MODELLING THE DISTRIBUTION OF ADVANCE REGENERATION IN
LODGEPOLE PINE STANDS IN THE CENTRAL INTERIOR OF
BRITISH COLUMBIA
by
Darin Warren Brooks
B.Sc. (Hons) University of Saskatchewan, 1996

THESIS SUBMITTED IN PARTIAL FULFILLMENT OF
THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE
IN
NATURAL RESOURCES AND ENVIRONMENTAL STUDIES
(GEOGRAPHY)

UNIVERSITY OF NORTHERN BRITISH COLUMBIA
December 2012
© Darin Brooks, 2012

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Abstract
The recent mountain-pine beetle outbreak in the Central Interior of British Columbia
is leaving unsalvaged stands with minimal silvicultural treatment, raising questions
about their ability to regenerate and die implications of this uncertainty to future
timber supply and habitat values. No system currently exists to predict, on a
landscape level, which pine stands will have adequate stocking of advance
regeneration suitable for release upon canopy death. My research takes a groundtruthed, landscape-level approach to modelling, predicting, mapping, and
prioritizing stands for salvage or rehabilitation. The resulting model, derived from
recursive partitioning of data from 964 sample plots, created a landscape level
output with a predictive accuracy of 78%. Across the Sub-Boreal Spruce study area,
I estimate that 58% of m ature pine-leading stands (approximately 840,000 ha) are
likely or very likely to be stocked with at least 600 stems/ha of living understory
trees.

ii

Table of Contents
Chapter One: Introduction................................................................................................... 1
Factors Impacting Advance Regeneration and Stand Recovery..................................6
Forest Management O ptions.......................................................................................... 13
Empirical Models of Species Distribution and Abundance....................................... 13
Recursive Partitioning and Classification Trees.......................................................... 15
Objectives..........................................................................................................................21
Chapter Two: M ethods....................................................................................................... 23
Study A rea........................................................................................................................23
Field Data Collection....................................................................................................... 25
Post-Field Data Organization......................................................................................... 31
Statistical A nalyses.......................................................................................................... 35
Geographical Information System (GIS) A nalyses..................................................... 36
Chapter Three: Results........................................................................................................ 40
Trends in Advance Regeneration D ensity................................................................... 40
Classification Tree A nalysis........................................................................................... 51
Applying the Classification Tree in a GIS M odel........................................................ 64
Chapter Four: Discussion and Recom m endations......................................................... 75
Application to Forest M anagem ent............................................................................... 78
Assessment of the Modelling A pproach...................................................................... 87
Chapter Five: Conclusions................................................................................................. 96
References...........................................................................................................................101
Appendix 1 ........................

118

Appendix 2 .........................................................................................................................119
Appendix 3 .........................................................................................................................138

List of Tables
Table 1. Number of advance regeneration plots per BEC unit......................................32
Table 2. Ecological variables from publicly available geospatial data layers..............37
Table 3. Number of regeneration plots sampled in different BEC u n it........................40
Table 4. Number of regeneration plots sam pled by age classes/ BEC u n it..................42
Table 5. Number of regeneration plots sampled by age classes and sites series........ 42
Table 6. Descriptive statistics for advance regeneration densities (BEC unit)............ 44
Table 7. Descriptive statistics for advance regeneration densities (age class).............44
Table 8. Descriptive statistics for advance regeneration densities (forest district).... 44
Table 9. Total num ber of stocked and not stocked plots across the study area.......... 45
Table 10. Key statistics describing the classification tree accuracy................................52
Table 11. List of im portant variables/significant ecological factors...............................58
Table 12. Classification tree variable importance for each stocking group................60
Table 13. Translation of classification tree model into textual rules (all trees).......... 61
Table 14. Translation of classification tree model into textual rules (conifer-only)... 62
Table 15. Translation of classification tree model into textual rules (MSSpa)............63
Table 16. Probability of being stocked for each BEC unit derived................................ 67
Table 17. Probability of being stocked for each NTS 1:250,000 m aptile.......................68
Table 18. Probability of being stocked for each forest district....................................... 69

List of Figures
Figure 1. Example of a classification tree illustrating predictor variable splits

17

Figure 2. Example of a ROC curve.................................................................................... 20
Figure 3. Study area.............................................................................................................24
Figure 4. Location of sampled stands (thesis plots)........................................................ 26
Figure 5. Cross section illustrating site mesoslope positions........................................ 29
Figure 6. Proportion of plot locations am ong different site meso-slope positions.... 41
Figure 7. Proportion of plots in pine-leading forest cover polygons (all trees)

46

Figure 8. Proportion of plots in pine-leading forest cover polygons (conifers-only). 46
Figure 9. Proportion of 964 plots in pine-leading forest cover polygons (MSSpa).... 47
Figure 10. Advance regeneration and plot basal area linear model..............................48
Figure 11. Advance regeneration and distance to seed source linear m odel.............. 49
Figure 12. Advance regeneration and m ean annual precipitation linear m o d e l

49

Figure 13. Advance regeneration density and projected height linear m odel............ 50
Figure 14. Advance regeneration density and projected age linear m odel................. 50
Figure 15. Example of a rule path in the conifer-only 600 stems/ha............................. 53
Figure 16. Final pruned classification tree model (all trees).......................................... 55
Figure 17. Final pruned classification tree model (conifer-only species)..................... 56
Figure 18. Final pruned classification tree model (MSSpa)........................................... 57
Figure 19. ROC curve chart illustrating model accuracy (all trees).............................. 65
v

Figure 20. ROC curve chart illustrating m odel accuracy (conifer-only species).........65
Figure 21. ROC curve chart illustrating m odel accuracy (MSSpa)................................66
Figure 22. Proportion of forest districts that are within the study area....................... 70
Figure 23. Colour themed map depicting probability of stocking (conifer-only)

71

Figure 24. Spatial extent of probability of stocking >80% for map tile NTS 93G ....... 73
Figure 25. Spatial extent of probability of stocking <20% for map tile NTS 93G ....... 74
Figure 26. Intersection of very likely and very unlikely stocked cells..........................77
Figure 27. Landscape view of m apped m odel output....................................................80
Figure 28. Advance regeneration location example (mature pine stands).................. 82
Figure 29. Advance regeneration location example (5 probability classes)................ 84
Figure 30. Location of large, very unlikely to be stocked m ature pine areas.............. 86

vi

Acknowledgements
I would like to thank the following people and agencies: Dr. Phil Burton, Dr. Roger
Wheate, and Dr. Michael Gillingham (my committee members), w ho provided me
with more latitude than I deserved. This thesis w ould not have been possible
without their patience, guidance, and support. They have been incredible m entors
... and consequently I am a better student, teacher, and mentor for having know n
them. Thank you from the bottom of my heart. I thank my wife, kids, and extended
families for their patience as they watched me sacrifice holidays, w eekends, family
nights and evenings of dance for this thesis; always graciously and unselfishly
supporting me in this dream, I can't imagine how I will begin to pay them back. To
David Kim from KFM in Prince George, BC: thank you for seeing the im portance of
this thesis and for providing me w ith the time, material, equipment, and m entorship
that was required. Thank you to everyone who provided funding (w hether
monetary or in kind): BC Forest Science Program, the Pacific Forestry Centre of the
Canadian Forest Service, PFC graduate scholarship, Kim Forest M anagem ent Ltd. A
special thanks to Heather and Talya for helping m e with field research and for
providing me w ith a couple of summers that I will never forget. I thank everyone
who provided data to the aggregate dataset: Dave Coates, Craig DeLong, Patience
Rakochy, Chris Hawkins, Brad Hawkes, Deb Cichowski, and Phil Burton. And
finally, thanks to the College of the North Atlantic for the use of m aterials and time
during the "final push".

Chapter One: Introduction

British Columbia's (BC) lodgepole pine (Pinus contorta var. latifolia) forests
have recently (-1999 to present) suffered from an epidemic of mountain pine beetles
(Dendroctonus ponderosae), hereafter MPB. Although such infestations are largely a
natural occurrence, the intensity and spatial extent of the present infestation are
unprecedented, such that attem pts to control the growing pest population have
failed (Stockdale et al., 2004; Burton, 2010). In 2004, Pedersen (2004, p. 11) noted
"despite the suppression measures, the epidemic as well as the am ount of beetlekilled wood continues to increase". The Provincial Aerial Overview Surveys of
Forest Health have indicated that the current epidemic reached its peak in 2005, and
although mountain pine beetles continue to attack pine stands throughout the
province, the outbreak will eventually subside by 2021 (Walton, 2012). In the
meantime, because pest-management intervention w as not sufficient to combat the
current damage, research interest has largely shifted to guide timber salvage and
regeneration operations. Social, economic, and operational limitations continue to
ham per those attempts to salvage the infested area (Stockdale et al., 2004). Those
constraints have contributed to predictions of a future severe timber shortage
(Pedersen, 2004; Burton, 2010). Immature pine stands, previously presum ed to be
immune to pine beetle attack and provide harvestable tim ber within the next few

1

decades, have become susceptible to pine beetle attack at the peak of the outbreak as
the older stands most susceptible to beetle-induced mortality were overrun w ith
beetles and their offspring become increasingly desperate for food (Maclauchlan,
2006). With most of the m ature pine forest killed, and with many of the plantations
established in the 1970s and 1980s equally compromised or unlikely to reach
maturity by the time salvage operations are completed, it is expected that BC will
soon be suffering from an unprecedented timber supply fall-down over the m idterm
of the next 10 to 50 years (Pousette and Hawkins, 2006; Snetsinger, 2011).
Advance regeneration consists of the seedlings, saplings or sprouts that have
naturally established in a forest understory before any large-scale disturbance, and
can be found naturally established under some m ature lodgepole pine stands
(Johnson et al., 2003; Burton, 2006). The survival and release of those understory
trees has been identified as a valuable m echanism to help avoid tim ber shortages
created by the MPB infestation (Burton, 2006; Coates, 2006; Greisbauer and Green,
2006; Pousette and Hawkins, 2006). The presence of advance regeneration decreases
the need for the use of more aggressive intervention and recovery m ethods to
regenerate forest stands by forest managers (Greene et al., 1999).
Forest planners are faced w ith the quandary of deciding which stands of trees
are unlikely to recover and, therefore, should be harvested and planted to speed

2

regeneration and which stands should be left to recover on their own. The lack of
knowledge regarding the capacity and growth of advance regeneration to respond
to a disturbance will be a major obstacle for the prediction of future harvests and the
development of appropriate response efforts (Messier et al., 1999). The ability of
advance regeneration to respond to a disturbance can be impacted by factors such as
the composition of species within the affected stand, the particular characteristics
(e.g., height, age, and diameter) of the trees involved, and the availability of light
determined by canopy gaps (Mitchell, 2005).
This potentially high variability among stands has limited advance
regeneration modelling using individual tree and stand models such as SORTIE
(Hawkins et al., 2012). It is this variability within and am ong stands that also
present a challenge to SORTIE's modelling. SORTIE develops an o utp u t that is
derived from complex interactions between light, growth, seed dispersal, and
mortality—all ecological factors that have a high variability between stands (Sattler,
2009). Coates (2006) suggests that the variability among stands is so great, that
stands can only be m anaged on an individual basis. A landscape-level m odel for
predicting the distribution of advance regeneration is critical for efficient and
effective forest planning, particularly in the context of the province's m anagem ent
unit objectives to ensure harvested areas in BC are adequately renewed through
stocking standards (McWilliams, 2009).
3

Despite the widespread occurrence of understory regeneration in lodgepole
pine forests, the question remains as to w hether those forests will rem ain adequately
stocked upon the death of the overstory. Stocking can be broadly defined through
current tree metrics (typically volume based) and early stand conditions that are
used to measure the probability of achieving long-term m anagement goals for that
stand (Martin et al., 2005; McWilliams, 2009). A fully stocked stand or sample plot is
one in which all open space is (or is projected to be) occupied by living trees. To
ensure that BC forests continue to return to their pre-harvested conditions, stocking
standards have been established to maximize the probability of successful
regeneration. It is, therefore, both critical and prudent, for forest planners to assess
stand regeneration at a landscape level. The stocking required to regenerate stands,
however, is not the same across the landscape (i.e., stands within different
biogeoclimatic unit and site series require different stocking standards to achieve
renewal). And in some cases harvested areas do not have timber production as their
primary objective (set by government and industry planners), and, therefore, have
different stocking standards to achieve their particular managem ent objectives.
Dhar and Hawkins (2011) identified three critical research-driven purposes
for advance regeneration assessment: forecasting long-term development (yield) of
attacked stands, selecting stands for further research, and forecasting impacts on
ecological attributes. The data to support estimates of stocking in stands following
4

MPB are available, but are addressed in several different research projects. There is
a need to collapse those data sets into a single usable form at (perhaps even
differentiating between predictive and operational) that can be used by industry,
research entities, and a variety of other stakeholders (Wilford, 2008; D har and
Hawkins, 2011).
The need to understand the patterns of advance regeneration occurrence has
an operational focus. Current reforestation stocking standards - designed prim arily
to guide the reforestation of clearcuts - m ay need to be revisited by forest planners.
Designation of preferred and acceptable species, as well as their densities, m ay need
to be altered or amended in order to economically utilize post-MPB advance
regeneration (Lewis, 2005; Greisbauer and Green, 2006). Commercial logging
strategies may also require adjustm ent on a stand-by-stand basis to provide
protection to advance regeneration that may or may not contribute to the m idterm
timber supply. Forest managers require a better understanding of the cost
implications associated with the retention of advance regeneration versus 'starting
over' with planting after logging in term s of facilitating important m idterm forest
harvesting opportunities (Dhar and Hawkins, 2011). Consideration m ust also be
provided to the potential effects of climate change on advance regeneration, and its
ability to sequester carbon and thereby mitigate some climate change impacts
(Brown et al., 2012). A more complete assessment of the distribution of advance

regeneration is required to identify the potential for future challenges such as
vulnerability to pests and diseases. As forests continue to respond to climate
change, so too do the populations and distributions of num erous insects and fungal
pathogens that may pose a threat to the regenerating species (Lewis, 2005).

Factors Impacting Advance Regeneration and Stand Recovery
Research on the recovery of stands following a disturbance through advance
regeneration is limited because the vast majority of studies have chosen to focus
only upon their early development (Messier et al., 1999). Patterns of understory
release in forests disrupted by natural disturbance, and the long-term grow th, yield
and habitat value of such forests are unfortunately poorly documented.
Natural disturbances are im portant ecological processes that drive observed
patterns in ecosystems. The study of disturbance regimes and the interaction of
disturbance agents has only recently become a central theme in ecology (Mori,
2011). Aspects of disturbance ecology that require further inquiry include
disturbance history, spatiotemporal dynamics, disturbance interactions,
regeneration response to disturbance, and the application of resistance and
resilience theory to ecosystem managem ent (Wright et al., 2000).
Ecological disturbances are defined as disruptive changes to an ecological
system by an external event that makes changes to the resources w ithin the system,
6

but does not necessarily result in the destruction of the ecological system itself
(White and Pickett, 1985; Pickett et al., 1989; Johnson and Miyanishi, 2007; Hughes,
2010). Studies indicate that disturbance impacts are defined by m ore than just the
affecting agent (i.e., whether it is insect, fire, wind, or other agents). Pickett et al.
(1986) state that the bases for understanding of an ecological disturbance are
threefold: 1) identifying the existing ecological system that may be affected by a
disturbance; 2) discerning only the changes to the ecological system that are a result
of a disturbance; and 3) understanding the consequences of the disturbance.
How effective will advance regeneration be in supporting stand recovery
after disturbance? Stand recovery rates vary through advance regeneration. For
example, the re-establishment of MPB attacked stands through regeneration can be
delayed by five to ten years due to species composition before the beetle attack and
the vigour of overstory trees (Bouchard et al., 2005; Coates, 2006). A m ore complex
example of stand recovery after disturbance is the creation of a thinning effect in
balsam fir (Abies balsamea) stands by spruce budw orm (Choristoneura fumiferana) in
eastern Canada. The natural regeneration is released post-budworm attack, only to
be attacked itself 30 or 40 years later - perpetuating a cycle of favourable conditions
for subsequent spruce budw orm attacks (MacLean and Anderson, 2008). The MPB
outbreak in BC is having a profound impact on the m akeup of the affected stands.
MPB is not unique as a disturbance agent that just kills the overstory, typically
7

serving as a means of releasing the understory regeneration and vegetation; this is
true of wind storms, other insect outbreaks, and root rot pockets, etc. (Gautreaux,
1999). Pine-dominated forests have varying amounts of live trees, saplings and
seedlings remaining after they have been attacked by MPB, which are collectively
referred to as "secondary stand structure" or "secondary structure" (Coates et al.,
2006).
Whereas forest fire will kill most seedlings and saplings, w indthrow and
insect infestations typically kill the overstory trees, but not the regeneration, thereby
facilitating its release (Johnson et al., 2003; Roberts, 2004; Burton, 2008b). N atural
methods of forest regeneration can be particularly attractive to forest planners w hen
stocking is reliable, or economic and operational factors prohibit the large-scale use
of artificial regeneration strategies. Natural regeneration - whether by seed or
through the release of existing seedlings -- offers several advantages to alternative
approaches. For example, natural regeneration is cost-effective w hen com pared to
more interventionist reforestation strategies and helps to protect the forest's natural
diversity (Weetman and Vyse, 1990).
Forest understory species m ay thrive following bark-beetle attack and this
will cause a dominant species shift w ithin the stand. The dwarf shrubs
kinnikinnick (Arctostaphylos uva-ursi) and twinflower (Linnaea borealis) have been
documented to increase in cover following MPB-induced canopy opening (Williston
8

et al., 2006). Other studies indicate that plant species richness (particularly grasses)
is measurably higher in post-MPB attacked stands and non-tree vegetation can
represent one to two-thirds of the CO 2 uptake contribution in these stands (Stone
and Wolfe, 1996; Bowler et al., 2012). Therefore, the beetle outbreak m ay be
regarded as a stand-releasing event that causes the understory vegetation to assume
a more dominant position within the stand as it grows to take the place of the lost
canopy trees (Greene et al., 1999; Burton, 2008a; Lindenmayer et al., 2008). Young
trees and other vegetation surviving in the understory have a strong potential to
thrive because of the new availability of resources created by the lost stand
members (Coates et al., 1994). Stands w ith a healthy understory m ay recover from
MPB attack to yield harvestable timber within a timeframe of 40 to 80 years (Coates
and Hall, 2005; Coates et al., 2006).
Understory light availability increases in natural canopy gaps (resulting from
the mortality of one or more m ature trees) and after forest harvesting (Palik et al.,
1997; Burgess and Wetzel, 2000; Oguchi et al., 2006; Boucher et al., 2007), and larger
gaps provide more light than smaller gaps (McGuire et al., 2001; Gray et al., 2002;
Palik et al., 2003). Large canopy gaps due to dead trees can result in reduced
evapotranspiration and, therefore, decrease sum m er groundwater depletion (Helie
et al., 2005). Light availability is also greater near gap edges than in forest interior
positions (Matlack, 1993; Heithecker and H alpem , 2007). High light availability is
9

associated w ith greater light-saturated photosynthetic rates (Ellsworth and Reich,
1992; Bond et al., 1999) so any death or removal of overstoiy trees should prom ote
increased growth of advance regeneration (Williams et al., 1999). The new
availability of increased light that results from the loss of shading crowns leads to
the stimulation of germination and seedling release in m any shade-tolerant trees
such as Abies spp. (McCarthy, 2001). The adaptability of these shade-tolerant
species is responsible for their establishment in the understory and further supports
their recruitment into the canopy of the stand (Messier et al., 1999). As a result,
some tree species are more likely than others to be found within the advance
regeneration stratum. For example, shade tolerant species such as the subalpine fir
and interior white spruce (a natural hybrid of Picea engelmannii and P. glauca,
common throughout the BC Central Interior) are species commonly found among
the advance regeneration found in BC's sub-boreal forests (Coates et al., 1994;
Kneeshaw and Burton, 1997). The distribution of other plant species w ithin a region
can also impact the success of advance regeneration strategies. For example, the
presence of aggressive non-tree vegetation can negatively impact the ability of
advance regeneration to respond to overstory m ortality (Bassman et al., 1992; Stone
and Wolfe, 1996). Knowledge of sapling and seedling grow th is also an essential
element for the formulation of accurate predictions of future stand conditions
(Wright et al., 2000). The species composition w ithin the understory itself m ay also
10

have an influence on the density of advance regeneration. Advance regeneration is
generally more abundant w hen accompanied by a greater diversity of tree species
within the overstory (Amup, 1996).
Particular characteristics allow some species to respond more positively than
others after an insect outbreak. For example, the relative availability of shade and
sunlight has been highlighted as particularly influential for advance regeneration.
Wright et al. (2000, p. 1528) found "a clear relationship between shade tolerance and
the magnitude of the effects of past periods of suppression and release on sapling
growth." Species able to tolerate conditions of low light have a propensity to thrive,
and possibly adapt to variable light regimes due to changing canopy structure
within the understory through advance regeneration (Oliver and Larson, 1996;
Messier et al., 1999; McCarthy, 2001). Understory light m ay remain relatively
unchanged for up to five years after a MPB attack because it takes that long for the
dead foliage to fall and the residual canopy will continue to shade the vegetation in
the understory (Coates and Hall, 2005). Furthermore, pine snags are another
enduring source of shade for plants w ithin the understory (Coates and Hall, 2005).
The shade from these snags and any surviving trees can help to prevent understory
trees from being out-competed by other vegetation (Lieffers and Stadt, 1994).
Although some lodgepole pine seedlings can establish under full canopies, it
is generally classified as a shade-intolerant species (Bums and Honkala, 1990; Klinka
11

et al., 2000). Shade-intolerant spedes tend to be less likely to respond well w ithin
the cohort of advance regeneration following a disturbance because they have a
more fixed, less adaptable structure and physiology (Messier et al., 1999). Its status
as a shade-intolerant spedes, however, does not p red u d e lodgepole pine from being
found as a natural component of the secondary stand structure surviving an MPB
outbreak. The presence of lodgepole pine regeneration within a m ature forest can
be explained by the presence of uneven canopy closure, which perm its sunlight to
reach the light-demanding young pines (McCarthy, 2001). Indeed, in cold dry
environments where other tree spedes are at a competitive disadvantage, lodgepole
pine may be the dom inant spedes of advance regeneration, and can release to create
an uneven-aged stand after MPB attack (Axelson et al. 2009).
Finally, there is evidence that natural regeneration may be assisted through
seed rain recruitment (the deposition of seeds spread by bird, wind, hum ans, and
animals) by some spedes (Moles and Drake, 1999), although Burton (2006) found
inconsistendes in the relationship between regeneration densities and proxim ity to
non-pine conifer seed sources. Leadem et al. (1997) state that successful
regeneration of stands relies on seed production and dispersal, so there m ust be
some fundamental dependency on the availability of seed from shade-tolerant
spedes, either within the stand or from nearby on the landscape.

12

Forest Management Options
Standard industrial forestry in the form of even-aged management and
dearcut harvesting promotes the development of simplified stand structures
through the application of homogeneous treatm ents across stands at fixed intervals
that are often shorter than the return intervals of natural disturbances in the same
region (Coates and Burton, 1997; Palik et al., 2002; Seymour et al., 2002). The loss of
structural complexity in m anaged forests presents concerns for conserving
biodiversity, sustaining key ecosystem functions, and maintaining ecological
resilience in the face of a changing climate (Franklin et al., 2002; Lindenm ayer and
Franklin, 2002; Palik et al., 2002; Tews and Jeltsch, 2004; Drever et al., 2006). These
concerns over the ecological consequences of simplified forest structures have
created interest in developing novel silvicultural systems that promote more natural
patterns of stand development by emulating the frequency, scale, and severity of
natural disturbances (Coates and Burton, 1997; Franklin et al., 1997,2002; Palik et al.,
2002; Seymour et al., 2002).

Empirical Models of Species Distribution and Abundance
Ecologists have spent a great deal of time examining the interaction betw een
plant species and their micro- and macro-environments. Through the collection and
examination of environmental data, ecologists attem pt to discover patterns that
assist them in predicting the presence or absence of a particular species, community,
13

or ecosystem (e.g., Franklin, 2009). Unfortunately, the environmental variables used
in predictive models are complex and covarying. Their interaction w ith each other
can vary by simply changing where they exist in time or space. For example, even if
we understand how variables interact w ith each other, our understanding can
change when the variables are examined at a slightly higher elevation or on a
warm er day. This ties a model to a particular geographical context, as the derived
model may encounter accuracy errors w hen the geography changes, even if the
combination of variables remains the same (Guisan et al., 1999). Furthermore,
environmental variables can be significantly affected by unknown additional
lurking variables, (such as anthropogenic interferences) or a sophisticated
interaction of multiple variables. That is, our understanding of the variable
interaction between variablex+ variabley + variablez can change if an additional
unknown and unseen variableu is present. These limitations are especially
problematic for ecology, where variability and deviations occur in nature as the
norm, not the exception.
General linear models have traditionally been used by ecologists to describe
the relationship between causal factors and an observed response (Draper and
Smith, 1981; Burnham and Anderson, 2002). Yet despite the well docum ented
drawbacks of relying on techniques such as stepwise m ultiple regression, the use of

14

these procedures for ecological studies are prevalent (Stephens et al., 2005). Many
ecologists sacrifice the potential of m aking erroneous conclusions in the search for
the most parsimonious model. This is im portant in datasets that have factor
interactions too complex for parametric models (Freedman, 1983; Derksen and
Keselman, 1992). Recent studies have show n that classification trees, or recursive
partitioning, can be more reliable and accurate than traditional param etric linear
models (Friedl et al., 1999; Hansen et al., 2000).

Recursive Partitioning and Classification Trees
Classification and regression trees are the statistical application of binary
trees first introduced by Breiman et al. (1984). Classification trees are an intuitive
and easily interpreted type of supervised learning m ethod used in exploring
relationships in data. Further, w hen the explored relationships in the data take the
form of a decision tree and are then applied to new data to predict new values, the
classification tree becomes a predictive tool (Han et al., 2011). Classification trees
are equipped to deal with continuous and categorical data, missing values, and
outliers (Moisen, 2008). But unlike linear regression models, which identify and
measure the relationship between the response and explanatory variables,
classification trees divide the explanatory variables into homogenous groups
through a series of recursive partitions. Botanists employ dassification-style
decision trees in the form of the routinely used dichotomous keys for the correct
15

identification of a plant by following a tree of if-then statements. Classification trees
are also prevalent in the fields of medicine and psychology for diagnosis and
decision making (Ripley, 1996).
In a standard classification tree, the idea is to split the dataset based on
homogeneity of data. The goal is to achieve pure homogeneous groupings of data
to 1) describe the systematic structure of the data; and 2) predict unobserved data
(De'ath and Fabricius, 2000). For example, consider two variables, tree age and tree
vigour, that predict w hether a tree is likely to be attacked by mountain pine beetle
(1), or not (0). If 90% of the trees that are >80 years old in our training data showed
signs of beetle attack, we can split the data here and age becomes a top node in the
tree. Further, if it is discovered that any tree w ith a vigour less than five (ten being
the healthiest and one being the unhealthiest), is attacked 80% of the time, then
vigour <5 or >5 would be the second branch in the tree. Graphically it w ould look
like the sequence of decisions portrayed in Figure 1.

16

ALLTREES

A 6F

> 8 0 YEARS

< 8 0 YEARS

ATTACKED

WOT ATTACKED

20 %

VIGOUR

> 5 .0

< 5 .0

ATTACKED

WOT ATTACKED

Figure 1. Example of a classification tree illustrating predictor variable splits. Note that the
first split at age >80 years old is an internal node, i.ev other nodes can branch from this
node. The next split at vigour >5.0 is a terminal node, signalling the end of the branch.

Classification trees are a useful tool for analyzing data because of their visual
simplicity. The trees are rules for predicting or explaining the response category
using hierarchical binary splits of tire explanatory variables. When predicting the
category of response, classification trees are used as an algorithm to classify new
data. An observation will follow a path in the tree starting in the top or root node
and follow its individual splits at the interior or branch nodes, dow n the path until
it reaches a terminal or leaf node w here no m ore splitting occurs (Kim and Yates,
2003). The criteria used to split the branches to achieve the nodes represent the "ifthen" model. Classification trees are used to predict membership of cases or objects
in the classes of a categorical dependent variable from their measurements on one or

17

more predictor variables. Classification tree analysis is one of the m ain techniques
used in data mining (Hastie et al., 2001).
Each predictor variable is examined to see how well it can divide the node
into two groups. If the predictor is continuous, a trial split is made betw een each
category (every unique value is a 'category') of the variable. The process is repeated
by moving the split point across all possible division points in the training data until
the best improvement is found. This split point is saved as the best possible split for
that predictor variable in this node. The process is then repeated for each of the
other predictor variables.
A well-recognized advantage of the decision tree representation of a m odel is
that the paths through the decision tree can be interpreted as a collection of rules.
The information associated with the textual rules include a node num ber for
reference, a decision of 0 or 1 to indicate (in the application considered here)
whether the plot is stocked or not stocked, the num ber of training observations and
the strength or confidence of the decision.
The measurement of predictive accuracy of a variable (i.e., m ean decrease in
accuracy) is the more meaningful importance indicator (Berk, 2005). The m ean
decrease in accuracy is defined as the normalized difference between classification
accuracy and the accuracy when the variable values have been random ly perm uted.

18

Higher mean decrease in accuracy indicates that a variable is more im portant to the
accuracy of the classification.
The Receive Operating Characteristic (ROC) curve, a diagnostic m easure
(represented by a graphic curve and a numerical score) that plots false positive
against true positive rates, is generally described as one of the most accurate ways to
measure the discriminatory power of the resultant classification tree m odel through
comparison of the relationship between sensitivity (in this case, true positives) and
specificity (false positives) (Hanley and McNeil, 1982; Beck and Schultz, 1986; Krivec
and Matjaz, 2011). In other words, specificity of the tree is the probability that one
more not stocked point added to the analysis will be correctly classified as not
stocked; and conversely, sensitivity is the probability that one more stocked point
added to the analysis will be correctly classified as stocked (Feldman and Gross,
2003). A perfect test (100% sensitive and 100% specific) would score a ROC value of
1.0. The closer the value is to 1.0 (100%), the better the distinguishing capability of
the classification tree model. The ROC graphic is a curved line that extends from
the 45 degree line to the upper left comer; higher model accuracy is associated w ith
a sharp distinct curve that approaches the top left com er of the graph (Figure 2).
The ROC curve is essentially the m easurem ent of the trade-off between sensitivity

19

1.0

> 0.5 and
< 1.0

0)->
•+

ns
pH
0)

>

0.5

•J3

o

Ph
QJ
3
i- i

b

£
ca

e
0)

</5

1- Specificity (False Positive Rate)
Figure 2. Example of a ROC curve illustrating the trade-off between sensitivity and
specificity. A ROC score of 1.0 is a perfect model fit and 0.5 is a purely random model fit.

and specificity. A perfect model w ould be able to correctly classify all stocked
stands as stocked and it would never incorrectly classify a stocked stand as not
stocked. A perfect model (represented by the red line on the ROC curve in Figure 2)
would follow the y axis to the top of the graph (zero false positives, i.e., zero
incorrectly identified) and then follow the x axis along the top of the graph (all true
20

positives, i.e., all correctly identified). A random model (represented by the 45
degree black line in Figure 2) w ould indicate that every true positive has an equally
likely false positive. A ROC value of 0.5 (50% sensitive and 50% specific)
demonstrates no discriminative value and is equivalent to assigning true positives
with a coin flip (Sherrod, 2006). The strength of the final classified m odel can be
interpreted by assessing the ROC value, also know n as AUC (area under the curve).

Objectives
The objectives of my thesis are t o : 1) devise a predictive m odel of forest
understory stocking, based on publicly available digital data with long shelf-life,
that provides forest managers w ith a decision model to assist in post-beetle stand
management planning; and 2) apply the model in a Geographic Inform ation System
(GIS) to generate a series of colour-themed maps portraying the probability of
understory stocking in stands dom inated by m ature lodgepole pine in Sub-Boreal
Spruce biogeodimatic zone.
Many factors such as proximity to potential non-pine seed sources,
biogeodimatic subzone, mean annual predpitation, crown dosure, and site
productivity may im p ad advance regeneration and stand recovery in the lodgepole
pine forests of central British Columbia. Literature suggests that patterns in the
abundance of advance regeneration are evident, such that the proper use of stand
variables should make a predictive model possible (Kneeshaw and Burton, 1997;
21

Kayes and Tinker, 2012). Given the far-reaching geographic spread of MPB-affected
stands (and the inability of industry to harvest these stands), and the fact that there
seem to be some consistent trends in the distribution of advance regeneration, it
seems likely that a relatively accurate landscape-level predictive m odel could be
useful (Hawkes et al., 2003). My thesis explores the use of a statistical data-mining
technique known as recursive partitioning, or Classification and Regression Tree
Analysis, and its integration with GIS geospatial modelling. The results illustrate
how the combination of a priori information and recursive partitioning can provide
an accurate, stable and reliable predictive model of the likely distribution of advance
regeneration.

22

Chapter Two: M ethods
Study Area
The study area was restricted to the dk, dw2, dw3, mc2, mc3, m k l, mw, and
w k l biogeodimatic ecosystem dassification (BEC) units of the Sub-Boreal Spruce
(SBS) biogeodimatic zone (Klinka et al, 2000) located in central BC (Figure 3). I
selected this study area because of the abundance of predominantly even-aged
m ature pine stands. As a consequence of its composition, the study area selected
was one of the hardest hit MPB-attacked regions in BC (Parkins and MacKendrick,
2007), making it a critical area in which to consider the potential for stand recovery.
In order to report the results within a forest industry recognized context, the data
were clipped to 1:250,000 NTS m ap tiles 93F, 93G, 93J, 93K, and 93L. The 1:250,000
NTS map tile dataset also allows for logical, effident data storage and organized
dissemination of the resultant data.
The SBS occurs mostly in the central region of BC and dominates the gently
rolling Nechako Plateau between the Coast Range and the Cariboo and Rocky
Mountains (Meidinger et al. 1991). It ranges from valley bottoms to 1300 m
elevation, receives 400-900 mm of precipitation annually, and has a m ean
tem perature range of below 0°C in w inter to above 10°C in the sum m er (M eidinger
et al. 1991). The SBS zone is characterized by ten subzones and four com m on site
assodations: from driest to wettest, these are referred to as the Lodgepole pine 23

Study Area Geographic Extents

Figure 3. Study area as defined by six National Topographic Survey (NTS) 1:250,000 map sheets (crosshatched). Grey or green lines denote forest district boundaries.

Huckleberry—Cladonia plant community, the H ybrid spruce - Huckleberry Highbush-cranberry plant community, the H ybrid spruce - Oak fern plant
community, and the Hybrid spruce - Devil's club plant community (Meidinger et al.
1991).

Field Data Collection
I selected my sampled stands through a stratified sampling design/ using
biogeodimatic subzone as strata (Figure 4) because previous research had indicated
strong differences among subzones in the abundance of advance regeneration
(Burton, 2006; Coates et al. 2006). Suitable stands, which I referred to as target
stands, met the following attribute criteria: stand spedes composition is lodgepole
pine (coded as PL or PLI in the Province of BC's Vegetation Resource Inventory,
VRI) as the leading spedes with a m inim um of 50 percent basal area (as specified
by VRI attribute: SPEC_CD_1 and SPEC_PCT_1)-, the stand has an average age of
greater than 60 years, weighted by basal area of the dom inant trees for the leading
spedes (specified by VRI attribute: AGE_1); and the stand is adjacent to a m ature
stand dominated by conifer spedes other than lodgepole pine.
My field sampling was designed to test and calibrate distance-related fadors
affecting the density of advance regeneration in m ature stands dom inated by
lodgepole pine. In particular, the effects of proximity to potential seed sources from
m apped stands or landscape positions dom inated by non-pine trees guided the
25

SMITHERS

P rin cT G eo rg e

Q uesnel
SBSdk
SBSdw2

SBSmkl

SBSdw3

SBSmw
SBSwkl

Figure 4. Location of sampled stands (thesis plots) within study area SBS BEC units.

sampling design. Consequently, m y sample plots were positioned at 50-m intervals
at transects extending from potential seed sources (for hybrid white spruce [Picea
engelmannii x glauca], subalpine fir [Abies lasiocarpa], or Douglas-fir [Pseudotsuga
menziesii]) into pine stands for distances up to approximately 700 m. The num ber of
plots per stand typically varied from 5 to 10, depending on the size of die stand
being sampled. Stands dom inated by those non-pine species were identified from
VRI (forest cover) m aps considered current to May 2006 and interpretation of colour
1:15000 digital orthophotos compiled from 2004.
Utilizing a GIS software package, I isolated VRI stand polygons that met
suitable target stand criteria. Because a straight transect from the edge of the target
stand through the target stand was required, I established a transect point of
commencement (POC) for each target stand through computer on-screen digitizing
and geographic coordinates (Universal Transverse Mercator Easting (x) and
Northing (y)) for the POC and coordinates for each subsequent plot 50 m along the
transect line. I transferred the UTM to a handheld global positioning system (GPS)
unit. A hardcopy m ap w ith UTM coordinates, num ber of intended plots, transect
bearing, and target stand attributes was created for every target stand before I left
for field sampling. This was particularly useful when I encountered target stands
that had been logged and were no longer useful for data collection. The GPS unit
helped me locate the target stand POC in the field and establish a proper bearing
27

line along the intended transect. Both GPS locations and compass bearings were
used to ensure the predetermined transect line w as being followed. Once the exact
location of the POC was located in the field, the predeterm ined bearing into the
candidate stand was established and data collection plots were collected every 50 m
until the stand was fully transected.
I established my sample plots by driving a semi-permanent num bered m etal
pigtail stake into the ground (with a unique num ber derived from the sam ple date,
transect number, and plot number). A GPS coordinate was collected and recorded
for the plot center. An overall site description was recorded, including: the percent
slope gradient (measured with a clinometer), slope aspect (measured by compass in
degrees), and mesoslope position (Figure 5).
At each plot center, I dug a 50 cm deep soil pit to accurately assess the soil
texture (the relative proportions of sand, silt, and clay) and the percentage of coarse
fragments. The soil properties and plot position allowed for identification of both
soil nutrient regime (amount of essential soil nutrients that are available to the
vegetation) and soil moisture regime (the average am ount of soil w ater annually
available for evapotranspiration by vegetation).
Using the appropriate BEC unit edatopic grid from field guides site
identification and interpretation for the Southwest, Southeast, and N orth Central

28

portion of the Prince George Forest Region (DeLong et al., 1993; DeLong, 2003;
2004), I was able to assign a field-based site series designation for each plot location.

_

0
©

i
i
!

uni
Figure 5. Cross section illustrating site mesoslope positions along a hill.
A cruise plot sweep was conducted at each plot center for basal area
estimates using a prism w ith a basal area factor (BAF) of 4.0. To supplem ent the
cruise data, a plot-level estimate of the num ber of years since MPB attack was
determined by examining the trees for MPB bore holes, pitch tubes, and vigour. I
established 3.99-m (50 m2) and 5.64-m (100 m 2) radius fixed-area sam ple plots by
attaching a m etered tether to the metal pigtail at plot center and flagging the radius.
Dominant plant species within the 3.99-m radius were identified. Through ocular
estimate, the percent cover and average height (cm) of each species w ere recorded.
29

Also within the 3.99 radius sample plot, all seedlings (0 cm -130 cm tall) were
tallied by species, w ith their vigour, height (cm), and distance to the nearest
seedling/sapling recorded. In die 5.64 radius sample plot, all saplings (130 cm tall to
7.5 cm in diameter as m easured at 1.3 m height) were tallied by species, w ith their
vigour, diameter at breast height (dbh), and distance to the nearest seedling/sapling
recorded. The num ber of tree seedlings (>10cm tall) and saplings at each plot
represented the am ount of advance regeneration. This num ber was extrapolated to
estimate the num ber of stems/ha of advance regeneration per plot. The stems/ha of
all conifer regeneration >30 cm in height represented the target or response variable
for much of the classification tree analysis. At each of my plot locations, a camera
tripod (with built-in level) was placed and levelled at plot center. Digital oblique
and upward-directed hemispherical ("fisheye") photographs were taken to assist in
site description and subsequent incoming light/canopy openness studies
respectively. Finally, three m ature trees, that were indicative of the stand's average
age, were cored using an increment borer. The cores were protected in soda straws,
and tree rings were counted post-field to estimate approximate stand age.
Additional data used for my thesis included an aggregation of raw field data
collected from advance regeneration studies in the study area from 1996 to 2007.
Although the studies may not have had similar objectives or deliverables as my
thesis, I was able to extract portions of the raw data that w ere suitable inputs for my
30

analysis. In total, I collected data from 162 plots within 37 stands (sam pled in 2006
and 2007). These data were combined w ith data collected in a similar m anner (i.e.,
along transects from non-pine stands into pine-dom inated stands) by P.J. Burton
and K.D. Coates (Coates et al. 2006), and other analogous plot data designed to
representatively sample entire pine-leading stands rather than specifically the
effects of plot distance from a non-pine seed source (e.g., Dhar and Hawkins, 2011).
In total, 4241 plots were aggregated into a single plot dataset. Although I only
collected 162 plots in support of this analysis, the study derives its conclusions from
a 964 plot subset of the aggregated plot dataset. Table 1 lists the source, num ber of
plots, and BEC units of all data used as inputs for the thesis classification tree m odel
development. The 964 plots were selected by a GIS query that isolated only those
plots within m ature pine-leading stands (>50% lodgepole pine by basal area and
m apped as >60 years old at the time of sampling) w ithin the SBS dk, dw2, dw3, mc2,
mc3, m kl, mw, and w kl BEC units of 1:250,000 NTS m ap tiles 93E, 93F, 93G, 93J,
93K, and 93L.

Post-Field Data Organization
I organized the data from the 964 plot sam ple data in an ArcGIS (ESRI, 2011)
file geodatabase. I subsequently used this dataset as the training data for the
classification tree analysis. A common table attribute (advance regeneration

31

stems/ha) was established and populated with field collected data. Classification
tree analysis requires the variable being predicted to be categorical.
Table 1. Number of advance regeneration plots sam pled per BEC unit by data
source.
Source

Year

dk

Brooks
2007
Burton
2005
CarrotLake 2006
Cichowski 2005
2005
Coates
DeLong
2005
Fluxnet
2006
Hawkes
2002
2005
Hawkins
NIVMA
1996 - 2001
Rakochy
2004

5
38
10
77
4
150

Total Plots

292

dw2

-

-

8

21

-

-

-

-

23
1
-

45

BEC Unit (SBS)
mc2
mc3
dw3
m kl
59
54
36
138
5
100
18
55
9
6
9
53
13
8
1
4
42
-

-

-

-

-

141

259

-

w kl
14
-

-

-

-

-

-

-

3
-

-

-

143

67

mw

Total Plots

-

-

127
208
100
23
93
25
9
77
92
18
192

3

14

964

-

-

As my thesis objective was to build a m odel that assists in predicting the stocking
status of stands, it was necessary to convert the advance regeneration stems/ha to a
Boolean attribute of stocked or not stocked. An im portant qualification should be
made with regards to my thesis' use of the attribute "stocked". I applied a
conservative estimate of stocking, as the data only refers to the stocking of seedlings
(>10cm tall but less than 130cm tall) and saplings (>130cm tall but less than 7.5 cm
dbh). My analysis does not take into account germ inants (<10 cm tall) or existing
trees (>7.5 dbh), even though both could be considered important elements of
advance regeneration. Germinants are not infrequent in the understories of the

32

more moist zones of the SBS (Vyse et al., 2009). I also m ake the assum ption that all
pine trees >7.5 can dbh within the plot will not survive post MPB, and therefore are
not considered in the stocking calculation. This becomes an important consideration
when we consider the growing space actually available to the advance regeneration.
The results are consequently a conservative estimate of stocking and could be better
identified as "stocked with seedlings and saplings".
I selected a threshold of 600 stems/ha to separate stocked from not stocked
stands as several studies referring the percentage of plots meeting or exceeding
minimal stocking standards have used 600 stems/ha as the baseline (Bulmer et al.,
2002; Burton, 2006; Vyse et. al., 2009). 600 stems/ha is widely recognized as the
minimum well-spaced preferred trees/ha in in stocking guidelines for the
regeneration of clearcuts (e.g., British Columbia Ministry of Forests 2000), and is
threshold beneath which stand rehabilitation measures m ight be undertaken. Based
on that threshold, I created two new attributes in the geodatabase, nam ed
alltrees600 and conifers600. The alltrees600 attribute was populated w ith a 1 if the
advance regeneration total stems/ha for the sample plot w as equal to or greater than
600 stems/ha and populated with a 0 if the advance regeneration total stem s/ha was
less than 600 stems/ha. This attribute applied to all tree species within the sample
plot.

A second 600 stems/ha attribute, conifer600, was also populated w ith a 1 or 0

following the same criteria as the alltrees600 attribute, bu t only counting those
33

conifer species in the sample plot. In addition, a third threshold group, MSSpa, w as
established to assign a stocking value of one or zero according to the appropriate
minimum stocking standard of preferred and acceptable species found in the
Establishment to Free Growing Guidebook for the Prince George Forest Region
(British Columbia Ministry of Forests, 2000). Using the Establishment to Free
Growing Guidebook the MSSpa, I identified criteria for each biogeodimatic unit and
site series pairing that contained a study plot. The published MSSpa values and
conditions were used to define the level of stocking against which to assess seedling
and sapling densities (Appendix 1). MSSpa can be as low as 200 stem s/ha to as high
as 700 stems/ha in the subzone/site series present in my study area (British
Columbia Ministry of Forests, 2000). Plots that h ad less than the prescribed MSSpa
were considered not stocked and plots that met or exceeded the prescribed MSSpa
were considered stocked. The "well-spaced" requirem ent for counting regeneration
was ignored, as this value (which typically ranges from 1.0 to 2.5 m between
seedlings) is arbitrary and depends on the silvicultural prescription and grow th
modelling assumptions, while fully m ature trees are often observed w ith stem bases
growing <1.0 m apart. This simple bu t conservative measurement of understory
stocking (designed to be applied under open-growing conditions) was critical to the
classification tree development and subsequent GIS m apping model.

34

Statistical Analyses
Initially, basic descriptive statistics were applied to the data to examine
patterns in the variables. T-tests, R package t.test (R Core Team, 2012), were
conducted to examine the contribution of non-conifers to the advance regeneration
densities. Linear regression models, R package glm (R Core Team, 2012), were
applied to the data to explore the possibilities of relationships between advance
regeneration densities and several key variables. The prim ary objective of building
a predictive geospatial model of the probability distribution of advance regeneration
in target pine stands was pursued by developing classification tree m odels in
DTREG (Sherrod, 2006) and R (R Core Team, 2012), using a recursive partitioning
package called rpart (Themeau et al., 2012). The classification-tree m odel required a
binary response variable (stocked or not stocked) and publicly available explanatory
variables that currently exist in digital format. Therefore, any data I collected in the
field that could not be derived from publicly available geospatial data sets (e.g.,
understory plant cover) were not used as a potential explanatory (predictor)
variable. I determined that data derived from: 1) the Vegetation Resource Inventory
(VRI, 2006); 2) Predictive Ecosystem Modelling (PEM, 2008); and 3) interpolated
and elevation adjusted climate data calculated using ClimateBC (W ang et al. 2006)
were all publicly accessible and contained key potential predictors. The three
datasets together yielded 54 potential predictors (Table 2). The intention w as to find

35

the best combination of potential predictors that could be used to create a
parsimonious predictive model to accurately classify each 1-ha cell section w ithin
target stands across the study area as stocked (1) or not stocked (0). Additionally,
each cell would not only be designated as stocked or not stocked, but w ould also be
assigned the probability of being stocked or not stocked. A cross validation
argument cv.tree function was applied to the full tree to minimize the
misclassification error associated w ith overfitting of the tree. The cross validation
pruned back the tree to the optimal num ber of splits/node pairs. See A ppendix 3 for
a more detailed description of recursive partitioning, tree pruning using crossvalidation, and variable importance calculation.

Geographical Inform ation System (GIS) Analyses

The second objective of my thesis w as to create a geospatial m odel that
assists in converting the probability of stocking into a geospatial environm ent.
Through the use of classification tree modeling, the rules for determining stocked or
not stocked and the probabilities of stocking were determined. One of the passive
inputs (included in the model developm ent but not used as a key predictor) into the
classification tree analysis was the geographic coordinates of the 100 m cells. The
themed polygons portraying the likely distribution and location of stocked and
unstocked stands dom inated by m ature lodgepole pine in Sub-Boreal Spruce

36

Table 2. Ecological variables from publicly available geospatial data(evaluated as potential inputs) to the
probability of stocking classification tree model.
Variable
Elevation
Leading Spedes Live Volume per Hectare at 12.5 cm
Leading Spedes Live Volume per Hectare at 17.5 cm
Second Spedes Live Volume per Hectare at 12.5 cm
Second Spedes Live Volume per Hectare at 17.5 cm
Leading Spedes Dead Volume per Hectare at 12.5 cm
Leading Spedes Dead Volume per Hectare at 17.5 cm
Mean Annual Temperature
Mean Warmest Month Temperature

Source Type
GIS
2
VRI
2
VRI
2
2
VRI
VRI
2
VRI
2
2
VRI
2
C*c
2
C?c

Variable
UTM coordinate (easting)
UTM coordinate (northing)
Forest District
Biogeodimatic Subzone/Variant
Site Series
Soil Moisture Regime
Soil Nutrient Regime
Absolute Moisture Regime
Surface Expression

Source Type
GIS
2
GIS
2
VRI
1
VRI
1
PEM
1
VRI
1
VRI
1
VRI
1
VRI
1

Modifying Process

VRI

1

Mean Coldest Month Temperature

C*c

Mesoslope Position

VRI
VRI

1

Temperature Difference Between MWMT and MCMT

2

Mean Annual Predpitation

dc
c*c

Quadratic Diameter at 12.5 cm

Mean Summer (May to Sept.) Predpitation
Annual Heat: Moisture Index

C bc

Summer Heat: Moisture Index
Degree-Days Below 0°C

C bc

2
2
2
2
2

Quadratic Diameter at 17.5 cm
Crown Closure

VRI
VRI

2

Site Index

VRI
VRI

2

VRI

Degree-Days Above 5°C

dc
dc

Degree-Days Below 18°C
Degree-Days Above 18°C

&

2

c*c

2

Basal Area

2
2

C *c

2
2

Spedes Composition of Leading Spedes

VRI
VRI

1
1
1

Leading Spedes Percentage

VRI

2

Number of Frost-Free Days

C *c

2

Spedes Composition for Second Spedes
Second Spedes Percentage
Percent of Pine in Leading Spedes

VRI
VRI
VRI

1
2

Frost-Free Period
Predpitation as Snow
Extreme Minimum Temperature over 30 Years

&

2

2
2
2

Percent of NonPine in Stand

VRI

2

Hargreaves Reference Evaporation

VRI
VRI
VRI

2
2
2

Hargreaves Climatic Moisture Defidt
Distance (m) to Nearest Nonpine Seed Source (SW direction)
Species Composition of Nearest Nonpine Seed Source

d*
dc

2

Ratio of Pine to NonPine in Stand

GIS
GIS

2
1

T ree Cover Pattern
Vertical Complexify

Projected Age for Leading Species
Prcjeded Height for Leading Spedes

d*
C *c

Data Source: VRI (Vegetation Resource Inventory), PEM (Predictive Ecosystem Mapping), O (ClimateBQ, GIS (derived
data using ArcGIS) Data Type: 1 (categorical), 2 (continuous)

2

2

biogeodimatic zone. The GIS m odel incorporates the exported rules from the
dassification tree to isolate criteria identified in each branch. Each of the term inal
nodes in the dassification tree could be extracted from the resultant tree
individually through a series of single program m ing statements, w ith each properly
executed statement resulting in a queried output. This, however, w ould be an
ineffident use of the final model, as the result w ould be a series of if-then strings
that would each have to be applied against test data. By creating a dassification tree
and the splitting rules that make u p the tree as a model, all the branches leading to
all the terminal nodes could be applied against test data simultaneously. Because
the model dataset contained geographical coordinates, the dataset could be
imported into a GIS. The resultant is a spatially attributed file that identifies the
variables used in the model, the predicted target value for every 100-m raster cell (as
stocked or not stocked), the terminal node used for each predicted value, and a
probability value for the designation of stocked or not stocked for every 100-m
raster cell. The probability value is the critical attribute that is used in creating the
predictive colour-theme map. Much like the classification tree output, ArcGIS
models are components linked together through connectors such as tools, variables,
and iterators (Allen, 2011). The final model output is an extensible geospatial m odel
that can be run within the ArcGIS environment. The m odel automates the

38

geoprocessing tasks that are required to prepare the data for modelling, geospatial
analysis, and colour-themed mapping.

39

Chapter Three: Results
Trends in Advance Regeneration D ensity
A total of 243 pine-leading stands (containing the 964 plots) w ere field
sampled. A majority of these plots were located in the SBSdk, SBSdw3, SBSmc2, and
SBSmc3 biogeodimatic units and on 01,03,04, or 05 site series (Table 3).
Table 3. Num ber of regeneration plots sam pled in pine-dominated stands on
different site series in different biogeodim atic subzones.
BEC Unit
dk
dw2
dw3
mc2
mc3
m kl
mw
w kl
Total

01
142
16
38
97
20
12
1
0
326

02
71
0
2
21
0
2
0
0
96

03
52
6
27
1
2
16
0
7
111

04
0
13
45
0
114
4
2
3
181

Site Series
07
05
06
3
2
21
2
1
2
39
14
73
13
5
0
2
0
5
9
0
23
0
0
0
1
0
3
137 58
23

08
0
0
3
0
0
0
0
0
3

09
0
4
16
0
0
1
0
0
21

10
1
1
2
4
0
0
0
0
8

Total
292
45
259
141
143
67
3
14
964

The 964 plots were located on a range of topographic locations. The percentages on
the site meso-slope cross section (Figure 6) quantify the location of the 964 plots
according to their topographical locations (as determ ined by intersection w ith VRI
digital data). It should be noted that although site mesoslope position w as one of
the potential predidors, it was a more general topographic descriptor nam ed
surface expression (VRI, 2006) that became a key predictor variable.

40

57-5%

3.8%

1.8%

3.6%

Stockad Plots 0.0%

0.4%

63.3%

4.9%

12%

5.3%

M iddle

L ow er

*

►

1
1
1
1
1
«
«
1
«
1

c
.2
0}

sa
s

L evel

0.4%

C re st

0.1%

U pper

All Mots

t of Plots
Site Position Meoo
NA
crest

31*

fUtOeveO

35

lower slope
middle slope
toe

37
554
17
4

1

* NA * 32.8%

Figure 6. Proportion of the stu d y area p lo t locations (n=964) am ong different site m eso­
slope positions. N A represents plots for w hich m eso-slope value was n o t available in the
VRI

The distribution of plots reflects the current age class structure of pine forests in the
Northern Interior, with many m apped as being greater than 100 years of age, but
w ith "old-growth" lodgepole pine and natural stands under 80 years of age m uch
more difficult to find. The distribution of plots by stand age and BEC subzone is
shown in Table 4. Cross-tabulating plots by site series and age class, a
concentration of sampling in circum-mesic stands 80 to 140 years of age is evident
(Table 5). Note that site series 07,08,09,10 have been binned into a single "m oist
41

Table 4. Num ber of regeneration plots sampled in pine-dominated forest cover
polygons by age classes* and biogeodim atic subzones.
BEC Unit
dk
dw2
dw3
mc2
mc3
m kl
mw
w kl
Total

4
9
4
2
0
14
0
0
0
29

5
63
4
103
2
5
32
0
14
223

Nominal M apped Age Class *
9
7
8
6
55
64
101
0
24
0
10
3
22
0
42
90
2
23
104
10
1
0
105
18
4
31
0
0
3
0
0
0
0
0
0
0
113
242
354
3

Total
292
45
259
141
143
67
3
14
964

* age class 4 is 61 to 80 years, age class 5 is 81 to 100, age class 6 is 101 to 120, age
dass 7 is 121 to 140, age class 8 is 141 to 240, and age class 9 is 240+ years.
Table 5. N um ber of regeneration plots sam pled in pine-dom inated stands b y age classes*
and sites series, across all biogeodim atic subzones.

Site Series
01
02
03
04
05
06
07,08,09,10
Total

4
6
8
3
10
0
1
1
29

5
28
27
37
22
64
28
17
223

Nominal M apped Age Class *
7
9
6
8
76
2
48
166
16
1
8
36
17
0
23
31
99
0
10
40
19
45
0
9
5
14
0
10
10
0
22
5
242
354
3
113

* age dass 4 is 61 to 80 years, age class 5 is 81 to 100, age class 6 is 101 to 120, age
dass 7 is 121 to 140, age class 8 is 141 to 240 years, and age dass 9 is 240+ years.

42

Total
326
96
111
181
137
58
55
964

site" category in order to increase sample size. Across all 964 plots, advance
regeneration by all species (>10cm tall) averaged a m ean density of 1268 stems/ha
and a median density of 600 stems/ha. This means that one-half of the plots
sampled had more than 600 stems/ha of advance regeneration (my thesis threshold
for designating a plot as stocked), and one-half of the plots sampled had less.
A paired-samples t-test was conducted to determine if there was a significant
difference between the m ean densities of advance regeneration w hen calculations
included and excluded non-conifer species. I found that there was not a significant
difference in the mean density between conifers only (mean=1267.87, s.d.=1911.90
stems/ha) and all species (mean=1289.02, s.d.=1909.36 stems/ha) across the study
area; t963=4.42, P = 0.08. This result suggests that non-conifer species do not
significantly influence the mean density of advance regeneration, and by extension,
the stocking status of the stand.
An examination of advance regeneration across biogeodim atic subzones shows that
mean densities across all subzones exceed the 600 stem s/ha— except in the SBSmw,
a subzone with only three samples. Comparison of m ean and median advance
regeneration densities across the thesis study area proved to be quite valuable, as
this comparison indicates; most sub-populations are not normally distributed.
Mean regeneration densities for each BEC unit, age dass, and forest district
respectively are presented in Tables 6 through 8.
43

Table 6. Descriptive statistics for advance regeneration densities (stems/ha) for all sam ple
plots in each BEC unit. Mean, m edian, stan d ard deviation, and interquartile ran g es are
reported.

BEC Unit
dk
dw2
dw3
mc2
mc3
m kl
mw
w kl

n
287
45
262
143
143
61
3
20

Mean
743
1504
1278
1086
2120
2077
266
2035

s.d
1342
1649
1661
1414
2992
2263
115
1571

25%
0
200
200
200
200
400
200
850

Median
200
1200
750
600
600
1200
200
1650

75%
800
1700
1600
1400
3250
2700
300
3750

Table 7. Descriptive statistics for advance regeneration densities (stems/ha) for all sam ple
plots per age class. Mean, m edian, stan d ard deviation, and interquartile ranges are
reported.

Age Class
4
5
6
7
8
9

n
29
223
113
242
356
1

Mean
231
1221
1132
1399
1387
2800

s.d
355
1597
1435
2082
2136
na

25%
0
200
200
200
200
2800

Median
100
600
600
600
600
2800

75%
300
1700
1600
1675
1613
2800

Table 8. Descriptive statistics for advance regeneration densities (stems/ha) for all sam ple
plots p er forest district. M ean, m edian, stan d ard deviation, and interquartile ran g es are
reported.

Forest District
Fort St. James
Nadina
Prince George
Quesnel
Vanderhoof

n
1
350
275
4
334

Mean
1200
746
1410
900
1762

44

s.d
na
1283
1663
621
2446

25%
1200
0
300
500
200

Median
1200
400
900
900
750

75%
1200
1000
1750
1300
2375

Across the entire study area, there w as a near equal distribution of stocked and
not stocked across the 964 sample plots for all three stocking groups (Table 9).
Table 9. Total num ber of stocked and n o t stocked sam ple plots across the stu d y area based
on three different definitions of acceptable stocking (stocking groups).

Stocked

N ot Stocked

All Tree Species (600 stem s/ha)

510

454

Conifer Species only (600 stems/ha)

496

468

M inim um Stocking S tandards *

460

504

Stocking G roup

Based on the sampling within the study area, all bu t two BEC units (SBSdk
and mw) are greater than 50% stocked for all stocking groups, and as high as 70%
stocked in the m k l and w kl BEC units (Figures 7 , 8 , and 9). The biogeoclimatic
unit SBSmw had no stocked plots within the study area. It is worth noting that
there were only three plots gathered in the mw subzone variant, all collected from
the same stand.
In an attempt to identify any key variables that m ay have a direct (positive or
negative) effect on the advance regeneration densities, several potential key
variables were examined through a simple linear regression model. This exercise
was conducted for the purposes of data exploration and description only, searching
for any potential relationships between the advance regeneration
45

100%
90%
jj i

80%

|

70%

|

60%

S

50%

e

40%

|

30%

.2

S 20%
**

10%
0%
dk

dw 2

dw 3

m c2

m c3

m kl

mw

w kl

B io g eo c lim a tic U n it

Figure 7. Proportion of 964 plots in pine-leading forest cover polygons in th e N o rth ern
Interior Forest Region that m eet a 600 stem s/ha stocking density threshold (for all tree
species).
100%
^

90%

|

80%

55

70%

|

60%

5

50%

e

40%

'€

30%

| 20%
10%
0%
dk

dw 2

dw 3

m c2

m c3

m kl

mw

w kl

B io g eo c lim a tic U n it

Figure 8. Proportion of 964 plots in pine-leading forest cover polygons in th e N o rth ern
Interior Forest Region that m eet a 600 stem s/ha stocking density threshold (for conifer
species).

46

100%
na 90%
|

80%

35 70%
|

60%

£
o
e

40%

50%

•S 30%
g1 20%
10%
0%
dk

dw 2

dw 3

m c2

m c3

m kl

mw

w kl

B io g eo c lim a tic U n it

Figure 9. P roportion of 964 plots in pine-leading forest cover polygons in the N o rth ern
Interior Forest Region th a t m eet a prescribed stocking density threshold (for m in im u m
stocking stan d ard s - preferred and acceptable species).

(positive or negative) effect on the advance regeneration densities, several potential
key variables w ere examined through a simple linear regression model. This
exercise was conducted for the purposes of data exploration and description only,
searching for any potential relationships between the advance regeneration
stems/ha of each stand and basal area (from VRI), distance to nearest seed source
(calculated using GIS), live pine volume per ha (VRI), dead pine volum e per ha
(VRI), mean annual precipitation (ClimateBC), m ean annual tem perature
(ClimateBC), stand height (VRI), and stand age (VRI). The results of the models,
presented in Figures 10 through 14, are represented as scatterplots. The exercise did
not uncover any variables that had a strong (r2 >0.5) linear relationship w ith density
of advance regeneration. Only distance from nearest seed source yielded a

47

statistically significant result (P=0.007). The r2(0.008), however, indicates that
distance from nearest seed source explains less than 1% of the variation in advance
regeneration stems/ha. The resulting linear regression equation for distance from
nearest seed source is total stems/ha = 1462.0493 - 0.5851 * m to nearest seed source.

18000

•
16000

1 14000

JiCO
12000

•

I 10000
4>
s60V

*

•
a

8000

<
uu

I

•

d

6000

■■................

4000

.....

• •
i••

.

5 M

< 2000

•
* * ------1
•

0 , , » M
20

40

60

80

100

120

140

Basal Area (m2/ha)

Figure 10. Scatterplot of advance regeneration density vs. stan d basal area (r2 = 0.0002315,
P = 0.637, F = 0.2228, n = 964).

48

18000

m 16000
*5
14000

a
~

12000

i
*•2 io o o o
8w

s

8000 ■* '
bO
u
LV
B3
w
u

# * # «* • .. •
•*

* -

200

400

y • -0.5851X +1462
R 2 = 0.0075

<
600

800

1000

1200

1400

1600

Distance to Nearest Non-Pine Seed Source (m)
Figure 11. Scatterplot of advance regeneration density vs. distance to the n eare st non-pine
seed source (r2 = 0.008, P = 0.007, F= 7.239, n = 964).
18000
« 16000
14000
12000
•-C 1 0 0 0 0

2000
-T -

200

400

600

800

1000

M e a n A n n u a l P recin itatin n (m m )
Figure 12. Scatterplot of advance regeneration density vs. distance to the n eare st non-pine
seed source (r2= 0.003, P = 0.058, F= 3.596, n = 964.)
49

18000
16000
14000

12000

10000

0

5

10

15

20

25

30

35

Projected Height For Leading Species (m)
Figure 13. Scatterplot of advance regeneration density vs. stan d projected h eig h t (r2 = 0.001,
P = 0.436, F= 0.6068, n = 964).

m1
<5
CD
5QJ ■
CO.

1 *

I

V
ft
60
V
6
V
V
V

■a

<

0

50

100

150

200

250

300

Projected Age For Leading Species (yr)
Figure 14. Scatterplot of advance regeneration density vs. stan d projected age (r2 = 0.003,
P = 0.076, F= 3.147, n = 964).
50

Classification Tree Analysis
My model derived from the rpart module in R classified the presence/absence
of advance regeneration stocking w ith an accuracy of 77% (11 terminal nodes) for
all-tree stocking, 78% (13 terminal nodes) for conifer-only stocking, and 78% (14
terminal nodes) for MSSpa stocking. As expected, the identity and order of
predictors deemed im portant by the models were similar for each of the three
stocking groups. The final tree for all three stocking groups had BEC unit, distance
to nearest non-pine seed source, projected stand age, and basal area as their top four
im portant variables. It is also interesting that all three stocking groups utilized the
categorical variable BEC unit as their initial split, making it the most im portant
variable for all three groups. This w ould appear to indicate that the density of
advance regeneration is influenced by the broad factors associated w ith
biogeoclimatic subzones (i.e., climate, vegetation, soil) and may im ply that the
model is suitable as an overarching landscape-level predictor.
The critical statistical outputs for the final model (Table 10) indicate that in
all three stocking groups, the resultant final tree w as larger than it needed to be (i.e.,
the num ber of terminal nodes before pruning was overfitting the data) and that a
simpler tree with fewer terminal nodes could achieve the same (or better) accuracy.
The num bers of terminal nodes after pruning are the final number of nodes
associated w ith the best fitting and m ost parsimonious classification tree model.
51

Table 10. Key statistics describing the classification tree accuracy for the advance
regeneration prediction model. The classification tree size, accuracy, and evaluation are
listed for all three stocking groups. MSSpa is the Minimum stocking standard (various
stems/ha) of preferred and acceptable species, particular to each site series in each BEC unit.

600 stems/ha
(all tree)

600 stems/ha
conifers)

MSSpa

Number of terminal nodes
(before turning)

24

31

29

Number of terminal nodes
(after pruning)

11

14

14

Number of splits
(after pruning)

10

13

13

Sensitivity
(true positive rate)

82.45%

80.85%

71.99%

Specificity
(false positive rate)

71.33%

74.15%

83.63%.

Misclassification rate

0.2282

0.2241

0.2189

Model accuracy

77.18%

77.59%

78.11%,

ROC score

0.8386

0.8327

0.8528

The red arrows in Figure 15 illustrates the path of a rule from initial split to term inal
node. The initial split at SUBZVAR (BEC unit) is governed by the rule that the plot
m ust be located in SBSdk or SBSmw to follow this branch.

52

YES

SU BVAR = dk, mw
^

NO

DISTAN CEnear >= 544

BASAL AREA >=39

SURFACE_EXPRESSION = N,
51% of 150

84% of 44

PROJ_H EIGHT <21
100% of 8

74% of 34

79% of 14

Figure 15. Example of a rule path in the conifer only 600 stems/ha classification tree. The
tree begins with an initial split of BEC unit and terminates after a split based on surface
expression. This rule can be found in Table 15 as rule number 10.

The second split at DISTANCEnear (distance to nearest non-pine seed source) is
governed by a threshold of 544 m to the nearest non-pine seed source. If the nearest
distance to a non-pine seed source is >544 m, then the rule follows to the left and
53

terminates at the dark green node classified as 0, or not stocked. The rule indicates
that 96 plots are present in the split. The rule stipulates that there are only 96 plots
that fit both splits (BEC unit and distance to nearest seed source) and that the
likelihood of those 96 plots being not stocked is 17%. This provides a low
confidence that BEC unit and distance from nearest non-pine seed source alone are
good indicators for predicting stocking. If the plot is <544.3 m to the nearest non
pine seed source, then the rule follows the branch to the right where it encounters a
split at basal area. If the basal area is <39.34 m2/ha, then the rule follows to the right
where it encounters its last split of surface expression being either U (undulating) or
M (rolling). The plot terminates as a stocked node, where 100% of the 8 plots in the
964 plot dataset that conformed to this set of rules were correctly classified as
stocked.
The rule in text form reads as follows:
SUBZVAR=dk, or mw
DISTANCEnear<544.3 m
BASAL_AREA<39.34 m2/ha
SURFACE_EXPRESSION=M (rolling), or P (undulating)
The fully pruned classification trees (for all three stocking groups) provide
sets of rules for the prediction of stocked with seedlings and saplings (Figure 16,17,
18). The trees are interpreted (as per Figure 14) by following the splits in the
branches — to the left if the split value in the tree is true and to the right if the split

54

Projected Age < 7* yi»

Diitanceto nwraM non-pin* tourc* > ■ SS7m

Saul Aim >* 39 m2Ai*

in
in

Surfec* Expression * It U

9*%af 1 8 / U m f c ^ lm O ^ V b iu m .p - lta c ttm c ttm M -

Sped** of n**r*st non-pin* m uk* • AU&ft&Sx

Meen ennuil temperature >■ 4 ariciue

0
57*o« 10«

Projected Height < 21m

0
61%of 91

Figure 16. Final pruned (using 10-fold cross-validation) classification tree model for predicting the probability of stocking by all
tree species

m

nan Sutaons-d^mwfBTI

0

0

Dbta«K»tOMMftno(V{Mmsourc*>-344m

Prc|aaad Aga < 7®yvs

UKHngSpadaiOtadVbkmaparMKtam<4JmMia

Raul Ana >wMma/ha

SurfxaEjpasta-ttU

SpactesofManatnor-pinasuica- M
JEaSw^c

ManamualMnpanOm>-«cddui

1

44%of553

Ln

o>
ReactedHaight<2ira

T
[M % o f» 1

\

Bmdon<733*1

SpKtMofiMna nc»vp*»«ourc# mttff f t f i f i *

J

ftqfKtsdMgM»- 19m
74*0(34

79%S ill

OWanots nH fut ikihiIm m m > « ic fn

Figure 17. Final pruned (using 10-fold cross-validation) classification tree
model for predicting the probability of stocking by conifer only species.

PrcfKiodAg»<7Yyti

•wriAnb>■19mMwi

LoadingSpactoDoadUbfemoporHactam<42mart*

Otoncetoneaiesineiw0iesoira>■ssmi
12% Of212

SwracoBtpPHM
Dn- N,u

l/lJ
N

SpadMOfMarMnoivpiMSOuffia-ALSw.SR

SubBMadW^IKl

M m annul pradpiMon< Siam */ t
Ita m o f a J

SgadH of rwaraot notvfUnt some* - I tfifib j*

Figure 18. Final pruned (using 10-fold cross-validation)
classification tree model for predicting the probability of
MSSpa stocking.

ftqfKMIWghUKiri

value in the tree is false, until a terminal node is reached. The num ber of root-toterminal nodes range from a minimum of two splits to a maximum of 14 splits.
The key to building the classification tree is the identification of the im portant
variables used, as they are the only variables used in the resultant rules. The order
of appearance in the classification tree does not necessarily indicate the strength or
overall importance of a particular variable. W hat is m ore important is the variable's
overall contribution to the m odel (i.e., is the model worse without it?)
The important variables for predicting the probability of stocking for all three
stocking groups remained consistent. Even though the classification m odel had
access to an input of 54 equally weighted potential predictors, Table 11 details the
important variables (and therefore significant ecological factors) selected for each
classification tree.
Table 11. List of important variables/significant ecological factors involved in the final
model predicting the probability of stocking. MSSpa is the Minimum stocking standard
(various stems/ha) of preferred and acceptable species, particular to each site series in each
BEC unit.
Variable/Ecological Factor
Biogeoclimatic Unit
Projected Height for Leading Species
Leading Species Dead Volume/ha at 12.5 cm
Elevation
Basal area
Projected Age for Leading Species
Species Composition of Nearest Non-pine Seed Source
Distance (m) to Nearest Non-pine Seed Source (SW direction)
Mean Annual Temperature
Surface Expression
Mean Annual Precipitation
Leading Species Live Vohime/ha at 12.5 cm

58

Classification Tree
all trees
conifers MSSpa
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓

The variable importance for each stocking group is based on the m ean decrease in
accuracy. The higher the m ean decrease in accuracy, the more im portant the
variable is for the overall predictive accuracy of the model (Table 12).
The classification tree branches are translated into textual paths that can be
interpreted as a collection of rules (Tables 13-15). They are listed in the order of
their strength, i.e., highest probability in predicting the target variable (stocked or
not stocked). For example: there are 11 textual rules for the stocking group all tree
species (listed in Table 13). The two strongest and highest probability rules are:
Predictive Rule (Rank 1) probability = 1.00
biogeoclimatic unit = dk, or m w
distance to the nearest non-pine seed source <557 m
stand basal area <39 m2/ha
surface expression = M (rolling), or P (undulating)
Following the tree in Figure 16, the above predictive rule terminates at node 23. The
probability of 1.00 relates to the node text 1:100% of 8. The 1 indicates that the rule
results in the prediction of a stocked cell. The 100% of 8 indicate that 8 of the 964
plots remain in the predictive solution at this point of the tree. And of the
remaining 8 plots, all 8 plots are both actually stocked and predicted to be stocked,
resulting in a 100% prediction or 1.00 probability. This set of rules has the highest
confidence for predictive power on test plots. The rule set with the second strongest
predictive power terminates at node 29 in Figure 16. The following path through
the classification tree (represented by textual rules below) indicates that 13 of the
59

Table 12. Classification tree variable importance (in order of importance) for each stocking
group. Order of importance is determined by the mean decrease accuracy value; a higher
mean decrease accuracy values indicate a more important variable for prediction.
all tree species stocking group

1
2
3
4
5
6
7
8
9
10

Variable Importance

MeanDecreaseAcccuracy

Biogeoclimatic Unit
Distance (m) to Nearest Non-pine Seed Source (SW direction)
Projected Age for Leading Species
Leading Species Dead Volume per Hectare at 12.5 cm
Basal area
Projected Height for Leading Species
Mean Annual Temperature
Species Composition of Nearest Non-pine Seed Source
Elevation
Surface Expression

1.01
0.93
0.93
0.91
0.86
0.86
0.85
0.83
0.81
0.44

conifer only stocking group

1
2
3
4
5
6
7
8
9
10

Variable Importance

MeanDecreaseAcccuracy

Biogeoclimatic Unit
Distance (m) to Nearest Non-pine Seed Source (SW direction)
Leading Species Dead Volume per Hectare a t 12.5 cm
Projected Age for Leading Species
Basal area
Projected Height for Leading Species
Species Composition of Nearest Non-pine Seed Source
Mean Annual Temperature
Elevation
Surface Expression

1.02
0.90
0.90
0.89
0.88
0.87
0.87
0.86
0.84
0.54

MSSpa stocking group

1
2
3
4
5
6
7
8
9
10

Variable Importance

MeanDecreaseAcccuracy

Biogeoclimatic Unit
Leading Species Dead Volume per Hectare at 12.5 cm
Projected Age for Leading Species
Basal area
Distance (m) to Nearest Non-pine Seed Source (SW direction)
Projected Height for Leading Species
Leading Species Live Volume per Hectare at 12.5 cm
Mean Annual Precipitation
Species Composition of Nearest Non-pine Seed Source
Surface Expression

1.04
1.01
0.96
0.95
0.92
0.92
0.91
0.88
0.88
0.59

60

Table 13. Translation of classification tree model for predicting the probability of stocking
in all tree species 600 stems/ha stocking threshold into textual rules.
600 stemsAta (all trees)
stocked
1 allsp600“ l prob=1.00
SUBZVAR=dk,mw
DJSTANCEnear< 557.4
BASAL_AREA< 38.78
SUKFACE_EXPRESSION=M,P

not stocked
6 allsp600=0 prob=0.37
SUBZVAR-dw2,dw3,mc2,mc3,mkl ,wkl
PROJ_AGE_l>=77.5
DEAD_VOL_PER_HA_SPPl_125< 4233
SPECIES_CD_lnear-AT,EF,SW,SX

2 allsp600*1 prob-O.85
SUBZVAR=dw2,dw3,mc2,mc3,mkl,wkl
PROJ_AGE_l>-77.5
DEAD_VOL_PER_HA_SPPl_125< 42.33
SPEOES_CD_lnear*SSB

7 allsp600=0 prob-0.31
SUBZVAR*dk,mw
DISTANCEnear< 557.4
BASAL_AREA< 38.78
SURFACEJEXFRESS!ON=N,U
PROJ_HEIGHT_l< 2135

3 allsp600*l prob-0.75
SUBZVAR-dk,mw
DISTANCEnear< 557.4
BASAL_AREA< 38.78
SURFACE_EXFRESSION*N,U
PROJ_HEIGHT_l>=21.35
4 allsp600=l prob=0.69
SUBZVAR-dw2,dw3,mc2,mc3,mkl,wkl
PROJ_AGE_l»77.5
DEAD_VOL_PER_HA_SFPl_125>-4233
MAT>=4.05
Elevation>=722.5
5 allsp600*l prob=0.68
S UBZVAR=dw2,dw3,mc2,mc3,mkl,wkl
PROJ_AGE_l >*77.5
DEAD_VOL_PER_HA_SPPl_125>=42.33
MAT< 4.05

8 allsp600*0 prob=0.21
SUBZVAR*dw2/dw3,mc2,mc3,mkl,wkl
FROJ_AGE_l>-77.5
DEAD_VOL_PER_HA_SPP1.125>=42.33
MAT>*4.05
Elevation< 722.5
9 allsp600=0 prob=0.20
SUBZVAR=dk,mw
DISTANCEnear< 557.4
BASAL_AREA>*38.78
10 allsp600=0 prob=0.17
SUBZVAR=dk,mw
DISTANCEnear>=557.4
11 allsp600-0 prob=0.06
SUBZVAR=dw2,dw3,mc2,mc3,mkl ,wkl
PROJ_AGE_l< 77.5

61

Table 14. Translation of classification tree model for predicting the probability of stocking
in conifer-only 600 stems/ha stocking threshold into textual rules.
600 stems/ha (conifers only)
___________________stocked_________
1 conifer600=l prob=1.00
SUBZVAR=dk,mw
DBTANCEneaK 544.3
BASAL_AREA< 39.34
SURFACE_EXPRESSION=M,P
2 conifer600=l prob=0.90
SUBZVAR*dw2,dw3,mc2,mc3,mkl ,wkl
PROJ_AGE_l>-77.5
DEAD_VOL_PER_HA_SPPl_125>-42.33
MAT< 4.05
SPECIES_CD_lneai=AT,EP,FD,FDtS,SX
PROJ_HHGHT_l< 19.25
3 conifer600-l prob-0.85
SUBZVAR=dw2,dw3,mc2,mc3,mkl,wkl
PROJ_AGE_l >-77 3
DEAD_VOL_PER_HA_SPPl_125< 42.33
SPEQES_CD_lnear=S,SB
4 conifer600=l prob=0.79
SUBZVAR=dk,mw
DISTANCEnear< 5443
BASAL_AREA< 39.34
SURFACE_EXPRESSKDN=N,U
PROJ_HEIGHT_l >=21.35
5 conifer600”l prob-0.74
SUBZVAR=dw2,dw3,mc2,mc3,mkl ,wkl
PROJ_AGE_l>-77.5
DEAD_VOL_PER_HA_SPPl _125>=42.33
MAT< 4.05
SPEOES_CD_lnear=BLSB,SW,SXW
6 conifer600=l prob=0.69
SUBZVAR=dw2,dw3,mc2,mc3,mkl ,wkl
PROJ_AGE_l>-77.5
DEAD_VOL_PER_HA_SPPl_125>-42.33
MAT>=4.05
Elevation>=722.5

___________________ not stocked________
8 conifer600=0 prob=0.40
SUBZVAR-dw2,dw3,mc2,mc3,mkl ,wkl
PROJ_AGE_l>=77.5
DEAD_VOL_PER_HA_SPPl_125>=42.33
MAT< 4.05
SPECIES_CD_lnear=AT,EP,FD,FDI,S,SX
FROJ_HElGHT_l>=19.25
DBTANCEnear>-l 82.4
9 conifer600=0 prob=0.36
SUBZVAR=dw2,dw3,mc2,mc3,mkl ,wkl
PROJ_AGE_1>-77 3
DEAD_VOL_PER_HA_SPPl_125< 42.33
SPECIES_CD_lnear-AT,EP5W,SX
10 conifer600=0 prob-0.26
SUBZVAR=dk,mw
DBTANCEneaK 544.3
BASAL_AREA< 39.34
SURFACE_EXPRESS!ON=N,U
PROJ_HEIGHT_l< 21.35
11 conifer600-0 prob=0 21
SUBZVAR=dw2,dw3,mc2,mc3,mkl ,wkl
FROJ_AGE_l>=77.5
DEAD_VOL_PER_HA_SPPl_l 25>«42.33
MAT>-4.05
Elevation< 722.5
12 conifer600-0 prob=0.17
SUBZVAR=dk,mw
DBTANCEnear>-544.3
13 conifer600=0 prob=0.16
SUBZVAR=dk,mw
DBTANCEneaK 5443
BASAL_AREA>-39.34
14 conifer600”0 prob-0.06
SUBZVAR“dw2,dw3,mc2,mc3,mkl ,wkl
PROJ_AGE_l< 77.5

7 conifer600=l prob=0.63
SUBZVAR=dw2,dw3,mc2,mc3,mkl,wkl
PROJ_AGE_l >=77.5
DEAD_VOL_PER_HA_SPPl_125>=42.33
MAT< 4.05
SPECIES_CD_lnear“AT,EP>FD/FDkS,SX
PROJ_HEKj HT_1>=19.25
DBTANCEneaK 182.4

62

Table 15. Translation of classification tree model for predicting the probability of stocking
in all minimum stocking standards stocking threshold into textual rules.
MSSpa (preferred and acceptable)
stocked
1 MSSpa-l prob-1.00
SUBZVAR=dk,mw
BASAL_AREA< 38.78
DBTANCEnear< 557.4
SURFACE_EXPRESSION=M,P

not stocked
8 M5Spa=0 prob-0.30
SUBZVAR-dw2,dw3,mc2,mc3,mkl,wkl
FROJ_AGE_l >-79.5
DEAD_VOL_PER_HA_SPPl_125< 42.33
SFECIES_CD_lnear-AT,SW,SX

2 MSSpa-l prob-0.78
SUBZVAR=dk,mw
BASAL_AREA< 38.78
DISTANCEnear< 557.4
SURFACE_EXPRESSION-N,U
MAP>=510

9 MSSpa-0 prob-0.24
SUBZVAR=dw2,dw3,mc2,mc3,mkl,wkl
PROJ_AGE_l>-79.5
DEAD_VOL_PER_HA_SPPl_l 25>-42.33
SUBZVAR-dw3,mc2
DEAD_VOL_PER_HA_SPPl_l 25>-l 42.8
UV E_VOL_PER_HA_SPP1_125>=72.22
SPECIES_CD_1near-AT,S ,SB,SX

3 MSSpa-l prob-0.75
SUBZVAR=dw2,dw3,mc2,mc3,mkl,wkl
PROJ_AGE_l>»79.5
DEAD_VOL_PER_HA_SPPl_125< 42.33
SPECIES_CD_lnear=EP,S,SB
4 MiSpa-1 prob-0.71
SUBZVAR-dw2,dw3,mc2,mc3,mkl,wkl
PROJ_AGE_l>=79.5
DEAD_VOL_PER_HA_SFPl_125>=42.33
SUBZVAR-dw2,mc3,mkl,wkl
5 MSSpa-l prob-0.68
SUBZVAR=dw2,dw3,mc2,mc3,mkl ,wkl
PROJ_AGE_l>-79.5
DEAD_VOL_PER_HA_SPPl_125>-42.33
SUBZVAR=dw3,mc2
DEAD_VOL_PER_HA_SPPl_125< 142.8
6 MSSpa-l prob-0.59
SUBZVAR=dw2,dw3,mc2,mc3,mkl,wkl
PROJ_AGE_l>-79S
DEAD_VOL_PER_HA_SPPl _ 125>=42.33
SUBZVAR=dw3,mc2
DEAD_VOL_PER_HA_SPPl_125>-142.8
LTVE_VOL_PER_HA_SPP1_125>=72.22
SPECIES_CD_lnear-EP,FD,SW
FROJ_HEIGHT_l>=24.75
7 MSSpa-l prob-0.58
SUBZVAR-dw2,dw3,mc2,mc3,mkl,wkl
PROJ_AGE_l >-79.5
DEAD_VOL_PER_HA_SPPl_125>=42.33
SUBZVAR-dw3,mc2
DEAD_VOL_PER_UA_SPPl_125>-142.8
UVE_VOL_PER_HA_SPPl_125< 7222

10 MSSpa-0 prob-0.21
SUBZVAR=dk,mw
BASAL_AREA< 38.78
DISTANCEnear< 557.4
SURFACE_EXFRESSION=N,U
MAP< 510
11 MSSpa-0 prob-0.16
SUBZVAR=dk,mw
BASAL_AREA< 38.78
DISTANCEnear>=557.4
12 MSSpa-0 prob=0.12
SUBZVAR=dw2,dw3,mc2,mc3,mkl,wkl
PROJ_AGE_l>=79.5
DEAD_VOL_PER_HA_SPPl_125>-42.33
SUBZVAR-dw3,mc2
DEAD_VOL_PER_HA_SPPl_125>=142.8
UVEJVOL_PER_HA_SFPl_125>=72.22
SPECIES_CD_lnear-EP,FD,SW
PROJ_HEIGHT_l < 24.75
13 MSSpa=0 prob=0.12
SUBZVAR-dk,mw
BASAL_AREA>=38.78
14 MSSpa-0 prob=0.05
SUB2TVAR-dw2,dw3,mc2,mc3,mkl,wkl
PROJ_AGE_l< 79.5

63

964 plots remaining in the predictive solution at this point of die tree are correct
with 85% prediction or 0.85 probability.
Predictive Rule (Rank 2) probability = 0.85
biogeoclimatic unit = dw2, dw3, mc2, mc3, m kl, or w k l
stand age >78 yrs
stand estimated dead volume <42 m 3/ha
species of the nearest non-pine seed source = Spruce
The ROC evaluations for all three stocking groups indicate that m y predictive
model is a useful application, as all the ROC scores are above 0.83 (0.5-0.7 are
considered low accuracy, 0.7-0.9 are considered useful, and ROC values > 0.9
indicate high accuracy) (Manel et al., 2001). The area under the ROC curve (AUC)
represents the probability that the model will rank a randomly chosen positive
instance (true positive) higher than a random ly chosen negative one (false positive).
The AUC scores are 84%, 83%, and 85% for all tree species, conifers only, and
MSSpa respectively (Figures 19,20, and 21).

Applying the Classification Tree in a GIS M odel
Maps illustrating the probability of stocking were generated for each of the
three stocking groups per 1:250,000 m ap tile. A full series of maps, depicting the
probability of stocking themed by five probability classes, for the 1:250,000 m ap tiles
covering the study area are presented in Appendix 2.

64

ROC for allsp600 = 1

0.0

0.1

0.2

0.3

0.4
0.5
0.6
False Positive Rate

0.7

0.8

0.9

1.0

Figure 19. ROC curve chart illustrating the accuracy of the classification tree model (all tree
species 600 stems/ha threshold) through area under curve (AUC) statistic.

ROC for conifer600 = 1

F a s t Positive Rate

Figure 20. ROC curve chart illustrating the accuracy of the classification tree model
(conifer-only threshold) through area under curve (AUC) statistic.

65

ROC for M SS d s = 1

0.0

0.1

0.2

0.3

0.4
0.5
0.6
False Positive Rats

0.7

0.8

0.9

1.0

Figure 21. ROC curve chart illustrating the accuracy of the classification tree model
(minimum stocking standard threshold) through area under curve (AUC) statistic.
The probability of stocking tables indicate that approximately 63% of the
study area (when m easured by a stocking threshold of 600 stems/ha for all tree
species) is likely to very likely stocked; approximately 60% of the study area (when
stocking is m easured by a 600 stems/ha threshold for conifers only) is likely to very
likely stocked; and approximately 44% of the study area (when stocking is
measured by MSSpa) is likely to very likely stocked (Tables 16, 17, and 18).
Translated into area, this m eans that the study area (comprised of 1.4 million ha of
m ature pine stands) can be expected to have up to 616,000 ha of stocked w ith
seedlings and saplings (measured by MSSpa), 833,000 ha of stocked w ith seedlings
and saplings (measured by 600 stems/ha all tree species), or 878,000 ha of stocked
with seedlings and saplings (measured by600 stems/ha conifers only).
66

Table 16. Probability (as a percentage) of being stocked for each BEC unit derived from the
classification tree rule set for conifer only 600 stems/ha stocking threshold.

BEC unit

M ature
Pine (ha)

0-20
Very Likely
Not Stocked

Probability of Being Stocked (as percentage)
60.1-80
20.1-40
40.1-60
Likely
Likely
As Likely
Not Stocked
Stocked
Stocked As Not

80.1-100
Very Likely
Stocked

SBSdk all trees
SBSdk conifers
SBSdkMSSpa

282539

40
40
46

16
18
14

0
0
6

5
5
21

39
37
12

SBSdw2 all trees
SBSdw2 conifers
SBSdw2 MSSpa

80876

18
17
36

15
13
13

7
0
10

36
49
21

23
21
20

SBSdw3 all trees
SBSdw3 conifers
SBSdw3 MSSpa

291425

15
15
32

15
13
17

9
0
7

32
47
22

29
25
22

SBSmc2 all trees
SBSmc2 conifers
SBSmc2 MSSpa

479996

16
26
34

15
11
10

11
0
9

27
37
21

31
27
26

SBSmc3 all trees
SBSmc3 conifers
SBSmc3 MSSpa

77284

15
41
39

7
5
11

9
0
12

31
26
16

38
28
22

SBSmkl all trees
SBSmkl conifers
SBSmkl MSSpa

259730

14
14
31

6
11
13

5
0
3

37
37
15

38
38
38

SBSmw all trees
SBSmw conifers
SBSmw MSSpa

5283

71
70
92

13
17
0

0
0
0

3
3
6

13
9
2

SBSwkl all trees
SBSwkl conifers
SBSwkl MSSpa

22014

18
14
23

3
12
29

8
0
1

28
36
29

44
38
17

Study Area all trees
Study Area conifers
Study Area MSSpa

1499147

20
25
36

13
12
13

7
0
7

26
33
20

33
30
24

67

Table 17. Probability (as a percentage) of being stocked for each 1:250,000 NTS maptile
derived from the classification tree rule set for conifer only 600 stems/ha stocking threshold.
NTS 1:250,000
Maptfle

Mature
Pine (ha)

0-20
Very Likely
Not Stocked
20
35
33

Probability of Being Stocked (as percentage)
20.1-40
40.1-60
60.1-80
Likely
As Likely
Likely
Not Stocked
Stocked As Not
Stocked
27
16
11
11
0
34
9
12
11

80.1-100
Very Likely
Stocked
27
20
36

93E all trees
93E conifers
93E MSSpa

161479

93F all trees
93F conifers
93F MSSpa

360025

29
38
41

14
13
9

4
0
10

19
16
24

34
33
16

93G all trees
93G conifers
93G MSSpa

220916

21
16
35

14
15
13

7
0
8

33
48
24

25
20
20

93J all trees
93J conifers
93J MSSpa

278669

13
14
29

9
12
18

6
0
4

35
38
13

36
36
36

93K aH trees
93K conifers
93K MSSpa

305215

16
20
36

14
10
11

9
0
6

26
36
26

35
34
20

93L an trees
93L conifers
93L MSSpa

172843

20
23
39

13
15
16

8
0
5

17
34
16

42
29
24

68

Table 18. Probability (as a percentage) of being stocked for each forest district derived from
the classification tree rule set for conifer only 600 stems/ha stocking threshold.
Forest District
Mature
Pine (ha)

Probability of being stocked (as percentage)
20.1-40
40.1-60
60.1-80
likely
as likely
likely
not stocked
stocked
stocked as not
3
14
13
33
6
0
18
3
34

0-20
very likely
not stocked
34
23
28

80.1-100
very likely
stocked
37
38
18

Skeena Stikine all trees
Skeena Stikine conifers
Skeena Stikine MSSpa

21505

Mackenzie all trees
Mackenzi conifers
Mackenzi MSSpa

6769

6
9
11

23
11
12

9
0
1

21
48
63

41
32
14

Fort St. James all trees
Fort St. James conifers
Fort St. James MSSpa

219378

13
16
40

5
10
8

6
0
4

38
40
20

38
33
29

Nadina all trees
Nadina conifers
Nadina MSSpa

554084

26
33
42

14
13
12

7
0
7

20
27
17

33
27
22

Prince George all trees
Prince George conifers
Prince George MSSpa

285404

19
14
31

8
13
16

6
0
3

36
44
17

30
29
33

Vanderhoof all trees
Vanderhoof conifers
Vanderhoof MSSpa

376145

17
26
30

20
13
13

7
0
12

21
28
27

34
33
18

Quesnel all trees
Quesnel conifers
Quesnel MSSpa

22746

10
39
38

19
13
19

18
0
15

16
31
5

37
17
23

North Island-Central Coast all trees
North Island-Central Coast conifers
North Island-Central Coast MSSpa

13115

9
47
28

18
5
1

40
0
24

18
30
23

14
19
23

69

It is important to note that although study plots were located in the Skeena Stakine,
Mackenzie, and North Island - Central Coast forest districts, only a fraction of these three
forest districts intersected with the study area of interest (Figure 22). Caution should be
used when drawing any conclusions involving the probability of stocking within a forest
district context.
Mackenzie

_(0.6%)_

Figure 22. Map illustrating the proportion of forest districts that are within the study area
(NTS 1:250,000 93E,F,G,J,K,L).
Figure 23 is an example of a 1:250,000 m ap predicting the probability of
MSSpa stocking in m ature pine-leading stands for m ap tile NTS 93G.

The five

colours in the legend correspond to a likelihood of stocking (red=0-20%, orange=2040%, yellow=40-60%, light green=60-80%, and dark green=80-100%). This m ap and
those in Appendix 2 also have a shaded relief in the background for elevation
context, major lakes (blue polygons), and major roads (symbolized by black lines).
70

Predicted Locations a n d Stocking Probability of A dvance R eg en eratio n U nder
M ature Pine S ta n d s in Central British Colum bia

93G
Probability of
being Stocked
0- 20%

20-40%
140-60%
I 60-80%
80-100%

600 stems/ha
conifers only

tit
ffU

0 5 10

20 km

1 . . ■ i____ i

Figure 23. Colour themed map depicting probability of being stocked for conifer only
600 stems/ha stocking threshold within NTS 1:250,000 map tile 93G.

Once the classification tree results are in a geospatial environment, specific
probability of stocking percentages can be displayed in isolation of the rem aining
probability classes and can be provided spatial context. By placing large areas of
"very likely" and "very unlikely" stocking in a spatial context, the data can be used
as a GIS layer for more sophisticated analysis regarding forest management. For
example, Figure 24 shows the isolation of areas that have a >80% probability of
stocking. These isolated areas can be easily identified as cells that are very likely to
recover naturally without intervention. Conversely, large areas can also be
identified as priorities for salvage or rehabilitation operations. Figure 25 shows that
by isolating areas that have a <20% probability of stocking, areas that may require
rehabilitation (including planting) can be targeted. The isolated areas can be
combined with datasets such as proximity to mill sites to determine economic
viability. Further, they may be targeted for rehabilitation, i.e., treatm ent to knock
dow n and pile trees, grinding them for pellet fuels or other bioenergy (depending
on markets) or burned, and then planted. The large contiguous areas classified as
very likely stocked (green pixels in Figure 24) become an im portant GIS layer with
regards to coordinating logging activity. Perhaps these stands could be allocated as
no logging or rehabilitation zones. It is recommended that these stands be
identified for natural (unaided) recovery. They m ay be important as a m id-term
supply of timber, or for habitat value.

P redicted L ocations an d Stocking Probability of A dvance R egeneration U nder
M ature Pine S ta n d s in C entral British Colum bia

93G
Probability of
being Stocked
80- 100 %

>600 stems/ha
conifers only

Jt £

MJ?
****
0 5 10

Figure 24. Spatial extent of probability of stocking for map tile NTS 93G. Green areas
denote >80% probability of stocking (conifers-only).

20 km

Predicted L ocations an d Stocking Probability of A dvance R egeneration U nder
M ature Pine S ta n d s in C entral British Colum bia
*

4

93G
Probability of
being Stocked
0 - 20 %

>600 stem i/ha
conifer* only

/

5 10

Figure 25. Spatial extent of probability for map tile NTS 93G. Red areas denote <20%
probability of stocking (conifer-only).

20km

C hapter Four: Discussion and Recom m endations

The main objective of my thesis was to develop a model predicting the
distribution of advance regeneration using publicly available data. M any of the
initial inputs to my model have been explored for their predictive strength in
previous studies. The resultant m odel was applied within a study area (NTS
1:250,000 93E, F, G, J, K, L m ap tiles) and probability m aps were constructed
(Appendix 2).

As per the Establishment to Free Growing Guidebook (BC Ministry

of Forests, 2000), MSSpa criteria and thresholds vary w ith BEC unit and site series.
These conclusions are consistent w ith several current advance regeneration
publications such as Vyse et al. (2009) w ho found that m ore than half of all plots
surveyed in lodgepole pine stands in the Kamloops Timber Supply A rea exceeded a
threshold of 600 stems/ha. This is echoed in a study by N igh et al. (2008), which
states that over half the stands sam pled in the Montane Spruce zone of southern
British Columbia had enough advance regeneration (>1000 stems/ha) to form new
stands of adequate density. Another study reports 44% to 98% stands contained
sufficient stems after MPB attack to be considered stocked (Hawkins et al., 2012). A
survey of pre-harvest industrial records has indicated that the percentage of pine
stands with a greater than 600 stems/ha are highest in the moist cool (mk) subzone
followed by the moist cold (me) subzone, and then by the dry warm (dw) and dry
cool (dk) subzones of the SBS (Burton, 2006). Studies also suggest that SBSdk is
75

unlikely to provide a significant contribution to the m id-term timber supply; in
contrast, the SBSdw and SBSmc are thought to be contributors to both the m id- and
long-term supplies (Hawkins and Rakochy, 2007). The overall distribution and
probability of stocking predicted here aligns well w ith these conclusions. A closer
examination of the resultant data (tabular and spatial) provides evidence to this
claim. The SBSmk had the largest likely/very likely stocked probability (as high as
75% for the all trees stocking group) for all BEC units. The results also support the
assessment by Hawkins and Rakochy (2007) that SBSdw and SBS me w ill likely be
the largest contributor to mid- and long-term timber supplies. In the conifer only
stocking group, SBSdw has a 71.2% likely/very likely stocked probability (-208,000
ha) and SBSmc2 and SBSmc3 have a 63.3% (-304,000 ha) and 53.8% (-42,000 ha)
likely/very likely stocked probability, respectively. The total area associated w ith
these probabilities is - 554,000 ha of potential advanced regeneration >600 stems/ha
or roughly one-third of the existing total ha of the study area.
A closer examination of the colour-themed m aps reveals the utility of
translating the tree/text based rules into a geospatial output. The m aps present the
probability of stocking in five coloured classes, and because the scale of the m ap is
known, an ocular estimate of the area of contiguous areas or distance betw een
proximal areas for any of the probability classes can be m ade. For example, large
areas of likely/very likely stocked polygons that are interrupted by sm aller areas
76

very unlikely to be stocked (Figure 26) can be identified and subsequently visited
and assessed using ground-based advance regeneration grid sampling.

Probability of Stocking

■ B o-20%
20-40%
d ] 40-60%
60-80%
I^Heo-100%

Figure 26. A portion of the mapped final model that illustrates the intersection of large very
likely stocked areas (green pixels) with very unlikely stocked cells (red pixels).

The results generated from the classification tree model also support the
preliminary results in Hawkins and Rakochy (2007), where it is reported that there
was measurably less regeneration in the SBSdk and SBSdw2 than in the SBSdw3 and
SBSmc. My classification tree model show s that the predicted probability of the
MSSpa group being stocked in SBSdk (12%) is close to half of the probability in

77

SBSdw (25%) and SBSmc (22%). Vyse et al. (2009) also state that the m ean density of
stems increased w ith moisture and elevation, both critical elements in determ ining
the biogeoclimatic subzone of a site. This generalization is further supported by my
findings, as mean annual precipitation and BEC unit are defined as im portant
variables in the resulting predictor model. The resultant model indicated that the
following variables are key predictors in m odelling stocking status: BEC unit,
distance to the nearest non-pine seed source in a southwest direction, projected age
of the leading species, basal area, leading species of dead volume per hectare at 12.5
cm, surface expression, spedes composition of the nearest non-pine seeds source,
mean annual temperature, m ean annual precipitation, projected height of the
leading spedes, and elevation. The key variables selected through recursive
partitioning are consistent with other study condusions, specifically w ith regards to
overstory height (Griesbauer and Green, 2006), overstory mortality (leading spedes
dead volume; Lewis, 2011), basal area (Coates and Sachs, 2012; Nigh et al., 2008),
distance to nearest seed sources (LePage et al., 2000; Kaufmann et al., 2008), and
moisture (predpitation; Kayes and Tinker, 2012).

Application to Forest M anagem ent
A landscape-level planning tool is useful for several different aspects of forest
planning and management. At the provindal level, this study's m odel can assist in
the implementation of the Forests for Tomorrow Current Reforestation and Timber
78

Supply Mitigation Strategic Plan 2011-2015 (Ministry of Forests, Lands, and N atural
Resource Operations, 2011) by providing critical data to m eet several goals.
First and foremost, the resultant of my m odel (hardcopy m aps and textual
rule sets) can assist forest managers in the establishment of new and up-to-date
assessments of potential timber supply. Tools such as this can play a p art in helping
estimate the new baseline that will be used for forecasting and planning. The need
for current information is echoed in a June 8,2012, memo from the Inventory
Section, Forest Analysis and Inventory Branch: Approach of the inventory program in
2012-13 to improve inventory information in MPB-affected management units (Ministry of
Forests, 2012). The working memo states that the provincial inventory program is
placing a high priority on improving information related MPB-affected areas. The
memo specifically states that the advance regeneration in the understory is critical to
mid-term timber supply and that the assessment of stocking under these MPBaffected stands is important. The model developed here can play a large role in
assisting inventory personnel "short-list" stands that may potentially have this
critical mid-term timber supply. The scale of the output is not necessarily fine
enough to generate reliable determinations of stand-level stocking, b u t it is highly
useful for directing field validation programs. O n a landscape level, the resultant
stocking data can be used for more general land-use and resource m anagem ent

79

plans. By examining the data, areas of sporadic distribution, large anomalies, and
"salt and pepper" occurrences can be identified (Figure 27).

Probability of Stocking

|HM0-20%
I H xmok
I 140-60%
meo-ao%
80-100%

Figure 27. Landscape view of mapped model output. Blue circles indicate large anomalies
that are easily identified at a broad scale.

The tabular results from exercising the classification tree have generated
important information about how m any hectares of likely/very likely to be stocked
there are within a defined area. They are, however, limited in their explanatory
power, as there is a distinct difference in know ing how m any hectares of >80% (very
likely to be stocked) probability of stocking and w here these very likely to be

80

stocked areas are on the landscape. Importing the tabular stocking inform ation into
a GIS allowed me to spatially locate how the five stocking classes are distributed
across the landscape. The ability to spatially locate each of the probability of
stocking classes enhances the decision making pow er of m y decision model.
Consider the following example, where a forest m anager w ants to
understand the advance regeneration attributes of a particular m anagem ent area
(Figure 28). Knowing the total hectares of the m anagem ent area (65180 ha) and total
hectares of m ature pine within the management area (29815 ha), the forest m anager
is now in a position to estimate the num ber of hectares of mature pine that could
possibly have advance regeneration. According to the areas reported, the am ount of
advance regeneration cannot exceed 45% of the m anagem ent area (or ~ 29,000 ha) as
there are only 29,000 ha of m ature pine within the area. Assume further that a
classification tree model has been used to calculate the probabilities of stocking as
per the following: 1) 4858 ha are very unlikely to be stocked; 2) 3210 ha are unlikely
to be stocked; 3) 0 ha are as equally likely to be stocked as no t stocked; 4) 10280 ha
are likely to be stocked; 5) 11467 ha are very likely to be stocked.
The detailed information regarding areas of stocking likelihood provides the
forest manager with valuable information regarding the amount of potential

81

Figure 28. Example of a management area of interest in which a forest manager would like to calculate the
amount of advance regeneration under mature pine forest stands by using a probability of stocking model. The
grey polygons indicate mature pine forest stands.

advance regeneration in the management area. W ithout spatial context, however,
the planner can only know the probability of stocking w ith regards to advance
regeneration. An assumption regarding the spatial distribution of the likely or
unlikely stocked areas cannot be m ade w ith the information in hand, i.e., the
manager can only know how m uch stocking is in the management area b u t no t if
the stocking is restricted to one particular area or widely dispersed throughout the
area. By providing a geospatial context to the probability information, a m uch
clearer and complete picture is provided w ith regards to stocking (Figure 29).
Patterns of large contiguous areas of very unlikely and likely stocking become
evident. Large patches can be quickly identified and used to supplement landscape
level plans. This information can be used as a landscape level planning tool for
activities such as annual allowable cut (AAC) allocation, post-MPB m anagem ent
planning, and even identification of mid- and long-term timber supply stands
suitable for future research projects. In a VRI newsletter, Martin (2012) identifies
one of the goals for inventory information is to know more about stocking by
gathering information regarding small trees under a dead overstory. The prim ary
goal of the BC Government's "Forest for Tomorrow" program, namely to im prove
the mid- and long-term timber supply and establish resilient forest ecosystems,
specifies the need to focus on restoration and reforestation through the
identification of sites which have had the greatest negative impact on the m id- and
83

Probability of Stocking

mm0-20%

mm

20- 40%

[

140-60%

m

60-80%

■ ■

80-100%

Figure 29. Example of a BEC area of interest in which a forest manager would like to calculate the probability of
stocking. Probability of stocking is depicted in the five coloured classes. Spatial patterns of stocking are evident
when viewing data in a geospatial context

long-term timber supplies. To effectively mitigate m id-term timber supply
shortfalls, it is imperative to have an overarching plan that helps differentiate
between stands that have sufficient advance regeneration (and therefore represent
the mid-term supply) and stands that will not be contributing to the m id- to long­
term timber supply. Stands that do not have sufficient advance regeneration can be
identified through the use of a landscape level model and then targeted for
harvesting and subsequent replanting. Alternatively, a working know ledge of the
percent of m ature pine without adequate advance regeneration m ay be useful for
old forest retention in the quest for biodiversity conservation and preservation of
critical wildlife habitat. Large areas of m ature pine that are classified as very
unlikely to be stocked pose no benefit to the mid- and long-term tim ber supply.
These areas can be prioritized for logging efforts; effectively removing post-MPB
stands from the inventory w ithout removing any potential mid- and long-term
timber represented as advance regeneration, especially large areas classified as very
unlikely to be stocked (Figure 30). Roads (red lines with black borders in Figure 30)
and existing cutblocks (thick black lines) are added to the maps to provide context
for accessibility. The red pixels represent areas very unlikely to be stocked areas.
Goal three in "Forest for Tomorrow's" strategic plan is to develop and implement
innovative approaches to reforesting forests dam aged by catastrophic disturbance.
One of the strategies to achieve this is to engage stakeholders in the developm ent of
85

a strategic and tactical plan. W hether the stakeholders are the Province, the
licensees / stewards of the forest, non-traditional users of the forest, or the public,
strategic plans m ust begin w ith the m ost current and accurate knowledge possible.
The predictive m odel can help provide a region-wide overview of w here the highest
potential for mid- and long-term timber supply is located. A GIS-ready dataset of
this scale can be used as an informative base layer for refining existing land use
plans.

Probability of Stocking

H

0-20%

H

I 20-40%

1....... 1 40-60%
H I 60-80%
■ ■ 80-100%

Figure 30. A portion of the final model map that illustrates the location of large, very
unlikely to be stocked mature pine areas (red pixels). These areas can be targeted for large
scale logging and silviculture programs.

86

Griesbauer and Green (2006) identify two potentially dangerous and
expensive scenarios associated w ith the perceived need to tend advance
regeneration: supplementing advance regeneration through planting of unstocked
patches and the requirement for thinning of overstocked understories. Both present
a potential danger in the form of falling MPB-killed snags and would require the
removal of snags for safety reasons. For the planting scenario, Griesbauer and
Green (2006) suggest restricting planting only to highly productive sites that have
little advance regeneration. The predictive model outputs can be used as a GIS
overlay to help forest managers find the intersection betw een highly productive
sites (site index layer) and probability of stocking (generated by the classification
tree model). This model may help to economically identify areas that could have
regeneration augmented through planting. Conversely, stands predicted to be
stocked on highly productive sites m ay also be identified and flagged for field
inspection.

Assessment of the M odelling Approach
R (R Core Team, 2012), DTREG (Sherrod, 2006), and ArcGIS (ESRI, 2011)
were used to establish an intuitive workflow to create fully attributed feature classes
using publicly available digital data input. The resulting feature classes have correct
projection and coordinate systems, are topologically clean, fully attributed, and are
GIS-ready for input as a working dataset. The working parts of the m odel are
87

extensive yet invisible to the user. The users cannot add more tools or explanatory
variables to the model w ithout building a new model, as this would jeopardize the
integrity of the classification tree solution. To create a stocked / not stocked m ap for
another study area or for pine stands that do not fit the m ature pine criteria, the
models w ould have to be recreated and re-run in both R and ArcGIS.
This working model is interpolative, in that its training data were sparsely
distributed and it cannot make predictions w ith regards to advance regeneration
stocking beyond the limits of data used to create the model. In the case of my
model, the limitations lie more in the organization and definition of variables, rather
than quantitative maximum and m inim um values.
It w ould be misleading to claim that the model developed in this study is
unique. Other software packages have been used to predict natural regeneration
under mountain pine beetle attacked stands, m ost notably SORTIE and
PROGNOSIS80 (Smith, 1990; Ferguson and Carlson, 1993; Ribbens, 1994; Sattler,
2009). The distinction, however, is not in the intended application of the m odel b u t
rather the scale and ownership of the m odel input variables and the ultim ate utility
of the model output. Although those are mechanistic simulation models, and the
work reported here resulted in an empirical statistical model, perhaps the key
distinction is the emphasis on the ability to map predicted stocking across a broad

88

region. My study input data are derived solely from publicly available geospatial
data that can be downloaded from provincial online repositories or requested from
BC government agencies such as British Columbia's Land and Resource Data
Warehouse (LRDW) and its Integrated Land Management Bureau (ILMB). Most
forest planners and managers with access to the internet or an internal data
warehouse have access to my m odel's inputs. The model does not require
additional field data collection on the part of the analyst.
SORTIE, a spatially explicit, mixed species forest dynamics simulator, relies
heavily on the complex field-based m easurem ents of light transmitted through
forest canopies and gaps (Canham et al., 1999). PROGNOSIS80, a grow th and yield
model, is fueled by tree counts w ithin a stand and dbh measurements for each tree
and requires one record of data per tree in the input .txt files.
Although PROGNOSIS80 and SORTIE-ND modelling may be superior in
their ecological portrayal of the mechanisms of stand development, they require
considerable detail for input data that limits their application to case study
simulations in a few representative stand types. LeMay et al. (2002) used
PROGNOSIS 80 to examine the natural regeneration beneath complex stands in the
Interior Douglas-Fir biogeoclimatic zone in the Nelson, Kamloops, and Cariboo
Forest Regions. Their final report states that PROGNOSIS80 is best suited for

89

models with a ground-based inventory. Similarly, the data needed to feed a
SORTIE-ND and PROGNOSIS80 hybrid m odel for predicting natural regeneration in
MPB-attacked stands in central and southeastern BC necessitated the collection of
ground-based measurements such as individual tree dbh, total tree height, height to
live crown, maximum crown diameter, and ratio of live crown to tree height (Sattler,
2009).
In contrast, the landscape-level geospatial approach developed here can be
applied across a large range of geographic variability and forest stand types w ith a
simple probability of occurrence output. The model uses coarsely collected
variables for its input (a majority derived from Vegetation Resource Inventory GIS
files), and consequently sacrifices individual stand anomalies for a broad-brush
overview of all stands within a study area of interest. This empirical m odel does not
simulate or otherwise address specific understory dynamics (e.g., in term s of
growth release, competition among trees or with brush). The ultimate intention of
the model is to create the most parsimonious algorithm derived from the most
publicly available data. The more complicated the model becomes, the m ore limited
its function.

The process of creating predictive models for the field of ecology is highly
contentious. At times, models are built w ith good intentions only to fall into disuse,

90

or worse, misuse (Bunnell, 1989). There are multiple ways to look at m odelling
ecological processes, and therefore there are m ultiple ways to build a model. The
inherent strength of my decision tree m odel is that it accommodates the possibility
of multiple models by creating multi-branches of rules that all represent a possible
predictive algorithm, with each branch assigned a probability of accuracy. A single
regression model could provide a single parsim onious equation that draw s from the
most significant variables as they apply to the dataset used to create the model.
This, however, "locks" the model into a coefficient + variablei + variable 2 + variablen
format, resulting in a single equation to fit the snapshot of data used to build it.
With a static list of key predictor variables (and coefficients associated w ith these
variables) the model weakens w hen key variables are missing from subsequent
datasets. Through concepts such as surrogate splitters, the decision tree m odel can
adapt to missing input data and can result in m any rule sets with m any
combinations of contingency that result in a stand, or indeed parts of a forest stand,
being stocked with advance regeneration or not. The forest response to MPB or
other canopy disturbances is complex, and therefore cannot be easily m odeled w ith
a simple catch-all equation. Many stands sharing the same characteristics m ay
respond differently to disturbance. A m odel that allows for combinations of
contingency provides a more multi-faceted approach to predicting the probability of
stocking.
91

With each statistical m ethod used to create models, come m ultiple
assumptions, limitations, and biases. The tem ptation to explore more complex
interactions between variables, and therefore create more complex m odels is fueled
by the ease of data accessibility and increased computing power. The m ore complex
the model, the more difficult it becomes to evaluate (Bunnell, 1989; Kimmins, 2005).
Just because a complex model can be built, doesn't necessarily mean it should be
built.
It is important to recognize that even the m ost inappropriate and unrelated
variables thrown together into a modelling process may result in a predictive
algorithm. Like parametric models, the addition of variables (overfitting) tends to
increase the model fit. Variables, however, that have little connection to each other
or the ecological process that they are trying to model tend to create a "snapshot"
model. A model that fits only the dataset from which it was derived therefore
defeats the predictive purpose of the model. The reliance on predictor variables that
were derived from static snapshot datasets run into problems when validation is
required and in most cases the model misfires (Thompson, 1995; Graham, 2001;
Knapp and Sawilowsky, 2001). The variables used in the development of my m odel
were based on known or hypothesized ecological mechanisms and results from
preliminary studies.

92

A second consideration in developing predictive models is the tem ptation to
prioritize all the variables determ ined from a purely a priori approach. This is best
described by Thompson's basketball team paradox. Thompson (1995) suggests that
modelling is similar to a basketball team picking the best player first, the secondbest player second (in the context of the first player's strengths and weaknesses),
etc.. This is in direct contrast to the "all possible players'" approach used in
constructing a second team, where the five players that play together best as a team
are selected. This leaves the distinct possibility that the second team m ay have a
roster that does not include one of the first team players. H e goes further to state
that the "best team," although possibly comprised of w eaker players, m ay still be
stronger as a team, than one made of all-stars selected through a purely linear
process (Thompson, 1995). It was im portant in the development of this study's
model that all combinations of variables were tested to ensure that the "best team "
was selected. This can be illustrated in my thesis by examining the potential key
variable distance from nearest non-pine seed source. The r2 value of density of
advance regeneration when plotted against distance to seed source was only 0.0064,
(P = 0.007, n = 964). This means that as a single variable considered alone, distance
to seed source explains less than 1% of the variance in regeneration density. Yet it
was one of the top five important variables, i.e., factor w here a split in the decision
tree occurred, for all three stocking groups (and one of the top two for conifer only
93

and all trees, second only to BEC unit in both cases). W hen taken into account w ith
other predictors, the strength of distance to seed source increases and its im portance
as a primary splitter in the decision tree becomes evident.
The goal of predictive ecological models should be intuitiveness, parsim ony
and extensibility, namely the ability to add on or modify the model w ithout
breaking w hat is already there. The final key im portant variables included in my
study's model are ecologically sound and publicly available data that form an
intuitive parsimonious model that has both explanatory and predictive value.
This study began with two main objectives: to create an accurate predictive
model of understory stocking probability in m ature pine-leading stands for forest
planners to use in mid- to long-term planning initiatives, and to create cartographic
and tabular output portraying the results of the predictive model. The first objective
was accomplished by collecting advance regeneration data in the sum m ers of 2006
and 2007 and combining it with collaborator data to produce an extensive, geo­
referenced data library. The second objective was achieved by creating a recursively
partitioned classification tree m odel using R rpart. The m odel input variables were
limited to readily and publicly available data sources. The final m odel was
composed of data from the Vegetation Resource Inventory, ClimateBC, and the
biogeoclimatic ecosystem classification system

The resulting model achieved a

78% accuracy in correctly predicting stocked and non-stocked locations in m ature
94

pine-leading SBS forests. For the final objective, the predictive model generated
using the R package rpart was applied against a study area by creating a geospatial
model in ArcGIS 10. The geospatial model partitions the data into the following
probability of being stocked classes: 0-20%, 20-40%, 40-60%, 60-80%, and 80-100%.
Area statistics were gathered for each membership class and a large-format colour
themed m ap was generated to display the results for each NTS 1:250,000 m ap tile.
The variables used in the most parsim onious predictive model are consistent w ith
those reported as ecologically im portant in a num ber of similar studies (e.g.,
Ferguson, 1984; M urphy et al., 1998; Sattler, 2009; Coates et al., 2009).
With BC's interior tim ber supply compromised by one of the largest
disturbances in history, forest m anagers and planners are implementing strategies
to help understand the mid- and long-term implications. These implications reach
further than timber supply and will directly impact wildlife, carbon storage,
hydrology, and tourism (Coates et al., 2009). Most of these strategies require
current and accurate knowledge of the forest land base in the wake of the m ountain
pine beetle outbreak. The need for inventory data, not only what is in the canopy
but also what is beneath it, is obvious. Hopefully, the provincial governm ent is
paying close attention to new inventories, or their proxy in the form of modelling
output, before it proceeds w ith new harvesting, rehabilitation, and silviculture
regulations.
95

Chapter Five: Conclusions
The results of m y thesis show that one way to predict the presence or absence
of advance regeneration beneath m ature pine stands in BC's northern interior is to
create a model that works w ith the complex scenarios supportive of understory
development, rather than trying to simplify them. The response of m ature pine to
the MPB events of the last decade is complicated, and therefore requires a multiple
model approach to prediction. The classification decision tree developed in this
thesis provides a multiple branch m odel that proved to be 78% accurate in
predicting whether a stand was stocked or not w ith seedlings and saplings (>600
stems/ha). Further, a geospatial link between the predictive model and GIS
provides an enhanced understanding of the prediction, assisting forest m anagers to
discover spatial patterns and the clustering or dispersion of seedling and sapling
stocking at a landscape level.
The work presented in my thesis contributes to the ongoing effort to better
understand British Columbia's forests post-MPB. Several studies have examined
the key variables involved in predicting advance regeneration at a stand level. The
model developed in this thesis fills a gap in knowledge w ith regards to
understanding the likely distribution of understory stocking at a landscape level.
An accurate broad-brush tool is necessary in assisting w ith broad-brush
management strategies. My predictive model is built to help forest m anagers make
96

decisions at the landscape level. Although m y m odel o utput generates a resultant
probability of stocked pixels at a 100m size, it is the patterns of aggregated pixels
that contain the information and not the single pixels themselves. The results of this
thesis also contribute to the scientific community w ith the introduction of recursive
partition analysis for stocking presence evaluation. Although not a new technique,
it is presented here as a viable alternative to the m ore traditional step-wise
regression statistical techniques. A second contribution, and an area for future
research, is the integration of recursive partitioning and GIS. By providing
geospatial awareness to predicted stocking probabilities across a landscape-wide
area of interest, patterns previously unseen at a local scale may now emerge and
potentially drive new research.
By using the outputs of my model, forest planners may also have the
information needed to augment silviculture strategies such as variable-retention
harvesting. Variable-retention harvest systems have been developed as one m ethod
for creating more natural stand structures, particularly in forest types that rarely
experience stand-replacing natural disturbances such as severe forest fires. Variable
retention harvest systems retain living and dead structural elements of the p re­
harvest stand to restore structural complexity in m anaged forestlands (Franklin et
al., 1997). The relative novelty of formal variable-retention harvest systems,
however, leaves many questions about their impacts on stand development
97

unanswered. Simple questions such as how different patterns of overstory retention
influence the development of regeneration and grow th in residual trees cannot be
readily answered for most forest types (Gordon, 1973). M ore importantly, we have
only anecdotal evidence gathered from studies of tree responses to natural
disturbances or more traditional m anagem ent practices to link regeneration and
residual tree dynamics following variable retention harvesting to the underlying
physiological mechanisms that drive these responses. Overstory density reductions
and canopy gap formation alter resource availability, which should im pact tree
physiological performance and growth. The planning of salvage logging operations
after MPB, whether by clearcut or variable-retention harvesting, is further
complicated by the presence of tree species other than lodgepole pine w ithin the
impacted stands. A significant percentage of the pine stands contain other
coniferous tree species in both the overstory and the understory (Coates et al., 2009).
Incomplete forest inventories, coupled with the w idespread use of unsuitable
growth and yield models, appear insufficient to account for these stand and
understory variations. Therefore, there exists a need to develop strategies for
information gathering to augment these models and to subsequently aid in the
strategic planning of salvage and regeneration responses. My model's ability to
predict the probability of stocking can aid in the adoption of forestry techniques
such as variable-retention.

The m odel's efficiency and efficacy, however, could be significantly
supplemented with a broader geographic (i.e., biogeoclimatic) range of input data
and the addition of several unused variables, such as prevailing w ind speed and
direction. The predictive model is interpolative and therefore can only be used to
predict within the limits of the input data. In this study's case, only plot data from
the SBS dk, dw2, dw3, mc2, mc3, m kl, mw, and w k l were used to develop the
model. Further study incorporating a more diverse sample of biogeoclimatic zones
(or perhaps using tem perature and precipitation relationships to extrapolate the
equivalence of subzones not sampled) is suggested to enhance the m odel from a
central British Columbia based model to a province-wide model. A lthough climate
data were selected by the model construction algorithm, w ind direction and speed
data were not considered in this model iteration. W ind data can be generated in a
GIS environment; I did not, however, have access to a landscape level w ind dataset
at the time of this study. Research has indicated that prevailing w ind direction and
speeds clearly play a role in the recruitm ent of seeds that contribute to the advance
regeneration (Smidt and Blinn, 1995; Pardy, 1997; Wieland et al., 2011). In addition
to the availability and favourability of substrate, abundance and proxim ity to seed
sources (such as parent trees) are considered to be key variables in advance
regeneration (Astrup et al., 2008). Given that a majority of the m ature pine
understories sampled in my study area were populated w ith species other than
99

pine, advance regeneration establishment m ust have been aided by some form of
seed recruitment mechanism such as wind. Incorporating the wind data into the
existing model as an extensible component seems to be a logical extension to this
project.
This study's predictive m odel provides forest planners with a unique
perspective on advance regeneration inventory. By looking at the landscape as a
series of predicted probabilities, detailed inventory work and the continuation of
stand-level advance regeneration studies can be focused. Finally, by combining
w hat is known about understories from stand-level advance regeneration studies
w ith a landscape level probability model, forest planners can provide legislators and
the public with varying scales of m anagem ent plans and proactive forest health
mitigation strategies.

100

References
Acuna, E., and C.A. Rodriguez. 2004. Meta analysis study of outlier detection
methods in classification. Technical paper, Departm ent of Mathematics, University
of Puerto Rico at Mayaguez. Available from academic.uprm.edu/eacuna/
paperout.pdf. In proceedings IPSI2004, Venice.
Allen, D. W. 2011. Getting to Know ArcGIS ModelBuilder. ESRI Press. Redlands,
CA.
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117

Appendix 1
The attached table are the published MSSpa values and conditions that w ere used to
define the level of stocking against which to assess seedling and sam pling densities.
Minimum Stocking Standards (MSSpa) for preferred and acceptable species
(BC Ministry of Forests, 2000)
BEC U n it

SiteS eries

T SS pa

M SSpa

M S Sp

SB Sdk

1

1200

700

600

SB Sdk

2

1000

500

400

SB Sdk

3

1200

700

600

SB Sdk

5

1.200

700

600

SB Sdk

6

1200

700

600

SB Sdk

7

1000

500

400

SBSdw 2

1

1200

700

600

SBSdw 2

6

1200

700

600

SBSdw 2

8

1200

700

600

SBSdw 2

9

1200

700

600

1200

700

600

SBSdw 3

1

SBSdw 3

3

1200

700

600

SBSdw 3

4

1200

700

600

SBSdw 3

5

1200

700

600

SBSdw 3

6

1200

700

600

SBSdw 3

7

1200

700

600

SBSdw 3

8

1200

700

600

SBSdw 3

9

1000

500

400

SBSdw 3

10

400

200

200

SBSm c2

1

1200

700

600

SBSm c2

3

1200

700

600

SBSm c2

5

1200

700

600

SBSm c2

6

1200

700

600

SBSm c2

10

1000

500

400

SBSm c3

1

1200

700

600

SBSm c3

4

1200

700

600

SBSm c3

5

1200

700

600

SBSm c3

7

1200

700

600

S B Sm kl

3

1200

700

600

S B Sm kl

5

1200

700

600

SB Sm w

1

1200

700

600

S B S w kl

5

1200

700

600

118

Appendix 2

Colour themed maps depicting probability of being stocked w ithin NTS 1:250K
map tiles 93E,F,G,J,K,L
The following m aps are colour-themed m aps built from the classification tree m odel
rules presented in this thesis. This is a full series of probability of stocking m aps for
all three stocking groups: 1) >600 stems/ha conifer only; 2) >600 stems/ha all tree
species; and 3) MSSpa (minimum stocking standards for preferred and acceptable
species).

119

Predicted Locations and Stocking Probability of Advance Regeneration Under
Mature Pine Stands in Central British Columbia

93E
Probability of
being Stocked
0-20%
20-40%

40-60%
60-80%
80-100%
120

>600 stems/ha
all trees

I 93L

■
0

3

93K

93J

93F

93G

10

30km

--1 1__1____ I

Predicted Locations and Stocking Probability of Advance Regeneration Under
Mature Pine Stands in Central British Columbia

Predicted Locations and Stocking Probability of Advance Regeneration Under
Mature Pine Stands in Central British Columbia

93G
Probability of
being Stocked
0-20%

20-40%

jM

40-60%
60-80%
80-100%
>600 stems/ha
all trees

1 93L
I

93K

93J

1 93E
L_____ 9 3 F f f l

0

S

1 I

10

20km

I_____I

Predicted Locations and Stocking Probability of Advance Regeneration Under
Mature Pine Stands in Central British Columbia

93J
Probability of
being Stocked
0-20%

20-40%
4060%
6060%
80100%
>600 stems/ha
all trees

93L

93E

0
1

5
I

93F

93G

10
20km
1_______ I

Predicted Locations and Stocking Probability of Advance Regeneration Under
Mature Pine Stands in Central British Columbia

93K
Probability of
being Stocked
0-20%
20-40%
40-60%
60-80%
80-100%

>600 stems/ha
all trees

0

5

1 I

10

20km

I_____1

Predicted Locations and Stocking Probability of Advance Regeneration Under
Mature Pine Stands in Central British Columbia

93L
Probability of
being Stocked
0-20%

2040%
40-60%
60-80%

80-100%
>600 stems/ha
all trees

■

93K

93J

93E

93F

93G

0 5
1 I

10
20km
I_______ I

L'

Predicted Locations and Stocking Probability of Advance Regeneration Under
Mature Pine Stands in Central British Columbia

93E
Probability of
being Stocked
0-20%

20-40%
40-60%
60-80%
80-100%
126

>600 stems/ha
conifers

m

0

93K

93J

93F

93G

5 10

20 km

____
1
l__ 1-----------1

Predicted Locations and Stocking Probability of Advance Regeneration Under
Mature Pine Stands in Central British Columbia

93F
Probability of
being Stocked
0- 20%

20-40%
40-60%
60-80%
80-100%
>600 stems/ha
conifers

93L

93K

93E

0

93G

5 10

1 I

93J

20km

1_____I

Predicted Locations and Stocking Probability of Advance Regeneration Under
Mature Pine Stands in Central British Columbia

93G
Probability of
being Stocked

Jr '

»,

. nxT'.j'gm
"T*#■*

**, <r

vtr*

0- 20%
.

20-40%
40-60%
60-80%
80-100%

128

>600 stems/ha
conifers

93L

93K

93E

93F

93J

a*

0

5 10

1

i

L_

20 bn

_J

Predicted Locations and Stocking Probability of Advance Regeneration Under
Mature Pine Stands in Central British Columbia

93J
Probability of
being Stocked

40-60%
H

80-100%

>600 stems/ha
conifers

j 93L
!
!
1 93E

93K

SI

93F

93G

0

10

20km

5

1 l

I_____ I

Predicted Locations and Stocking Probability of Advance Regeneration Under
Mature Pine Stands in Central British Columbia

93K
Probability of
being Stocked
0-20%

20-40%
40-60%
60-80%
80-100%
U
oJ

>600 stems/ha
conifers

93L H

93E

0

B

93J

93F

93G

5 10

1 I

20km

I------- 1

Predicted Locations and Stocking Probability of Advance Regeneration Under
Mature Pine Stands in Central British Columbia

93L
Probability of
being Stocked
- %

0 20

.

40-60%

B l 60-80%
( j | | 80-100%
131

>600 stems/ha
conifers

0

5

93K

93J

93F

93G

10

20 km

_
1_ I---1------- 1

Predicted Locations and Stocking Probability of Advance Regeneration Under
Mature Pine Stands in Central British Columbia

93E
Probability of
being Stocked
0-20%

20-40%
40-60%
60-80%
80-100%
132

Minimum Stocking
Standards (MSSpa)

93L

■

93K

93J !

93G

w

0 5 10

20km

1 i I------- 1

Predicted Locations and Stocking Probability of Advance Regeneration Under
Mature Pine Stands in Central British Columbia

93F
Probability of
being Stocked
0-20%

2040%
40-60%
60-80%
80-100%
Minimum Stocking
Standards (MSSpa)

93L

93K

93E

0

93G

5 10

1 i

93J

20km

I------- 1

Predicted Locations and Stocking Probability of Advance Regeneration Under
Mature Pine Stands in Central British Columbia

93G
Probability of
being Stocked
0-20%

2040%
40-60%

60-80%
80-100%
134

Minimum Stocking
Standards (MSSpa)

' 'rtr
/ 4 ***

93L

93K

93E

93F

0

5 10

1 l

93J

20km

I------- 1

Predicted Locations and Stocking Probability of Advance Regeneration Under
Mature Pine Stands in Central British Columbia

93J
Probability of
being Stocked
0- 20%

20-40%
40-60%
160-80%
I80-100%
u>
Ol

Minimum Stocking
Standards (MSSpa)

j93L
r

93K IttlH

L_...

j 93E
i

93F

93G j

0

10

20km

5

1 l

I_____ I

Predicted Locations and Stocking Probability of Advance Regeneration Under
Mature Pine Stands in Central British Columbia

93K
Probability of
being Stocked
0 -20%

20-40%
40-60%
60-80%
80-100%
136

Minimum Stocking
Standards (MSSpa)

93L H H H 93J

93E

93F

93G

0

10

20km

5

1 I

I_____I

Predicted Locations and Stocking Probability of Advance Regeneration Under
Mature Pine Stands in Central British Columbia

93L
Probability of
being Stocked
0-20%

20-40%
40-60%
60-80%

80-100%
137

Minimum Stocking
Standards (MSSpa)

93J
93E

03F

93G

0

10

20km

I

5

1 I

1_____I

Appendix 3

Classification Tree Analysis: Recursive Partitioning, Cross Validation, and
Variable Importance
For classification trees built w ith a categorical target variable, the
determination of w hat category to assign a node is more complex: it is the category
that minimizes the misdassification cost for the observations in the node. In the
simplest case, every row that is m isdassified has a cost of 1 and every row that is
correctly dassified has a cost of 0.
A problematic issue in recursive partitioning is the decision of how large to
build the tree (Breiman et al., 1994; Khoshgoftaar and Allen, 2001). Too large a tree
means excessive branches, which in turn, m ean excessive nodes. This represents an
over-fitting of the model. If two trees provide equivalent predictive accuracy, the
simpler tree is preferred because it is less sensitive to outliers and spurious
observations, easier to understand, and faster to use for making predictions. Limits
m ust be placed on the size of the resultant tree. W ithout limits, a tree could be built
so large that there is terminal node for every case in the original dataset. In addition
to it being computationally expensive, this situation w ould represent a solution that
would be too difficult to interpret and it w ould have no applicability to new cases,
i.e., the model would be over-fit. Pre-pruning of the tree can occur by simply

138

providing limits to the classification routine. The analyst can either delim it the
number of observations necessary for a node split or program the m axim um
number of branch levels allowed to be calculated. Both methods will artificially
stop the classification splitting before the tree becomes too large.
Generally, the classification is provided a generous berth and stops w hen
there are no more statistically significant splits to be made, (i.e., maxim um purity of
nodes is achieved). This strategy usually results in a larger tree than necessary w ith
over-fitting. A tree with maximum nodes will result in the best fit m odel for the
dataset. This, however, is not necessarily the best model for all datasets. There is a
decision cost associated with producing an overfitted model, necessitating the
identification of the optimal sized tree that will best fit subsequent datasets.
Parametric models use penalization strategies such as Akaike Information Criterion
(AIC) model fit measurements to ensure parsimony is achieved. In fire case of
nonparametric modelling, a widely accepted m ethod of model fit is tree pruning
(Strobl, 2009). Through the use of v-fold cross validation - one pruning m ethod —
the resultant can be pruned back to an optimal tree size (Dhurandhar and Dobra,
2008). Cross validation is widely used statistical strategy to evaluate or compare
learning algorithms or decision tree models through a generalization error. The role
of the v-fold cross validation is to separate the data into a test group and a
validation group (folds). These groups, however, are created in such a m anner that
139

each point is 'crossed-over' between being a test point and validation point,
ensuring that every data point is evaluated (Refaeilzadeh et al., 2009). This m ethod
differs from the hold-out method, where data isolated as a validation set are never
evaluated. In v-fold cross validation, the working dataset is separated into v equal
parts (10 equal parts in the case of 10 v-fold). A test classification tree is built w ith v
- 1 held back for validation. The training data are run and the test data are run as
an independent check against the training data for accuracy. The results of both are
compared and then stored as the initial test. The process of splitting off the first v-1
test data against training data is automatically conducted nine more times (in the
case of 10 v-fold), each time with a new independent validation dataset. Once the
process has been run 10 times, the classification error rate calculated for each of the
ten test runs are averaged together to provide a generalization error or crossvalidation cost (Dhurandhar and Dobra, 2008). The tree size that produces the
minimum cross validation cost is pruned to the num ber of nodes m atching the size
that produces the minimum cross validation cost. The literature does not indicate
that using more than ten folds improves the accuracy of the generalized error
Backward pruning requires significantly more calculations than forw ard pruning,
b u t the tree sizes are much more optimally calculated (Sherrod, 2006).
When the target variable and the predictor variables are categorical (and both
are multivariate, i.e., more than two categories), this creates a more m athematically
140

complex process. To perform an exhaustive search, the classifier m ust evaluate a
potential split for every possible combination of categories of the predictor variable.
The num ber of splits is equal to 2(k'h -l where k is the num ber of categories of the
predictor variable. For example, if there are 5 categories, 15 splits are tried; if there
are 10 categories, 511 splits are tried; if there are 16 categories, 32,767 splits are tried;
if there are 32 categories, 2,147,483,647 splits are tried. Because of this exponential
growth, the computation time to do an exhaustive search becomes prohibitive w hen
there are more than about 12 predictor categories (Sherrod, P.H. DTREG Predictive
Modeling Software, personal communication, March 10,2011).
If the target variable is binary and has only two possible categories, as is the
case for a stocked or non-stocked condition as posed in m y thesis, the exhaustive
search is conducted with efficiency. The ideal split would divide a group into two
nodes in such a way that all of the observations in the left node are the same (have
the same value as the target variable) and all of the observations in the right node
are the same - but different from the left node. This is referred to as purity. If such a
split can be found, then you can exactly and perfectly classify all of the observations
by using just that split, and no further splits are necessary or useful. Such a perfect
split is possible only if the observations in the node being split have only two
possible values of the target variable.

141

Unfortunately, perfect splits do not occur often in nature, so it is necessary to
evaluate and compare the quality of imperfect splits. Various criteria have been
proposed for evaluating splits, bu t they all have the same basic goal, w hich is to
favour homogeneity within each right/left node and heterogeneity betw een the
right/left nodes. The heterogeneity, or dispersion, of target categories w ithin a node
is called the "node impurity". The goal of splitting is to produce nodes w ith
minimum impurity.
The impurity of every node is calculated by examining the distribution of
categories of the target variable for the rows in the group. A "pure" node, w here all
rows have the same value of the target variable, has an impurity value of 0 (zero).
When a potential split is evaluated, the weighted average of the im purities of the
two nodes is subtracted from the im purity of the node from which they w ere split.
This reduction in impurity is called the im provem ent of the split. The split w ith the
greatest improvement is the one used. Im provem ent values for splits are show n in
the node information that is part of the generated report.
Variable importance is the relative importance that each variable plays in the
splitting of the tree into nodes, both as prim ary or surrogate splitters. A surrogate
splitter is an imputation technique that is employed w hen rows of the dataset have
missing values. If a variable is called on as a primary splitter in the building of a
tree and it has missing data, the developed surrogate will take its place and conduct
142

the split as it was developed in the initial tree building (Acuna and Rodriquez,
2004). It is im portant to note that a variable's importance is not m easured solely by
how early it enters the tree to act as a splitter. A strong surrogate splitter may be
more "important" to the classification model even though it enters the tree later
than a weaker primary splitter (Lewis, 2000; Sherrod, 2006). The loss of an
important variable in the decision m odel will likely weaken the m odel as a whole.
Variable importance can also act as a recruiter for subsequent analysis, as it is clear
that a variable with a higher variable importance score is likely a significant
predictor of the response variable (Breiman, 2001). The variable that contributes the
highest improvement measure (i.e., the variable that has the greatest effect on error
rate increase) achieves a score of 100 (Banerjee et al., 2008). The m easures are based
on the num ber of times a variable is selected for splitting, weighted by the squared
improvement to the model as a result of each split, and averaged over all trees
(Friedman and Meulman, 2003; Strobl et al., 2007). The relative influence (or
contribution) of each variable is scaled so that the sum adds to 100, w ith higher
numbers indicating stronger influence on the response (Elith et al., 2008). The
remaining contributing predictor variables are scored relative to the m ost im portant
variable. Importance, however, may refer to how im portant a variable is to the
overall goodness of model fit, or it may refer to how im portant the variable is to the
model's predictive ability.