CONSERVING AVIAN BIODIVERSITY ON MANAGED FOREST LANDSCAPES: THE
IMPORTANCE OF PATTERN AND SCALE
By
Andrew Donald Crosby

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degrees of
Fisheries and Wildlife – Doctor of Philosophy
Ecology, Evolutionary Biology, and Behavior – Dual Major
2017

ABSTRACT
CONSERVING AVIAN BIODIVERSITY ON MANAGED FOREST LANDSCAPES: THE
IMPORTANCE OF PATTERN AND SCALE
By
Andrew Donald Crosby
The shift in forest management goals over the last several decades to meet societal
demands for more non-timber benefits has led to a move towards ecosystem-based approaches to
management, with biodiversity conservation being a major objective. Within this context,
maintaining the richness and diversity of bird species on working forest landscapes has
continued to be a priority in sustainable forest management. Ecosystems are heterogeneous in
space and time, and regional species diversity is maintained by spatial patterns of heterogeneity
at multiple scales. Understanding how patterns of heterogeneity in forest composition and
structure influence species diversity is crucial to sustainable forest management. However,
despite a great deal of research on habitat relationships of forest bird species, there is little
understanding of how patterns of heterogeneity across scales influence regional bird species
diversity. Therefore, my research goal was to investigate the relationship of bird species diversity
to patterns of forest composition and structure across multiple spatial scales on a managed forest
landscape. The first chapter investigates how patterns of heterogeneity in stand-level attributes
impact patterns of bird community diversity across multiple spatial scales. Chapter 2
demonstrates a novel application of the conservation filters strategy to maintaining avian
diversity on managed forests by working at 2 different operational scales. The third chapter looks
at monitoring beta diversity in bird communities at multiple spatial scales as an alternative
paradigm to species-level strategies for tracking changes in regional biodiversity.

The research in these chapters draws several conclusions that are fundamental to the
problem of maintaining regional biodiversity on managed forest landscapes. The first is that the
relationship of environmental heterogeneity to bird community diversity changes across spatial
scales. The second conclusion is that uncommon vegetation community types have a greater
relative contribution to regional diversity, and the importance of specific compositional and
structural attributes changes among types. Third, quantifying beta diversity of bird communities
(differences among spatial units within a region) across multiple scales, using a hierarchical
cluster sampling design, reflects environmental heterogeneity and offers an efficient and
effective system for monitoring changes in regional biodiversity.
The research presented in this dissertation offers an expanded and integrated view of the
problem of maintaining biodiversity on managed forests. I have demonstrated that large-scale
management systems must explicitly address how forest planning will impact patterns at multiple
scales simultaneously, and maintain both homogenous and heterogeneous landscapes at the
appropriate scales. My work offers an integrated set of guidelines for biodiversity conservation
on managed forests that explicitly accounts for the multiple scales at which biodiversity is
generated and maintained. I believe that this research provides ecologists, land managers, and
planners with an improved framework for managing forests under the ecosystem management
paradigm.

Copyright by
ANDREW DONALD CROSBY
2017

This dissertation is dedicated to the memory of my father, Donald Charles Crosby, who
loved nature and cared deeply about protecting it throughout his life. Thank you Dad for setting
me on my path and giving me the skills and passion I needed to walk it.

v

ACKNOWLEDGEMENTS

This work was made possible through funding provided from the Boone and Crockett
Club through the Boone and Crockett Quantitative Wildlife Center at Michigan State University.
Additional support was provided by the Michigan State University Graduate School through the
University Distinguished Fellows program and by Frontier Renewable Resources LLC.
I would like to thank my major advisor, Dr. William F. Porter, for help and guidance
throughout the research process and for providing a first-class working environment. I would
also like to thank the members of my graduate committee, Drs. Gary Roloff, Scott Winterstein,
and David MacFarlane, for their valuable assistance with this work. Additionally, I must express
my extreme gratitude to my fellow lab-mates in the QWC (past and present, in no particular
order): Chad Parent, Amy Dechen Quinn, Bryan Stevens, Heather Porter, Nathan Snow, Andrea
Bowling, Jodi Kreuser, Marta Jarzyna (Vegetable), David Williams, Sonja Christensen, Kathryn
Frens, Rebecca Cain, Chris Hoving, Jon Cook, Jennifer Smith, and Leslie Skora. I could not
have asked for a better group of people to work with these past five years.
Dr. Mike Walters from the Department of Forestry and Dr. Jiangua (Jack) Liu from the
Center for Systems Integration and Sustainability at Michigan State University generously
provided the data used in this research. Dr. Walters also provided invaluable advice concerning
the details of the data. Appreciation also goes to Dr. Pen Holland from the University of York for
generously supplying me with the Python and R code for simulating landscapes with spatially
correlated pixel values.
Finally, and most importantly, I need to thank my family for their love and support. My
wonderful wife Andrea and our beautiful son Sebastian; Mom and Dad (who set me on my path

vi

supported me the entire way); and my brother and sisters who kept me honest by asking
(continually) when I was going to be done with school. Thank you all.

vii

TABLE OF CONTENTS

LIST OF TABLES ...........................................................................................................................x
LIST OF FIGURES ....................................................................................................................... xi
PROLOGUE ....................................................................................................................................1
CHAPTER 1: DIFFERENTIAL IMPACTS OF LANDSCAPE PATTERN ON BIODIVERSITY
ACROSS MULTIPLE SPATIAL SCALES ....................................................................................7
ABSTRACT ................................................................................................................................7
1.1. INTRODUCTION ...............................................................................................................8
1.2. METHODS ........................................................................................................................11
1.2.1. Study area and sampling design .................................................................................11
1.2.2. Bird community data ..................................................................................................13
1.2.3. Forest composition and structure data ........................................................................14
1.2.4. Data analysis ..............................................................................................................15
1.3. RESULTS ..........................................................................................................................19
1.3.1. Bird community analysis ............................................................................................19
1.3.2. Additive partitioning ..................................................................................................19
1.3.3. Heterogeneity and diversity .......................................................................................20
1.4. DISCUSSION ....................................................................................................................22
CHAPTER 2: APPLYING CONSERVATION FILTERS TO CONSERVING BIRD
DIVERSITY ON MANAGED FORESTS ....................................................................................28
ABSTRACT ..............................................................................................................................28
2.1. INTRODUCTION .............................................................................................................29
2.2. METHODS ........................................................................................................................34
2.2.1. Study area and plot selection ......................................................................................34
2.2.2. Bird community and forest data .................................................................................35
2.2.3. Bird species analysis and plot-level diversity contribution ........................................37
2.2.4. Coarse filter: identifying high-value community types..............................................38
2.2.5. Mesofilter: attributes of high-contribution plots ........................................................39
2.2.6. Bird species relationships to high-contribution plots .................................................40
2.3. RESULTS ..........................................................................................................................41
2.3.1. Bird community composition .....................................................................................41
2.3.2. Coarse filter: identifying high-value community types..............................................41
2.3.3. Mesofilter: attributes of high-contribution plots ........................................................42
2.3.4. Species-level relationships .........................................................................................50
2.4. DISCUSSION ....................................................................................................................52
2.5. MANAGEMENT IMPLICATIONS..................................................................................55

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CHAPTER 3: MONITORING BETA DIVERSITY OF BIRD COMMUNITIES AS AN
ALTERNATIVE PARADIGM FOR TRACKING CHANGES IN REGIONAL
BIODIVERSITY............................................................................................................................57
ABSTRACT ..............................................................................................................................57
3.1. INTRODUCTION .............................................................................................................58
3.2. METHODS ........................................................................................................................60
3.2.1. Study area and data acquisition ..................................................................................60
3.2.2. Environmental heterogeneity and beta diversity ........................................................64
3.2.3. Landscape and species simulation..............................................................................65
3.2.4. Sample design comparisons .......................................................................................68
3.3. RESULTS ..........................................................................................................................70
3.3.1. Bird community and beta diversity ............................................................................70
3.3.2. Simulation analysis ....................................................................................................71
3.4. DISCUSSION ....................................................................................................................72
EPILOGUE ....................................................................................................................................79
APPENDICES ...............................................................................................................................83
APPENDIX A: MULTI-SPECIES OCCUPANCY-ABUNDANCE MODEL ........................84
APPENDIX B: MULTI-SPECIES OCCUPANCY-ABUNDANCE
MODEL CODE .........................................................................................................................87
APPENDIX C: PYTHON CODE FOR LANDSCAPE SIMULATION ..................................91
APPENDIX D: R CODE FOR SPECIES SIMULATION .......................................................96
LITERATURE CITED ................................................................................................................102

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LIST OF TABLES

Table 2.1. Total number of plots among six primary forested community types, number of plots
with a high contribution to overall regional diversity, and the direction (+ or ─) and strength of
the relationship between forest compositional and structural variables and diversity
contributions ..................................................................................................................................44
Table 2.2. Bird species used in diveristy contribution analysis from the western Upper Peninsula
of Michigan, USA. Average plots are those below the third quantile of diversity cotribution
scores. High-contribution plots are those above the third quantile. Species in bold are those that
had a significanlty higher abundance in high-contribution plots (P < 0.05) .................................47
Table 2.3. Top 5 indicator species or combinations for high-contirbution plots within 6
ecosystem types in the western Upper Peninsual of Michigna, USA. Numbers in parantheses are
the probabilities of being a high-contribution site, given that combination of species is found
there. See Table 2 for species associated with four-letter codes....................................................51
Table 3.1. Parameters used for simulating landscape gradients, where pixel values are randomly
drawn from a beta distribution with parameters 𝛼 and 𝛽, and spatial correlation in parameter
values specified by the H-value in the midpoint displacement method.........................................66
Table 3.2. Parameters used to simulate species occurrence probabilities along 2 environmental
gradients using the package coenocliner in program R. Parameters for each species were drawn
randomly from probability distributions. Max psi represents the maximum occurrence
probability, modal abundance represents the point on the gradient where maximum occurrence is
achieved, and range of occurrence represents the limits of occurrence along the gradient ...........68

x

LIST OF FIGURES

Figure 1.1. Diagram of additive partitioning of species diversity across multiple scales. At the
smallest scale, 𝛼1 is the mean within-point diversity and 𝛽1 is diversity among points. Points are
nested into landscapes, and so 𝛼2 is the mean within-landscape diversity and 𝛼1 + 𝛽1 = 𝛼2. The
relative contribution of each scale to overall diversity is described by 𝛼1 + 𝛽1 + 𝛽2 = 𝛾. Adapted
from Gering et al. (2003) .................................................................................................................9
Figure 1.2. Hypotheses about the effect of environmental conditions and heterogeneity on the
contribution of a spatial unit to overall regional diversity, where diversity contribution is an
additive result of species richness and distinctiveness. A: at the point level, greater distance from
mean environmental conditions may increase distinctiveness, leading to higher diversity
contribution. B: Competing hypotheses, (1) more heterogeneous landscapes are more diverse,
leading to higher species richness and therefore increased contribution, and (2) homogeneous
landscapes favor more specialist species, leading to higher distinctiveness and therefore
increased diversity contribution .....................................................................................................11
Figure 1.3. Location of the 4000 km2 study area in the western Upper Peninsula of Michigan,
USA, where bird community and vegetation data were collected in 2001─2003 .........................12
Figure 1.4. Hierarchical cluster sampling design used for estimating bird community diversity
across four spatial scales: 50-m-radius sampling plots; ecological neighborhoods where each plot
is ≤1000 m from at least one other plot; management areas defined by the Michigan Department
of Natural Resources or private industrial forest owners; and ecological subsections (here
referred to as ecoregions) defined by McNab et al. (2007) nested within the 4000 km2 study
area .................................................................................................................................................13
Figure 1.5. Percentages of total bird species diversity contributed by the alpha and beta
components across 4 spatial scales, estimated by additive diversity partitioning, for species
richness, Shannon diversity, and Simpson diversity. The number at the top of the richness bar is
the total number of species detected (gamma diversity) ................................................................20
Figure 1.6. Scatterplot and best-fit line showing the relationship between the ln distance from
mean vegetation conditions (dispersion distance) for 50-m-radius plots in a multivariate
dispersion analysis and the ln of the contribution of the plot to regional bird diversity. Dispersion
distance is a measure of how marginal a plot was in terms of vegetation composition and
structure, relative to all measured plots .........................................................................................21
Figure 1.7. Scatterplots with best-fit lines showing the relationship of within-unit environmental
heterogeneity with bird community beta diversity and the contribution of a unit to regional
diversity..........................................................................................................................................22
Figure 2.1. Operational scales of the conservation filter concept. The coarse filter seeks to
conserve most species by retaining the full range of community types within a region. The

xi

mesofilter increases the conservation value of community types by retaining structures and
processes that may be overlooked at the coarse filter level. The fine filter consists of specieslevel conservation efforts aimed at rare or highly specialized species that may fall through the
higher-level filters (adapted from Zenner et al., 2010) ..................................................................31
Figure 2.2. Study area in the western Upper Peninsula of Michigan, totaling 4000 km2, sampled
for bird species and forest composition and structure in 2001–2003 ............................................34
Figure 2.3. Comparison of conservation index values between forested community types in the
western Upper Peninsula of Michigan relative to bird species diversity. The light gray bars
represent the proportional representation of each community type in the dataset, pink bars
represent their proportional representation among plots in the upper 25% of diversity
contribution. Conservation value is represented by the green bars as the contribution index
calculated by dividing the pink bar by the gray bar .......................................................................43
Figure 2.4. Median (bars) and interquartile range values (black lines) of forest compositional
and structural variables between plots with high relative contribution to regional bird diversity
(the top 25%; green bars) and remaining plots (gray bars) within the same community type.
Community types are coded as: NH = Northern Hardwood; UC = Upland Conifer; UM = Upland
Mixed; ES = Early-successional; C = Cedar; and LC = Lowland Conifer. Basal area (BA) is
measured in m2/ha. Large trees (≥50 cm diameter) and snags (standing dead trees ≥25 cm
diameter) are measured in trees per hectare. Seedling density (trees ≥25 cm tall and <1.5 m tall)
is measured in stems/m2. Diameter distribution is the ln chi2 departure from an idealized even
distribution of 20 trees per hectare in each 5-cm size class ...........................................................45
Figure 3.1. Study area and study design map showing: (A) sampling plots within ecological
neighborhoods; (B) neighborhoods within management areas; (C) management areas within
ecological subregions; and (D) study area location within the Upper Peninsula of Michigan,
USA................................................................................................................................................61
Figure 3.2. Simulated ecological gradients used for simulating species occurrence based on
randomly generated beta distributions. Landscape dimensions were 500x700 pixels ..................67
Figure 3.3. Hierarchical partitioning of simulated landscape used to compare the effectiveness of
different study designs for estimating species diversity across scales ...........................................69
Figure 3.4. A: Linear regression of the relationship between environmental heterogeneity and
bird community beta diversity within ecological neighborhoods (all points ≤1000 m from at least
1 other point). B: Correlation of the same relationship for forest management areas as defined by
the Michigan Department of Natural Resources or private industrial forest landowners ..............71
Figure 3.5. Comparison of the estimates from 4 different sampling designs to known
contribution of alpha and beta components of diversity to overall gamma diversity across 5
hierarchically-partitioned spatial scales in a simulated landscape. Each design contained 450
sampling points. The systematic sample was an 18x25 grid of points spread evenly across the

xii

landscape, the stratified random sample was stratified at the beta.4 level, and the cluster sample
was hierarchically partitioned across all scales .............................................................................72

xiii

PROLOGUE

Over the past several decades there has been a shift in the focus of natural resource
management towards a more holistic, ecologically-based approach generally referred to as
ecosystem management (Christensen et al., 1996; Fuhlendorf et al., 2012). Ecosystem
management is a landscape-level approach to planning for the management of natural resources
that emphasizes a central goal of maintaining the sustainability of the ecological system
(Christensen et al., 1996; Haufler et al., 2002). The ecosystem management paradigm can be
traced back to the writings of Aldo Leopold, who developed the idea of conservation as a way of
utilizing natural resources while still maintaining the integrity of the biotic community (Leopold,
1949; Fuhlendorf et al., 2012). Leopold viewed conservation as a scientifically-based form of
management that preserved all of the constituent parts of the system (Leopold, 1949). Leopold’s
view underlies one of the central goals of ecosystem management, which is the conservation of
biological diversity.
Ecosystem management and the conservation of biodiversity is central to the practice of
sustainable forestry (Carey and Curtis, 1996). As such, the importance of maintaining
biodiversity is reflected in the standards of sustainable forestry certification programs such as the
Sustainable Forestry Initiative (SFI, 2015) and the Forest Stewardship Council (FSC, 2010).
Regional biodiversity is driven by many ecological factors that can be affected by management
across a range of spatial and temporal scales (Levin, 2000; Bestelmeyer et al., 2003). Therefore,
if sustainable forestry certification standards are to be met it is vital that forest managers
understand how ecosystems respond to management decisions across multiple scales
(Bestelmeyer et al., 2003).

1

Ecosystems are heterogeneous in space and time, and ecosystem composition and
structure are determined by processes occurring at multiple spatial and temporal scales (Levin,
2000; Fuhlendorf et al., 2006). The dynamics of these processes impact the diversity and
complexity of the ecosystem as well as the amount and distribution of resources that species
depend on for survival (Wiens, 1976). Ecologists recognize that patterns of spatial and temporal
heterogeneity are critical factors determining ecosystem function and sustainability, and provide
the underlying basis for maintaining biological diversity (Christensen, 1997; Levin, 2000;
Fuhlendorf et al., 2006). The fact that processes determining these patterns of heterogeneity
operate at multiple scales means that diversity patterns change across scales as well (Levin,
2000; Crist et al., 2003) which has important implications for landscape-scale conservation
planning when biodiversity conservation is a goal.
Biodiversity is a complex idea encompassing many aspects of the ecosystem, but
generally refers to the variety of species and the interactions among them across all scales and
levels of biological organization (Noss, 1990; Hooper et al., 2005). In concrete terms, changes in
biodiversity involve changes in the distribution and abundance of organisms at any scale. These
changes can have profound effects on ecosystem properties, functioning, and resilience, and so
the human-induced alteration of biodiversity is of primary concern for the continuing production
of ecosystem goods and services (Folke et al., 2004; Hooper et al., 2005). The importance of
maintaining biodiversity to the functioning and resilience of ecosystems makes it vital to the
sustainability of managed forests (Lindenmayer et al., 2000).
In ecosystem management, conservation of biodiversity is usually thought of in terms of
preventing reductions in species richness and changes in composition across a region of concern
(Carey and Curtis, 1996). Within this context, maintaining the richness and diversity of bird

2

species on managed forest landscapes has been a continuing focus in forest conservation (Hansen
et al., 1991; Sallabanks and Arnett, 2002; Mahon et al., 2016). Birds provide many ecologically
and economically important functions in forested ecosystems, such as nutrient transfer, insect
control, and seed distribution (Sekercioglu, 2006), as well as being important indicators of
ecological conditions and ecosystem integrity (Canterbury et al., 2000; O'Connell et al., 2000).
The distribution of bird species and communities across a forested landscape is partly determined
by spatial patterns of forest composition and structure (Verschuyl et al., 2008; Mahon et al.,
2016), and forest management systems impact these patterns across multiple spatial and temporal
scales (Boutin and Hebert, 2002). Therefore, forest management affects bird community
diversity at multiple scales, which is an important aspect of sustainable forest management
planning.
The effect of pattern and scale on our understanding of how species diversity is
established and maintained is a longstanding problem in ecology (Wiens, 1989; Levin, 1992;
Levin, 2000). Whittaker (1960) first articulated the link between spatial scale and species
diversity by defining alpha (𝛼; within-unit), beta (𝛽; among-unit), and gamma (𝛾; total) diversity
(Gering et al., 2003). The relative contributions of these components to regional diversity can
change at different spatial scales, reflecting differences in ecological patterns across scales (Crist
et al., 2003). Because patterns of diversity change across scales, the way we define and measure
species diversity, and at what spatial scales, is central to our understanding of how management
will affect biodiversity. This means that managing forests with the objective of maintaining
regional biodiversity (gamma diversity) requires knowledge of how species and communities
respond to landscape patterns across multiple spatial scales; from stand-level forest conditions
(alpha diversity) to the distribution of community types and successional stages among

3

landscapes, ownerships, and ecoregions (reflecting beta diversity across multiple spatial scales).
Despite this need, there is little research on how patterns of forest conditions across multiple
scales affect regional species diversity.
My overall research goal was to investigate the response of bird community diversity to
patterns of forest composition and structure across multiple spatial scales on a managed forest
landscape. I estimated avian distribution and abundance and forest composition and structure
across a range of ecosystem types present in the western Upper Peninsula of Michigan, USA. At
the stand level, I focused on attributes of the vegetation that described forest community type and
successional stage. At the landscape level, I focused on patterns of heterogeneity in those
attributes. The results of my research are presented in 3 separate chapters.
The first chapter investigates how patterns of heterogeneity in stand-level attributes
impact patterns of bird community diversity across multiple spatial scales. The problem of
pattern and scale pervades our understanding of ecological relationships (Wiens, 1989; Levin,
1992), and different patterns and drivers of diversity emerge at different spatial scales (Levin,
2000; Crist et al., 2003). Therefore, understanding the drivers of regional species diversity
requires disentangling the effects of environmental conditions, landscape pattern, and spatial
scale. My objective was to investigate how regional bird community diversity was impacted by
spatial patterns of vegetation composition and structure across four spatial scales in a managed
forest landscape. Specifically, I looked at which spatial scales had the biggest influence on
diversity and how environmental heterogeneity within and among spatial units at different spatial
scales affected their contribution to regional bird species diversity.
The second chapter demonstrates a novel application of the conservation filters strategy
to maintaining avian diversity on managed forests. The coarse filter conservation strategy

4

focuses on retaining the full range of vegetation community types on the landscape as a way to
conserve the vast majority of species, while the mesofilter strategy seeks to maintain important
structural features of ecosystems to increase biodiversity on managed areas (Hunter, 2005).
Coarse filters and mesofilters are 2 of the primary strategies used by planners to aid in managing
for biodiversity conservation (Schulte et al., 2006). However, these strategies operate at different
spatial scales and are traditionally applied independently. In chapter 2 I proposed applying an
integrated coarse filter-mesofilter conservation strategy to the problem of maintaining regional
bird diversity on a managed forest landscape. This application uses the diversity contribution
approach of Lu et al. (2007) to prioritize ecosystem types for conservation (the coarse filter
scale) and estimate the compositional and structural attributes of forest stands that have a high
relative contribution to regional diversity (the mesofilter scale). My objective was to evaluate a
strategy for multi-scale management planning that would aid in the maintenance of biodiversity.
The third chapter looks at monitoring beta diversity in bird communities as an alternative
paradigm to species-level strategies for tracking changes in regional biodiversity. Approaches to
biodiversity monitoring have typically been focused at the species level, with a great deal of
controversy over which species can act as indicators of regional biodiversity (Manley et al.,
2004; Noon et al., 2012). Monitoring of beta diversity at multiple scales offers an alternative that
focuses on how patterns of diversity change across scales, reflecting environmental changes that
drive these patterns (Marsh and Ewers, 2013). I propose a system that focuses on species-level
monitoring of bird communities for the estimation of beta diversity using a hierarchical sampling
design. More specifically, I investigate the link between beta diversity and environmental
heterogeneity and compare the abilities of different sampling designs to estimate patterns of beta
diversity across scales. Being able to effectively monitor changes in diversity patterns across

5

scales is a key to understanding if management systems are accomplishing the objective of
maintaining regional diversity.
Collectively, these chapters address questions that are fundamental to the problem of
maintaining regional biodiversity on managed forest landscapes. The research presented here
represents a step forward in our understanding of how forest management decisions might
impact regional bird species diversity. By improving our understanding of how forest patterns at
multiple scales impact biodiversity, I have begun to address a critical knowledge gap for making
management decisions under the ecosystem management paradigm.

6

CHAPTER 1
DIFFERENTIAL IMPACTS OF LANDSCAPE PATTERN ON BIODIVERSITY
ACROSS MULTIPLE SPATIAL SCALES
ABSTRACT
Addressing the issue of pattern and scale is critical to our understanding of the factors
governing the maintenance of biodiversity across the landscape. I examined how patterns of bird
species diversity changed across spatial scales in a managed northern forest landscape and
investigated how heterogeneity affected the contribution of individual spatial units at multiple
scales to regional diversity. I estimated bird community occupancy and abundance for individual
sampling plots within a 4000 km2 area in the western Upper Peninsula of Michigan, USA. Using
a hierarchical sampling design, I applied additive partitioning of species diversity at 4 nested
spatial scales: 50-m-radius sampling plots, ecological neighborhoods (1–3 km2), management
areas (100–1000 km2), and ecoregions (1000–3000 km2) to determine the scales most important
for driving regional diversity. I further estimated the relative contribution of individual spatial
units to regional diversity across scales and analyzed how within-unit environmental
heterogeneity related to diversity contribution and bird community beta diversity. I found that
beta diversity among plots and neighborhoods provided the largest relative contribution to
regional diversity. Uniqueness of a sampling plot relative to mean conditions, in terms of
vegetation structure and composition, had a significant positive correlation with diversity
contribution. Within-neighborhood heterogeneity was positively correlated with beta diversity
but showed no relationship to diversity contribution. Conversely, heterogeneity within
management areas was positively correlated with diversity contribution. My results illustrate that
the effect of landscape pattern on regional species diversity changes across scales, and that

7

variation in pattern as well as in habitat conditions is important to the maintenance of regional
biodiversity.
1.1 INTRODUCTION
The problem of pattern and scale in ecology has long presented challenges to our
understanding of how species diversity is established and maintained across the landscape
(Wiens, 1989; Levin, 1992; Levin, 2000). The primary issue is that the patterns observed in
ecology depend to a large degree on the scales at which they are viewed (Wiens, 1989).
Ecosystems are heterogeneous in space and time, and patterns of heterogeneity are determined
by processes operating at multiple spatial and temporal scales (Fuhlendorf et al., 2006). The
dynamics of these processes determine the amount and distribution of resources that species
depend on for survival, and so provide the underlying basis for maintaining biological diversity
(Levin, 2000; Fuhlendorf et al., 2006). Because the processes that drive patterns operate at
multiple scales, diversity is not distributed evenly across space or time and different patterns and
drivers of diversity emerge at different spatial and temporal scales (Levin, 2000; Crist et al.,
2003). As a result, addressing the issue of pattern and scale is critical to our understanding of the
factors governing the distribution of biodiversity across landscapes (Wiens, 1989; Bestelmeyer et
al., 2003).
Whittaker (1960) first articulated the link between spatial scale and species diversity by
defining alpha (𝛼; within-unit), beta (𝛽; among-unit), and gamma (𝛾; total) diversity (Gering et
al., 2003). Gamma diversity can be additively partitioned into the alpha and beta components
(𝛼 + 𝛽 = 𝛾) so that the contributions of each can be directly compared (Lande, 1996). This
approach treats alpha diversity as the average within-unit diversity at a given scale and beta as
the average diversity among all units (Lu et al., 2007), and makes it possible to estimate the

8

relative contributions of alpha and beta diversity across multiple spatial scales (Fig. 1.1; Lande,
1996; Gering et al., 2003). Beta diversity, then, represents the spatial component of diversity and
describes the proportion of gamma diversity contributed at a given scale (Gering et al., 2003;
Marsh and Ewers, 2013). This means that spatial scales with greater beta diversity have a greater
contribution to overall (gamma) diversity, and so heterogeneity among units at those scales
should be an important driver of regional diversity. However, diversity is not distributed evenly
among units and so the contributions of individual units to total diversity at any scale are not
equal (Wagner and Edwards, 2001; Lu et al., 2007).

Figure 1.1. Diagram of additive partitioning of species diversity across multiple scales. At the
smallest scale, 𝛼1 is the mean within-point diversity and 𝛽1 is diversity among points. Points are
nested into landscapes, and so 𝛼2 is the mean within-landscape diversity and 𝛼1 + 𝛽1 = 𝛼2. The
relative contribution of each scale to overall diversity is described by 𝛼1 + 𝛽1 + 𝛽2 = 𝛾. Adapted
from Gering et al. (2003).
The relative contribution of a spatial unit at a given scale to regional (gamma) diversity
depends in part on species richness within that unit (an index of alpha diversity) and in part on
how distinct the species composition is from other units at the same scale, which is an aspect of
beta diversity (Lu et al., 2007). At the smallest spatial scales, marginality of a spatial unit in
terms of habitat conditions may have a large impact on diversity contribution. Marginality refers

9

to how different the habitat conditions are relative to average conditions among all units.
Marginal habitats are likely to support more uncommon species (Wagner and Edwards, 2001;
Heino and Gronroos, 2014), thus making them more distinctive in terms of species composition
(Fig. 1.2A). At larger scales, there are two potentially contradictory hypotheses about how
patterns of heterogeneity influence regional diversity (Fig. 1.2B). On one hand, past research has
shown that there is a positive correlation between within-unit environmental heterogeneity and
beta diversity (Fuhlendorf et al., 2006; Astorga et al., 2014), and so more heterogeneous units
may contribute more to regional diversity through increased niche diversity and greater overall
species richness. On the other hand, homogeneous landscapes have been shown to support more
specialist species (Devictor et al., 2008; Katayama et al., 2014), which may increase their
diversity contribution through greater distinctiveness. It is also possible that the effect of
environmental heterogeneity on diversity contribution is scale-dependent, and so different
relationships may emerge at different scales. Therefore, understanding the drivers of regional
species diversity (gamma diversity) requires disentangling the effects of environmental
conditions, landscape pattern, and spatial scale.
The goal of my research was to investigate the impacts of landscape pattern and spatial
scale on regional biodiversity. Specifically, I investigated how regional bird community diversity
was impacted by spatial patterns of vegetation composition and structure across four spatial
scales in a managed forest landscape. My objectives were to examine how regional bird species
diversity was partitioned across scales, and investigate how patterns of heterogeneity influenced
the contributions of individual spatial units to overall diversity at multiple scales. I hypothesized
that marginality of a spatial unit in terms of habitat conditions would be positively correlated

10

with diversity contribution. I also examined two competing hypotheses (Fig. 1.2B) about the
effect of environmental heterogeneity on diversity contribution at 2 different spatial scales.

Figure 1.2. Hypotheses about the effect of environmental conditions and heterogeneity on the
contribution of a spatial unit to overall regional diversity, where diversity contribution is an
additive result of species richness and distinctiveness. A: at the point level, greater distance from
mean environmental conditions may increase distinctiveness, leading to higher diversity
contribution. B: Competing hypotheses, (1) more heterogeneous landscapes are more diverse,
leading to higher species richness and therefore increased contribution, and (2) homogeneous
landscapes favor more specialist species, leading to higher distinctiveness and therefore
increased diversity contribution.

1.2 METHODS
1.2.1. Study area and sampling design
My study was conducted in a 4000-km2 area in the western upper peninsula of Michigan,
USA (Fig. 1.3). This is an ecologically-diverse northern forest landscape, with variability driven
by glacial topography, soil, and differences in deer browse and forest management across
ownerships (Laurent et al., 2005). The region is dominated by upland northern hardwood forests,
and also includes upland and lowland conifer, early-successional, and upland mixed forest types
11

(Millington et al., 2011). Dominant tree species include sugar maple (Acer saccharum) in the
northern hardwood types, red pine (Pinus resinosa) and white pine (Pinus strobus) in the upland
conifer types, northern white cedar (Thuja occidentalis) in lowland forest areas, and aspen
(Populus spp.) and white birch (Betula papyrifera) in the early-successional areas. The majority
of the land is state-owned or private industrial forest managed for timber production. The most
prominent management practice is selective cutting of northern hardwoods, primarily sugar
maple, however plantation management for pine and clear-cut management of aspen also occur
(Millington et al., 2011).

Figure 1.3. Location of the 4000 km2 study area in the western Upper Peninsula of Michigan,
USA, where bird community and vegetation data were collected in 2001─2003.
I used data on bird species and vegetation variables collected in 2001-2003 from a
regional study of bird species in forested habitats (Laurent et al., 2005; Millington et al., 2011).
Sample plots were selected according to what was known as the GRAIN protocol (Laurent et al.,
2005), where the landscape was gridded into ~1,000 ha sections and 2-8 plots were placed within

12

randomly selected sections. See Laurent et al. (2005) for more detail on the plot selection
protocol. This plot selection system allowed me to impose a hierarchical study design on the data
(Fig. 1.4). In this design, individual plots were clustered into ecological neighborhoods where
each plot was ≤1000 m from at least one other plot. Neighborhoods were nested into
management areas defined by the state management system or by private industrial landowners,
and management areas were further nested into ecological subsections as defined by McNab et
al. (2007), hereafter referred to as ecoregions.

Figure 1.4. Hierarchical cluster sampling design used for estimating bird community diversity
across four spatial scales: 50-m-radius sampling plots; ecological neighborhoods where each plot
is ≤1000 m from at least one other plot; management areas defined by the Michigan Department
of Natural Resources or private industrial forest owners; and ecological subsections (here
referred to as ecoregions) defined by McNab et al. (2007) nested within the 4000 km2 study area.
1.2.2. Bird community data
To characterize bird communities, I used data from fixed-radius point counts (Ralph et
al., 1995) collected from all sampling plots in 2001–2003. Each plot was sampled 3–4 times

13

between June 4 and July 3 (1 plot was visited twice) in either 2001, 2002, or 2003 between
sunrise and 5 hr post-sunrise. All birds detected within a 10-min timeframe were recorded to
species. I limited my analysis to birds that were detected within 50m of the plot center. Because
my objective was to model resident species that could be indicative of community structure and
habitat conditions within a plot, I excluded large raptors (families Accipitridae, Cathartidae,
Falconidae, Strigidae), and large corvids (Corvus corax and C. brachyrhynchos), because their
large home ranges and ubiquitous distributions make their status as residents questionable
(Crosby et al., 2015). I also considered species that were detected at <1% of plots, as well as
waterfowl (family Anatidae) to be incidentals and excluded them from the analysis (Crosby et
al., 2015; Mahon et al., 2016).
1.2.3. Forest composition and structure data
I characterized forest composition and structure within each plot using 11 variables
derived from measurements taken at the plots concurrent with the bird data and from remotelysensed elevation data. Basal area (BA; m2/ha) for trees ≥10 cm diameter at breast height (DBH)
was measured using a 10-factor prism at 3 subplots within each plot located at the vertices of an
equilateral triangle surrounding the plot center. The first point of the triangle was placed 15 m
from the center at a random azimuth, and the succeeding points were 25 m from the initial point
and 15 m from the center (Laurent, 2005). From the prism measurements I also estimated
proportion of BA in conifers, proportion of BA in deciduous trees other than maple, and stem
density (trees/ha) of snags ≥25 cm DBH and large trees ≥50 cm DBH (sensu McGee et al., 1999;
Millington et al., 2011). Canopy openness was measured at each of the three subplots using a
spherical densitometer and calculated as the average of measurements taken while facing in each
of 4 directions (north, south, east, and west) (Comeau et al., 1998). Stem density of trees <10 cm

14

DBH was measured using 5-tree distance sampling (Lessard et al., 2002) at 9 subplots spaced on
a 3x3 grid centered on the plot center, with subplots 16 m apart (Laurent, 2005). From this I
calculated stems/m2 of seedlings (trees ≥25 cm tall and <1.5 m tall) and canopy recruits (trees
≥1.5 m tall and <10 cm DBH), and the proportion of seedlings that were conifers. To
characterize size structure of the stand, I calculated an index of diameter distribution as the
departure from an idealized even size class distribution of 20 trees per hectare in each 5-cm size
class, where the value was the log-transformed chi-square value measuring departure from the
idealized distribution (Tyrrell and Crow, 1994). Finally, I indexed soil moisture in each plot
using a modification of the topographic wetness index called the SAGA wetness index (SWI;
Olaya and Conrad, 2009), where topography was derived from the U. S. Geological Survey
National Elevation Dataset 1/3 arc-second 2013 maps (https://lta.cr.usgs.gov/NED; accessed
August 21, 2016).
1.2.4. Data analysis
To describe patterns of bird diversity, I estimated the occupancy probability and
abundance of each species at each plot using a multi-species occupancy-abundance model
(Appendix A). Multi-species models have been developed recently as a way to account for
detection probability while retaining information on rare species and thus improve estimates of
community-level parameters such as species richness (Zipkin et al., 2010; Yamaura et al., 2016).
Previous versions of such models have either estimated only occupancy or used global
occupancy estimates to account for undetected species and estimated site-level occupancy as a
derived parameter based on the assumed mathematical relationship with abundance (Wenger and
Freeman, 2008; Yamaura et al., 2016). The model that I developed, however, treats occupancy
and abundance as separate but related processes and estimates them individually. There are three

15

important reasons for doing this. The first is that occupancy patterns and local abundance can
arise from separate processes operating at different scales (Wenger and Freeman, 2008), and so
may not follow assumed mathematical relationships. The second is that it allows the model to
account for the covariance between global occupancy and abundance as a way to improve
estimates (Royle and Dorazio, 2009). Finally, estimating occupancy explicitly allows the model
to take advantage of spatial correlation in occupancy in order to discriminate between plots
(Hines et al., 2010; Mattsson et al., 2013), given that no habitat variables were used in the
estimation process. Through this method, I modeled occupancy explicitly at each plot using the
spatial correlation among plots within 1000 m to improve estimates (sensu Mattsson et al.,
2013). I modeled survey-specific detection probability as a linear function of standardized
covariates for Julian day (linear and quadratic) and time as measured in minutes from sunrise
(Zipkin et al., 2010).
I fit the model in a Bayesian framework with programs R (Version 3.3.0) and JAGS
(Version 4.2.0; Plummer, 2003) using the package runjags with parallel chains, with
uninformative prior distributions for all parameters and hyperparameters. I ran 3 chains of
300,000 iterations with a burn-in of 50,000 and a thinning ratio of 10, and assessed convergence
using the Gelman and Rubin R-hat statistic (Brooks and Gelman, 1998). The occupancyabundance analysis was performed using data from all sample plots where point counts were
done. However, for the additive partitioning and beta diversity analyses described below I
limited the data set to plots within neighborhoods containing ≥3 plots within management areas
containing ≥3 such neighborhoods (Anderson, 2006; Marsh and Ewers, 2013).
To meet my first objective of examining how bird species diversity is partitioned across
scales, I used additive diversity partitioning of species richness, Shannon diversity, and Simpson

16

diversity. Lande (1996) showed that an index of biodiversity can be additively partitioned across
scales provided the index is strictly concave, meaning the value of the index for a pooled set of
units is equal to or greater than the average value within those units (Gering et al., 2003). The
overall regional diversity of an area is the sum of alpha and beta diversity when alpha is the
average within-unit diversity and beta is diversity among units (Lande, 1996). If partitioning is
across multiple scales, then alpha diversity at a given scale is the sum of alpha and beta diversity
at the next lowest scale. In terms of my study, this means that 𝛼1 represents the average bird
species diversity within all plots, 𝛽1is the diversity among plots, 𝛽2 is the diversity among
neighborhoods, 𝛽3 is diversity among management areas, and 𝛽4 is diversity among ecoregions.
Therefore, overall bird species diversity of my study area is equal to 𝛼1 + 𝛽1 + 𝛽2 + 𝛽3 + 𝛽4
(sensu Gering et al., 2003). The 3 indices used in my analysis give information on different
aspects of diversity, where richness looks at the pure effect of species and the Shannon and
Simpson indices look at combined richness and relative abundance (Gering et al., 2003). The
Shannon and Simpson indices are dominance measures that differ in their sensitivity to rare
species, where the Shannon index is weighted equally between common and rare species and the
Simpson index is weighted towards common species (Gering et al., 2003). I used occupancy
estimates to calculate species richness and abundance estimates for Shannon and Simpson
Diversity
Lu et al. (2007) extended this additive partitioning approach to calculate the contribution
of each spatial unit to regional diversity at each scale. They did this by decomposing diversity
contribution into 2 separate components: within-unit diversity (𝛼𝑆(𝑘) ) and distinctiveness of the
species within the unit (𝛽𝑆(𝑘) ) for the kth unit at each spatial scale so that 𝛼𝑆(𝑘) + 𝛽𝑆(𝑘) = 𝐶𝛾𝑆(𝑘)
where 𝐶𝛾𝑆(𝑘) is the contribution of the kth unit to overall species diversity (Lu et al., 2007).

17

Because of the additive partitioning approach, ∑ 𝐶𝛾𝑆(𝑘) at each scale is equal to overall regional
diversity. Using this approach, I estimated the contribution of each spatial unit to overall regional
diversity across all scales used in my sampling design using occupancy estimates.
To meet my second objective of investigating factors that make spatial units at different
scales important contributors to biodiversity, I used multivariate dispersion analysis to estimate
marginality of habitat conditions, environmental heterogeneity, and bird community beta
diversity. Multivariate dispersion arranges environmental or species data in principal coordinate
space around a group centroid, where the distance from the centroid acts as a measure of
dissimilarity (Anderson, 2006). This allows environmental heterogeneity or beta diversity to be
estimated as the average distance of individual units to the group centroid and provides a robust
test for differences in beta diversity among spatial units (Anderson et al., 2006).
To test the hypothesis that diversity contribution is positively correlated with the habitat
marginality of a plot, I estimated multivariate dispersion among all plots and calculated
marginality of a plot as the distance of that plot from the overall centroid. I used linear regression
to test for a significant relationship between ln(distance to centroid) and ln(diversity
contribution). At the neighborhood and management area levels, I used multivariate dispersion
analysis to estimate environmental heterogeneity and bird community beta diversity within
spatial units and test for significant differences among units. I estimated environmental
heterogeneity using the Euclidean distance for the normalized forest composition and structure
variables, and beta diversity of bird communities using the Bray-Curtis index for multi-species
abundance estimates (Anderson et al., 2006). I then used linear regression to test the
hypothesized relationships of environmental heterogeneity with beta diversity and diversity
contribution at the neighborhood level. My data did not meet regression assumptions at the

18

management area level due to a small sample size, so I calculated the correlation coefficients
between the variables at this level. Correlation assumes a linear relationship between the
variables and that they are drawn from a bivariate normal distribution. Because there may be a
relationship between within-unit sample size and the unit’s environmental heterogeneity, beta
diversity, and diversity contribution I removed any possible effect by using residuals from
regressions of each of the 3 estimates against the number of plots within the unit (Veech and
Crist, 2007). I performed all analyses using program R. The multivariate dispersion analyses was
done using the betadisper function in package vegan with type = “centroid” specified. Statistical
significance was assessed at the 𝛼 = 0.1 level.
1.3. RESULTS
1.3.1. Bird community analysis
A total of 433 sample plots were surveyed for bird species in this study, and 59 species
met my criteria for being included in the analysis. The distribution of occupancy rates among all
species was strongly right-skewed, ranging from 0.015─0.823 with a median of 0.182, showing
few common species and a large number of uncommon species. Mean estimated species richness
among all sites was 13.869 (variance = 5.306). The subset of the data that was used for the
additive partitioning and beta diversity analyses included 232 plots nested within 36 ecological
neighborhoods and 5 management areas. Neighborhoods ranged from 105─313 ha with a mean
of 174 ha. Management areas ranged from 12,428─75,850 ha with a mean of 45,343 ha.
1.3.2. Additive partitioning
Additive partitioning of species richness indicated that the majority of diversity was
contributed at smaller spatial scales (Fig. 1.5). The largest amount of diversity in species richness
came from diversity among plots (𝛽1; 37%), followed by diversity among neighborhoods (𝛽2;

19

34%) and within-plot diversity (𝛼1 ; 23%). For both the Shannon and Simpson indices the
majority of diversity was accounted for by within-plot diversity, although there were differences
between the indices with the Simpson index attributing a greater percentage to diversity within
plots (Fig. 1.5).

Figure 1.5. Percentages of total bird species diversity contributed by the alpha and beta
components across 4 spatial scales, estimated by additive diversity partitioning, for species
richness, Shannon diversity, and Simpson diversity. The number at the top of the richness bar is
the total number of species detected (gamma diversity).
1.3.3. Heterogeneity and diversity
There was a significant positive relationship between the marginality of habitat
conditions within a plot and the contribution of the plot to overall regional diversity (df = 230, β
= 0.186, P < 0.001; Fig. 1.6), although marginality explained only a small amount of the
variability in the model (R2 = 0.07). The tests of multivariate dispersion showed significant
differences in environmental heterogeneity among neighborhoods (df = 35, F = 2.886, P < 0.001)
but not among management areas (df = 4, F = 1.774, P = 0.135). Bird community beta diversity,

20

on the other hand, showed significant differences in multivariate dispersion both among
neighborhoods (df = 35, F = 2.151, P = 0.001) and among management areas (df = 4, F = 3.278,
P = 0.012).

Figure 1.6. Scatterplot and best-fit line showing the relationship between the ln distance from
mean vegetation conditions (dispersion distance) for 50-m-radius plots in a multivariate
dispersion analysis and the ln of the contribution of the plot to regional bird diversity. Dispersion
distance is a measure of how marginal a plot was in terms of vegetation composition and
structure, relative to all measured plots.
As expected, there was a significant positive correlation between environmental
heterogeneity and beta diversity within units at the neighborhood level (df = 34, β = 0.024, P =
0.003) and a strong correlation at the management area level (r = 0.796) (Fig 1.7). There was no
apparent relationship between environmental heterogeneity and diversity contribution at the
neighborhood level (df = 34, β = -0.007, P = 0.938). However, at the management area level
there was a moderately strong positive correlation (r = 0.668) (Fig 1.7).

21

Figure 1.7. Scatterplots with best-fit lines showing the relationship of within-unit environmental
heterogeneity with bird community beta diversity and the contribution of a unit to regional
diversity.
1.4. DISCUSSION
Understanding how patterns of heterogeneity interact across scales to influence regional
species diversity is fundamental to deciphering the processes that generate and maintain
biodiversity. My study showed that regional bird species diversity is most strongly influenced by
beta diversity at smaller spatial scales (among sampling plots and ecological neighborhoods),
and demonstrated the scale-dependent effects of landscape pattern on regional diversity. In
particular, there were differential effects of spatial heterogeneity in forest structure and

22

composition at different scales, illustrating how variation in heterogeneity patterns helps to
maintain regional diversity.
The tests of my competing hypotheses, asking whether homogeneous or heterogeneous
areas contribute more to regional biodiversity, seemed to show that it depends on the scale at
which the heterogeneity is measured. This should not be considered surprising, as scale plays a
powerful role in the patterns observed in ecology (Wiens, 1989; Levin, 1992). In my analysis, I
did not explicitly define areas as either homogeneous or heterogeneous, but rather estimated the
level of heterogeneity as a continuous variable using multivariate dispersion. As such, areas with
low heterogeneity were considered more homogeneous and I tested for a correlation between
diversity contribution and the level of heterogeneity within a spatial unit. Previous studies of the
effects of heterogeneity on biodiversity have used different metrics, such as beta diversity
(Fuhlendorf et al., 2006; Astorga et al., 2014), species richness (Morelli et al., 2013; Katayama et
al., 2014), or abundance of individual species (Julliard et al., 2006; Devictor et al., 2008), and
have tended to view diversity at only a single scale (but see Veech and Crist, 2007). To my
knowledge, this study is the first to look at how heterogeneity affects diversity contribution
across multiple scales, and illustrates the importance of pattern and scale in the maintenance of
biodiversity.
At the smallest scale used in this study, that of an individual survey plot, the relative
marginality of a plot in terms of its habitat had a significant impact on its contribution to regional
bird species diversity. This is consistent with the results of Wagner and Edwards (2001) who
found that habitat specificity values (an alternative measure of diversity contribution) were
consistently higher for the least common habitat types in an agricultural matrix. The habitat types
used by Wagner and Edwards (2001) were discreet classifications rather than continuous

23

measures, as in our study. The conclusion, however, is the same: the more marginal the habitat
conditions in a spatial unit, the greater it tends to contribute to regional diversity. The fact that
marginal habitat conditions support more distinctive species is also consistent with the work of
Heino and Gronroos (2014) on the relationship between niche position and occupancy rates of
stream invertebrates. Heino and Gronroos (2014) found that stream invertebrates that relied on
more marginal habitat conditions also had much lower occupancy rates, meaning that the areas
they occupied were likely to have a more distinctive species composition. This relationship
between occupancy rate, habitat marginality, and diversity contribution is logically intuitive but
to my knowledge has not been examined until now.
The explanatory power of the regression model of the relationship between habitat
marginality and diversity contribution was low, however this is not unexpected because of the
way diversity contribution is defined and estimated. This is because habitat marginality only
speaks to the 𝛽𝑆(𝑘) component of diversity contribution, which describes the distinctiveness of
species in that unit (Lu et al., 2007). The other component of diversity contribution is 𝛼𝑆(𝑘) , or
species richness within the unit. While species distinctiveness is related to habitat marginality,
species richness of an equal-sized area may not be (Wagner and Edwards, 2001; Lu et al., 2007),
Therefore, it is likely that a large part of the unexplained variability in this model comes from the
species richness component of diversity contribution.
At intermediate scales (~1–3 km2; the ecological neighborhoods in this study), withinunit heterogeneity had the expected positive correlation with beta diversity but seemed to have
no effect on the contribution of a spatial unit to overall regional diversity. This means that high
within-unit beta diversity did not necessarily equate with high diversity contribution at the
neighborhood scale. There are two possible explanations for this. One is that there is simply no

24

relationship between within-unit environmental heterogeneity and diversity contribution at the
neighborhood scale. On the other hand it may indicate the opposite: that both heterogeneous and
homogenous units are important for maintaining biodiversity. This post-hoc hypothesis fits with
my finding that beta diversity among neighborhoods had one of the highest impacts on regional
diversity in the additive partitioning analysis. The hypothesis is also consistent with the findings
of Julliard et al. (2006) and Devictor et al. (2008), showing that specialist and generalist species
are spatially segregated between homogenous and heterogeneous landscapes, respectively. This
suggests that having both homogenous and heterogeneous units at the neighborhood scale should
have a positive impact on regional species richness. If true, this would show that among-unit
heterogeneity in landscape pattern at certain scales may be as important as within-unit
heterogeneity in habitat conditions.
In contrast to the neighborhood scale, within-unit heterogeneity at the management area
scale (~100–1000 km2) appeared to have a positive correlation with diversity contribution. While
the lack of a statistical test due to the small sample size did not offer definitive evidence for this,
the high correlation coefficient is noteworthy nonetheless. The fact that the relationship between
the two patterns appears to change at different scales speaks directly to the scale-dependent
nature of many relationships in ecology (Wiens, 1989; Levin, 1992; Levin, 2000). These results
may represent an example of separate domains of scale, as proposed by Wiens (1989). Domains
of scale are areas of the scale continuum along which a pattern remains constant or changes
monotonically, bounded by sharp transitional zones between adjacent domains (Wiens, 1989).
Such domains are defined by the scale at which the landscape changes as well as the scale at
which species respond to the landscape (Wheatley, 2010). My results suggest that neighborhoods

25

and management areas may represent separate scale domains in terms of the effect of
heterogeneity on bird community diversity contribution.
The fact that I found a difference in bird community beta diversity among management
areas, but not in environmental heterogeneity, suggests that there are environmental differences
driving species composition among management areas unaccounted for in my analysis. My
estimate of heterogeneity using multivariate dispersion examined heterogeneity among plot-level
compositional and structural features, which represents only one aspect of landscape pattern. The
spatial arrangement of these features relative to each other is likely to have an impact on
community composition within management areas (Fahrig, 2003), and this arrangement is not
accounted for in the multivariate dispersion analysis. Another possibility is that differences in
climate and landform between ecoregions impacted bird community composition enough to
create differences that were not reflected in plot-level vegetation measurements.
Similar to Gering et al. (2003), my additive partitioning analysis reflected the differing
influences of rare and common species on driving within-unit versus among-unit diversity.
Specifically, the fact that the Shannon and Simpson indices were dominated by within-plot
diversity while species richness was dominated by beta diversity suggests that common species
are the primary drivers of alpha diversity while uncommon species drive beta diversity among
units (Crist et al., 2003). Gering et al. (2003) and Crist et al. (2003) found similar patterns for
beetle diversity while sampling over a much larger area with substantial differences among
ecoregions at the largest scale. The ecological implication of this is that biodiversity is driven by
patterns of heterogeneity that maintain common species while creating diversity in uncommon
species among sites (Gering et al., 2003). This pattern maintains species richness as well as the
functional roles driven largely by common species (Gering et al., 2003).

26

Variation in patterns across multiple spatial scales provides the underlying foundation for
maintaining biological diversity by magnifying underlying patterns of environmental variability
(Levin, 2000). Historically, however, studies of biodiversity have focused on alpha and gamma
diversity at a single spatial scale with little research on how patterns occurring at different scales
impact regional diversity (Marsh and Ewers, 2013). My research shows that the environmental
patterns contributing to diversity change across scales, and that variability in patterns of
heterogeneity is important to the maintenance of regional biodiversity.

27

CHAPTER 2
APPLYING CONSERVATION FILTERS TO CONSERVING BIRD
DIVERSITY ON MANAGED FORESTS

ABSTRACT
Maintaining the richness and diversity of bird species on working forest landscapes has
long been one of the major themes in sustainable forest management. However, managers face a
great deal of uncertainty as to the impacts of management decisions on species diversity because
of the difficulty of accounting for all species simultaneously. This difficulty has led to the
development of conservation strategies to be used as tools in the decision-making process.
Among these strategies, the use of conservation filters has been prominent over the last several
decades. I demonstrate a novel application of the conservation filter strategy to the problem of
maintaining bird species diversity on managed forest landscapes utilizing a diversity contribution
approach. Using data on bird community composition, I estimated the relative contributions of
individual plots to regional bird species diversity on a 4,000 km2 area in the western Upper
Peninsula of Michigan managed primarily for timber production. At the coarse filter level I was
able to identify community types and areas that were priorities for conservation. At the
mesofilter level, I described compositional and structural attributes of high value sites within 6
different community types relative to average sites. I identified bird species that were positively
associated with high-contribution sites as well as indicator species for high value sites within the
community types. I found that the conservation value of a community type was inversely
proportional to its representation on the landscape. There were differences among community
types in the relationship between diversity contribution and forest composition and structure
variables, but the commonality was an increase in structural complexity within high value plots.

28

There was a significant negative relationship between species overall abundance and the
probability of being positively associated with high value sites. Managers can use this
application of the conservation filter strategy as a planning tool in the face of uncertainty about
how management decisions affect regional biodiversity.
2.1 INTRODUCTION
The shift in forest management goals over the past several decades to meet societal
demands for more non-timber benefits, such as wildlife habitat and biodiversity conservation,
has led to a move towards ecosystem-based approaches to management (Zollner et al., 2008).
Ecosystem management is a landscape-level approach to planning for the management of natural
resources that emphasizes a central goal of maintaining the sustainability of the ecological
system (Christensen et al., 1996; Haufler et al., 2002). One of the primary ecological goals of
ecosystem management is the maintenance of regional biodiversity, which is typically defined as
preserving the full complement of native species and biological processes within the area of
interest (Haufler et al., 2002). Meeting this objective in forests managed for timber production,
however, is a complex process that requires long-term planning at multiple scales (Haufler et al.,
2002; Crous et al., 2013). A large part of the difficulty of planning for the conservation of
multiple species across a heterogeneous landscape is that managers are often charged with
making decisions in the face of incomplete information on how those decisions might impact
biodiversity (Schulte et al., 2006).
Within the ecosystem management context, maintaining the richness and diversity of bird
species has continued to be one of the major themes in sustainable forest management (Hansen et
al., 1991; Sallabanks and Arnett, 2002; Mahon et al., 2016). Birds provide many ecologically and
economically important functions in forested ecosystems, such as nutrient transfer, insect

29

control, and seed distribution, as well as being important indicators of ecological conditions (e.g.
vegetation composition and structure, landscape composition) (Canterbury et al., 2000;
O'Connell et al., 2000; Sekercioglu, 2006). The distribution of bird species and communities
across a forested landscape is determined by spatial patterns of forest composition and structure
(Verschuyl et al., 2008; Mahon et al., 2016), and forest management systems impact these
patterns across multiple spatial and temporal scales (Boutin and Hebert, 2002).
A great deal of the literature on how forest management impacts species diversity focuses
on forest fragmentation and species richness (e.g. O'Connell et al., 2000; Zipkin et al., 2009), or
uses coarse-resolution cover types to predict occupancy (e.g. Schwenk and Donovan, 2011;
Mahon et al., 2016). As a result, there is little information on how the majority of species
respond to forest composition and structure across a range of forest community types (but see
Cushman and McGarigal, 2004). This lack of information makes it impossible to account for
each species individually in management planning (Noss, 1987), and leads to a great deal of
uncertainty about how management decisions will impact regional species diversity.
Consequently, planners and managers have developed a number of scientifically-based
conservation strategies that can be used as tools for conservation planning in the face of this
uncertainty (Noss, 1987; Schulte et al., 2006; Zenner et al., 2010).

30

Figure 2.1. Operational scales of the conservation filter concept. The coarse filter seeks to
conserve most species by retaining the full range of community types within a region. The
mesofilter increases the conservation value of community types by retaining structures and
processes that may be overlooked at the coarse filter level. The fine filter consists of specieslevel conservation efforts aimed at rare or highly specialized species that may fall through the
higher-level filters (adapted from Zenner et al., 2010).
The coarse filter–fine filter approach to conservation (Fig. 2.1) has been one of the
primary conservation strategies in North America since being introduced by The Nature
Conservancy (TNC) in the 1980’s (Noss, 1987; Schulte et al., 2006; Beier et al., 2015). The
original conception of this strategy (Noss, 1987) is based on the idea that a majority of species
can be conserved by creating a reserve network that retains the full complement of native
community types within a region (Hunter et al., 1988). The reserve network represents a coarse
filter, and is the most commonly-applied strategy in large-scale forest conservation planning
(Schulte et al., 2006). Even then, a certain number of rare or endangered species fall through this
coarse filter, and thus require specialized management practices to maintain their populations
(Noss, 1987). This specialized management represents the fine filter, and extends to areas outside
the coarse filter network to protect vulnerable species (Hunter, 2005). Hunter (2005) introduced

31

the complementary idea of mesofilter conservation, which requires conserving important
structural features within managed areas outside of the coarse filter reserve network. The
mesofilter is seen as a way of extending coarse filter efficiencies to many species that do not
warrant fine filter treatment by maintaining features and processes that increase species richness
of areas within the matrix. In managed forests, these strategies are traditionally applied
independently, with coarse filters applied at the regional level to ensure that all native
community types are represented and the mesofilter strategy applied to stand-level structural
retention (Lindenmayer et al., 2006; Villard and Jonsson, 2009). However, explicitly combining
2 or more of these strategies may offer advantages for conservation planning on managed forests.
In working forest landscapes, where the majority of the land is managed for timber
production under multiple ownerships, creating a connected reserve network representing all
native community types may not be a realistic goal. To address this issue, Haufler et al. (1996)
proposed an alternative approach to the coarse filter as providing adequate distribution of all
community types across the landscape based on their historical range and variability. The ability
to maintain desired distributions of all community types within a region, however, might not be
possible in regions where there are multiple, fragmented ownerships with differing priorities and
management objectives. In such a case, a modified version of this coarse filter approach might be
more appropriate. Because some community types may have a larger impact on biodiversity,
either because of their relative scarcity or because they support higher species richness
(Lindenmayer and Cunningham, 2013), the coarse filter can be re-conceived as a system of
prioritizing community types in terms of their conservation value. Similarly, mesofilter strategies
can go beyond simple structural elements to incorporate multiple compositional and structural
attributes that increase the conservation value of an area through increased complexity or

32

ecological distinctiveness (Crosby, chapter 1 this dissertation; Lindenmayer et al., 2006).
Implementing a strategy that combines these modified coarse filter and mesofilter concepts
requires a method for estimating the value of individual community types or areas.
Lu et al. (2007) proposed a method for estimating the contribution of individual areas to
overall regional diversity as a combination of the number of species in that area (species
richness) and how uncommon those species are throughout the region (distinctiveness relative to
other plots). The diversity contribution approach uses data on community composition from a
given taxon to estimate the additive contributions of all sampled areas to regional diversity of
that taxon (Lu et al., 2007). In practice, this approach provides a quantitative method for ranking
specific areas according to their importance for regional diversity. Explicitly applying the
diversity contribution approach within the context of the combined filter strategy can, therefore,
be used as a tool for maintaining bird species diversity on working forest landscapes.
My goal was to apply an integrated coarse filter-mesofilter conservation strategy to the
problem of maintaining bird species diversity on a managed forest landscape. At the coarse filter
level, my objective was to compare the conservation value of the primary community types on
the landscape. At the mesofilter level, my objective was to investigate the compositional and
structural features of sites with a high contribution to regional diversity relative to other sites
within the same community type. Finally, at the species level my objective was to examine
which species had the strongest relationship with high-contribution sites, and if any species could
act as indicators of high-contribution sites within ecosystem types.

33

2.2 METHODS
2.2.1. Study area and plot selection
To investigate the use of the combined filter approach in forest management, I used data
from a 4000-km2 area in the western upper peninsula of Michigan, USA (Fig. 2.2). This is an
ecologically-diverse northern forest landscape, with variability driven by glacial topography,
soil, and differences in deer browse and forest management across ownerships (Laurent et al.,
2005). The region is dominated by upland northern hardwood forests, and is interspersed with
upland and lowland conifer, early-successional, and mixed upland forest types (Millington et al.,
2011). Dominant tree species include sugar maple (Acer saccharum) in the northern hardwood
types, red pine (Pinus resinosa) and white pine (Pinus strobus) in the upland conifer types,
northern white cedar (Thuja occidentalis) in lowland forest areas, and aspen (Populus spp.) and
white birch (Betula papyrifera) in the early-successional areas. There are also small amounts of
non-forested areas throughout the region.

Figure 2.2. Study area in the western Upper Peninsula of Michigan, totaling 4000 km2, sampled
for bird species and forest composition and structure in 2001–2003.

34

The majority of the land is state-owned or private industrial forest managed for timber
production, and northern hardwood stands are primarily mature second-growth. The most
prominent management practice is selective cutting of northern hardwoods, primarily for sugar
maple, although plantation management for pine and clearcut management of aspen also occurs
(Millington et al., 2011). I used data on bird species and vegetation variables collected in 20012003 from a large-scale study of bird species in managed forests (Laurent et al., 2005; Millington
et al., 2011). Sample plots were selected according to what was known as the GRAIN protocol
(Laurent et al., 2005), where the landscape was gridded into ~1,000 ha sections and 2-8 plots
were placed within randomly selected sections.
2.2.2. Bird community and forest data
Data on bird community composition at each plot were collected using fixed-radius point
counts (Ralph et al., 1995). Each plot was sampled 3–4 times between June 4 and July 3 (1 plot
was visited twice) in either 2001, 2002, or 2003. Point counts were conducted between sunrise
and 5 hr post-sunrise, and all birds seen or heard within a 10-min period were recorded and
assigned to distance bands of 30 m, 50 m, 100 m, and >100 m from the plot center. I limited my
analysis to birds recorded within 50 m of the plot center to coincide with the scale at which
vegetation data were collected. Because the purpose of my analysis was to describe bird
community composition of resident species that would be indicative of habitat conditions within
a plot, I considered species that were detected at <1% of plots, as well as waterfowl (family
Anatidae), to be incidental detections and excluded them from the analysis (Crosby et al., 2015;
Mahon et al., 2016). I also excluded large raptors (families Accipitridae, Cathartidae,
Falconidae, Strigidae) and large corvids (Corvus corax and C. brachyrhynchos) because their

35

large home ranges and ubiquitous distributions make their status as residents difficult to verify
(Crosby et al., 2015).
To characterize environmental conditions within each plot I estimated 6 variables
describing forest composition and structure derived from measurements taken at the plots
concurrent with bird surveys. Basal area (BA; m2/ha) by species for trees ≥10 cm diameter at
breast height (DBH) was measured using a 10 basal area factor prism at 3 subplots within each
plot located at the vertices of an equilateral triangle surrounding the plot center. The first point of
the triangle was placed 15 m from the center at a random azimuth, and the succeeding points
were 25 m from the initial point and 15 m from the center (Laurent, 2005). From the prism
measurements I estimated total BA, proportion BA in conifers, stem density (trees/ha) of snags
≥25 cm DBH and large trees ≥50 cm DBH (sensu McGee et al., 1999; Millington et al., 2011). I
also estimated the proportion of BA in species of trees used to describe specific community types
(see below). Stem density of trees <10 cm DBH was measured using 5-tree distance sampling
(Lessard et al., 2002) at 9 subplots spaced on a 3x3 grid centered on the plot center, with
subplots 16 m apart (Laurent, 2005). From this I calculated stems/m2 of seedlings (trees ≥25 cm
tall and <1.5 m tall). To characterize size structure of the stand, I calculated an index of diameter
distribution as the departure from an idealized even size class distribution of 20 trees per hectare
in each 5-cm size class. where the value was the log-transformed chi-square value measuring
departure from the idealized distribution (Tyrrell and Crow, 1994). This metric is an index of the
distribution of trees in different size classes within the stand, and is strongly correlated with
stand age among northern hardwood stands in Michigan (Tyrrell and Crow, 1994).

36

2.2.3. Bird species analysis and plot-level diversity contribution
I estimated the occupancy probability and abundance for each species at each plot using
an integrated, multi-species occupancy-abundance model. These estimates provided plot-level
occupancy and abundance estimates without the use of habitat variables (Appendix A). Previous
versions of such models have either estimated only occupancy or used global occupancy
estimates to account for undetected species and estimated plot-level occupancy as a derived
parameter based on its assumed mathematical relationship with abundance (Wenger and
Freeman, 2008; Yamaura et al., 2016). My model treats occupancy and abundance as separate
but related processes, and incorporates the covariance between occupancy and abundance
directly into the model (Royle and Dorazio, 2009). Through this method, I modeled occupancy
explicitly at each plot using the spatial correlation among plots within 1000 m to improve
estimates (sensu Mattsson et al., 2013). I modeled survey-specific detection probability as a
linear function of standardized covariates for Julian day (linear and quadratic) and time as
measured in minutes from sunrise (Zipkin et al., 2010).
I fit the model in a Bayesian framework with programs R (Version 3.3.0) and JAGS
(Version 4.2.0; Plummer, 2003) using the package runjags with parallel chains, with
uninformative prior distributions for all parameters and hyperparameters. I ran three chains of
300,000 iterations with a burn-in of 50,000 and a thinning ratio of 10, and assessed convergence
using the Gelman and Rubin R-hat statistic (Brooks and Gelman, 1998). The occupancyabundance analysis was performed using data from all sample plots where point counts were
conducted. However, for further analyses we used only the subset of plots where vegetation data
were collected.

37

To estimate the relative contribution of each plot to overall regional bird diversity, I
applied my estimates of occupancy probability to the method developed by Lu et al. (2007). This
method estimates the contribution of plots to regional diversity by decomposing diversity
contribution into 2 separate components: within-unit diversity (𝛼𝑆(𝑘) ) and distinctiveness of the
species within the unit (𝛽𝑆(𝑘) ) for the kth unit so that 𝛼𝑆(𝑘) + 𝛽𝑆(𝑘) = 𝐶𝛾𝑆(𝑘) , where 𝐶𝛾𝑆(𝑘) is the
contribution of the kth unit to overall species diversity (Îł; gamma diversity) (Lu et al., 2007). This
is an additive approach, so that 𝛾 = ∑ 𝐶𝛾𝑆(𝑘) , meaning that 𝐶𝛾𝑆(𝑘) represents the diversity
contribution relative to all other plots within the sample. I then designated high-contribution
plots as those above the third quantile in diversity contribution scores (i.e. the top 25% of plots in
terms of diversity contribution).
2.2.4. Coarse filter: identifying high-value community types
To meet my first objective of estimating the relative conservation value of different
community types, I designated each plot as one of 8 primary community types found in the
region. These types were derived from definitions from the Michigan Department of Natural
Resources (MDNR) in the Integrated Forest Monitoring Assessment and Prescription (IFMAP)
protocol (Space Imaging Solutions, 2001) as: Non-forested, Northern Hardwood Association,
Upland Conifer, Upland Mixed, Early-successional, Cedar, Lowland Conifer, and Other. Nonforested areas were those with <25% canopy cover of trees. Northern Hardwood Association was
defined as having a combination of maples (Acer spp.), American beech (Fagus grandifolia),
basswood (Tilia americana), white ash (Fraxinus canadensis), cherry (Prunus spp.), and yellow
birch (Betula alleghaniensis) >60% of the basal area. Upland conifer was defined as having a
combination of balsam fir (Abies balsamia), European larch (Larix decidua), white spruce (Picea
glauca), jack pine (Pinus banksiana), red pine (Pinus resinosa), white pine (Pinus strobus), and

38

eastern hemlock (Tsuga canadensis) >60% of the basal area. Upland Mixed forest contained
between 40% and 60% conifers. Early-successional forest had >40% of the basal area in aspen
(Populus spp.) and white birch (Betula papyrifera). Cedar consisted of >50% of the basal area in
Northern White Cedar, and Lowland Conifer had >50% of basal area in Tamarack (Larix
laricina) and Black Spruce (Picea glauca). Other was defined as forested areas that did not fit
any of the other categories.
To estimate the relative conservation value of each community type, I created an index
from the ratio of the proportional representation of each community type among highcontribution plots to the proportional representation among all plots:
𝐶𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑖𝑛𝑑𝑒𝑥𝑖 =

𝑝𝑟𝑜𝑝𝑖 (𝐻𝑖𝑔ℎ)
𝑝𝑟𝑜𝑝𝑖 (𝐴𝑙𝑙)

where “High” refers to the high-contribution plots and “All” refers to all plots, for community
type i. If the value of the index was 1, the proportional representation of that ecosystem type
among high-contribution plots was equal to its proportional representation among all plots, and it
could be thought of as neutral in terms of conservation value. An index value greater than 1
would suggest an ecosystem type with high conservation value, and vice versa.
2.2.5. Mesofilter: attributes of high-contribution plots
To meet my objective of identifying important compositional and structural attributes at
the mesofilter level, I compared forest measurements between high-contribution plots and the
remaining plots within the 6 forested community types (Northern Hardwood, Upland Conifer,
Upland Mixed, Early Successional, Cedar, and Lowland Conifer). I did not perform formal
statistical tests for differences in mean values because 4 of the 6 community types were
represented by fewer than 20 plots, leading to small sample sizes for comparison and a
subsequent inability to meet statistical assumptions. Instead I compared medians and

39

interquartile ranges between high-contribution plots and the remaining plots for the 6 measured
variables representing stand compositional and structural attributes. I considered there to be a
strong relationship between a variable and diversity contribution if interquartile ranges did not
overlap between average and high-contribution plots, and a moderate correlation if at least one of
the interquartile ranges did not overlap with the median of the other category.
2.2.6. Bird species relationships to high-contribution plots
To examine the species-level relationship of birds to high-contribution plots, I tested
which species had higher abundances in high-contribution plots and examined whether any
species could act as indicators of high-contribution plots within each ecosystem type. I tested for
a significant difference in individual species abundances between high-contribution plots and
average plots using a Student’s t-test with unequal variances. I also used logistic regression to
test for a relationship between overall mean abundance among plots for each species and the
probability of having a higher mean abundance in high-contribution plots.
To examine if species could be used as indicators of high-contribution plots within
forested community types, I used indicator analysis with two-species combinations (De CĂĄceres
et al., 2012). This technique allows for the possibility that the joint occurrence of ≥2 species may
be a more reliable indicator than the target plot is a member of a discreet group, but includes
single species in its rankings of indicator values as well (De CĂĄceres et al., 2012). Within each
forested community type, I tested which species or combinations of species might act as
indicators of high-diversity plots relative to average plots.

40

2.3 RESULTS
2.3.1. Bird community composition
A total of 433 sample plots were surveyed for bird species in this study, and 59 species
met the criteria for being included in the analysis. There were 335 plots at which vegetation data
were collected to be used in our diversity contribution analysis. The distribution of occupancy
rates among these plots was strongly right-skewed, ranging from 0.007─0.894 with a median of
0.170, showing few common species and a large number of uncommon species. Mean estimated
species richness among all plots was 13.767 (variance = 5.081).
2.3.2. Coarse filter: identifying high-value community types
The coarse filter analysis found large differences among community types in terms of
their conservation value (Fig. 2.3). The dominant ecosystem type on the landscape was Northern
Hardwoods, representing 48% of all plots in the dataset. Besides Early-successional, no other
ecosystem type constituted >7% of the dataset, with the least common being Cedar (2.7%) and
Lowland Conifer (2.4%). The contribution index values for each ecosystem type were inversely
proportional to their representation on the landscape, although this was not a constant
relationship (Fig. 2.3). Upland Conifer, Upland Mixed, Cedar, and Non-forested all had
contribution index values >2, which corresponded with their low occurrence rates in the dataset.
Northern Hardwoods and Early-successional both had contribution indices of <1.
The total number of high-contribution plots was not evenly distributed across community
types either, however the relationship was less consistent then with the contribution index.
Despite its low relative conservation value, Northern Hardwoods supplied the greatest number of
high-contribution plots at 25. Early-successional, Upland Conifer, and Non-forested areas

41

supplied 10, 11, and 11 high-contribution plots, even though they represented 20.3%, 5.7%, and
6% of the plots, respectively.
2.3.3. Mesofilter: attributes of high-contribution plots
The comparison of forest compositional and structural attributes between highcontribution plots and the remaining plots showed a great deal of variation among community
types (Table 2.1; Fig. 2.4). On the whole, high-contribution plots tended to have lower basal area
than average, with the effect being most pronounced among Northern Hardwood, Cedar, and
Lowland Conifer community types (Fig. 2.4). For the proportion of basal area in conifer, the
only community type that showed a moderate difference was Northern Hardwoods, where the
median value among average plots was 0.0 and among high-contribution plots was 0.02.
Community types that had a strong conifer component showed moderate negative relationship,
suggesting that greater numbers of deciduous trees had a positive effect on diversity contribution
in these community types.

42

Figure 2.3. Comparison of conservation index values between forested community types in the
western Upper Peninsula of Michigan relative to bird species diversity. The light gray bars
represent the proportional representation of each community type in the dataset, pink bars
represent their proportional representation among plots in the upper 25% of diversity
contribution. Conservation value is represented by the green bars as the contribution index
calculated by dividing the pink bar by the gray bar.

43

Total
Count

HighContribution
Count

162

26

Upland Conifer

19

11

─

Upland Mixed

15

8

Early-successional

68

Cedar

9

Community Type
Northern
Hardwood

Total
Proportion
Basal
BA in
Area
Conifer
─
+
a
Moderate
Moderate

Large
Tree
Density

Snag
Density

Seedling
Density

Diameter
Distribution

+

0

+

─

─
Moderate

0

─

+
Moderate

+
Moderate

─

─
Moderate

+
Moderate

0

+
Moderate

+

10

+

0c

0

0

+

─

4

─
Strongb

─
Moderate

+
Moderate

+

+
Moderate

+

─
+
─
+
0
0
Strong
Strong
Strong
Table 2.1. Total number of plots among six primary forested community types, number of plots with a high contribution to overall
regional diversity, and the direction (+ or ─) and strength of the relationship between forest compositional and structural variables and
diversity contributions†.
†
Based on the difference between median and interquartile range between high-contribution plots and average plots.
a
Indicates that at least one of the interquartile ranges did not overlap with the median of the other category.
b
Indicates that interquartile ranges did not overlap between high-contribution plots and average plots.
c
Medians of both categories were equal to zero.
Lowland Conifer

8

3

44

Figure 2.4. Median (bars) and interquartile range values (black lines) of forest compositional
and structural variables between plots with high relative contribution to regional bird diversity
(the top 25%; green bars) and remaining plots (gray bars) within the same community type.
Community types are coded as: NH = Northern Hardwood; UC = Upland Conifer; UM = Upland
Mixed; ES = Early-successional; C = Cedar; and LC = Lowland Conifer. Basal area (BA) is
measured in m2/ha. Large trees (≥50 cm diameter) and snags (standing dead trees ≥25 cm
diameter) are measured in trees per hectare. Seedling density (trees ≥25 cm tall and <1.5 m tall)
is measured in stems/m2. Diameter distribution is the ln chi2 departure from an idealized even
distribution of 20 trees per hectare in each 5-cm size class.
The density of large trees ≥50 cm DBH showed a positive relationship with diversity
contribution among the Northern Hardwood, Upland Mixed, and Cedar ecosystem types,
however the relationship was weak in Northern Hardwoods and only moderate in the 2 others
(Table 2.1). These large trees were not common in any of the community types, and median

45

values were 0 in 3 of the 6 types. The upper end of the interquartile range was substantially
higher in high-contribution plots among all community types except Lowland Conifer (Fig. 2.4).
The density of snags ≥25 cm DBH was lower than that of large trees (Fig. 2.4), and showed
almost no relationship with diversity contribution in any of the community types. The median
value was 0 in all but 2 instances and interquartile ranges showed little variation between
average and high-contribution plots in any of the community types. The only exceptions were in
Upland conifers, where snag density was much higher among average plots, and Cedar, where
snag density was much higher among high-contribution plots, with both relationship being weak.
Seedling density showed a positive relationship with diversity contribution among all
community types. The relationship with diversity contribution in Lowland Confer was
considered strong, and all others were moderate except for Early-successional and Northern
Hardwoods. Median values of seedling density were, on average, 1.8 times higher in highcontribution plots and the low end of the interquartile range averaged 2.2 times higher. Finally,
diameter distribution did not vary greatly between average and high-contribution plots, with the
only real exception being among Lowland Conifer plots. The Lowland Conifer plots showed that
high-contribution plots had smaller departure from the low-density, even-age-class distribution
as measured by the chi-square value. Upland Conifer also showed a moderate effect, with highcontribution plots showing a greater departure from the idealized distribution.

46

Species

Mean Abundance

HighAOU
Average contribtion
Code
Common Name
Scientific Name
Plots
Plots
ALFL
Alder Flycatcher
0.090
0.600
Empidonax alnorum
AMGO American Goldfinch
1.662
2.545
Spinus tristis
AMRE American Redstart
0.683
1.828
Setophaga ruticilla
AMRO American Robin
2.139
2.220
Turdus migratorius
AMWO American Woodcock
0.024
0.551
Scolopax minor
BAOR
Baltimore Oriole
0.208
0.318
Icterus galbula
BAWW Black-and-white Warbler
0.528
1.088
Mniotilta varia
BBCU
Black-billed Cuckoo
0.121
0.286
Coccyzus erythropthalmus
BLWA Blackburnian Warbler
0.655
1.124
Setophaga fusca
BCCH
Black-capped Chickadee
2.763
3.831
Poecile atricapillus
BTBW Black-throated Blue Warbler Setophaga caerulescens
0.273
0.780
BTNW
Black-throated Green Warbler
2.365
2.052
Setophaga virens
BLJA
Blue Jay
2.642
3.194
Cyanocitta cristata
BHVI
Blue-headed Vireo
0.671
0.858
Vireo solitarius
BWWA Blue-winged Warbler
0.121
0.339
Vermivora cyanoptera
BWHA Broad-winged Hawk
0.402
0.569
Buteo platypterus
BRCR
Brown Creeper
1.545
1.555
Certhia americana
BRTH
Brown Thrasher
0.132
0.427
Toxostoma rufum
CEDW
Cedar Waxwing
1.555
2.389
Bombycilla cedrorum
CSWA
Chestnut-sided Warbler
1.423
2.713
Setophaga pensylvanica
CHSP
Chipping Sparrow
0.341
0.864
Spizella passerina
COYE
Common Yellowthroat
0.203
1.255
Geothlypis trichas
Table 2.2. Bird species used in diveristy contribution analysis from the western Upper Peninsula of Michigan, USA. Average plots are
those below the third quantile of diversity cotribution scores. High-contribution plots are those above the third quantile. Species in
bold are those that had a significanlty higher abundance in high-contribution plots (P < 0.05).

47

Table 2.2 (cont’d)
Species
AOU
Code
DEJU
DOWO
EABL
EAKI
EAWP
GCKI
GCFL
HAWO
HETH
INBU
LEFL
MAWA
MODO
MOWA
NAWA
NOFL
NOPA
NOWT
OVEN
PIWO
PIWA
PUFI
RBNU

Common Name
Dark-eyed Junco
Downy Woodpecker
Eastern Bluebird
Eastern Kingbird
Eastern Wood-Pewee
Golden-crowned Kinglet
Great-crested Flycatcher
Hairy Woodpecker
Hermit Thrush
Indigo Bunting
Least Flycatcher
Magnolia Warbler
Mourning Dove
Mourning Warbler
Nashville Warbler
Northern Flicker
Northern Parula
Northern Waterthrush
Ovenbird
Pileated Woodpecker
Pine Warbler
Purple Finch
Red-breasted Nuthatch

Scientific Name
Junco hyemalis
Picoides pubescens
Sialia sialis
Tyrannus tyrannus
Contopus virens
Regulus satrapa
Myiarchus crinitus
Picoides villosus
Catharus guttatus
Passerina cyanea
Empidonax minimus
Setophaga magnolia
Zenaida macroura
Geothlypis philadelphia
Oreothlypis ruficapilla
Colaptes auratus
Setophaga americana
Parkesia noveboracensis
Seiurus aurocapilla
Dryocopus pileatus
Setophaga pinus
Haemorhous purpureus
Sitta canadensis

48

Mean Abundance
HighAverage contribtion
Plots
Plots
0.253
0.843
0.446
0.342
0.187
0.397
0.107
0.533
1.337
1.402
0.464
1.541
1.049
1.385
0.838
0.888
2.318
2.262
0.970
1.949
1.298
1.227
0.707
0.985
0.323
0.552
1.210
1.533
2.445
3.533
1.043
1.162
0.375
0.956
0.193
0.343
3.777
2.895
0.182
0.301
0.199
0.613
0.331
0.619
0.651
1.009

Table 2.2 (cont’d)
Species

AOU
Code
REVI
RBGR
RTHU
RUGR
SASP
SCTA
SOSP
SWSP
VEER
WBNU
WTSP
WIWR
YBSA
YRWA

Common Name
Red-eyed vireo
Rose-breasted Grossbeak
Ruby-throated Hummingbird
Ruffed Grouse
Savannah Sparrow
Scarlet Tanager
Song Sparrow
Swamp Sparrow
Veery
White-breasted Nuthatch
White-throated Sparrow
Winter Wren
Yellow-bellied Sapsucker
Yellow-rumped Warbler

Scientific Name
Vireo olivaceus
Pheucticus ludovicianus
Archilochus colubris
Bonasa umbellus
Passerculus sandwichensis
Piranga olivacea
Melospiza melodia
Melospiza georgiana
Catharus fuscescens
Sitta carolinensis
Zonotrichia albicollis
Troglodytes hiemalis
Sphyrapicus varius
Setophaga coronata

49

Mean Abundance
HighAverage contribtion
Plots
Plots
3.853
3.171
3.063
2.614
0.300
0.532
0.597
0.618
0.019
0.098
0.896
0.743
0.191
1.004
0.121
0.759
0.584
0.807
0.659
0.947
0.817
1.466
0.603
1.015
2.192
2.083
1.535
2.449

2.3.4. Species-level relationships
The Student’s t-tests identified 35 of 59 species that had significantly higher mean
abundance in high-diversity plots than average plots (Table 2.2). There was a significant
negative correlation between the probability of having a higher mean abundance in highcontribution plots and overall mean abundance (β = -0.804; P = 0.015), meaning that lesscommon species tended to be better represented in high-contribution plots. In the indicator
species analysis, 5 of the 6 forest types had single species as either the best or second-best
indicator of high-contribution plots (Table 2.3). The species acting as indicators were not
necessarily uncommon (e.g. Red-eyed Vireo) or strongly associated with those forest types (e.g.
Eastern Kingbird in Northern Hardwoods). Positive predictive value, or the probability that the
plot belonged to a specific group given that the species was found there (also called specificity),
ranged from very high (>0.9 in high-contribution Lowland Conifer plots) to moderate (0.6 for
high-contribution Upland Mixed plots) (Table 2.3).

50

Ecosystem Type

1
2
3
4
5
EAKIa
OVEN+EAKI
REVI+EAKI
BTNW+EAKI
HETH+EAKI
Northern Hardwoods
(0.850)
(0.850)
(0.850)
(0.850)
(0.829)
CSWA
NAWA+CSWA OVEN+CSWA
RBNU
NAWA_RBNU
Upuland Conifer
(0.851)
(0.849)
(0812)
(0.811)
(0.794)
OVEN+YBSA
OVEN
BRCR
OVENI+BRCR
REVI+BRCR
Upland Mixed
(0.621)
(0.603)
(0.584)
(0.584)
(0.584)
LEFL+NOOR
LEFL+CSWA
LEFL+MOWA
SCJU
OVENA+SCJU
Early-successional
(0.898)
(0.888)
(0.877)
(0.867)
(0.867)
BHVI+BLWA
VEER
REVI+VEER
NAWA+VEER
BLJA+VEER
Cedar
(0.813)
(0.807)
(0.807)
(0.807)
(0.807)
CEDW
NAWA+CEDW
CEDW+BLJA
REVI+CEDW
OVEN+CEDW
Lowland Conifer
(0.906)
(0.906)
(0.906)
(0.875)
(0.875)
Table 2.3. Top 5 indicator species or combinations for high-contirbution plots within 6 ecosystem types in the western Upper
Peninsual of Michigna, USA. Numbers in parantheses are the probabilities of being a high-contribution site, given that combination of
species is found there. See Table 2 for species associated with four-letter codes.
a
Standardized species codes used by the American Ornithologist’s Union (AOU).

51

2.4. DISCUSSION
My research demonstrates that a novel application of the conservation filter strategy can
be used for the prioritization of ecosystem types and habitat conditions that are critical to the
maintenance of species diversity in managed landscapes. My work focused on bird community
conservation in areas that are actively managed for timber production, however this method is
easily applicable to other taxa and other systems. In particular, the diversity contribution
approach can be used to identify areas and ecosystem types that are important for maintaining
regional species diversity and provide guidelines for site-level management that will enhance
biodiversity value. Combining coarse filters and mesofilters in this way facilitates the multi-scale
planning that is an integral part of the ecosystem management paradigm and the effort to
conserve species diversity across managed landscapes. Therefore, this novel approach provides
an additional tool that managers can use in making management decisions in the face of
uncertainty about the effects on biodiversity.
The diversity contribution approach I employed here was proposed a decade ago (Lu et
al., 2007), and is an extension of the concept of habitat specificity (Halvorsen and Edvardsen,
2009). The idea behind habitat specificity is that individual species will be dependent to a degree
on individual spatial elements (i.e. habitats) within the landscape, with specificity being
measured as the proportion of occurrences of that species that fall into that spatial element
(Wagner and Edwards, 2001). Thus, the contribution of an individual unit to regional diversity is
the sum of the specificity scores of the species that occur there (Wagner and Edwards, 2001). Lu
et al. (2007) extended this idea by decomposing diversity contribution into richness and
distinctiveness components within an additive framework so that spatial units are described
according to their relative contribution to regional diversity, thus providing a robust method for

52

ranking and prioritizing areas for conservation. To date, these methods have been applied
primarily to plants and invertebrates in terrestrial systems (e.g. Halvorsen and Edvardsen, 2009;
Saraiva et al., 2015), and I know of no instances where they have been employed in planning or
management decisions.
My finding that the conservation value of a community type, as defined by my
contribution index, is inversely proportional to its representation on the landscape (Fig. 2.3) is
logically intuitive, and aligns with the idea of habitat specificity (Wagner and Edwards, 2001).
This effect of proportional representation is because diversity contribution is largely determined
by the distinctiveness of species within a site (Lu et al., 2007), which is strongly associated with
the distinctiveness of the environmental conditions relative to the rest of the landscape (Crosby,
chapter 1 this dissertation). The strong influence of uncommon species on regional diversity is an
aspect of the beta component of diversity (the difference among spatial units within a region;
Whittaker, 1972), which has been shown to be a major driver of diversity among birds and other
taxa (Crist et al., 2003; Veech and Crist, 2007). The effect of proportional representation,
however, was not constant. My results show that Upland Mixed and Upland Conifer forests both
had a higher conservation value than Cedar and Lowland Conifer, even though Upland Mixed
and Upland Conifer were nearly twice as common. Although I did not examine the relative
influences of richness and distinctiveness on the diversity contribution scores, it is possible that
Cedar and Lowland Conifer support fewer species on average. Species richness as reflected in
alpha diversity is a component of diversity contribution (Lu et al., 2007), and so it is possible that
lower species richness may have accounted for the lower conservation value of these community
types.

53

It was clear at the mesofilter level that different compositional and structural attributes
affected diversity contribution within different community types (Fig. 2.4), however the
commonality seemed to be that they created more structural complexity within plots. For
example, the proportion of BA in conifer had a positive correlation with diversity contribution in
Northern Hardwood community types, but a negative correlation in Upland Conifer and Upland
mixed community types (Fig. 2.4B). Similarly, high-contribution plots among Northern
Hardwoods and Cedar community types had lower total basal area while basal area seemed to be
neutral in Upland Conifer and Upland Mixed plots, which had lower basal area on average to
begin with. The relationship between structural complexity and diversity was first demonstrated
by MacArthur and MacArthur (1961), and has guided some forest conservation efforts under the
concept that “diversity begets diversity” (Schulte et al., 2006; Hunter and Schmiegelow, 2011).
My research suggests that increasing the compositional and structural complexity of forest stands
increases not just species richness, but also the contribution to overall regional diversity, by
increasing habitat specificity within those stands.
The fact that the abundance of less-common bird species was more likely to be positively
related to high-contribution plots also corresponds to the idea of habitat specificity. Heino and
Gronroos (2014) showed that niche marginality among stream invertebrates, which is akin to
habitat specificity, had a significant negative relationship with occupancy rates. This relationship
between specificity, occupancy, and diversity contribution is important for our understanding of
the drivers of regional species diversity (Crosby, chapter 1 this dissertation). Knowing which
species rely more strongly on high-contribution sites is important for managers in determining
monitoring and habitat conservation priorities. Because these species tend to be less common
regionally, they have increased importance for the maintenance of regional diversity.

54

In my application, the coarse filter strategy is not focused on creating reserves, as it
traditionally has been (Noss, 1987; Hunter, 2005), or on maintaining a certain distribution of
ecosystem types as suggested by Haufler et al. (1996). Rather, my application focuses on
prioritizing community types throughout the landscape in terms of their conservation value and
identifying sites of high conservation value among all community types. I then integrate the
mesofilter with the coarse filter by describing those high-value sites in terms of compositional
and structural attributes that set them apart from other sites within the same community type.
This approach is distinctly different from the traditional practice of prioritizing areas for
conservation based on species richness (Lu et al., 2007), which is problematic for a number of
reasons (Palmer and White, 1994). The key here is that conservation value is defined not in terms
of species richness but rather in the contribution to overall regional diversity (i.e. gamma
diversity), and so emphasizes uncommon species and community types within the context of the
broader biological community (Wagner and Edwards, 2001; Lu et al., 2007).
My application is based on the idea that, while all ecosystem types are important, some
sites have scarcity value because of their low occurrence rates on the landscape (Wagner and
Edwards, 2001). Within all ecosystem types, however, there will always be some that support
more or different species because of specific compositional and structural attributes (Hunter,
2005; Crous et al., 2013). Taken together, this represents the integration of coarse filter and
mesofilter strategies, and the diversity contribution approach provides a quantitative method for
applying this combined strategy on managed forest landscapes.
2.5. MANAGEMMENT IMPLICATIONS
At the coarse filter operational scale, it is important to be able to identify high-value
ecosystem types on the landscape and ensure that these are maintained in suitable amounts. The

55

actual amount and distribution of such types needs to be guided by the biophysical template, as
well as some sense of historical range and variability (Haufler et al., 2002; Keane et al., 2009),
however forest production goals and other objectives can also play a role and may even be
advantageous to both biodiversity and timber production (Zenner et al., 2010). For example, pine
plantations have high economic value, bur are often considered to have low value in terms of
biodiversity (Bremer and Farley, 2010). In my study area, however, pine forests were relatively
rare and so had high conservation value. Therefore, maintaining pine plantations in this study
area could have a positive impact on regional biodiversity. This illustrates the importance for
managers of recognizing and maintaining native community types that are regionally uncommon,
but also shows how economic and ecological interests can be sometimes serve a common goal.
At the mesofilter scale, understanding the compositional and structural attributes of highcontribution plots within a specific community type may hold the key to increasing the overall
biodiversity value throughout a region. When supplied with this knowledge, managers can use it
to modify management prescriptions to increase the conservation value of forest harvesting
activities and maintain diversity across the landscape. Because specific attributes, such as total
basal area or percent conifer, have differential impacts among community types, it is critical for
managers to understand this and be able to adjust harvest and retention guidelines based on the
community type of a particular area to be harvested.

56

CHAPTER 3
MONITORING BETA DIVERSITY OF BIRD COMMUNITIES AS AN
ALTERNATIVE PARADIGM FOR TRACKING CHANGES IN REGIONAL
BIODIVERSITY
ABSTRACT
Regional monitoring of biodiversity is consistently recognized as one of the primary
requirements of any long-term conservation program. Despite this recognition, examples of
monitoring programs that can link changes in biodiversity to environmental changes at scales
relevant to land management and conservation planning (1–1000 km2) are uncommon. To
address this issue, I propose a monitoring system based on beta diversity of bird communities at
multiple spatial scales. Beta diversity has been shown to reflect environmental heterogeneity in
several systems, and bird community diversity in particular is reflective of ecological conditions.
My proposed system focuses on species-level monitoring of bird communities for the estimation
of beta diversity using a hierarchical sampling design. I analyzed bird community and habitat
data from the western Upper Peninsula of Michigan collected using a hierarchical sampling
design to test the link between beta diversity and environmental heterogeneity at different spatial
scales. I then used simulations of species and landscapes to compare capabilities of different
sampling designs for detecting patterns of diversity across multiple spatial scales. My results
show a positive relationship between heterogeneity and diversity at 2 management-related scales
(1–3 km2 and 100–1000 km2). The hierarchical sampling design was superior to systematic,
random and stratified random sampling designs because it is able to detect patterns at finer
spatial scales. The fact that bird communities are relatively easy to monitor, are reflective of
ecological conditions at multiple scales, and generate so much interest with the general public
makes them the most appropriate taxon for regional biodiversity monitoring. The system I

57

propose here can provide a baseline monitoring program that is logistically feasible and
ecologically useful for assessing and guiding regional conservation policy.
3.1. INTRODUCTION
Regional monitoring of biodiversity is consistently recognized as one of the primary
aspects of any long-term conservation program (Yoccoz et al., 2001; White et al., 2013). Despite
this recognition, examples of landscape scale species-level monitoring programs are uncommon
because of the high costs of surveying a large and diverse group of species (Manley et al., 2004;
Noon et al., 2012). The few broad-scale monitoring programs available, such as the North
American Breeding Bird Survey (Sauer et al., 2003) or state-level breeding bird atlas programs
(Zuckerberg and Porter, 2010), are too coarse-grained in both space and time to track the way
typical land management activities impact biodiversity. As a result, there is little geographically
extensive information that can link changes in species diversity to environmental changes at
spatial and temporal scales at which management and conservation planning typically occur (1–
1000km2; Bestelmeyer et al., 2003; Noon et al., 2012).
To date, most biodiversity monitoring schemes have focused on determining which few
species offer the best indices of environmental conditions, and therefore may be useful as
surrogates for tracking biodiversity at large spatial scales (Manley et al., 2004). While this
strategy is intuitively appealing, the assumption that the status of one or a few species is
indicative of broad-scale ecological conditions has often been challenged (Manley et al., 2004;
Wiens et al., 2008). On the other hand, ecologists recognize that spatial and temporal patterns of
heterogeneity in the environment at multiple scales are the precursor for biological diversity
(Christensen, 1997; Levin, 2000), and research suggests that maintaining patterns of
environmental heterogeneity should be the focus of ecosystem management and conservation

58

efforts (Fuhlendorf et al., 2006; Veech and Crist, 2007; Fuhlendorf et al., 2012; Astorga et al.,
2014). Therefore, a monitoring system for tracking biodiversity and environmental heterogeneity
across scales while still providing valuable species-level data would provide important
information for our understanding of land-use impacts on biodiversity and long-term
conservation planning.
Species diversity is traditionally partitioned into three components related to spatial scale,
where 𝛼 is within-unit diversity, 𝛽 is the diversity among units, and 𝛾 as the overall regional
diversity (Whittaker, 1960). Among these, 𝛽-diversity represents a useful spatial component of
diversity, and can provide information about how diversity is distributed across the landscape
(Marsh and Ewers, 2013). 𝛽-diversity of specific taxa has been shown to reflect compositional
and structural heterogeneity within ecosystems (Fuhlendorf et al., 2006; Astorga et al., 2014),
suggesting that species diversity within selected groups can act as an index of environmental
heterogeneity. Lande (1996) showed how 𝛼-, 𝛽-, and 𝛾-diversity can be additively partitioned at
multiple spatial scales to investigate how diversity patterns are distributed across scales (Gering
et al., 2003). Monitoring of 𝛽-diversity at multiple scales, then, offers an alternative to traditional
surrogate-species approaches for tracking ecological conditions and indexing biodiversity at
regional scales.
I propose that measuring beta diversity of bird communities at multiple spatial scales
offers an efficient and effective way to monitor regional biodiversity. Bird community
composition has been used in the past as an indicator of ecological conditions (Canterbury et al.,
2000; O'Connell et al., 2000) and environmental heterogeneity (Fuhlendorf et al., 2006; Veech
and Crist, 2007), and birds are known to respond strongly to land-use change (DeGraaf et al.,
1998). Additionally, monitoring bird species is relatively easy and efficient compared to most

59

other taxa, and there is a great deal of interest within the general public for bird species
conservation. My goal was to evaluate a hierarchical sampling design intended to characterize
regional beta diversity at multiple spatial scales. My objectives were to test the hypothesis that
bird community diversity reflects environmental heterogeneity across spatial scales and evaluate
the effectiveness of different sampling designs for estimating beta diversity at multiple spatial
scales. I used bird community and environmental data within a hierarchical sampling design to
investigate the relationship between heterogeneity and beta diversity, and simulated landscape
and community data to evaluate sampling designs. My approach demonstrates the
appropriateness of birds as biodiversity indicators and offers insights into the impact that
sampling designs can have on biodiversity estimates.
3.2. METHODS
3.2.1. Study area and data acquisition
To meet my first objective, I tested the link between beta diversity of bird communities
and environmental heterogeneity across scales using bird community and forest data from a
4000-km2 area in the western upper peninsula of Michigan, USA. This is an ecologically diverse
northern forest landscape, with variability driven by glacial topography, soil, and differences in
deer browse and forest management across ownerships (Laurent et al., 2005). The majority of the
land is state-owned or private industrial forest managed for timber production. Upland northern
hardwood forests make up the majority of the landscape, interspersed with upland and lowland
conifers and areas of early successional forest. The primary species in northern hardwood stands
is sugar maple (Acer saccharum), while red pine (Pinus resinosa) and white pine (P. strobus)
dominate the upland conifer communities. Northern white cedar (Thuja occidentalis) is the main

60

tree species in lowland areas, and aspen (Populus spp.) and white birch (Betula papyrifera) cover
most of the early-successional areas.
I used data on bird species and vegetation variables collected in 2001–2003 from a largescale study of bird species in forested habitats (Laurent et al., 2005; Millington et al., 2011).
Sample plots were selected according to what was known as the GRAIN protocol (Laurent et al.,
2005), where the landscape was gridded into ~1,000 ha sections and 2–8 plots were placed
within randomly selected sections. This plot selection system allowed me to impose a
hierarchical study design on the data (Fig. 3.1). Individual plots were clustered into ecological
neighborhoods where each plot was no more than 1000 m from at least one other plot.
Neighborhoods were nested into management areas defined by the state forest management
system or by private industrial landowner, and management areas were further nested into
ecological subsections defined by McNab et al. (2007).

Figure 3.1. Study area and study design map showing: (A) sampling plots within ecological
neighborhoods; (B) neighborhoods within management areas; (C) management areas within
ecological subregions; and (D) study area location within the Upper Peninsula of Michigan,
USA.

61

I used data from all birds detected within 50 m of the plot center during standard 10-min
point counts (Ralph et al., 1995). Each plot was sampled 3–4 times between June 4 and July 3 (1
plot was visited twice) in either 2001, 2002, or 2003 between sunrise and 5 hr post-sunrise. I
estimated the abundance for each species at each site using a multi-species occupancy-abundance
model that provided site-level abundance estimates without the use of habitat variables
(Appendix A). This model estimated occupancy and abundance as separate but related processes,
and accounted for spatial correlation in occupancy within a neighborhood distance of 1000 m
(sensu Mattsson et al., 2013). I modeled survey-specific detection probability as a linear function
of standardized covariates for Julian day (linear and quadratic) and time as measured in minutes
from sunrise (Zipkin et al., 2010). Because my purpose was to sample resident species indicative
of community structure and habitat conditions, I regarded species that were detected at <1% of
plots, as well as waterfowl (family Anatidae), as incidental detections and excluded them from
the analysis (Crosby et al., 2015; Mahon et al., 2016). I also excluded large raptors (families
Accipitridae, Cathartidae, Falconidae, Strigidae) and large corvids (Corvus corax and C.
brachyrhynchos) because their large home ranges and ubiquitous distributions make their status
as residents difficult to verify (Crosby et al., 2015). I fit the model in a Bayesian framework with
programs R (Version 3.3.0) and JAGS (Version 4.2.0; Plummer, 2003) using the package runjags
with parallel chains, with uninformative prior distributions for all parameters and
hyperparameters. I ran three chains of 300,000 iterations with a burn-in of 50,000 and a thinning
ratio of 10, and assessed convergence using the Gelman and Rubin R-hat statistic (Brooks and
Gelman, 1998). The multi-species occupancy-abundance analysis was performed using data from
all sample plots where point counts were done. However, for the beta diversity analyses

62

described below I limited the data set to plots within neighborhoods containing ≥3 plots within
management area containing ≥3 such neighborhoods (Anderson, 2006; Marsh and Ewers, 2013).
I characterized forest composition and structure within each plot center using 11 variables
derived from measurements taken at the plots concurrent with bird surveys and from remotelysensed elevation data. Total basal area (BA; m2/ha) for trees ≥10 cm diameter at breast height
(DBH) was measured using a 10-factor prism at 3 subplots within each plot located at the
vertices of an equilateral triangle surrounding the plot center. The first point of the triangle was
placed 15 m from the center at a random azimuth, and the succeeding points were 25 m from the
initial point and 15 m from the center (Laurent, 2005). From the prism measurements I also
estimated proportion BA in conifers, proportion BA in deciduous trees other than sugar maple,
and stem density (trees/ha) of snags ≥25 cm DBH and large trees ≥50 cm DBH (sensu McGee et
al., 1999; Millington et al., 2011). Canopy openness was measured at each of the three subplots
using a spherical densitometer and calculated as the average of measurements taken while facing
in each of 4 directions (north, south, east, and west) (Comeau et al., 1998). Stem density of trees
<10 cm DBH was measured using 5-tree distance sampling (Lessard et al., 2002) at 9 subplots
spaced on a 3x3 grid centered on the plot center, with subplots 16 m apart (Laurent, 2005). From
this I calculated stems/m2 of seedlings (trees ≥25 cm tall and <1.5 m tall) and canopy recruits
(trees ≥1.5 m tall and <10 cm DBH), and the proportion of seedlings that were conifers. To
characterize size structure of the stand, I calculated an index of diameter distribution as the
departure from an idealized even size class distribution of 20 trees per hectare in each 5-cm size
class, where the value was the log-transformed chi-square value measuring departure from the
idealized distribution (Tyrrell and Crow, 1994). Finally, I indexed soil moisture in each plot
using a modification of the topographic wetness index called the SAGA wetness index (SWI;

63

Olaya and Conrad, 2009), where topography was derived from the U.S. Geological Survey
National Elevation Dataset 1/3 arc-second 2013 maps (https://lta.cr.usgs.gov/NED; accessed
August 21, 2016).
3.2.2. Environmental heterogeneity and beta diversity
I evaluated the appropriateness of my chosen environmental variables for modeling
community composition by estimating the correlation among variables and testing for their
influence on niche separation among species in an outlying mean index (OMI) analysis. OMI is a
constrained ordination technique that estimates the niche position of species relative to average
environmental conditions, and total inertia reflects the influence of the environmental variables
on the species’ niche separation (Dolédec et al., 2000). To test whether the chosen variables
described niche separation, I employed a permutation test of the total inertia calculated from the
OMI analysis using species abundance estimates at each plot for the analysis. The permutation
test randomizes the communities among sites and tests the null hypothesis that the species niche
separation is not influenced by the environmental variables (DolĂŠdec et al., 2000). I ran 1000
permutations and compared the average marginality from the randomized data to the observed
average marginality and evaluated significance as the proportion of permutation values higher
than the observed value.
To describe the influence of environmental heterogeneity on diversity, I measured
environmental heterogeneity and bird community beta diversity across scales using multivariate
dispersion analysis (Anderson et al., 2006). Multivariate dispersion estimates the ecological
distance of each point to a group centroid based on species composition or environmental
variables, and the mean of these distances within a group can be used as a measure of beta
diversity or environmental heterogeneity, respectively (Astorga et al., 2014). I estimated

64

environmental heterogeneity at the neighborhood and management area scales using Euclidean
distance for the normalized environmental variables, and to estimate beta diversity of bird
communities using the Bray-Curtis index at the same scales (Anderson et al., 2006). Because
there may be a relationship between beta diversity and sampling area, I used the residuals
obtained from linear regressions of beta diversity and environmental heterogeneity against the
number of points in the unit for which the estimate was obtained for neighborhoods and
management areas (Veech and Crist, 2007). I used linear regression to test for a relationship
between environmental heterogeneity and beta diversity at the neighborhood level. Due to small
sample size, my data did not meet regression assumptions at the management area level so I
looked at correlations between variables among management areas. I performed all analyses
using program R. The multivariate dispersion analyses was done using the betadisper function in
package vegan with type = “centroid” specified. I considered tests to be statistically significant
at p < 0.1.
3.2.3. Landscape and species simulation
To meet my second objective of evaluating sampling designs for monitoring beta
diversity, I simulated a landscape to represent 2 separate, large-scale primary gradients, each
following a different direction and changing at a different spatial scale. Within these large-scale
directional gradients were small-scale secondary gradients changing in random directions at
varying spatial scales, where the spatial scale was dependent on the level of aggregation within
that subsection of the landscape. The full simulated landscape was 500x750 pixels. I simulated
the composition of the first 2 primary gradients according to probability density functions
determined by a beta distribution and configuration specified as the H-value in the midpoint
displacement method (sensu Holland et al., 2009). The first primary gradient was composed of 3

65

separate 500 x 250 pixel landscapes increasing in average value and spatial aggregation from
west to east according to the increasing H-value (Table 3.1). In this method, an H-value of -2.0
would represent a random landscape, but because such a landscape would be highly unlikely in
nature smallest H-value used in my simulations was -0.2. The second primary gradient was
composed of 4 separate 125x750 pixel landscapes decreasing in average value from north to
south and unchanging in spatial aggregation (Table 3.1). The simulation of spatial aggregation
created the secondary gradients, where a low level of spatial aggregation caused the secondary
gradients to change over a smaller spatial scale relative to areas with higher spatial aggregation
(Fig. 3.2).
Primary Gradient
1: West to East

2: North to South

𝛼

𝛽

H-value

3.0

3.0

-0.2

5.0

3.0

0.0

7.0

2.5

2.0

4.0

1.0

0.0

3.0

2.0

0.0

2.0

3.0

0.0

1.0

4.0

0.0

Table 3.1. Parameters used for simulating landscape gradients, where pixel values are randomly
drawn from a beta distribution with parameters 𝛼 and 𝛽, and spatial correlation in parameter
values specified by the H-value in the midpoint displacement method.

66

Figure 3.2. Simulated ecological gradients used for simulating species occurrence based on
randomly generated beta distributions. Landscape dimensions were 500x700 pixels.
I populated the landscape by simulating 100 species with differing responses to the
environmental gradients according to randomly generated beta distributions using the
coenocliner package in program R version 3.1.1. The coenocliner package simulates species
occurrence or abundance data along gradients according to Gaussian or beta response curves
(Simpson, 2016). I drew species response parameters from random distributions to reflect a
range of responses from rare to common and generalist to specialist (Table 3.2). I increased all
probabilities by a factor of x = 100 million using the equation 1 − (1 − 𝑝𝑠𝑖)𝑥 to approximate a
realistic range of occupancy probabilities in a natural bird community. I also simulated a
response resembling a climate effect, where some species had a reduced occupancy probability
in the northern half of the landscape. To do this, I randomly chose which species would be
affected with a 0.5 probability. I then randomly assigned the strength of the effect by multiplying
the initial occupancy probability by a random draw from a uniform (0.1, 0.9) distribution.

67

Response parameter

Distribution

Max psi

Gradient 1

Gradient 2

Species set 1

beta (5, 2)

Species set 2

beta (7, 1)

Modal abundance

uniform (min, max)†

Range of occurrence

uniform (0.01, 0.5)

𝛼

uniform (0.5, 7.0)

𝛽

uniform (0.5, 7.0)

Modal abundance

uniform (min, max) †

Range of occurrence

uniform (0.01, 0.9)

𝛼

uniform (0.5, 7.0)

𝛽

uniform (0.5, 7.0)

Table 3.2. Parameters used to simulate species occurrence probabilities along 2 environmental
gradients using the package coenocliner in program R. Parameters for each species were drawn
randomly from probability distributions. Max psi represents the maximum occurrence
probability, modal abundance represents the point on the gradient where maximum occurrence is
achieved, and range of occurrence represents the limits of occurrence along the gradient.
†
min and max are the minimum and maximum gradient values, respectively.
3.2.4. Sample design comparisons
I compared the effectiveness of different sample designs in estimating beta diversity
across scales using additive partitioning of diversity components (Gering et al., 2003). Additive
partitioning separates diversity into 𝛼, 𝛽, and 𝛾 components where 𝛼 + 𝛽 = 𝛾 provided that the
diversity metric is strictly concave, meaning that the value of the metric for a pooled set of
communities is ≥ the average value within those communities (Lande, 1996; Gering et al., 2003).
Such metrics can be partitioned across multiple scales when 𝛾 for a level is measured as the

68

average 𝛼-diversity at the next higher level. I used species richness as my diversity measure and
separated the landscape into 5 levels corresponding to those typically used in management (Fig.
3.3). From highest to lowest levels: I vertically separated the landscape into 2 climatic zones
measuring 250 x 750 pixels; each climatic zone was split into 3 regions of 250 x 250 pixels; each
region was separated into 25 management areas of 50 x 50 pixels, and each management area
was separated into 100 neighborhoods of 5 x 5 pixels. Each pixel was considered an individual
plot.

Figure 3.3. Hierarchical partitioning of simulated landscape used to compare the effectiveness of
different study designs for estimating species diversity across scales.

I first calculated the known diversity at all levels using all 375,000 plots. I then estimated
diversity by sampling 450 individual pixels using 4 different sampling designs: systematic,
random, stratified random, and a hierarchical cluster sampling design (Thompson, 2012). The
systematic sampling design was based on an 18x25 grid spaced evenly across the landscape. For

69

the random sample, I randomly chose plots without replacement from across the entire
landscape. In the stratified random sample I randomly chose 75 plots from within each of the 6
regions. In the hierarchical cluster design, I randomly selected 5 management areas from within
each region, 5 neighborhoods from within each of the management areas, and 3 plots from each
of the neighborhoods. I drew 100 individual samples using each design (except for the
systematic design) and compared the results at each level using means and 95% confidence
intervals.
3.3. RESULTS
3.3.1. Bird community and beta diversity
The bird community analysis estimated occupancy and abundance from 433 plots. The
hierarchical dataset included 232 point count plots within 36 ecological neighborhoods divided
among 5 management areas and 2 ecological subsections. Neighborhoods ranged from 105─313
ha with a mean of 174 ha. Management areas ranged from 12,428─75,850 ha with a mean of
45,343 ha. There were 3 moderate correlations among the environmental variables: total BA with
canopy openness (-0.542); total BA with sapling density (-0.494); and density of seedlings with
density of saplings (0.437). All other correlations were between -0.4 and 0.4. The permutation
test showed that the environmental variables increased total inertia by 2.33/1 over random. This
increase was significant (P = 0.003). Bird community beta diversity was significantly correlated
with environmental heterogeneity in the linear regression at the neighborhood level (df = 34, β =
0.024, P = 0.003) and showed a strong correlation at the management area level (r = 0.796) (Fig.
3.4).

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Figure 3.4. A: Linear regression of the relationship between environmental heterogeneity and
bird community beta diversity within ecological neighborhoods (all points ≤1000 m from at least
1 other point). B: Correlation of the same relationship for forest management areas as defined by
the Michigan Department of Natural Resources or private industrial forest landowners.
3.3.2. Simulation analysis
The simulation analysis showed that the hierarchical cluster design performed better than
any of the other sampling designs in estimating diversity across scales. In particular the
systematic, random, and stratified random designs were all unable to detect beta diversity among
plots. These designs also captured an average of only 21% of the beta diversity among
neighborhoods and overestimated beta diversity among management areas by an average of
2.086/1. The hierarchical cluster design gave the most accurate estimates of beta diversity at the
beta.1, beta.2, and beta.3 levels and gave similar estimates to the other sampling designs for
beta.4, beta.5, and gamma (Fig. 3.5). All 4 designs were able to accurately estimate plot-level
alpha diversity (alpha.1), and all of them overestimated diversity at large scales (beta.4, beta.5)
and underestimated gamma diversity (Fig. 3.5).

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Figure 3.5. Comparison of the estimates from 4 different sampling designs to known
contribution of alpha and beta components of diversity to overall gamma diversity across 5
hierarchically-partitioned spatial scales in a simulated landscape. Each design contained 450
sampling points. The systematic sample was an 18x25 grid of points spread evenly across the
landscape, the stratified random sample was stratified at the beta.4 level, and the cluster sample
was hierarchically partitioned across all scales.

3.4. DISCUSSION
The foundation of ecosystem management is the conservation of pattern and process,
which maintains the spatial and temporal patterns of heterogeneity that underlie biodiversity
conservation (Fuhlendorf et al., 2012). These patterns of diversity change across scales because
the processes that drive them operate at multiple spatial and temporal scales (Levin,
2000).Therefore, the key to measuring and monitoring biodiversity at large spatial extents is
using metrics that reflect heterogeneity across multiple scales. My findings show that bird
community diversity reflects environmental heterogeneity at multiple spatial scales relevant to
forest management, and that a hierarchical cluster sampling design estimates diversity across

72

scales much more accurately than the random, stratified random, and systematic sampling
designs that are used more commonly in large-scale sampling. These findings illustrate the
advantages of using communities rather than individual species as surrogates for biodiversity
monitoring, which is that they can be used to index environmental differences among spatial
units across scales. My results also show the advantage of using hierarchical sampling designs in
large scale biodiversity monitoring rather than the classical designs more commonly employed
by researchers.
The application of a hierarchical cluster sampling design for large-scale monitoring
systems derives from 2 complementary ideas: that cluster sampling is much more efficient for
sampling in large landscapes (Hines et al., 2010; Aing et al., 2011); and that a cluster-based
sampling design is optimal for estimating beta diversity across multiple spatial scales (Marsh and
Ewers, 2013). Cluster sampling is more efficient because it reduces travel time between
sampling sites (Aing et al., 2011), and it is often done by default in monitoring programs in an
effort to overcome logistical difficulties (Hines et al., 2010). Hierarchical cluster designs are
better able to estimate beta diversity across scales because they naturally sample processes
occurring at multiple spatial scales (Marsh and Ewers, 2013), thus providing greater resolution
and accuracy of diversity patterns (Fortin et al., 1989). As in my analysis, Marsh and Ewers
(2013) showed that the spatial configuration of sampling points can have a large impact on beta
diversity estimates at different scales. When compared to more-common sampling designs, their
fractal-based cluster design gave better estimates of beta diversity and was the only design that
could successfully partition diversity at all scales (Marsh and Ewers, 2013). What my results
show is that a fractal-based design is not necessary for sampling multi-scale beta diversity as
long as some form of hierarchical, cluster-based design is employed.

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My landscape simulation created a complex landscape with multiple gradients changing
in different directions, and the scale of the gradients changing in different parts of the landscape.
Such a simulation is likely to be more reflective of natural ecological conditions than the
simplified, single directional gradients simulated by Marsh and Ewers (2013). Therefore I
believe my analysis to be a more realistic evaluation of the ability of different sampling designs
to estimate diversity at multiple scales. Given that, my additive partitioning results were not
dissimilar from Marsh and Ewers (2013) with all sampling designs underestimating small-scale
diversity and overestimating large-scale diversity. This result is to be expected because of the
inability of any sampling design to detect all species within a region. Because the estimates are
additive, any overestimation in one part must inevitably lead to an underestimation in another
part. Although such inherent deficiencies can never be entirely overcome, it is likely that they
can be mitigated using models that account for unobserved species in the samples such as multispecies occupancy or abundance models (Yamaura et al., 2016).
Other factors that may affect the accuracy of diversity estimates across scales are the
multiple scales and directions at which ecological gradients change across the landscape.
Because ecological patterns change in different directions and at different scales (Levin, 1992),
and species respond to conditions individually (Taper et al., 1995), there is little possibility that
any sampling design can estimate changes in diversity across large spatial scales with complete
accuracy. This does not, however, preclude the benefits of obtaining the best possible estimates
for use in ecological investigations, conservation planning, and management decision-making.
The link between heterogeneity and biodiversity has been investigated before with other
taxa and at different scales. The hypothesis that heterogeneity is the precursor to biodiversity,
and therefore should be the basis for conservation has been around for some time (Christensen,

74

1997; Ostfeld et al., 1997). Astorga et al. (2014) showed that habitat heterogeneity was the
biggest factor driving the geographic distribution of beta diversity of stream invertebrates in New
Zealand. Veech and Crist (2007) drew the link between beta diversity of bird communities and
habitat and climate heterogeneity at large spatial scales (across large landscapes and ecological
provinces). My analysis is also similar to the work of Fuhlendorf et al. (2006) which showed that
managing for heterogeneity in rangeland systems increased bird community diversity over
standard management systems, although theirs was not an explicit measure of beta diversity and
did not consider multiple spatial scales. The difference in my work is that I show the usefulness
of the heterogeneity-biodiversity relationship at multiple scales appropriate to management (1–
1000km2; Bestelmeyer et al., 2003), using compositional and structural variables affected by
management. Monitoring bird communities in this way can help researchers and managers draw
the explicit link between biodiversity, forest management systems, and large-scale conservation
planning.
Using bird community composition as an index of ecological conditions is not new either.
Bird communities have been used in the past as indicators of biotic integrity (O'Connell et al.,
2000; Glennon and Porter, 2005), and individual species have often been seen as surrogates for
specific habitat types: e.g. spotted owls in the northwestern United States, (Caro and O'Doherty,
1999) or white-backed woodpeckers in Europe (Roberge et al., 2008) as indicators of old-growth
forest. Bird communities have several characteristics that make them the best choice among taxa
for this type of monitoring system:
1. They are known to respond to commonly-measured variables that are affected by
management (DeGraaf et al., 1998).

75

2. Communities respond to conditions at multiple spatial scales relevant to management
(Cushman and McGarigal, 2004).
3. Breeding birds are easy to monitor relative to other taxa, and can be monitored noninvasively (Ralph et al., 1995; O'Connell et al., 2000).
In addition to these advantages, there is expertise and enthusiasm among the general public for
surveying birds. This is evinced by the many citizen science programs that use volunteers to
collect scientifically-defensible bird community data such as the North American Breeding Bird
Survey (Sauer et al., 2014) and many state-level and national breeding bird atlas projects (e.g.
McGowan and Corwin, 2008; Balmer et al., 2013). Combining this expertise and enthusiasm
with the proper sampling design and survey protocol could provide the most reliable and costeffective biodiversity monitoring system available.
Under the monitoring system suggested here, changes in the amount of diversity
explained within levels would indicate changes in landscape pattern. For example, if proportion
of diversity explained among neighborhoods was reduced while that explained among
management areas increased, that could indicate homogenization at the neighborhood levels but
greater variability among management areas as a consequence of management decisions (Zollner
et al., 2008). Management for contiguous areas of specific habitat types might result in such a
pattern, and be beneficial to area-sensitive species such as many forest interior birds and
mammals (Robbins et al., 1989; Zollner et al., 2008). On the other hand, higher diversity at small
scales coupled with low diversity at large scales would suggest a highly fragmented landscape
that does not change much over a large area, as in a heavily-managed area undergoing shortrotation timber harvest. Understanding these dynamics can help managers estimate how
management alternatives at different scales interact to influence regional biodiversity.

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While the diversity metrics described here show how bird communities can act as
indicators of environmental heterogeneity, and thus as an index biodiversity, alternative analyses
using the same type of data can give more specific information. For example, ordination
techniques can be used to investigate which species are most vulnerable as well as which
environmental conditions are most important for maintaining those species at the appropriate
scales (e.g. Thuiller et al., 2005; Mahon et al., 2016). A contribution-diversity approach (Lu et
al., 2007) can be applied to find which areas contribute the most to diversity across scales and
what the characteristics of such areas are (Crosby, chapter 2 this dissertation). Ordinations can
also be applied to data from different time periods to gauge how conditions have changed and
investigate the drivers of those changes (e.g. Coppedge et al., 2001).
The appropriateness of using surrogate species for monitoring biodiversity has been
debated in the literature for several decades, and the limitations of this approach are well-known
and documented (Caro and O'Doherty, 1999; Lindenmayer et al., 2000; Manley et al., 2004).
There are two primary issues with the use of surrogate species. First, species respond to changes
in environmental conditions individually, and so the use of a few indicator species as an index of
the broader community is not a viable strategy (Taper et al., 1995). Second, it cannot be assumed
that the status of a few species indicates the condition of the ecosystem (Manley et al., 2004).
Therefore, rather than suggesting the use of a few surrogate species whose relationship to
ecological conditions is presumed to be known, we propose the use of bird community beta
diversity as an efficient and effective alternative. The general monitoring system proposed here
can provide regional managers with a set of metrics that act as reliable indices of environmental
heterogeneity over a range of relevant spatial scales. These metrics can then be used to make

77

inferences about how management affects biodiversity, which is a fundamental question under
the ecosystem management paradigm (Christensen et al., 1996).
It is not known how reliably bird community diversity can predict diversity in other taxa,
but the few studies that have examined this question so far have shown promise (Vielliard, 2000;
Aslan et al., 2015). It must be understood, though, that bird communities cannot possibly act as a
perfect index of biodiversity but only of a few important aspects of it. Other information must be
brought to bear if we are to better understand and predict how land management decisions will
affect biodiversity conservation at large scales. The status of rare or endangered species and the
continued functioning of vital ecosystem processes are other important aspects of conservation.
However, monitoring bird communities using a hierarchical sampling design across appropriate
spatial scales represents an ecologically sound and logistically feasible alternative to traditional
approaches to biodiversity monitoring for large scale management and conservation planning.

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EPILOGUE

The purpose of this dissertation was to address the problem of maintaining biodiversity
on managed forest landscapes. More specifically, my goal was to investigate the response of bird
communities to patterns of forest composition and structure across multiple spatial scales. In the
first chapter, I investigated how patterns of heterogeneity in stand-level attributes impact patterns
of bird community diversity across multiple spatial scales. In the second chapter, I demonstrated
a novel application of the conservation filters strategy to maintaining avian diversity on managed
forests. In the third chapter, I looked at monitoring beta diversity in bird communities as an
alternative paradigm to indicator-based strategies for estimating changes in regional biodiversity.
The research in these chapters draws several conclusions that are fundamental to the
problem of maintaining regional biodiversity on managed forest landscapes. The first is that the
effect of environmental heterogeneity on bird community diversity changes across spatial scales.
This conclusion is important to understand because forest management systems affect spatial
patterns at multiple scales. Therefore, sustainable forest management planning requires an
understanding of how spatial patterns at multiple scales will impact regional diversity. The
second conclusion is that uncommon ecosystem types have a greater relative contribution to
regional diversity, and the importance of specific compositional and structural attributes changes
among types. This has important implications for how different areas are prioritized for
conservation and how structural retention guidelines are written because it underlies the patterns
that maintain diversity at different operational scales. Finally, quantifying beta diversity of bird
communities (differences among spatial units within a region) across multiple scales, using a
hierarchical cluster sampling design, reflects environmental heterogeneity and offers an efficient

79

and effective system for monitoring regional biodiversity. Bird community beta diversity, then,
provides an alternative to species-based strategies for indexing biodiversity, and can provide an
important contribution to our understanding of how and why biodiversity changes through time.
The first chapter addressed the issue of how pattern and scale impact our understanding
of the factors governing the maintenance of biodiversity across the landscape. I examined how
patterns of bird species diversity changed across spatial scales in a managed northern forest
landscape and investigated the effect of environmental heterogeneity on the contributions of
individual spatial units at multiple scales to regional diversity. I found that beta diversity at
smaller spatial scales (1–300 ha) provided the largest relative contribution to regional bird
diversity. Uniqueness of a sampling plot relative to mean conditions, in terms of vegetation
structure and composition, had a significant positive correlation with diversity contribution. At
medium scales (100–300 ha), within-unit heterogeneity was positively correlated with beta
diversity but showed no relationship to diversity contribution. Conversely, within-unit
heterogeneity was positively correlated with diversity contribution at large scales (100–1000
km2). Thus I were able to show the differential effects of heterogeneity patterns on diversity
across scales.
Chapter 2 addressed the issue of management planning for regional bird diversity on
managed forest landscapes. There is usually a great deal of uncertainty about how management
decisions will impact biodiversity, and so scientifically-based strategies are often employed as
tools in the planning process (Schulte et al., 2006). The coarse filter and mesofilter strategies
(Hunter, 2005) are two of the most common strategies, however they are traditionally employed
independently. I showed that integrating coarse filter and mesofilter conservation strategies can
help prioritize ecosystem types for conservation and enhance management prescription

80

guidelines to increase the contribution of managed areas to regional diversity. Specifically, I
employed the diversity contribution approach of Lu et al. (2007) to prioritize ecosystem types for
conservation, and described compositional and structural attributes of high-contribution sites
relative to other sites within the same ecosystem type. This represented a novel application of the
conservation filter strategy in managed forests where reserve designation is not a viable option.
My application is an extension of the approach proposed by Haufler et al. (1996), which viewed
the coarse filter as maintaining the historical distributions of ecosystem types within a region.
My application is more appropriate in working forest landscapes with multiple ownerships and
diverse management objectives, as is the case in many regions.
In chapter 3, I addressed the issue of regional biodiversity monitoring. Historically,
biodiversity monitoring recommendations have focused on using one or a few species as
indicators of overall species diversity (Manley et al., 2004; Noon et al., 2012). Estimating beta
diversity (differences among spatial units), on the other hand, can be used as an indicator of
patterns of heterogeneity at multiple scales, which is strongly linked with biodiversity (Benton et
al., 2003). I proposed a monitoring system that focuses on species-level monitoring of bird
communities for the estimation of beta diversity using a hierarchical cluster sampling design. I
showed that beta diversity in bird communities is correlated with environmental heterogeneity
across multiple scales. Additionally, using simulated data, I were able to show that the
hierarchical sampling design is superior to more traditional designs for estimating beta diversity
across multiple scales.
The research presented in this dissertation offers an expanded and integrated view of the
problem of maintaining biodiversity on managed forests. In the first place, I demonstrated that
maintaining the mix of generalist and specialist species that leads to high regional diversity

81

requires maintaining heterogeneity at multiple scales. This means that large-scale management
systems must explicitly address how forest planning will impact patterns at multiple scales
simultaneously, and maintain both homogenous and heterogeneous landscapes at the appropriate
scales. Secondly, I showed the utility of using the diversity contribution approach to the
application of an integrated conservation filter strategy for maintaining regional bird diversity on
a managed forest landscape. Such an approach can be very important for making management
decisions in the face of uncertainty about how those decisions will impact biodiversity. Third, I
showed that monitoring bird communities using a hierarchical cluster sampling design offers a
viable alternative to traditional indicator species approaches to monitoring regional biodiversity.
My work offers an integrated set of guidelines for biodiversity conservation on managed forests
that explicitly accounts for the multiple scales at which biodiversity is generated and maintained.
I believe that this research provides ecologists, land managers, and planners with an improved
framework for managing forests under the ecosystem management paradigm.

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APPENDICES

83

APPENDIX A
MULTI-SPECIES OCCUPANCY-ABUNDANCE MODEL
Model description for a zero-inflated multi-species occupancy-abundance model accounting for
spatial correlation in occupancy by incorporating an autologistic parameter into the probability of
occupancy (sensu Mattsson et al., 2013). The model utilizes an augmented dataset (a set of allzero encounter histories) to account for unobserved species, and accounts for the covariance
between occupancy and abundance (sensu Royle and Dorazio, 2009).

Ecological model for occupancy:
Parameters:
𝜓𝑖𝑗 = the probability that species i occurs at site j
𝑙𝑜𝑔𝑖𝑡(𝜓𝑖𝑗 ) = 𝜑𝑖 + 𝛼𝑖 𝐴𝑖𝑗
1, 𝑖𝑓 𝑠𝑝𝑒𝑐𝑖𝑒𝑠 𝑖 𝑖𝑠 𝑖𝑛𝑐𝑙𝑢𝑑𝑒𝑑 𝑖𝑛 𝑡ℎ𝑒 𝑠𝑎𝑚𝑝𝑙𝑒 𝑜𝑓 𝑎𝑙𝑙 𝑠𝑖𝑡𝑒𝑠 (𝑤𝑖𝑙𝑙 𝑎𝑙𝑤𝑎𝑦𝑠 𝑏𝑒 1 𝑓𝑜𝑟
𝑤𝑖 = {
𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑 𝑠𝑝𝑒𝑐𝑖𝑒𝑠)
0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
𝑤𝑖 ~𝐵𝑒𝑟𝑛𝑜𝑢𝑙𝑙𝑖(Ω)
𝜑𝑖 = logit intercept for species i, representing the mean probability of occupancy for that species
among all sites.
𝜑𝑖 ~𝑁𝑜𝑟𝑚𝑎𝑙(𝜇𝑢 , 𝜎𝑢2 )
𝛼𝑖 = the spatial weights parameter, representing the change in the logit occupancy probability
conditional on the spatial weight assigned to species i at site j.
𝛼𝑖 ~𝑁𝑜𝑟𝑚𝑎𝑙(𝜇𝛼 , 𝜏𝛼 )
𝐴𝑖𝑗 =

∑𝑟 𝑧𝑖𝑟
𝑅𝑗

where 𝐴𝑖𝑗 is the proportion of sites r neighboring j that are occupied by
species i.

1, 𝑖𝑓 𝑠𝑝𝑒𝑐𝑖𝑒𝑠 𝑖 𝑖𝑠 𝑝𝑟𝑒𝑠𝑒𝑛𝑡 𝑎𝑡 𝑠𝑖𝑡𝑒 𝑗 (𝑤𝑖𝑙𝑙 𝑎𝑙𝑤𝑎𝑦𝑠 𝑏𝑒 1 𝑓𝑜𝑟
𝑧𝑖𝑗 = {
𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑 𝑠𝑝𝑒𝑐𝑖𝑒𝑠 𝑎𝑡 𝑠𝑖𝑡𝑒 𝑗)
0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
𝑧𝑖𝑗 |𝑤𝑖 ~𝐵𝑒𝑟𝑛𝑜𝑢𝑙𝑙𝑖(𝜓𝑖𝑗 )
Hyperparameters:
Ω~𝑈𝑛𝑖𝑓𝑜𝑟𝑚(0, 1)

This parameter describes the inclusion probability of any species
randomly chosen form the augmented dataset. The probability will be ≥

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n/nspec, where n is the number of observed species and nspec=n+the
number of added zeros in the augmented dataset.
𝜇𝑢 ~𝑁𝑜𝑟𝑚𝑎𝑙(0, 0.001)
𝜎𝑢 ~𝑈𝑛𝑖𝑓𝑟𝑜𝑚(0, 10)
𝜏𝑢 = 1/ 𝜎𝑢2

The mean and variance of the mean logit occupancy probability
across all species

𝜇𝛼 ~𝑁𝑜𝑟𝑚𝑎𝑙(0, 0.0001)
𝜏𝛼 ~𝐺𝑎𝑚𝑚𝑎(0.1, 0.1)

The mean and variance of the spatial weights parameter across
all species

Ecological model for abundance:
Parameters:
𝜆𝑖𝑗 = the mean abundance of species i at site j.
*𝑙𝑜𝑔(𝜆𝑖𝑗 ) = 𝛿𝑖
𝛿𝑖 = the log abundance intercept for species i, representing the mean abundance for that species
among all sites.

Covariance between occupancy and abundance:
To account for the known relationship between occupancy and abundance, we specify the
covariance between these 2 parameters. We let 𝑢𝑖 = 𝑙𝑜𝑔𝑖𝑡(𝜓𝑖 ) and 𝑣𝑖 = 𝑙𝑜𝑔(𝜆𝑖 ) and specify
heterogeneity in the parameters among species with a bivariate normal distribution:
𝑢𝑖
𝛽
( ) ~𝑁𝑜𝑟𝑚𝑎𝑙 (( ) , 𝚺)
𝑣𝑖
𝛼
2
where 𝚺 is a 2 x 2 matrix with diagonal element 𝜎𝑢 and 𝜎𝑣2 and whose off-diagonal elements, 𝜎𝑢𝑣
is the covariance between the diagonal elements (Royle and Dorazio, 2009). Parameters 𝛽 and 𝛼
represent the logit- and log-scale mean probability of occupancy and mean abundance,
respectively, among all species.
𝜐𝑖 = 𝜇𝑣 + (𝜌 × 𝜎𝑣 ⁄𝜎𝑢 ) × (𝜑𝑖 − 𝜇𝑢 )
𝛿𝑖 ~𝑁𝑜𝑟𝑚𝑎𝑙(𝜐𝑖 , 𝜎𝜂2 )
†
Equations drawn from KĂŠry and Royle (2009)
†

𝑁𝑖𝑗 = The abundance of species i at site j
𝑁𝑖𝑗 |𝑧𝑖𝑗 ~𝑃𝑜𝑖𝑠𝑠𝑜𝑛(𝜆𝑖𝑗 )
Hyperparameters:
𝜇𝑣 ~𝑁𝑜𝑟𝑚𝑎𝑙(0, 0.0001)
𝜎𝑣 ~𝑈𝑛𝑖𝑓𝑟𝑜𝑚(0, 10)
𝜏𝑣 = 1/ 𝜎𝑣2

The zero-inflated abundance estimate

The mean and variance of mean log abundance across all
species

85

𝜌~𝑢𝑛𝑖𝑓𝑜𝑟𝑚(−1, 1)
𝜎𝜂2 = 𝜏𝑣 /(1 − 𝜌2 )

The covariance parameter between 𝜓 and 𝜆
The variance of 𝛿𝑖 (the log mean abundance for species i)

Detection model
Parameters:
𝑝𝑖𝑗𝑘 = the probability of detection species i at site j.
𝑙𝑜𝑔𝑖𝑡(𝑝𝑖𝑗𝑘 ) = 𝜋𝑖 + 𝜷𝑖 𝑥′𝑗𝑘
𝜋𝑖 = the logit detection probability intercept for species i, representing the mean probability of
detection for that species among all sites.
𝜋𝑖 ~𝑁𝑜𝑟𝑚𝑎𝑙(𝜇𝑦 , 𝜎𝑦2 )
𝑥′𝑗𝑘 = the covariate values at site j during survey k that affect detection probability.
𝜷𝑖 = the covariate coefficients for species i affecting detection probability during a survey.
𝜷𝑖 ~𝑁𝑜𝑟𝑚𝑎𝑙(𝜇𝛽 , 𝜎𝜷2 )
𝑌𝑖𝑗𝑘 = the number of individuals of species i detected at site j during survey k.
𝑌𝑖𝑗𝑘 ~ 𝐵𝑖𝑛𝑜𝑚𝑖𝑎𝑙(𝑁𝑖𝑗 , 𝑝𝑖𝑗𝑘 )
Hyperparameters:
𝜇𝑦 ~𝑁𝑜𝑟𝑚𝑎𝑙(0, 0.0001)
𝜎𝑦 ~𝑈𝑛𝑖𝑓𝑟𝑜𝑚(0, 10)
𝜏𝑦 = 1/ 𝜎𝑣2

The mean and variance of mean logit detection probability across
all species

86

APPENDIX B
MULTI-SPECIES OCCUPANCY-ABUNDANCE MODEL CODE
# -------------------------------------------------------------------------------------# Zero-inflated Poisson-binomial Multi-species Abundance Model (ZIP-MSAM), where
# occupancy and abundance are modeled seperately and there is spatial correlation in
# the probability of occupancy for each species at each site. Correlation is specified
# with an autologistic parameter based on the number of sites within a 1km neighborhood
# of the site where the sepecies was detected .
# Author: Andrew D. Crosby
#
Quantitative Wildlife Center
#
Michigan State University
#
480 Wilson Road, Room 13 NR
#
East Lansing, Michigan 48824
# Date: 10 April 2016
# -------------------------------------------------------------------------------------# The point count data is a 3-dimensional array of sampling points x surveys x species
# nstats is the number of sampling points
# nspec is the number of species (including the augmented all-zero encounter histories)
# K is a vector of the number of surveys done at each sampling point
# day is Julian day, day2 is day-squared, time is minutes from sunrise
# weights is a sample points x species matrix of the proportion of sample points within the
#
neighborhood surrounding each sample point where the species was detected

# The code for the initial values was derived from Zipkin et al. (2010), and is very important
#
for model performance and convergence
data = list(nstats=nstats, Y=bird.comm.data, nspec=nspec, K=nsurvs,
day=day, day2=day2, time=time, weights=as.matrix(weights_aug))
params = c("N", "z", "Ntot", "zmean", "psi", "alpha")
Nst <- matrix(nrow=nstats, ncol=nspec)
for (j in 1:nstats) {
for (i in 1:nspec) {
Nst[j, i] <- max(bird.comm.data[j, ,i],na.rm=T)
}
}
zinit <- matrix(nrow=nstats, ncol=nspec)
for (j in 1:nstats) {
for (i in 1:nspec) {
zinit[j, i] <- min(1, max(bird.comm.data[j, ,i],na.rm=TRUE))
}

87

}
inits = function() {
omegaGuess = runif(1, n/(nspec), 1)
psi.meanGuess = runif(1, .25,1)
lambda.meanGuess = runif(1, .25,1)
pi.meanGuess = runif(1, .25,1)
rhoGuess = runif(1, 0,1)
sigma.uGuess = runif(1,0,1.5)
sigma.vGuess = runif(1,0,1.5)
sigma.piGuess = runif(1,0,1.5)
list(omega=omegaGuess, mu.u=psi.meanGuess, mu.v=lambda.meanGuess,
mu.pi=pi.meanGuess, sigma.u=sigma.uGuess,
sigma.v=sigma.vGuess,sigma.pi=sigma.piGuess,
rho=rhoGuess, w=c(rep(1, n), rbinom(nz, size=1, prob=omegaGuess)),
z=zinit, N=Nst, phi=rnorm(nspec, psi.meanGuess, sigma.uGuess),
delta=rnorm(nspec, lambda.meanGuess, sigma.vGuess),
pi=rnorm(nspec, pi.meanGuess, sigma.piGuess),
alpha=rnorm(nspec), beta1.pi=rnorm(nspec), beta2.pi=rnorm(nspec),
beta3.pi=rnorm(nspec))
}
sink("zip_msam_spatial.txt")
cat("
model{
# ------------------------------------#
# Hyper-priors on community parameters#
# ------------------------------------#
# The ecological process
# ---------------------# Hyper-parameter for inclusion probability
omega ~ dunif(0, 1)
# Hyper-parameter for occupancy random species effect
mu.u ~ dnorm(0, 0.0001)I(-5, 5)
sigma.u ~ dunif(0, 10)
tau.u <- pow(sigma.u, -2)
# Hyper-parameter for abundance random species effect
mu.v ~ dnorm(0, 0.0001)I(-5, 5)
sigma.v ~ dunif(0, 10)
tau.v <- pow(sigma.v, -2)
# Hyper-parameter for detection probability random species effect
mu.pi ~ dnorm(0, 0.0001)I(-5, 5)

88

sigma.pi ~ dunif(0, 10)
tau.pi <- pow(sigma.pi, -2)
# Hyper-parameters on the covariance matrix of psi and lambda
rho ~ dunif(-1,1)
var.delta <- tau.v/(1-pow(rho,2))
# Priors on the spatial weights parameter
mu.alpha ~ dnorm(0, 0.001)
tau.alpha ~ dgamma(0.1, 0.1)

# The detection process
# --------------------mu.beta1.pi ~ dnorm(0, 0.001)
mu.beta2.pi ~ dnorm(0, 0.001)
mu.beta3.pi ~ dnorm(0, 0.001)
tau.beta1.pi ~ dgamma(0.1, 0.1)
tau.beta2.pi ~ dgamma(0.1, 0.1)
tau.beta3.pi ~ dgamma(0.1, 0.1)
for(i in 1:nspec){
# Species-specific priors drawn from the hyper-priors
# --------------------------------------------------# Priors on the ecological processes
w[i] ~ dbern(omega)
phi[i] ~ dnorm(mu.u, tau.u)
alpha[i] ~ dnorm(mu.alpha, tau.alpha)

# Inclusion paramter for species i
# Mean species occupancy probability
# Spatial weights parameter

# Priors on the covariance matrix of psi and lambda
mu.delta[i] <- mu.v + (rho*sigma.v/sigma.u)*(phi[i]-mu.u)
delta[i] ~ dnorm(mu.delta[i], var.delta)
# Priors on the detection process
pi[i] ~ dnorm(mu.pi, tau.pi) # Mean species detection probability
beta1.pi[i] ~ dnorm(mu.beta1.pi, tau.beta1.pi)
beta2.pi[i] ~ dnorm(mu.beta2.pi, tau.beta2.pi)
beta3.pi[i] ~ dnorm(mu.beta3.pi, tau.beta3.pi)
# Ecological model for occupancy and abundance
for (j in 1:nstats) {
lpsi[j,i]<-phi[i]+alpha[i]*weights[j,i]
psi[j,i]<-exp(lpsi[j,i])/(1+exp(lpsi[j,i]))

89

# logit occupancy probability
# occupancy probability

mu.psi[j,i]<-min(0.999, max(0.001, psi[j,i]))*w[i]
on species inclusion probability
z[j,i]~dbern(mu.psi[j,i])
indicator (1 or 0)
log(lambda[j,i])<-delta[i]
lam.eff[j,i]<-z[j,i]*lambda[j,i]
conditional on occupancy
N[j,i] ~ dpois(lam.eff[j,i])

# occupancy probability conditional
# Occupancy

# log mean abundance
# mean abundance
# Abundance estimate

# Detection process model
for (k in 1:K[j]) {
lp[j,k,i]<-pi[i] + beta1.pi[i]*day[j,k] + beta2.pi[i]*day2[j,k] + beta3.pi[i]*time[j,k]
p[j,k,i]<-min(0.999, max(0.001, exp(lp[j,k,i])/(1+exp(lp[j,k,i]))))
Y[j,k,i] ~ dbin(p[j,k,i],N[j,i])
}
}
Ntot[i]<-sum(N[,i])
zmean[i]<-mean(z[,i])
}
}
",fill=TRUE)
sink()
ni<-2000
nc<-3
nb<-10000
nt<-50
system.time({
zip_msam_spat1000_full_parallel<-run.jags(model="zip_msam_spatial_full.txt",
monitor=params,
data=data, n.chains=nc, inits=inits, burnin=nb, sample=ni,
thin=nt, method="parallel", n.sims=3)
})

90

APPENDIX C
PYTHON CODE FOR LANDSCAPE SIMULATION
# Python code for simulating landscapes with spatially correlated pixel values
#
according to the diamond-square improvement on the midpoint displacement
#
method. Code was generously supplied by:
# Dr Pen Holland
# Ecology Teaching Fellow
# Department of Biology
# University of York
# Heslington
# York
# YO10 5DD
# UK
# Tel: work 01904 328734
# pen.holland@york.ac.uk
# For an example of the application of this code, see:
# Holland, E.P., Aegerter, J.N., Dytham, C., 2009. Comparing resource representations and
#
choosing scale in heterogeneous landscapes. Landscape Ecology 24, 213-227.
# This version of the code creates landscape value according to the beta distribution
# H is the value for the level of spatial correlation
# -----------------------------------------------------------------------------------------------------------------# -----------------------------------------------------------------------------------------------------------------# Python code for running the landscape simulation code (see below)
import diasq_beta
reload(diasq_beta)
H = 0.2
N=7
maxdim = 50
ydim = 100
a = 7.0
b = 2.5
folder = str(maxdim) + "_" + str(a) + "_" + str(b) + "_" + str(H)
surface = diasq_beta.make_landscape(H, N, maxdim, ydim)
pixellandscape = diasq_beta.revalue(surface, a, b)

91

diasq_beta.save_landscape(pixellandscape, maxdim, ydim, "for_age_" + folder + ".txt")
# -----------------------------------------------------------------------------------------------------------------# -----------------------------------------------------------------------------------------------------------------# Code for simulating the landscape; referred to as “diasq_beta” in the code to run the simulation
#
(see above)
import math, random
def randomdisplace(disheight):
return random.random()*disheight-0.5*disheight
def displacevals(p, disheight):
if len(p)==4:
pcentre = 0.25*sum(p)+randomdisplace(disheight)
elif len(p) == 3:
pcentre = sum(p)/3 + randomdisplace(disheight)
return pcentre
def check_diamond_coords(diax,diay,dim,i2):
if diax < 0 or diax > dim or diay <0 or diay > dim:
return []
if diax-i2 < 0:
return [(diax+i2,diay),(diax,diay-i2),(diax,diay+i2)]
if diax + i2 >= dim:
return [(diax-i2,diay),(diax,diay-i2),(diax,diay+i2)]
if diay-i2 < 0:
return [(diax+i2,diay),(diax-i2,diay),(diax,diay+i2)]
if diay+i2 >= dim:
return [(diax+i2,diay),(diax-i2,diay),(diax,diay-i2)]
return [(diax+i2,diay),(diax-i2,diay),(diax,diay-i2),(diax,diay+i2)]
#hlist = [-2.0, -1.0, -0.71, -0.43, -0.14, 0.0, 0.14, 0.28, 0.43, 0.71, 1.0, 2.0]

def make_landscape(H, N, maxdim, ydim):
displacementheight = 2.0
dim = 2**N + 1
if H == -2.0:
surface={}
for x in xrange(dim):
for y in xrange(dim):

92

surface[x,y] = random.random()
else:
surface={}
for x in xrange(dim):
for y in xrange(dim):
surface[x,y] = randomdisplace(displacementheight)
inc = dim-1
while inc > 1:
i2 = inc/2
#print 'inc', inc, 'i2', i2
#
print 'square'
for x in range(0,dim-1,inc):
for y in range(0,dim-1,inc):
# this fills in the centre of the square
surface[x+i2,y+i2] =
displacevals([surface[x,y],surface[x+inc,y],surface[x+inc,y+inc],surface[x,y+inc]],displacement
height)
#print 'diamond'
for x in range(0, dim-1, inc):
for y in range(0, dim-1,inc):
#print '*****', x, y, '*****'
#print x+i2,y
diaco = check_diamond_coords(x+i2,y,dim,i2)
# print diaco
diavals = []
for co in diaco:
diavals.append(surface[co])
surface[x+i2,y] = displacevals(diavals,displacementheight)
# print x,y+i2
diaco = check_diamond_coords(x,y+i2,dim,i2)
# print diaco
diavals = []
for co in diaco:
diavals.append(surface[co])
surface[x,y+i2] = displacevals(diavals,displacementheight)
# print x+inc, y+i2
diaco = check_diamond_coords(x+inc,y+i2,dim,i2)
# print diaco
diavals = []

93

for co in diaco:
diavals.append(surface[co])
surface[x+inc,y+i2] = displacevals(diavals,displacementheight)
# print x+i2, y+inc
diaco = check_diamond_coords(x+i2,y+inc,dim,i2)
# print diaco
diavals = []
for co in diaco:
diavals.append(surface[co])
surface[x+i2,y+inc] = displacevals(diavals,displacementheight)
displacementheight = displacementheight*2**(-H)
inc = inc/2

# maxdim = 40
if dim < maxdim:
maxdim =dim
trimmedsurf = {}
for x in xrange(ydim):
for y in xrange(maxdim):
# print x, y
if surface.has_key((x,y)):
trimmedsurf[x,y] = surface[x,y]
## fileout = open("surfconf.txt",'w',-1)
## for x in xrange(maxdim):
##
thisline = ''
##
for y in xrange(maxdim):
##
if surface.has_key((x,y)):
##
thisline = thisline + str(surface[x,y]) + '\t'
##
else:
##
thisline = thisline + '0\t'
##
thisline = thisline + '\n'
##
fileout.write(thisline)
## fileout.close()
return trimmedsurf
def save_landscape(surface, maxdim, ydim, fileoutname):
fileout = open(fileoutname,'w',-1)
for x in xrange(ydim):
thisline = ''
for y in xrange(maxdim):
if surface.has_key((x,y)):

94

thisline = thisline + str(surface[x,y]) + '\t'
else:
thisline = thisline + '0\t'
thisline = thisline + '\n'
fileout.write(thisline)
fileout.close()

def revalue(surface,a,b):
oldvals = surface.values()
oldvals.sort()
newvals = [random.betavariate(a,b) for i in xrange(len(oldvals))]
newvals.sort()
newsurface = {}
for k in surface.keys():
newsurface[k] = newvals[oldvals.index(surface[k])]
return newsurface

# -----------------------------------------------------------------------------------------------------------------# ------------------------------------------------------------------------------------------------------------------

95

APPENDIX D
R CODE FOR SPECIES SIMULATION
library(raster)
library(coenocliner)
library(reshape2)

memory.limit(size=20000) # This program can use a great deal of memory

# Create the location matrix from the text files representing the ecological gradients (i.e. raster
# maps)
matrix1<-as.matrix(read.table("TABLE_NAME.txt"))
matrix2<-as.matrix(read.table("TABLE_NAME.txt"))
matrix1.vec<-sort(matrix1, index.return=TRUE)
matrix2.vec<-sort(matrix2, index.return=TRUE)
loc1<- matrix1.vec$x
loc2<- matrix2.vec$x

# Simulate 50 spp using beta distribution
M<-50
# Number of species
A0 <- rbeta(M, 0.5, 1)
# max occupancy rate
m <- runif(M, min(loc1), max(loc1)) # location on gradient of modal abundance
r <- runif(M, 0.01, 0.5)
# species range of occurence on gradient
alpha<-round(runif(M, 0.5, 7), 1)
# shape parameter
gamma<-round(runif(M, 0.5, 7), 1) # shape parameter
alpha
gamma
pars<-list(A0=A0, m=m, r=r, alpha=alpha, gamma=gamma)
pbern<-coenocline(loc1, responseModel = "beta", params = pars, countModel = "bernoulli",
expectation=TRUE)
pbern
## plot
plot(pbern, type = "p", pch = 1) # a random realisation
lines(pbern, lty = "solid") # probability of occurrence
# Save the output as a matrix
trial.out<-pbern[1:length(loc1),1:M]
prob<-cbind(loc1, trial.out)

96

data<-matrix(0, length(loc1), M)
for(i in 1:dim(data)[1]){
for(j in 1:dim(data)[2]){
data[i,j]<-rbinom(1, 1, trial.out[i,j])
}
}

# Add the second gradient
# ----------------------m2 <- runif(M, min(loc2), max(loc2))# location on gradient of modal abundance
r2 <- runif(M, 0.01, 0.9)
# species range of occurence on gradient
alpha2<-round(runif(M, 0.5, 7), 1) # shape parameter
gamma2<-round(runif(M, 0.5, 7), 1) # shape parameter
pars2<-list(m=m2, r=r2, alpha=alpha2, gamma=gamma2)
params2<-list(px=pars, py=pars2)

# Create the location points for the individual grid sections
maxdim<-50
xdim<-dim(matrix1)[2]/maxdim
ydim<-dim(matrix1)[1]/maxdim
d<-f<-0
for(i in 1:xdim){
d<-0
for(j in 1:ydim){
assign(paste("loc1.", j, i, sep=""), sort(matrix1[(d+1):(d+maxdim),(f+1):(f+maxdim)],
index.return=TRUE))
assign(paste("loc2.", j, i, sep=""), sort(matrix2[(d+1):(d+maxdim),(f+1):(f+maxdim)],
index.return=TRUE))
d<-d+maxdim
}
f<-f+maxdim
}
# Run the simulations on each individual grid section
system.time({
for(i in 1:xdim){
for(j in 1:ydim){
locs<-expand.grid(x=get(paste("loc1.", j, i, sep=""))$x, y=get(paste("loc2.", j, i, sep=""))$x)
assign(paste("pbern2.", j, i, sep=""), coenocline(locs, responseModel = "beta", params =
params2,
countModel = "bernoulli", expectation=TRUE))
}
}

97

})
pbern2.11

# -----------------------------------------------------------------------------# Return values to matrix
# ----------------------# Re-cast all of the simulation output into arrays indexed by loc1 and loc2 values
for(i in 1:xdim){
for(j in 1:ydim){
t<-cbind(expand.grid(x=get(paste("loc1.", j, i, sep=""))$x, y=get(paste("loc2.", j, i,
sep=""))$x), get(paste("pbern2.", j, i, sep="")))
t.m<-melt(t, id=c("x", "y"), measured=seq(1, 10, 1))
assign(paste("t.cast_", j, i, sep=""), acast(t.m, x~y~variable))
}
}
f<-0
for(i in 1:xdim){
d<-0
for(j in 1:ydim){
mat1<-matrix1[(d+1):(d+maxdim),(f+1):(f+maxdim)]
mat2<- matrix2 [(d+1):(d+maxdim),(f+1):(f+maxdim)]
g<-array(NA, dim=c(maxdim, maxdim, M))
for(l in 1:maxdim){
for(m in 1:maxdim){
x<-which(dimnames(get(paste("t.cast_", j, i, sep="")))[[1]]==mat1[l,m])
y<-which(dimnames(get(paste("t.cast_", j, i, sep="")))[[2]]==mat2[l,m])
for(k in 1:M){
z<-get(paste("t.cast_", j, i, sep=""))[x,y,k]
g[l,m,k]<-z
}
}
}
assign(paste("bird.comm_", j, i, sep=""), g)
d<-d+maxdim
}
f<-f+maxdim
}

# Save all of the arrays
for(i in 1:xdim){
for(j in 1:ydim){

98

x<-get(paste("bird.comm _", j, i, sep=""))
save(x, file=paste("bird.comm _", j, i, ".Rdata", sep=""))
}
}

# Re-load all of the tables
for(i in 1:xdim){
for(j in 1:ydim){
load(paste("bird.comm_", j, i, ".Rdata", sep=""))
assign(paste("bird.comm_", j, i, sep=""), x)
}
}

# Combine the individual arrays into the entire map
library(abind)

birds.north<-abind(bird.comm_11, bird.comm_12, bird.comm_13, along=2)
birds.south<-abind(bird.comm_21, bird.comm_22, bird.comm_23, along=2)
birds.psimap<-abind(birds.north, birds.south, along=1)
dim(birds.south)
dim(birds.psimap)

# Create occupancy map
birds.zmap<-array(NA, dim=c(dim(birds.psimap)[1], dim(birds.psimap)[2],
dim(birds.psimap)[3]))
for(i in 1:dim(birds.zmap)[1]){
for(j in 1:dim(birds.zmap)[2]){
for(k in 1:dim(birds.zmap)[3]){
birds.zmap[i,j,k]<-rbinom(1, 1, birds.psimap[i,j,k])
}
}
}
hist(apply(birds.zmap, 3, sum)/15000)
# Increase occupancy probabilities
birds.psimap_new<-1-(1-birds.psimap)^100000000
hist(birds.psimap_new)

# Create occupancy map

99

birds.zmap_new<-array(NA, dim=c(dim(birds.psimap)[1], dim(birds.psimap)[2],
dim(birds.psimap)[3]))
for(i in 1:dim(birds.zmap)[1]){
for(j in 1:dim(birds.zmap)[2]){
for(k in 1:dim(birds.zmap)[3]){
birds.zmap_new[i,j,k]<-rbinom(1, 1, birds.psimap_new[i,j,k])
}
}
}
apply(birds.zmap_new, 3, sum)/15000
hist(apply(birds.zmap_new, 3, sum)/15000)
birds.zmap<-birds.zmap_new
# Add in the north/south climate gradient
C<-0.5 # The probability that the species is not affected by the gradient
clim<-rep(0, M)
for(i in 1:M){
clim[i]<-1*(runif(1) < C)
}
clim
clim.eff<-round(runif(M, 0.1, 0.9), 1)
clim.eff

# Re-do the north-half occupancy matrix using the climate filter
birds.north.zmap<-array(NA, dim=c(dim(birds.north)[1], dim(birds.north)[2], M))
for(i in 1:dim(birds.north)[1]){
for(j in 1:dim(birds.north)[2]){
for(k in 1:M){
birds.north.zmap[i,j,k]<-birds.zmap[i,j,k]*1*(runif(1) > clim[k]*clim.eff[k])
}
}
}

birds.clim.zmap<-abind(birds.north.zmap, birds.zmap[51:100,,], along=1)
dim(birds.clim.zmap)
apply(birds.clim.zmap, 3, sum)/15000
hist(apply(birds.clim.zmap, 3, sum)/15000)

save(birds.clim.zmap, file="birds.clim.zmap_1.Rdata")

100

# ---------------------------------------------------------------------------------# Create a new map using both data frames
# ---------------------------------------------------------------------------------# Bring in both arrays
load("birds.clim.zmap_1.Rdata")
load("birds.clim.zmap_3.Rdata")
hist(apply(birds.clim.zmap_1, 3, sum)/15000)
hist(apply(birds.clim.zmap, 3, sum)/15000)

# Combine both species arrays
birds.clim.zmap_full<-abind(birds.clim.zmap_1, birds.clim.zmap, along=3)
dim(birds.clim.zmap_full)
apply(birds.clim.zmap_full, 3, sum)/15000
hist(apply(birds.clim.zmap_full, 3, sum)/15000)

101

LITERATURE CITED

102

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