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Graduate Student Theses, Dissertations, & Professional Papers Graduate School
2010
Are black bears declining in Montana? Inference from multiple data sources in the face of uncertainty
Julie Ann Beston The University of Montana
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This Dissertation is brought to you for free and open access by the Graduate School at ScholarWorks at University of Montana. It has been accepted for inclusion in Graduate Student Theses, Dissertations, & Professional Papers by an authorized administrator of ScholarWorks at University of Montana. For more information, please contact [email protected]. ARE BLACK BEARS DECLINING IN MONTANA? INFERENCE FROM MULTIPLE DATA SOURCES IN THE FACE OF UNCERTAINTY
By
JULIE ANN BESTON
B.S. in Biology and Mathematics, Truman State University, 2005
Dissertation
presented in partial fulfillment of the requirements for the degree of
Doctor of Philosophy in Fish and Wildlife Biology
The University of Montana Missoula, MT
Fall 2010
Approved by:
Perry Brown, Associate Provost for Graduate Education Graduate School
Elizabeth Crone, Chair Wildlife Biology
Vanessa Ezenwa Division of Biological Sciences
Mark Hebblewhite Wildlife Biology
Scott Mills Wildlife Biology
Michael Mitchell Montana Cooperative Wildlife Research Unit
Beston, Julie, Ph.D., Fall 2010 Fish and Wildlife Biology
Are black bears declining in Montana? Inference from multiple data sets in the face of uncertainty
Chairperson: Dr. Elizabeth Crone
Carnivores are managed both to maintain populations and reduce conflict with humans, but data-based decision-making is difficult due to the expense of data collection. When new fieldwork is impossible, we can benefit from available data in assessing populations. I used demographic and harvest data to assess the population status of black bears (Ursus americanus) in Montana.
I conducted a hierarchical Bayesian meta-analysis of black bear demographic studies to evaluate geographic structuring and estimate vital rates and population growth rate. Adult survival is higher in the west than the east, but the reverse is true for fecundity. The mean population growth rate is 0.97 (0.93, 1.00) in the west, but variability among populations suggests many are increasing.
I analyzed the sex and age of bears harvested in Montana, 1985-2005, to estimate harvest rate and population size. The harvest rate of females is 4.3% and the total population is 30- 40000. Montana’s population is stable or increasing.
I modeled discrete and continuous spatial variation in population growth rate with varying movement and habitat distributions. In order for the entire population to be stable, fewer than 20% of individuals can disperse, which is reasonable based on the literature. Landscapes with 20-30% source habitat were generally able to sustain populations.
I applied a similar approach to brown bears (U. arctos) in British Columbia, where management of salmon and bears occur independently despite the reliance of brown bears on salmon. I conducted a demographic meta-analysis and used several models and parameter combinations to evaluate the consequences of salmon reduction and bear harvest. While both affect populations, bear harvest has a more dramatic effect.
My research highlights the application of available data when new fieldwork is not feasible. Both intensive, demographic data and extensive data, like statewide harvest information, are useful in evaluating population status and management actions.
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ACKNOWLEDGEMENTS
First and foremost, I would like to thank everyone at the University of Montana who made this work possible. Elizabeth Crone is a great advisor, and without her commitment,
I could not have succeeded. Jeanne Franz is an invaluable asset to the Wildlife Program who always had the answers or could direct me to someone who did. My committee; Scott
Mills, Mark Hebblewhite, Vanessa Ezenwa, and Mike Mitchell; were generous, both with criticism and support, and improved my ability as a scientist. Mike Mitchell, in particular, helped me land this great project and facilitated communication with the powers that be who were interested in my work.
Thanks also go to various funding sources. Elizabeth, the College of Forestry and
Conservation, and the Wildlife Program, largely thanks to Dan Pletcher, were essential in keeping me fed and working. Rick Mace and Montana Fish, Wildlife, and Parks provided guidance, data, and funding for my work on black bears. M. Sanjayan gave me the opportunity to get paid working on some vastly different questions with the Nature
Conservancy and also introduced me to Richard Geo, who was my connection for the final chapter of my dissertation on grizzly bears. I also received support through the National
Science Foundation’s EPSCoR program.
Many individuals and agencies provided information for the analysis in chapter 2, including: T. Berens, Northwest Territories Environment and Natural Resources; W.
Bolduc, R. Cross and J. Vashon, Maine Department of Inland Fisheries & Wildlife; K.
Bunnell, Utah Division of Wildlife Resources; K. Burguess, New Jersey Division of Fish and
Wildlife; J. Cardoza, Massachusetts Division of Fisheries & Wildlife; K. Cartwright,
Arkansas Game and Fish Commission; H. Hristienko, Manitoba Conservation; H. Jolicoeur,
Québec Ministère des Ressources Naturelles et de la Faune; E. Kowal, Saskatchewan iii
Environment & Resource; R. Mace, Montana Fish, Wildlife, & Parks; G. MacHutchon,
Wildlife Biology Consultant, British Columbia; P. Murphy, New Brunswick Department of
Natural Resources; M. Obbard, Ontario Ministry of Natural Resources; L. Olver, Wisconsin
Department of Natural Resources; C. Ryan, West Virginia Division of Natural Resources;
H. Spiker, Maryland Department of Natural Resources; S. Still, South Carolina
Department of Natural Resources; A. Timmins, New Hampshire Fish and Game
Department; R. Winslow, New Mexico Department of Game and Fish; P. Zager, Idaho
Department of Fish and Game. Thanks also to the many biologists and field technicians who collected those data.
Finally, the unwavering support and encouragement of my family helped pull me through the hard times and keep me focused on the light at the end of the tunnel. My husband, Adam, and my daughter, Journey, gave me the motivation to keep working toward the future that we envision together. My parents, Mike and Diana Bates, my sister,
Amanda Stephens, and my awesome niece, Wendy, were the best cheerleaders anyone could wish for. This dissertation is really for all of them.
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TABLE OF CONTENTS
ABSTRACT ...... ii
ACKNOWLEDGEMENTS ...... iii
LIST OF TABLES ...... vii
LIST OF FIGURES ...... viii
CHAPTER 1 – Introduction and overview ...... 1
CHAPTER 2 – Variation in life history and demography of the American black bear (Ursus americanus) ...... 6 Abstract … ...... 6 Introduction ...... 7 Methods…… ...... 10 Results...... 14 Discussion...... 16
CHAPTER 3 – What do harvest data tell us about American black bears? ...... 38 Abstract …...... 38 Introduction ...... 39 Methods …...... 43 Estimating harvest rate...... 43 Using harvest to detect declines ...... 47 Results …...... 48 Estimating harvest rate...... 48 Using harvest to detect declines ...... 50 Discussion ...... 50
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CHAPTER 4 – Spatial heterogeneity and population viability of American black bears ...... 69 Abstract …...... 69 Introduction ...... 70 Methods …...... 73 Discrete space model...... 74 Continuous space model ...... 76 Results …...... 79 Discrete space model...... 79 Continuous space model ...... 80 Discussion ...... 81
CHAPTER 5 – Population response of brown bears (Ursus arctos) to salmon escapement and harvest ...... 93 Abstract …...... 93 Introduction ...... 94 Methods …...... 96 Meta-analysis ...... 96 Fecundity functions ...... 97 Simulations ...... 99 Results …...... 101 Discussion ...... 103
BIBLIOGRAPHY ...... 115
APPENDIX – R and WinBUGS code for meta-analysis in Chapter 2 ...... 138
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LIST OF TABLES
CHAPTER 2. Table 2.1. Suite of models used in the meta-analysis to estimate black bear vital rates...... 21 Table 2.2. Parameter definitions for hierarchical models of vital rates presented in Table 2.1...... 22 Table 2.3. Demographic studies of black bears used in the meta- analysis…………………………………………………………………………..23 Table 2.4. Hierarchical structure of black bear study locations…...... 28 Table 2.5. Differences in deviance information criterion (ΔDIC) for geographic models of black bear vital rates. Models with the best support are shown in bold; those with substantial support are italicized...... 29 Table 2.6. Mean vital rates (95% credible intervals) of black bears in eastern and western North America...... 30 Table 2.7. Sensitivities and elasticities of female black bear vital rates for eastern and western North America and their 95% credible intervals...... 31
CHAPTER 5. Table 5.1. Demographic studies used in brown bear meta-analysis (see Methods for explanation of variables) ...... 106 Table 5.2. Average population growth rate of brown bears in British Columbia under four structural models (see Methods for explanation), three harvest rates with current salmon escapement, and four salmon escapement levels with no harvest...... 108
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LIST OF FIGURES
CHAPTER 2 – Figure Legends ...... 32 Figure 2.1. Locations of black bear demographic studies included in the hierarchical Bayesian meta-analysis…………..…………………………...... 33 Figure 2.2. Mean matrix models for bears in (a) eastern North America and (b) western North America based on vital rate values in Table 2.4...... 34 Figure 2.3. Mean cub survival values across black bear range estimated for each ecosystem division in the hierarchical Bayesian meta-analysis...... 35 Figure 2.4. The relationship between mean population growth rate and (a) mean adult survival and (b) mean fecundity for female black bears in eastern and western North America...... 36 Figure 2.5. Posterior probability distributions of the mean population growth rate and the expected population growth rates of individual populations in (a) eastern and (b) western North America...... 37
CHAPTER 3 – Figure Legends ...... 56 Figure 3.1. Black bear hunter days in Montana by season from 1996 to 2003 based on hunter surveys...... 58 Figure 3.2. Proportion of the Montana black bear harvest, 1985-2005, at each age that is composed of females ...... 59 Figure 3.3. The (a) proportion of females in the harvest and the (b) total harvest by age in a simulated population in which female vulnerability decreases by 50% at the age of primiparity, and the (c) actual proportion of females in Montana’s spring and fall harvests, 1985-2005 ...... 60 Figure 3.4. Estimated harvest rate for Montana as a function of the assumed ratio of natural male survival to natural female survival ...... 61 Figure 3.5. The (a) proportion of females in the harvest and the (b) total number harvested at each age in a simulated population in which male black bear non- harvest mortality is 96% of female natural mortality...... 62
viii
Figure 3.6. Estimates of harvest rate and associated confidence intervals for a simulated black bear population as more years of data are combined in the estimation ...... 63 Figure 3.7. Annual and pooled 5-year estimates of female black bear harvest rate in Montana, 1985-2005, assuming an initial sex ratio of 1:1 and equal male and female non-harvest mortality rates...... 64 Figure 3.8. Estimates of (a) annual harvest rate and the (b) age structure of the harvest through time as the harvest rate in a simulated population declines. .. 65 Figure 3.9. Estimates of black bear population size in Montana, 1985-2005, calculated from total reported black bear harvest divided by estimated harvest rate...... 66 Figure 3.10. Proportion of simulated populations in which a statistically significant negative trend was identified in the harvest data given stochastic or deterministic population growth and varying initial population size.... 67 Figure 3.11. Number of years of harvest data required to identify statistically significant declines in 90% of simulated populations with an initial population size of 30000 bears given the deterministic population growth rate ...... 68
CHAPTER 4 – Figure Legends ...... 87 Figure 4.1. Posterior probability density of black bear population growth rate in western North America (from Ch 2 this dissertation) ...... 89 Figure 4.2. The critical amounts of (a) source habitat in the discrete space model and (b) movement in the continuous space model that result in population growth rate greater than 1 as the habitat distribution varies, and the overall average population growth rate in (c) the discrete space model and (d) the continuous space model as the habitat distribution and the movement rate varies. The star (b) represents the best estimate of the mean and standard deviation of population growth rate. .. 90 Figure 4.3. Sensitivity of total black bear population growth rate (a) in the discrete space model to changes in the vital rates of the source and sink, the proportion of source habitat, and the proportion of subadults dispersing
ix
calculated for 1000 sample pairs of source and sink vital rates with 34% source habitat and 10% or 100% of subadults dispersing and (b) in the continuous space model to changes in the mean or standard deviation of overall population growth rate and movement rate calculated for 1000 samples of mean and standard deviation from their posterior distributions with 3% and 30% of all animals moving...... 91 Figure 4.4. Total population growth rate in the continuous space model given local movement rates that vary linearly with local population growth rate. Solid lines in panel (a) show preferences for good habitat, and dotted lines are when individuals prefer to remain in poor habitat. When the preference is not extreme, as in the bold lines of panel (a), populations do not necessarily grow or decline as we would expect based on free distributions or ecological traps, respectively. Whenever local movement rates are within the shaded area of panel (b), total population growth remains greater than or equal to 1...... 92
CHAPTER 5 – Figure Legends ...... 109 Figure 5.1. Central coastal British Columbia salmon (Oncorhynchus spp) escapement index, 1976-2000; the section after the dashed line, 1985-2000, is the portion used in simulations ...... 110 Figure 5.2. Posterior distributions of the means of female brown bear survival rates based on meta-analysis of demographic studies...... 111 Figure 5.3. Functions relating (a) brown bear fecundity to the proportion of their diet comprised of salmon and (b) fecundity to the index of salmon escapement with arrows indicating the observed range of salmon escapement in the focal population. Data for (a) from Hildebrand et al. (1999); see additional details in Methods ...... 112 Figure 5.4. Female brown bear population size over a 20 year times horizon under current salmon escapement and no harvest using Quinn’s asymptotic model; grey lines indicate the upper 75% and lower 25% of simulated populations ...... 113
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Figure 5.5. Change in female brown bear population growth rate due to changes in salmon escapement or bear harvest from current escapement or no harvest, respectively ...... 114
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CHAPTER 1 INTRODUCTION AND OVERVIEW
Carnivores are controversial yet charismatic species that frequently act as umbrella or keystone species in conservation planning (e.g. Maehr et al. 2001). They are often perceived as threats to humans or livestock, whether their actions support such beliefs or not (Karanth and Chellam 2009). Managers are faced with the dual goal of ensuring viability while reducing conflict. However, understanding the status of carnivores and the effects of management on their populations is problematic. Carnivores are often secretive and live at relatively low densities (Karanth and Chellam 2009). Observing these animals to assess population growth rate and response to management is difficult. The situation is even more problematic for large, long-lived carnivores. They are expensive to capture, and the relative rarity of births and deaths makes the estimation of survival and reproductive rates difficult.
One way to study these species is spend a lot of money collecting the specific data in which we are interested. In and around Glacier National Park, almost $5 million were used for a DNA study to estimate brown bear (Ursus arctos) population size (Kendall et al. 2008).
John McCain famously derided the expense during the 2008 presidential campaign. While this study on an endangered species may have been a justifiable use of public funds, his opinion underscores the fact that millions of dollars are not available for most carnivore populations. Moreover, continuous or repeated monitoring is required to determine population trend, which requires investing large amounts over a long period of time.
Because we are limited in the studies we can do, models of population dynamics often include parameters that researchers are unable to estimate directly. Evaluating the model across the possible ranges of unknown parameters can be helpful but results in
1 highly uncertain estimates of population growth rate. To reduce this problem, model output can be compared with known qualitative or quantitative patterns derived from animal sightings, short term studies, harvest or other data. Wiegand et al. (2004) used this approach and were able to greatly reduce the uncertainty in predictions from an individual- based model of reintroduced brown bears in Austria. In this case, the output of the model through time was compared with known locations of individual bears at various times to exclude models or parameter values that could not produce the observed patterns.
Another option is to quantitatively combine various data sources that are cheaper to collect but may be insufficient on their own. New developments in statistical catch-at-age analyses combine data collected from harvested individuals, which is relatively inexpensive, with information collected during concurrent mark-recapture or radio-telemetry studies
(Gove et al. 2002). Age-at-harvest and mark-recapture data have been combined using a
Bayesian framework to estimate harvest rate and population size of black bears (U. americanus) in Pennsylvania, as well as uncertainty in those estimates (Conn et al. 2008).
When available data come from different times and/or locations, finding meaningful ways to integrate them quantitatively may be impractical. Drawing on disparate data sources to address the same question may require a variety of estimation techniques as well as simulations. Advances in computer technology have made simulation studies easier to accomplish and understand, and this provides a way to analyze the limitations of available data and determine what additional data would be most useful. Simulations were used to examine likely disease dynamics during an outbreak of canine distemper virus in lions
(Panthera leo) when data were sparse (Craft et al. 2009). Data collected during other studies on lions were used to develop the model, and simulations could be done to explore spread of the disease, despite a lack of data from the original outbreak. Simulations have also been used to assess the ability of monitoring to detect trends in brown bear populations 2
(Stetz et al. 2010). Additionally, simulations were used to identify additional information needed to achieve research goals (Verbruggen et al. 2010). In short, when available data are limited or uncertain, simulations are an effective way to assess possible causes of observed patterns, identify power and biases of the data, and prioritize data collection.
American Black Bears and Brown Bears
For North American bears, the question of how to appropriately manage populations in the face of limited knowledge is particularly interesting. Historically, American black bears and brown bears were extirpated or diminished in much of their ranges in the lower
48 United States (Pasitschniak-Arts 1993, Lariviere 2001, Mattson and Merrill 2002).
Bears are of conservation value and interest but can also become troublesome and even dangerous near humans. Therefore management objectives include controlling populations and simultaneously preventing extinction. Designing a fail-safe management strategy that provides for removal of problem bears and some recreational harvest without jeopardizing population persistence could require the collection of an enormous amount of baseline information and extensive monitoring. Intensive data collection, such as repeated mark- recapture studies of bears with adequate sample sizes to estimate demographic parameters and population sizes for every managed population, is an unreasonable expectation.
Black bears are generalist omnivores that historically occurred throughout much of
North America (Lariviere 2001), but their range has shrunk within the United States
(Vaughan and Pelton 1995). They are harvested across much of their range (Vaughan and
Pelton 1995, Diefenbach et al. 2004), yet few long-term population studies have been undertaken to understand the effects of harvest (Lariviere 2001). The uncertainty in vital rate estimates from individual studies is often high, and all the vital rates needed for a population model are rarely estimated in the same study.
3
Grizzly or brown bears are an Holarctic species whose historic range encompassed much of North America, as well as northern Eurasia (Pasitschniak-Arts 1993). Like black bears, they are omnivorous, and though protected in the lower 48 states, they are harvested in Canada and Alaska. Due to their lower foraging efficiency on low density foods (Mattson et al. 2005), brown bears rely on foods that are readily available in large quantities for part of the year, such as spawning salmon or mast crops of whitebark pine (Robbins et al. 2004).
Fewer demographic studies have been done for brown bears than black in North America.
Both black and brown bears are both relatively long-lived with a low reproductive output (Pasitschniak-Arts 1993, Lariviere 2001). These traits make them susceptible to inadvertent overharvest (Sorensen and Powell 1998, Garshelis and Hristienko 2006). It is also difficult to collect reliable demographic data because births and deaths are relatively rare events, and researchers need to follow many animals over many years to achieve sufficient sample sizes for demographic parameter estimation (Williams et al 2002).
Therefore, it is not feasible to conduct detailed demographic studies of each population before implementing management.
Several data sources exist that are relatively inexpensive to collect and easy to maintain, but their usefulness in managing bears can be unclear. First and foremost, studies presented in peer reviewed and grey literature offer some insight into the demography of both species. The age and sex of harvested bears are also available in many jurisdictions. In Montana, as in many other jurisdictions, the age and sex of harvested black bears is collected as bears are brought through check stations. But this sample is not representative of the total standing population, and uncertainty in estimates of harvest rate, population size and growth rate derived from these bears is again a problem. Some information is available on other variables that may be important to these populations,
4 ranging from the amount of snowpack during the spring black bear harvest to the annual escapement of salmon in British Columbia.
I synthesize data and information on black bears and brown bears to examine the status of their populations and assess the value of a variety of data sources in guiding management. I focus specifically on management of black bears in Montana and brown bears in central coastal British Columbia. Both of these populations are harvested, and managers in both areas are expected to maintain viable populations, remove problem bears, and provide for harvest. Given limited resources, management requires efficient collection and use of information. Even relatively cheap data, like harvest data, require time and money to collect and analyze, and understanding what we can expect to gain from them is critical in determining whether the expense is worth it.
In the following chapter, I present a Bayesian hierarchical meta-analysis of black bear demography across their range. I investigated spatial structuring and used the vital rates to estimate population growth rates. In third chapter, I used the sex and age of harvested black bears to determine the status of bears in Montana and assess the utility of continued harvest data collection. Though the demography suggested black bears are declining in the West, harvest data from Montana suggested the population is stable or increasing. The fourth chapter reconciled these conclusions by showing that source-sink dynamics can create a situation where the average population growth rate is less than one but the population is increasing due to movement among habitat types. The final chapter addresses similar issues for brown bears in British Columbia. I conducted a demographic meta-analysis and used the vital rates to parameterize several models describing the relationship between salmon escapement and brown bear population dynamics. Despite the limitations of much available data, managers and researchers can use it to identify important parameters and evaluate the cost-effectiveness of continued data collection. 5
CHAPTER 2
VARIATION IN LIFE HISTORY AND DEMOGRAPHY OF THE AMERICAN BLACK BEAR (URSUS AMERICANUS)
Abstract
Variation in life history and demography across a species’ range informs researchers about regional adaptations and affects whether managers can borrow information from other populations in decision-making. The American black bear (Ursus americanus) is a long- lived game species whose continued persistence depends on management of harvest and reducing levels of human-bear conflict. Understanding the demography of black bears guides efforts at management and conservation, yet detailed knowledge of many populations is typically lacking. I performed a hierarchical Bayesian meta-analysis of black bear demographic studies across their geographic range to explore how vital rates vary across the range, what information they give us about population growth, and whether managers can justify borrowing information from other studies to inform management decisions. Cub, yearling, and adult survival and fecundity varied between eastern and western North America, whereas subadult survival did not show geographic structuring.
Adult survival and fecundity appeared to trade off, with higher survival in the western portions of their range and higher fecundity in the east. Although adult survival had the highest elasticity, differences in reproduction drove differences in population growth rate.
The mean population growth rate was higher in the east, 0.99 (95% credible interval: 0.96,
1.03) than the west, 0.97 (0.93, 1.01). Despite declining trends in the west, 34% of the distribution of population lambdas was great than 1, compared to 55% in the east. Further work needs to be done to address the cause of the apparent trade-off between adult survival and fecundity and explore how the estimated growth rates are likely to affect population
6 status of black bears. Because population growth rates are close to 1 and small deviations could impact whether a population is considered increasing or decreasing, managers need to employ caution in borrowing vital rates from other populations.
Introduction
Conservation and management decisions often rely on information about a species’ life history and demographic rates, and variation in these traits informs us about pressures populations face and potential impacts of management decisions. Variation in life history among populations of a particular species has been demonstrated in a variety of taxa, from fish (Johnson and Zuniga-Vega 2009) to deer (Nilsen et al. 2009). These differences affect population growth, persistence, and responses to management (Brown 1985, Dobson and
Murie 1987, Nilsen et al. 2009). Just as species that reproduce quickly recover more easily from disturbance and exploitation than long-lived species with slower reproduction, so too, populations within a species may differ in their response to management due to differences in population growth rates. These differences also affect whether we can generalize studies of individual populations to reduce costs of new studies and target gaps in the current knowledge base.
Many large carnivores have wide distributions in varied environments that may induce variation in life history. They are also frequently targets of harvest, control, or conservation actions, whose cost and effectiveness vary with life history and demography of individual populations. For example, brown bears (Ursus arctos) are more productive in their coastal North American range than in continental areas due to availability of spawning salmon (Hilderbrand et al. 1999). Coastal populations may sustain a higher harvest rate than inland populations due to greater reproduction. Likewise, the effect of extra wild dog (Lycaon pictus) helpers on reproduction varies spatially with ecological 7 conditions, and this affects the appropriate pack size for an enclosed reserve (Gusset and
Macdonald 2010).
Management can also induce important spatial variation. Cougars (Puma concolor) show strong source-sink dynamics when heavily harvested areas are adjacent to relatively undisturbed populations (Robinson et al. 2008, Cooley et al. 2009). Efforts at reduction of cougars in target areas were fruitless unless survival was suppressed over a wide area
(Cooley et al. 2009). Similarly, sanctuaries appear to provide some refuge for harvested black bear (U. americanus) populations in the southeast United States (Powell et al. 1996), and maintaining unhunted areas may bolster hunted populations on neighboring lands.
Spatiotemporal variation in historic overexploitation has also induced life history variation among sea otter (Enhydra lutris) populations in the North Pacific (Monson et al. 2000).
Populations that have not fully recovered exhibit higher weaning success than those that have reached carrying capacity (Monson et al. 2000). It is clear that spatial variation in vital rates and life history through natural variations or anthropogenic differences should affect management decisions. However, there have been few attempts to describe geographic structure in life history across the range of a large carnivore.
Black bears are widely distributed in a variety of ecosystems in North America, which could lead to variation in life history. They rely heavily on seasonally available hard and soft mast as well as prey, and variation in food has been shown to correlate with differences in reproduction and survival of young (Schwartz and Franzmann 1991).
Because they depend on primary productivity that varies among the biomes they inhabit, their life history and vital rates may also vary among populations in different biomes.
Variation in harvest pressure could also affect life history by depressing adult survival
(Czetwertynski et al. 2007, Obbard and Howe 2008), which generally has a strong impact on population growth of long-lived species (Heppell et al. 2000, Saether and Bakke 2000). 8
At a very broad scale, black bears in eastern North America were isolated from those in western North America during the Pleistocene (Wooding and Ward 1997), and there is a long-standing perception that populations in the two halves differ in population dynamics.
Researchers sometimes refer to the vital rates of “eastern” or “western” black bears in papers without explaining why such a distinction has been made (e.g. Rossell and Litvaitis
1994, Garrison et al. 2007, Baldwin and Bender 2009). Others have observed contrasts between estimates of vital rates, especially reproduction, from the two halves of their range
(Kasworm and Thier 1994), but to my knowledge there has been no systematic examination of how their life history varies across their range.
Regional differences in life history may determine the efficacy of management and conservation strategies for this charismatic carnivore. Black bears are hunted throughout much of their range and can become pests near agricultural and urban food sources
(Lariviere 2001, Hristienko and McDonald 2007). Managers are faced with the challenge of ensuring persistence while allowing for harvest and nuisance removals. Demographic differences can affect what management strategies are acceptable. Hristienko and
McDonald (2007) suggest that western and northern populations should be managed more conservatively because food is less abundant, presumably resulting in lower reproductive output. Alternatively, little variation in life history may mean information can easily be generalized to help guide management across the range.
Many demographic studies have been conducted on black bears, and this information may provide useful insights for managers and researchers. I synthesized work on black bear demography in a Bayesian meta-analysis to assess how their life history varies across space and whether managers can borrow information from other populations in making management decisions. I constructed a simple matrix population model to estimate population growth rate, compare population growth across their range, and 9 evaluate realized consequences of differences in vital rates (Wisdom et al. 2000). I explore whether the general pattern of high adult survival with high elasticity found in several studies of individual bear populations (Eberhardt 1990, Wielgus et al. 2001, Freedman et al. 2003) holds throughout the range of black bears. I also use model selection to test whether geographic structure is apparent among vegetation and climatic communities using ecoregions (Bailey 1998) and between eastern and western North America.
Methods
I conducted a literature search for black bear demography and used a citation search to identify further studies. I searched Web of Science and Google Scholar for “black bear and demography or life history or vital rate or survival or reproduction.” I sent information requests to every state and provincial agency mandated to manage black bears. I also included vital rates reported in papers or tables by third party authors where I could not acquire the original source. I recorded cub, yearling, subadult and adult survival, fecundity, age at primiparity, litter size, interbirth interval, sample sizes and standard errors, as well as location, time period, and whether the population was harvested. If two studies were based on the same data, I excluded the older study because the newer study usually either added data or improved the analysis. Bears are polygamous, and females drive population growth because a single male can impregnate several females (Lariviere
2001). Therefore, when different survival rates were reported for each sex, I used only information from female bears.
In order to combine estimates of vital rates from different studies in the meta- analysis, I used measures of precision to incorporate differing levels of uncertainty. I used the squared standard error to produce a measure of uncertainty associated with each vital
10 rate estimate. When standard error of survival, s, was not reported, I calculated it using the sample size, n, (Sokal and Rohlf 1995):
s(1 s) SE (s) n
When fecundity, f, and/or its standard error were not reported, I used ⁄ to calculate fecundity, where l is litter size and b is interbirth interval. This assumes a 1:1 sex ratio at birth. I then found the standard error by propagating the errors of litter size and interbirth interval:
2 2 f f SE ( f ) SE (l) SE (b) l b
If I could not employ these methods, I set the standard error equal to the greatest standard error recorded for the other estimates of that vital rate. I used the squared standard error to weight studies in the meta-analysis by adding it to the variance at the lowest level of the hierarchy. Studies with more precise estimates of vital rates therefore had greater weight in the model fitting and studies with large or unknown standard error had least weight.
I modeled age at primiparity with a stretched and translated beta distribution, which is very flexible and has upper and lower bounds that can be manipulated to suit the data. The youngest observed mean primiparity was 3 and the oldest was 8; so I set the limits at 2.5 and 8.5. To estimate the distribution, I converted the estimates to a standard beta scale, which is bounded by 0 and 1, by subtracting the lower limit, 2.5, and dividing by the range, 6. I assumed the probability of the mean age at primiparity being i was equal to the probability under the estimated stretched beta from i - 0.5 to i + 0.5.
I combined estimates of survival, fecundity, and age at primiparity using a set of six hierarchical models to identify the appropriate geographic structure for each vital rate
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(Tables 2.1, 2.2). I considered combinations of three intermediate geographic levels between the study level and the entire range: ecoregion provinces and ecoregion divisions
(Bailey 1998), and eastern and western halves of the continent. Ecoregions group areas with similar climate and vegetative communities, and each division is comprised of 1 to 4 provinces. For example, the most of the southeastern US is in the Subtropical Division, which contains 3 provinces: Mississippi riverine forests in the western part of the division, southeastern mixed forests in the center, and coastal plain forests in the east. There was a natural break in study locations, with none occurring between -95˚ and -105˚ longitude
(Figure 2.1), roughly corresponding to the Great Plains, which served as the divider between east and west. I made an exception for Obbard and Howe (2008) because the ecoregion it was in stretches across Canada and into Alaska, the other studies in this ecoregion were in the west, and the climate and population density more closely resemble the west than the east. The null model included no hierarchy. Three models incorporated a single level hierarchy; the studies were grouped by province, division, or half. Two further models had 2 levels, either province and half or division and half. I also included a set of models that incorporated harvest as an indicator variable, but these did not perform well, probably because harvest management likely varies widely among studies.
I fit models using package R2WinBUGS to call WinBUGS (Lunn et al. 2000) from R
(R Development Core Team 2009). I monitored convergence with the potential scale reduction factor, ̂ (Gelman et al. 2004, Sturtz et al. 2005). I compared models using the deviance information criterion, DIC, calculated with pV (Gelman et al. 2004). I conducted subsequent analyses using the best supported model for each vital rate.
I used the vital rates from the meta-analysis to parameterize a density-independent post-birth pulse matrix model (Caswell 2001):
12
0 0 m2 f m3 f m8 f m9 f s 0 0 0 0 0 0
0 s1 0 0 0 0
0 0 s2 0 0 0 0 0 0 0 0 0 0 0 0 0 s8 s9 where
sc for i 0 s y for i 1 si ss for i 2 s (1 p ) s p for i 3,...,8 s i a i sa for i 9 is the survival of bears from age i to age i+1 given stage specific survival of cubs (c), yearlings (y), subadults (s), and adults (a),
ss pi1 for i 2 mi ss ( pi1 pi ) sa pi for i 3,...,8 sa for i 9 is the proportion of i aged bears that will survive and be mature at age i+1, f is fecundity
(number of female cubs per female per year), and pi is the probability that the mean age at primiparity is i or younger. I assumed the age at which bears reach sexually maturity is constant within a given region, but unknown. I also performed analyses using an age- structured matrix in which all bears had the same age at primiparity, set to the mean of the region rounded to the nearest integer, and had a maximum age of 25 years
(Hebblewhite et al. 2003). This analysis led to essentially identical conclusions, so it is not discussed here.
I used the matrix model to calculate the asymptotic population growth rate, λ, and the sensitivities and elasticities of the survival and fecundity vital rates (Caswell 2001). I 13 bootstrapped survival and fecundity using their standard errors and variances among studies to find the posterior distributions of mean λ and population λs, respectively. While sensitivity describes the change in lambda with an incremental change in the vital rate, elasticity describes the change in lambda with a proportional change in a vital rate
(Caswell 2001). However, since the effects of vital rates on lambda also depend on the amount of variation in each vital rate (Wisdom et al. 2000), I also compared the pattern of variation in vital rates among areas with estimated population growth rates.
Results
I collected data on 86 black bear populations from 76 studies (Table 2.3). Fifty-nine populations were in eastern North America and 27 were in western (Table 2.4). Studies spanned the geographic range of black bears (Figure 2.1). The final dataset included 55 estimates of cub survival, 23 estimates of yearling survival, 23 estimates of subadult survival, 52 estimates of adult survival, 32 estimates of fecundity, and 35 estimates of age at primiparity.
Most vital rates appear to vary most between the east and west halves of the continent (Table 2.5). For fecundity, yearling and adult survival, and age at primiparity, the best model was structured by eastern and western North America. The best supported model for cub survival included division structuring. The highest cub survival values (0.64-
0.72) were found in more northerly divisions, and the lowest value (0.54) was, not surprisingly, from the desert southwest. To estimate population growth rates, I chose to use the halves model, which was also well-supported (ΔDIC = 1.455). Subadult survival data showed some support for the halves model (ΔDIC = 2.357), but the posterior distributions of the eastern and western means in the halves model overlapped greatly with
14 one another. I therefore chose to use the nonhierarchical model for subadult survival rate, which was the best supported one.
In the east, average adult female survival was 0.82 (95% credible interval: 0.77,
0.86) and fecundity was 0.58 (0.54, 0.62). In the west, adult survival was higher than in the east, 0.88 (0.83, 0.92), but fecundity was lower, 0.46 (0.36, 0.54). The mean age at primiparity in the east, 4.46 (4.02, 4.96), was also lower than that in the west, 5.58 (5.06,
6.07). There was an apparent negative relationship between adult survival and reproductive rate (Table 2.6). The pattern was also evident in the sensitivities and elasticities, with the sensitivity and elasticity of adult survival higher in the west than east and that of fecundity higher in the east than west (Table 2.7).
Analysis of the mean population growth rate, λ, for each half showed that population growth was positively correlated with both survival and fecundity (matrices, Figure 2.2; correlations, Figure 2.3). Eastern populations tended to have higher population growth despite their generally lower adult survival (Fig. 2.3A), indicating that larger differences in fecundity (a vital rate with lower sensitivity) between east and west outweighed smaller differences in survival (a vital rate with higher sensitivity). Black bears in eastern North
America had a mean λ of 0.99 (95% credible interval: 0.96, 1.03), and the mean λ in western
North America was 0.97 (0.93, 1.01). However, population growth rates also varied considerably among studies within each half of the continent. Using among-study variance in vital rates as an estimate of among-population variation, the posterior density for λ suggests that 55% of populations in the east and 34% of populations in the west have deterministic population growth rates greater than one (Figure 2.4).
15
Discussion
At a large scale across North America, adult survival of black bears appears to trade off with reproductive rate. The eastern half of the continent showed increased reproductive rate, decreased adult survival, and younger age at maturity than the western half. This may be accompanied by a north-south cline, because studies in the west were generally farther north than studies in the east. Trade-offs between reproduction and adult survival have been documented within other species as well as among species (Roff 2002). While a trade-off is plausible, no correlation was apparent between adult survival and reproductive rate in the few populations in which both were measured. It is possible that trade-offs occur in response to large scale conditions while other factors determine reproductive rate and survival at the population level. The apparent negative correlation at the continental scale could reflect differing habitat quality and/or differing mortality between eastern and western North America.
For example, following very poor hard or soft mast years, black bear reproduction often fails because mothers are in poorer condition going into winter dens (Eiler et al. 1989,
Elowe and Dodge 1989). The differences between east and west could result from increased abortion of reproductive attempts or death of neonates due to poorer nutrition in the west.
For this to cause the observed tradeoff, the more frequent reproduction in the east must extract a cost in terms of adult survival. Researchers have documented survival costs of reproduction for several mammals, including carnivores such as wolverines and badgers
(Clutton-Brock et al. 1983, Boyd et al. 1995, Woodroffe and Macdonald 1995, Persson 2005).
However, other studies have failed to find measurable costs of reproduction (Murie and
Dobson 1987, Millar et al. 1992). Although to my knowledge no one has examined the costs
16 of reproduction on adult survival in black bears, Atkinson and Ramsey (1995) found no apparent cost of reproduction on female polar bear (U. maritimus) survival.
Alternatively, increases in reproduction may be a response to decreased survival of adults. When life expectancy is shorter, animals should invest more in reproduction and less in survival. In hunted populations, harvest is the primary cause of mortality for adult black bears (Hellgren and Vaughan 1989, Schwartz and Franzmann 1991, Beringer et al.
1998, Koehler and Pierce 2005, Czetwertynski et al. 2007). Lower survival rates in the east suggest that these bears experience higher harvest and human-caused mortality, which would be expected from higher human population density in the east. Therefore, humans may be causing a shift in life history towards more and earlier reproduction by suppressing adult survival, both through harvest and through non-harvest human-caused mortality such as road kills and the removal of conflict bears. Shifts in life history and related traits due to harvest have been observed in species with stage- or sex-selective harvests (Ericsson
2001, Coltman et al. 2003, Jorgensen et al. 2009), and increasing harvest mortality selects for younger age at maturity regardless of the selectivity of harvests (Allendorf and Hard
2009, Darimont et al. 2009). Evidence for compensation in individual populations of black bears is equivocal (Beecham 1980, Czetwertynski et al. 2007, Obbard and Howe 2008), and responses may be confounded with effects of habitat and density (Czetwertynski et al.
2007). Further work needs to be done to assess whether the observed pattern between adult survival and reproduction is mainly the result of differences in habitat, harvest and human-caused mortality, or not an actual trade-off but a combination of these factors.
Black bears are long-lived with relatively low reproductive rates, and as expected, adult survival had the highest elasticity. However, population growth rate was higher in the east, suggesting that the differences in fecundity outweighed differences in adult survival. Generally, the vital rate with highest elasticity is expected to have low variation 17
(Gaillard et al. 1998, Pfister 1998, Wisdom et al. 2000), and in this case the relatively low spatial variation of adult survival decreases its importance for population growth rate.
Elasticity rankings do not necessarily correspond to a vital rate’s role in determining population growth rate (Wisdom et al. 2000). Importance of higher fecundity for higher population growth rates in the east mirrors other black bear studies showing that higher temporal variation in reproduction renders it most important in determining population growth rate (Beecham 1983, Mitchell et al. 2009). Unlike the results presented here,
Beckmann and Lackey (2008) found that an urban black bear population with higher fecundity and lower survival had a lower population growth rate than a wildland population. However, adult survival in the urban population was suppressed beyond its normal range due to human activities, essentially artificially increasing the spatial variation in the most elastic vital rate.
The mean population growth rates indicate that bear populations are probably stable in the east and may be slightly declining in western populations. This is counter to the general perception of managers that populations are increasing (Garshelis and
Hristienko 2006, Hristienko and McDonald 2007). Out of 11 provinces and 33 states, only two reported population decreases between 1988 and 2001 (Hristienko and McDonald
2007). It may be that the actual growth rates are in the right sides of the credible intervals, at or above one, and there is no real discrepancy between perceptions and reality. Bias in the areas studied could also affect estimates because studies are not spread evenly across bear range or representative of the proportion of bears living in any given habitat.
Moreover, many of the studies are decades old and may be outdated. Alternatively, increasing public sightings and complaints driven by an expanding human population could be masking stability or slow declines in bear populations (Garshelis and Hristienko 2006,
Lambert et al. 2006). Researchers in several areas have indeed found that local black bear 18 populations appear to be overharvested (Kasworm and Thier 1994, Powell et al. 1996,
Brongo et al. 2005, Clark and Eastridge 2006). Finally, it is also possible that movement from populations that are increasing may be subsidizing populations that would otherwise be declining (Hebblewhite et al. 2003). Even in the west, where the mean population growth rate is less than one, 34% of populations were estimated to be growing and could act as sources. Beckmann and Lackey (2008) propose that wildland bears are acting as a source for urban bear populations in Nevada, and bear sanctuaries like Pisgah in the southeast have been established with the intention of providing source populations for surrounding hunted populations (Powell et al. 1996).
Black bears are a charismatic species, and managers and conservationists face conflicting goals of ensuring population persistence and minimizing human-bear conflict.
Achieving both of these goals requires information on population growth. Because growth rates are close to 1, small inaccuracies in vital rate estimates could lead to incorrect conclusions about whether the population of interest is increasing or declining. Due to the apparent spatial variation, borrowing demographic information from other studies, especially from the opposite half of the continent, will introduce bias. However, these results provide probability distributions of vital rates that allow managers to incorporate uncertainty explicitly, perform sensitivity analyses, and target future work at the most important gaps.
General patterns are apparent in black bear life history at a broad scale, and despite black bears’ slow life history, their fecundity appears to be critical in determining population status. Vital rate variation among populations easily straddles the boundary between persistence and decline. Discrepancies between these data on black bears and our perceptions of population trend raise a red flag. Other data sources, including traditional mark-recapture and radio-telemetry, non-invasive DNA mark-recapture, and harvest 19 information, can help assure us that our indices of population status are accurate.
Moreover, the tradeoff between reproduction and adult survival deserves further exploration to determine the mechanism and implications for population persistence.
Research examining the costs of reproduction on survival may help elucidate physiological tradeoffs, and further work clarifying compensatory responses of harvested populations may reveal the role of increasing adult mortality in the relationship. This would allow managers to more accurately predict the effects of harvest and protected areas on populations.
20
Table 2.1. Suite of models used in the meta-analysis to estimate black bear vital rates.
Model Survival and Primipartiy Fecundity
Non-hierarchical s ~ A(, 2 ),B(, 2 ) s ~ LN(, 2 ) i i i i i 2 2 2 2 2 2 i SE i i SE i
Halves or 2 2 2 sij ~ A( j , ij ),B( j , ij ) sij ~ LN( j , ij ) 2 2 2 2 2 2 Divisions or ij j SE ij ij j SE ij ~ (a,b) ~ N(, 2 ) Provinces j j a a b a b 2 (a b) 2 (a b 1)
Divisions – Halves 2 2 2 sijm ~ A( jm , ijm ),B( jm , ijm ) sijm ~ LN(mj , ijm ) 2 2 2 2 2 2 or ijm jm SE ijm ijm jm SE ijm
~ (A( , 2 ),B( , 2 )) ~ N( , 2 ) Provinces – Halves jm m m m m jm m m 2 m ~ (a,b) m ~ N(, ) a a b a b 2 (a b) 2 (a b 1) where , N and LN refer to the beta, normal, and lognormal distributions, respectively, and
x x 2 A(x, y) x 1 y
x x 2 B(x, y) (1 x) 1 y are the shape parameters of the beta distribution with mean x and variance y.
21
Table 2.2. Parameter definitions for hierarchical models of vital rates presented in Table 2.1. Variable Meaning Vital rate estimate for the ith study si Vital rate estimate for the ith study in the jth province, division, or half sij Vital rate estimate for the ith study in the jth province or division in the sijm mth half Mean vital rate value for the jth province, division, or half j Mean vital rate value for the jth province or division in the mth half jm Mean vital rate value for the mth half m Overall mean vital rate value 2 Variance among studies i 2 Variance among study estimates within the jth province, division, or half ij 2 Variance among populations within the jth province, division, or half j 2 Variance among study estimates within the jth province or division in the ijm mth half 2 Variance among populations within the jth province or division in the mth jm half 2 Variance among provinces or divisions within the mth half m 2 Variance among studies, provinces, divisions, or halves Standard error estimate for the ith study SE i Standard error estimate for the ith study in the jth province, division, or SE ij half Standard error estimate for the ith study in the jth province or division in SE ijm the mth half
22
Table 2.3. Demographic studies of black bears used in the meta-analysis.
Survival Yearling Survival Subadult Survival Adult Survival Fecundity at Age Primiparity Hunted Ecoregion Province Study Cub Location Abler 1985 a 0.68 Y GA, Okefenokee Swamp 232 Alt 1980, 1981, 1989 b 0.84 0.74 3.20 Y PA, northeastern 212 Anderson 1997 c 0.50 0.93 N LA, Tensas River Basin 234 Bales et al 2005 0.74 0.90 0.58 N OK, Ouachita Mountains M231 Beausoleil 1999 c 0.57 0.57 N LA, Tensas River Basin 234 Beck 1991 d 0.56 Y CO M331 Beecham 1980 5.00 Y ID, west central (Lowell) M332 Benson and Chamberlain 0.99 N LA, Tensas River Basin, source 234 2007 Beringer et al 1998 0.53 0.82 N NC, Harmon Den Bear Sanctuary M221 Bertram and Vivion 2002 0.45 0.66 Y AK, Yukon Flats 139 Brandenburg 1996 c 0.71 N NC, Camp Lejeune 232 Brongo et al 2005 0.72 0.53 N NC, Pisgah Bear Sanctuary M221 Cardoza, pers comm 0.87 Y MA, Connecticut Valley M212 Carney 1985 b 0.70 0.93 0.50 4.00 N VA, Shenandoah National Park M221 AR, White River National Wildlife Clark and Eastridge 2006 0.41 0.94 N 234 Refuge Clark and Smith 1994 0.40 0.83 Y AR, Ozark Mountains M222 Clark and Smith 1994 0.65 0.95 Y AR, Ouachita Mountains M231 Costello et al 2001 0.55 0.97 0.89 0.90 0.43 5.45 Y NM, Gila National Forest M313 Costello et al 2001 0.55 0.75 0.86 0.92 0.55 5.56 Y NM, near Eagle Nest and Ute Park M331 Cunningham and Ballard 0.38 0.94 Y AZ, central unburned 313 2004
23
e
Survival Yearling Survival Subadult Survival Adult Survival Fecundity at Age Primiparity Hunted Ecoregion Provinc Study Cub Location Cunningham and Ballard 0.01 0.96 Y AZ, central burned 313 2004 Czetwertynski et al 2007 0.66 6.00 N Alberta, Cold Lake 132 Czetwertynski et al 2007 0.83 5.00 Y Alberta, Cold Lake 132 Diefenbach and Alt 1998 0.59 Y PA M221 Eiler et al 1989 0.62 0.55 4.60 N TN, Great Smoky Mountains M221 Elowe and Dodge 1989 0.59 0.66 3.70 Y MA, Western M212 Folta 1998 c 0.97 Y NC, Dare County Peninsula 232 Fuller 1993 d 0.53 Y MA M212 Fuller 1993 d 0.63 Y MA M212 Garrison et al 2007 0.46 0.57 3.25 N FL, Ocala National Forest 232 Garshelis et al 1988 d 0.85 Y MN 212 Garshelis et al 2005 0.67 N MN, Voyageurs National Park 212 Garshelis et al 2005 0.83 0.63 Y MN, Chippewa National Forest 212 Garshelis et al 2005 0.75 Y MN, Camp Ripley Military Reserve 222 Graber 1981 b 0.40 4.20 N CA, Yosemite National Park M261 Hamilton 1978 a 0.84 Y NC, southeastern coast 232 Hammond 2002 0.26 0.87 5.33 Y VT, Stratton Mountain M212 Hebblewhite et al 2003 0.64 0.67 0.77 0.84 0.47 N Alberta, Banff National Park M333 Hellgren 1988 c 0.72 0.78 0.76 N VA, Great Dismal Swamp 232 Hellgren and Vaughn 1989 0.87 0.57 4.00 N VA, Great Dismal Swamp 232 Hersey and Bunnell 2006 0.81 Y UT M331 Jolicoeur et al 2006 0.71 0.85 0.47 6.00 Y Quebec, La Verendrye 212 Jolicoeur et al 2006 0.96 0.58 5.33 Y Quebec, Pontiac 212
24
Survival Yearling Survival Subadult Survival Adult Survival Fecundity at Age Primiparity Hunted Ecoregion Province Study Cub Location Jonkel and Cowan 1971 0.86 0.38 0.48 0.86 0.28 6.40 Y MT, North of Whitefish M333 Kasbohm et al 1996 0.73 0.90 0.66 3.89 N VA, Shenandoah National Park M221 Kasworm and Thier 1994 0.79 0.27 6.00 Y MT, northwest M333 Kemp 1972 0.73 0.63 0.63 0.88 N Alberta, Cold Lake 132 Klenzendorf 2002 0.81 0.81 Y VA M221 Koehler and Pierce 2005 0.92 Y WA, Olympic M242 Koehler and Pierce 2005 0.93 Y WA, Snoqualmie M242 Koehler and Pierce 2005 0.95 Y WA, Okanogan M333 LeCount 1982 0.48 0.98 Y AZ, central burned M313 LeCount 1987 0.52 Y AZ, central M313 Lee and Vaughan 2005 0.87 0.87 Y VA, along border with WV M221 Lombardo 1993 c 0.53 0.53 0.69 N NC, Camp Lejeune 232 Maddrey 1995 c 0.64 0.64 Y NC, Neuse-Pamlico Peninsula 232 Martorello 1998 c 0.90 Y NC, Neuse-Pamlico Peninsula 232 Massopust et al 1984 d 0.94 Y WI 212 McConnell et al. 1997 0.72 0.94 3.00 N NJ 221 McDonald and Fuller 2001, 0.74 Y MA, Western M212 2005 McLaughlin 1998 0.79 0.78 0.84 0.96 0.58 4.91 Y ME, Stacyville 212 McLaughlin 1998 0.65 0.76 0.83 0.84 0.61 5.10 Y ME, Spectacle Pond 212 McLaughlin 1998 0.59 0.71 0.65 0.85 0.69 4.47 Y ME, Bradford M212 McLean and Pelton 1994 0.55 0.88 0.86 0.79 0.50 N NC, Great Smoky Mountain NP M221 Miller 1994 0.58 0.46 5.92 Y AK, Susitna River M135 Black Bear in NJ 2004 0.70 N NJ 221
25
Survival Yearling Survival Subadult Survival Adult Survival Fecundity at Age Primiparity Hunted Ecoregion Province Study Cub Location Ontario, Chapleau Crown Game Obbard and Howe 2008 0.46 0.76 0.76 0.87 7.81 N 132 Reserve Ontario, outside Chapleau Crown Obbard and Howe 2008 0.44 0.86 0.77 6.70 Y 132 Game Reserve Reynolds and Beecham 1980, 0.39 4.78 Y ID, west central (Council) M332 Beecham 1980 Rogers 1987 0.75 0.56 6.29 Y MN, Superior National Forest 212 Roof and Wooding 1996 c 0.99 N FL, Lake County 232 Ryan 1997 0.70 0.93 0.69 2.83 Y VA, southwest Virginia M221 Sargeant and Ruff 2001 0.71 N Alberta, Cold Lake 132 Schwartz and Franzmann 0.74 0.81 0.93 0.89 0.52 5.80 Y AK, Kenai Peninsula, 1947 burn 135 1991 Schwartz and Franzmann 0.91 0.73 0.66 0.85 0.56 4.57 Y AK, Kenai Peninsula, 1969 burn 135 1991 AR, White River National Wildlife Smith 1985 a 0.69 0.95 4.00 N 234 Refuge Sorensen and Powell 1998 0.71 0.79 0.75 N NC, Pisgah Bear Sanctuary M221 Ternent and Sittler 2007 0.62 3.53 Y PA, northcentral M221 Timmins 2008 0.74 0.87 Y NH, westcentral M212 Trauba 1996 0.60 N WI, Stockton Island 212 Visser, unpublished data b 0.59 0.55 4.60 Y MI, Drummond Island 212 Warburton 1993 c Y NC, Coastal 232 Weaver 1999 0.78 0.70 0.95 N LA, Tensas River Basin 234 White 1996 c 0.95 N AR, Mississippi Alluvial Valley 234 Wooding and Hardisky 1994 0.69 0.89 Y FL, Osceola National Forest 232
26
Survival Yearling Survival Subadult Survival Adult Survival Fecundity at Age Primiparity Hunted Ecoregion Province Study Cub Location Yodzis and Kolenosky 1986, 0.53 0.76 0.87 0.84 0.46 6.17 Y Ontario, Eastcentral 212 Kolenosky 1990 a) Table 3. Hellgren and Vaughan 1989. b) Table 2. Garshelis 1994. c) Table 2. Freedman et al 2003. d) Table 4.7. Hammond 2002.
27
Table 2.4. Hierarchical structure of black bear study locations. Division Province No. Studies East 210 Warm Continental 212 Laurentian Mixed Forest 13 Adirondack–New England Mixed Forest–Coniferous Forest–Alpine M210 M212 8 Meadow 220 Hot Continental 221 Eastern Broadleaf Forest (Oceanic) 2 222 Eastern Broadleaf Forest (Continental) 1 M220 M221 Central Appalachian Broadleaf Forest–Coniferous Forest–Meadow 12 M222 Ozark Broadleaf Forest–Meadow 1 230 Subtropical 232 Outer Coastal Plain Mixed Forest 13 234 Lower Mississippi Riverine Forest 7 M230 M231 Ouchita Mixed Forest–Meadow 2 West 130 Subarctic 132 Boreal Forests 6 135 Coastal Trough Humid Tayga 2 139 Upper Yukon Tayga 1 M135 M135 Alaska Range Humid Tayga–Tundra–Meadow 1 240 Marine M242 Cascade Mixed Forest–Coniferous Forest–Alpine Meadow 2 260 Mediterranean M261 California Coastal Chaparral Forest and Shrub 1 310 Tropical/ 313 Colorado Plateau Semidesert 2 Subtropical Steppe Arizona-New Mexico Mountains Semidesert–Open Woodland– M313 3 M310 Coniferous Forest–Alpine Meadow Southern Rocky Mountain Steppe–Open Woodland–Coniferous M330 Temperate Steppe M331 3 Forest–Alpine Meadow M332 Middle Rocky Mountain Steppe–Coniferous Forest–Alpine Meadow 2 Northern Rocky Mountain Forest-Steppe–Coniferous Forest–Alpine M333 4 Meadow
28
Table 2.5. Differences in deviance information criterion (ΔDIC) for geographic models of black bear vital rates. Models with the best support are shown in bold; those with substantial support are italicized.
Cub Yearling Subadult Adult Age at
Model Survival Survival Survival Survival Fecundity Primiparity
Null 12.84 0.51 0.00 0.10 12.12 7.64
Halves 1.46 0.00 2.36 0.00 0.00 0.00
Divisions 0.00 2.84 11.12 20.24 6.33 2.07
Provinces 9.60 11.21 17.28 27.69 7.35 1.28
Divisions – Halves 1.94 4.33 14.18 14.79 7.51 4.92
Provinces – Halves 7.89 12.16 19.86 24.33 8.92 3.50
29
Table 2.6. Mean vital rates (95% credible intervals) of black bears in eastern and western
North America.
Vital Rate East West
Cub Survival 0.65 (0.60, 0.70) 0.54 (0.43, 0.65)
Yearling Survival 0.74 (0.65, 0.81) 0.72 (0.57, 0.83)
Subadult Survival 0.77 (0.69, 0.83)
Adult Survival 0.82 (0.77, 0.86) 0.88 (0.83, 0.92)
Fecundity 0.58 (0.54, 0.62) 0.45 (0.36, 0.54)
Age at Primiparity 4.46 (4.02, 4.96) 5.58 (5.07, 6.07)
30
Table 2.7. Sensitivities and elasticities of female black bear vital rates for eastern and western North America and their 95% credible intervals. Yearling Subadult Adult Cub Survival Fecundity Survival Survival Survival Sensitivity 0.17 0.15 0.29 0.66 0.19 (95% CI) (0.15, 0.19) (0.13, 0.17) (0.27, 0.32) (0.62, 0.70) (0.17, 0.22) East Elasticity 0.11 0.11 0.22 0.55 0.11 (95% CI) (0.10, 0.13) (0.10, 0.13) (0.20, 0.25) (0.50, 0.60) (0.10, 0.13) Sensitivity 0.12 0.09 0.25 0.73 0.14 (95% CI) (0.9, 0.15) (0.07, 0.11) (0.20, 0.31) (0.67, 0.79) (0.11, 0.18) West Elasticity 0.07 0.07 0.20 0.67 0.07 (95% CI) (0.05, 0.08) (0.05, 0.08) (0.15, 0.25) (0.59, 0.74) (0.05, 0.08)
31
Figure Legends
Figure 2.1. Locations of black bear demographic studies included in the hierarchical
Bayesian meta-analysis.
Figure 2.2. Mean matrix models for bears in (a) eastern North America and (b) western
North America based on vital rate values in Table 2.4.
Figure 2.3. Mean cub survival values across the range estimated for each ecosystem division in the hierarchical Bayesian meta-analysis.
Figure 2.4. The relationship between mean population growth rate and (a) mean adult survival and (b) mean fecundity for female black bears in eastern and western North
America.
Figure 2.5. Posterior probability distributions of the mean population growth rate and the expected population growth rates of individual populations in (a) eastern and (b) western
North America.
Figure 2.1.
33
a)
[ ]
b)
[ ]
Figure 2.2.
34
0.64
0.63 0.72 0.59
0.69 0.61 0.54 0.64 0.57
Figure 2.3.
35
a) 1.1 East West 1.05
λ 1
0.95
0.9 0.7 0.8 0.9 1 Adult survival b) 1.1 East West 1.05
λ 1
0.95
0.9 0.2 0.4 0.6 0.8 Fecundity Figure 2.4.
36
a) 25 East 20
15 Mean λ Populations λs 10
5
0 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
b) 25
20 West
15 Mean λ 10 Populations λs
5
0 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
λ Figure 2.5.
37
CHAPTER 3
WHAT CAN HARVEST DATA TELL US ABOUT AMERICAN BLACK BEARS?
Abstract
Harvest data provide readily available and relatively cheap information about populations of game species. However, these data are not necessarily representative of standing populations and may have limited applicability in management. We applied a method of harvest data analysis based on the changing sex ratio of the harvest with age to black bear harvest data from 1985-2005 in Montana. We assessed the ability of this method to identify assumption violations and the extent of the resulting bias. One assumption we thought would be violated, due to protection of females with young, is that the relative vulnerability of the sexes does not change with age. Simulations in which vulnerability of females changed at primiparity did not replicate the pattern observed in Montana’s harvest, indicating that adult females with cubs are not as well protected as is generally assumed. Analyses of these harvest data also contradicted the hypothesis, based on meta- analysis of demographic data, that black bears are declining in Montana. Finally, we evaluated, in light of their limitations and biases, whether collection of harvest data are a cost-effective undertaking for Montana Fish, Wildlife, and Parks. Harvest data are cost- effective compared to DNA sampling when the goal is to cover the entire state of Montana, but across smaller areas DNA mark-recapture work would be preferable to continued collection of black bear harvest data.
38
Introduction
Wildlife managers are often charged with managing populations of game species that are rare or secretive, such as many furbearers and carnivores, using very limited resources. Many jurisdictions require hunters to bring harvested individuals through check stations where age and sex data are collected (Rupp et al. 2000), and in many cases, harvest data are the best or only source of information about the status of these populations. A variety of techniques, relying on different assumptions about population and harvest processes, can be used to estimate both harvest rates and population status or vital rates from these harvest data. However, it is surprisingly common for harvest data to be collected and not used or applied to management. For instance, in a survey of management agencies, Rupp and colleagues (2000) found that while almost all jurisdictions collected whitetail deer harvest data, a minority of them used the harvest data for population models. Four respondents stated that harvest data were collected but not actually used in decision-making, and most of the agencies used harvest data to estimate the total harvest but not harvest rate or population size and trend (Rupp et al. 2000). More generally, harvest management is often developed from a patchwork of interests and implemented piecemeal over a sometimes long time frame (Milner-Gulland and Rowcliffe 2007), making application of harvest data in decision-making that much more idiosyncratic. Basing decisions on harvest data may also not be a top priority when managers must incorporate public interests and input as well as budget priorities and constraints.
One reason harvest data are not used more thoroughly may be the limitations of available harvest data analysis methods. Methods with various assumptions and requirements have been used to estimate harvest rate and population status from harvest data, including those that rely on the age and sex structure of the data, like population reconstruction and change in ratio, and those that rely on combinations of surveys and 39
harvest data, like index removal and catch per unit effort (Roseberry and Woolf 1991).
Roseberry and Woolf (1991) reviewed nine methods and reported that half require data in addition to information on the harvested animals, such as harvest effort or a concurrent field study. Managers often lack such auxiliary information. Of those that do not require auxiliary data, several methods use the age structure of the harvest to infer information about survival rates or population trend. However, the composition of the harvest may not be representative of the living population (Litvaitis and Kane 1994) and the relative numbers of different ages may reflect the selectivity or effect of harvest more so than the population trend (Bunnell and Tait 1980; Noyce and Garshelis 1997). Estimates of harvest rate derived from harvest data are also more reliable when a large proportion of the population is removed each year (Harris and Metzgar 1987; Roseberry and Woolf 1991), which is thought not to be the case for many carnivores.
In this paper, we examine the robustness of a combination of the methods presented by Paloheimo and Fraser (1981) and Fraser (1984) for estimating harvest rate of black bears (Ursus americanus) in Montana, where data on sex and age of harvested bears are collected but little information has been gleaned from them before now. Because we also have total numbers of bears harvested, these estimates of harvest rate can then be used to estimate population size. The method we apply avoids some problems of other methods, such as the need for additional data, and explicitly models the differential vulnerability across groups. If one sex is more vulnerable to harvest than the other, the ratio of males to females in sequential harvests of a cohort will change as that cohort ages. Fraser (1984) showed that the inverse of the age at which the sex ratio of the harvest is even will approximate the average harvest rate. This simple estimate works best when the harvest rate is near 0.5 or the differential vulnerability is much less than the harvest rate.
Paloheimo and Fraser (1981) use the same principle, but relax these requirements by using 40
generalized least squares to estimate harvest rate and relative vulnerability using a model of harvest sex ratio at each age. However, their method requires additional information about harvest effort. Tag sales have been relatively constant for the past 20 years (R Mace;
Montana Fish, Wildlife and Parks (MTFWP), unpublished data), and evidence from hunter surveys suggests the harvest effort, measured in hunter days, was consistent for the period for which data are available (1996-2003, Figure 3.1). Therefore, we were able to avoid the approximations of Fraser’s method and relax the data requirements of Paloheimo and
Fraser. Both methods, as well as the approach we present, depend on a number of assumptions: the initial sex ratio is even, the differential vulnerability of the sexes is constant across ages, the harvest rate is constant across time, and the natural mortality rates are equal for both sexes. Harris and Metzgar (1987) found that violations of these assumptions biased estimates of harvest rate more when the harvest rate and/or differential vulnerability were low.
Because we also had estimates of total harvest, we were able to extrapolate population size from the harvest rate estimates. We used simulation studies to address whether the harvest data can indicate when key assumptions are violated, including the assumptions that relative vulnerability of males and females does not change with age, that male and female animals have equal mortality in the absence of harvest, and that harvest rates are constant through time. Given this information, we then examined the hypothesis that adult female black bears experience lower harvest than immature females because it is illegal to harvest a female when she is accompanied by young. Our expectation was that the vulnerability of female black bears in Montana decreases by 50% at primiparity because adult females spend about half their time accompanied by cubs.
We also assessed the hypothesis that black bears are declining in Montana, an unexpected conclusion based on a meta-analysis of demographic studies (Ch 2 of this 41
dissertation). The analysis indicated that, on average, black bears are declining in the western United States, at a rate of ~1-4%/year. This contradicted the general perception of managers that black bears are stable or slowly increasing throughout their range
(Garshelis and Hristienko 2006). The conclusion that populations are declining could result from biases in data available for meta-analysis, but it could also mean that our impressions of growth were incorrect (Garshelis and Hristienko 2006; Lambert et al. 2006). Harvest methods and tag sales have been consistent in Montana for the past 20 years (R Mace,
MTFWP, unpublished data; Figure 3.1). Therefore, if the bear population is declining we would predict either 1) the harvest rate is increasing and the total harvest is stable or 2) the harvest rate is stable and the total harvest is decreasing. After exploring the ability of harvest data to detect trends in harvest rate and population size through time, we used simulations to determine whether we would be likely to detect population declines under constant harvest rate using only total harvest. We then use the results of these simulations and the observed harvest trends to evaluate whether the results of the meta-analysis are supported by Montana’s harvest data.
An additional purpose of this study is to analyze whether the continued collection of harvest data is a cost-effective use of funding for Montana black bears. While harvest data are relatively inexpensive, they do come at a cost, both for aging teeth and the time spent collecting teeth from harvested animals. Recent developments in DNA mark-recapture work using hair samples from barbed wire corrals provide another option. The results of this analysis will help shed light on whether intensive DNA work that covers less geographic range is more cost-effective than collecting harvest data that cover the state but may provide less information.
42
Black Bear Hunting in Montana
In Montana, black bear range is restricted to the mountainous western portion of the state, and hunting is permitted in all 5 MTFWP regions where black bears occur. Bears are hunted in two seasons: in the spring from April 15 through mid-May to mid-June and in the fall from September 15 through late November. Black bear licenses for residents cost
$15-19 and permit the take of 1 black bear per calendar year. Hunting bears using bait or dogs has been illegal in Montana since the first half of the twentieth century. It is also illegal to harvest cubs (black bears under 1 year old) and mothers with young. Because family break-up occurs during the summer, a female with yearlings will be illegal to harvest in the spring but legal to harvest in the fall of the same year. In addition to direct protection when accompanied by cubs, females may tend to enter hibernation earlier and remain in hibernation later than males, especially when pregnant and/or nursing (Beecham et al. 1983). They may be in dens by mid-October and remain until late May (Jonkel and
Cowan, 1971, Beecham et al. 1983), missing most of both hunting seasons.
Methods
Estimating Harvest Rate
Given an average harvest rate of k and a difference in vulnerability 2v, such that the harvest rate of males is k+v and the harvest rate of females is k-v, then the ratio of males in the harvest, Hm, to females in the harvest, Hf, at age i can be written as
i1 i1 H m,i M1(1 (k v)) sm (k v) i1 i1 , H f ,i F1(1 (k v)) s f (k v) where M1 and F1 are the numbers of males and females, respectively, in the cohort when it enters the harvestable population and sm and sf are the natural survival rates of males and
43
females. This is essentially the same equation used by Paloheimo and Fraser (1981), replacing their vulnerabilities and hunter efforts with constant harvest rates.
Two methods can be used to estimate k and v based on this equation. We took the natural logarithm of both sides and used generalized least squares estimation to find k and v, following Paloheimo and Fraser (1981). Alternatively, we used information from the first harvest and the harvest in which the male:female ratio is 1:1 to create a system of 2 equations and solved them for the 2 variables, which was essentially the approach used by
Fraser (1984). In the first harvest,
H M (k v) m,1 1 , H f ,1 F1(k v) and at age y, the male and female harvests are equal, yielding
y1 y1 M1(1 (k v)) sm (k v) 1 y1 y1 . F1(1 (k v)) s f (k v)
We found that both methods produced similar results, and we present results from the latter method.
We estimated y, the harvest in which the sex ratio is 1:1, using black bear harvest data collected in Montana from 1985 to 2005. We assumed low natural mortality over the winter (Hebblewhite et al. 2003) and combined the fall harvest with the following spring harvest to calculate the total annual harvest. To find y, we first summed each age group over the entire 20 year harvest dataset. We then performed a regression of the proportion of females in the harvest at each age. We weighted the regression by total bears harvested at each age to account for smaller sample sizes at older ages. We solved the regression equation for 50% females in the harvest to estimate y.
One assumption made when using this method to estimate harvest rate is that the relative vulnerability of the sexes does not change as a cohort ages. In Montana, however,
44
the relative vulnerability of female black bears probably decreases at primiparity, especially during the spring season, because mothers accompanied by cubs are illegal to harvest. To assess biases due to varying relative vulnerability, we simulated populations with adult females harvested at half the rate of subadult females. We simulated 2500 replicate populations for 20 years using a 60×60, sex and age-based matrix model:
[ ] where si is the survival at each stage; cub (c), yearling (y), subadult (s), and adult (a); and f is the fecundity (female cubs per female per year). This model relies on the assumptions that cubs are born in a 1:1 sex ratio, which is likely true, and that non-harvest survival is the same for males and females, which we explored directly.
We parameterized the model with survival rates and variances from the western half of North America (Chapter 2 of this dissertation). Harvest rate, fecundity, and their variances, as well as age at primiparity, were based on data from Montana. Each year a harvest rate was selected from a beta distribution with mean equal to the initial estimate from the harvest data and variance based on the fluctuations seen in the total harvest, and adult female bears were harvested at half the rate of subadults. Then vital rates were
45
selected from beta distributions for survival and a lognormal distribution for fecundity and the population was multiplied by the matrix model. We compared estimated rates of harvest with the actual total female harvest rate and compared the pattern of proportion females in the harvest with the pattern observed in Montana.
Application of this method also assumes that the natural mortality is the same for both sexes. Male black bears may have lower natural survival than female black bears, especially as subadults (Hellgren and Vaughan 1989; Koehler and Pierce 2005). However, some studies have failed to find a significant difference between the survival of males and females (Kasworm and Thier 1994; Wooding and Hardisky 1994). Results are also confounded because harvest mortality is included in most survival estimates (e.g. Hellgren and Vaughan 1989, Kasworm and Thier 1994, Wooding and Hardisky 1994, Koehler and
Pierce 2005). We assessed the potential bias in differences in natural mortality by calculating male and female harvest rates using the Montana estimates of y and varying
s the ratio of male survival to female survival, m , from 0.9 to 1. We were specifically s f interested in the case where male survival is lower than female survival, which is the most likely situation for black bears, and we quantified the bias separately for male and female harvest rates. We also simulated populations as above, with male survival equal to 96% of female survival, and assessed changes in the harvest structure.
Another assumption that many harvest data sets may violate is that harvest remains constant across the years analyzed. Two types of violations, stochasticity or trends in survival and harvest rates, can affect results. If there are no temporal trends, combining several years of harvest information should ameliorate the annual variability and increase the precision of estimates. To assess how the length of harvest dataset affects the precision of estimates of harvest rate, we conducted stochastic simulations of harvested populations
46
using the model described above. We estimated harvest rate from the harvest age and sex structure beginning in year one. For each consecutive year, we estimated harvest rate using the sums of all bears harvested to date in each age and sex class.
When harvest rates changed through time, Harris and Metzgar (1987) pointed out that annual harvest estimates lagged several years behind. To assess possible trends in
Montana’s harvest rate, we estimated annual harvest rates using the age and sex structure of each year’s harvest. We also estimated harvest rates using non-overlapping 5 year sets to increase precision of estimates. We then conducted simulations with a decreasing trend in the harvest over the 20 year timeline and assessed the resulting age and sex structure and the length of lag.
Using Harvest to Detect Declines
Beston (Ch 2 this dissertation) conducted a Bayesian meta-analysis of vital rates for black bears in North America. The hierarchical analysis grouped studies geographically and weighted them using the uncertainty for each study, with more weight on studies with greater precision. Vital rates varied most between eastern and western North America.
The posterior probability distributions for each rate in each geographic grouping were then used to populate a matrix population model to estimate the probability distribution of population growth rate.
Sampling population growth rate from the posterior distribution for western North
America, we simulated an unstructured stochastic population beginning with 10000, 30000, and 50000 bears. This covers the likely range for Montana’s actual black bear population size based on the estimated harvest rates (see Results) as well as the best guess of managers as of 2001, which was 20-30000 (Hristienko and McDonald 2007). We harvested it for 50 years at 4% with standard deviation of 0.4%. For each simulation, we fit a linear regression to the total number of bears harvested each year, starting with just 3 years of 47
harvests and adding consecutive years through the end of the dataset. Each year, we checked for a statistically significant decline in harvest numbers by assessing whether the coefficient of year was less than 0 at p = 0.05. This was a worst case scenario because the spatial variation incorporated in population growth rate probably overestimated the temporal variation in any one population (because management and habitat varied widely among populations). We also performed a simulation with a deterministic population subjected to a stochastic harvest as a best case scenario.
Because the length of time to detection also depends on the rate of decline, we repeated the process with deterministic population growth and stochastic harvest and varied the population growth rate. We estimated the length of time it would take to reach
90% power in detecting a decline in the harvest for values of lambda between 0.95 and 1.
Results
Estimating Harvest Rate
The R2 of the regression of proportion females in Montana’s harvest from 1985 to
2005 against age was 0.94 and the estimated value of y, the age at which males and females are equally represented in the harvest, was 14.2 (Figure 3.2). The high R2 value implies that the basic tenets of this model are borne out by Montana’s data. The estimated annual harvest rates for male and female black bears in Montana were 10.6% and 4.3%, respectively, given a starting sex ratio of 1 and equal natural mortality rates for males and females.
Simulations where adult females were harvested at half the rate of subadult females produced proportions of females in the harvest that were not consistent with the observed annual proportions of females in Montana’s harvest (Figure 3.3a). At the age when vulnerability changes, a break is noticeable in both the proportion of females harvested and
48
in the number of females harvested at each age (Figure 3.3). When considering only the spring harvest, there is a slight drop in female vulnerability at 5-6 years of age (Figure 3.3 c), but females have generally reduced vulnerability in the spring through most of their lives and there is no dramatic change as produced in the simulations.
As the ratio of male survival to female survival decreased, the estimate of harvest rate decreased (Figure 3.4). An estimate assuming the ratio is 1 overestimated harvest rate if male survival was less than female survival. The bias was greater for male harvest rate than female harvest rate. If the natural survival was heavily biased towards females, the estimated harvest rate became negative to compensate for the changing sex ratio. This put a lower limit on the possible survival ratios. The sex and age structure of the harvest when male survival was 96% of female survival was not distinguishable from a scenario with a greater harvest rate and equal adult survival (Figure 3.5).
An increase in the number of years incorporated in the estimation yielded more precise estimates of the harvest rate. Given the levels of variance seen in black bear vital rates across the western half of their range, much improvement was gained in the first five years of data gathering (Figure 3.6). The variance in the estimate of harvest rate leveled out after about 15 years. Populations experiencing lower levels of variance would require fewer years to gain similar precision in harvest rate estimates.
Annual estimates of harvest rate and estimates using 5 year periods suggested a declining trend in Montana’s harvest rate with some autocorrelation evident in the annual estimates (Figure 3.7). Simulations indicated that estimates of harvest lag as much as 10 years behind actual changes in rates (Figure 3.8a). The age structure of the harvest, however, did not change over time (Figure 3.8b). Estimates of population size calculated from 5 year harvest rates and the reported total number of bears harvested each year depict a population that has risen from approximately 18000 bears in 1985 to between 49
30000 and 40000 bears in 2005 (Figure 3.9), for an average annual population growth rate of 1.02.
Using Harvest to Detect Declines
Given the estimated harvest rate and variation in Montana and the population growth rate and variance for western North America, a decline in the population was observed in the harvest in 70-82% of simulations after 15 years of harvest data collection
(Figure 3.10). Larger population sizes produced larger harvests and greater power to detect decline. Under ideal conditions, with no stochasticity in population growth itself, the decline was identified within 15 years 99% of the time.
As the population growth rate approached 1, the number of years required to reach
90% power in detecting declines using only the harvest numbers increased dramatically
(Figure 3.11). Populations decreasing at 1-5% a year were reliably identified with 10-20 years of harvest data; annual decreases of less than 1% a year took considerably longer to detect. After 5 years, only 20% of the most rapidly declining populations, λ=0.95, had statistically significant declines in the harvest numbers.
Discussion
Though estimation of harvest rate from the sex and age of harvested individuals has several limitations, the combination method we applied can produce usable harvest rate estimates and information on population status or trend that can be applied in decision- making. The confidence in these estimates is higher given more years of harvest data and/or adequately low stochasticity. Our results supported the hypothesis that at least some assumption violations of Fraser’s (1984) and Paloheimo and Fraser’s (1981) methods can be identified by the harvest data themselves. However, the hypotheses that adult females in Montana experience lower relative vulnerability than immature females due to
50
the protection of mothers with cubs and that Montana’s black bear population is declining were not supported.
Examination of harvest data can reveal whether some of the assumptions needed for this method are violated. If the relative vulnerability of the sexes changes with age, a discontinuity will be present at the transition age. We were unable to identify whether the assumption of equal natural mortality for both sexes was violated using harvest data.
However, estimates based on this assumption will be conservative when male survival is less than female survival, which is likely true in a variety of mammalian and avian species
(Promislow 1992, Promislow et al. 1992), because they will overestimate harvest rate.
Changing harvest rates will be apparent if annual sex and age structures are used to estimate yearly harvest rates, although the estimates will lag behind the actual value of harvest rate until it stabilizes.
It appeared unlikely that the vulnerability of female black bears to harvest in
Montana changes dramatically at the presumed age of primiparity, and this contradicts our prediction that protection of females accompanied by cubs reduces the vulnerability of adult females (McLoughlin et al. 2005). Estimates based on reproductive tracts suggest adult females spend half their time accompanied by cubs (R Mace, MTFWP, unpublished data), which implies that vulnerability of adults should be half that of subadults because females with young are illegal to take. A greater proportion of young female bears could be producing their own cubs or accompanying their mothers or siblings than we expect, giving them as much protection as adults. Alternatively, hunters could be taking females with cubs more often than previously assumed. If cubs are in trees or hiding as a hunter approaches, it may not be obvious to the hunter that the mother has young. Because bears are not baited or hunted with dogs, hunters may have less opportunity to observe young nearby. Hristienko et al (2004) estimated only a 2% orphaning rate for black bear cubs 51
during spring hunts in Manitoba. If we assume that females in Montana are harvested at about 4% and half of these are accompanied by cubs, we produce a similar orphaning rate.
Harvest data show annual autocorrelation in harvest rate as well as a recent declining trend in the harvest rate in Montana, and this trend remained when 5 year periods were pooled to increase precision. Autocorrelation can be induced even by weak responses by managers to change quotas each year and can make populations more variable and susceptible to decline (Fryxell et al. 2010). Though the harvest rate estimates in simulations lagged about ten years behind the actual harvest rate, the declining trend itself became obvious after only a few years. While harvest data may not be able to reveal the actual harvest rate as it changes, it can indicate a changing harvest rate fairly rapidly.
Because Montana’s harvest rate leveled out from 1997 onward, more recent estimates are probably more accurate.
In theory, the method we used can be applied to any game species with differential selectivity in the harvest for which we can collect sex and age data. Male-biased harvesting occurs in mammals with multiannual parental care, such as bears and elephants, when females with young are protected and when adult males are targeted as trophies
(McLoughlin et al. 2005). It is also intentionally applied in some ungulate systems because females are considered the limiting component of the population (Ginsberg and Milner-
Gulland 1994). In reality, harvests need to be large enough overwhelm demographic stochasticity and the nature and degree of assumption violations need to be explored.
While our method can be applied in principle to many game species, other methods may be more appropriate in some situations. For example, with species that are sufficiently numerous and conspicuous, like many ungulates, coupling field studies and harvest data in approaches like statistical catch-at-age analysis provides more information and requires fewer years to achieve reasonable accuracy (Gove et al. 2002). 52
Even when the age and sex structure are unavailable, the total number of individuals harvested may reflect changes in population size. However, identification of declines in harvest numbers lagged well behind changes in simulated population size, even when the population was declining relatively rapidly. Annual changes in environmental conditions affect the vulnerability of individuals to hunters, and the ability to detect changes in population size will depend on how variable that vulnerability is and how consistent harvest effort and methods are. Hristienko and McDonald (2007) suggested that occasional overharvest of black bears will not be a problem because managers will respond rapidly to reduce harvest in subsequent years. The time lags apparent in both the decline of harvest numbers and the estimates of harvest rate indicate that many managers cannot respond rapidly because they cannot discover the problem rapidly. It is encouraging that with more than 20 years of harvest data for Montana, we do not have evidence of a negative trend, let alone a statistically significant one. Indeed, annual estimates of harvest show that harvest rates have declined while the total harvest has been fairly stable. Because the same number of bears harvested represents a smaller proportion of the population (the harvest rate), these results suggest the population has increased.
On its face, this contradicts our hypothesis, based on the meta-analysis of demography (Ch 2 of this dissertation), that black bears are decreasing in Montana. The average population growth rate based on the demographic work was less than 1, but the harvest analyses indicate that, if anything, the population is increasing. The demographic work could be biased, or there may be other processes occurring for which we have not accounted. While demographic studies are often considered the gold standard, they are more limited in space and time, and therefore may not be representative of the true population status across large geographic areas. Demographic studies included in the meta-analysis had a median sample size of about 30 bear-years (Chapter 2 of this 53
dissertation). This corresponds to following 10 individuals for 3 years, and because adult female survival rates are close to 1 (0.88 in the west, Chapter 2 of of this dissertation), researchers might only observe 3 or 4 deaths over the course of such a study. These small sample sizes reduce precision of the resulting estimates and make added information from harvests even more valuable. Harvest data can provide another means of estimating population trends at large scales to check against intensive demographic studies at smaller scales.
Another possibility is that spatial structuring and source-sink dynamics allow growing populations to support those that would otherwise decline. Glacier National Park provides protection from harvest, and black bears living deep in the Bob Marshall and other
Wilderness Areas may be essentially inaccessible to most hunters. These regions could serve as source habitats that allow bears to persist despite low population growth rates elsewhere. It is unclear whether typical dispersal rates seen for black bears or the 34% of populations believed to be growing (Chapter 2 of this dissertation) would be enough to support a viable population.
Management Implications
Recent work on accurately estimating harvest rates in terrestrial systems is an encouraging trend for more effective management of game species. While harvest data are relatively easy and inexpensive to collect, their limitations may render even this small investment unprofitable. For bears, advances in noninvasive DNA sampling may render it more cost-effective to invest in these DNA mark-recapture efforts rather than collection and aging of teeth of harvested individuals. Evaluation of the trade-off requires an assessment of how much each type of data collection costs as well as their abilities and limitations.
The harvest data analysis methods we employed can give useful estimates of black bear harvest rates. However, the need for many years of data for sufficient precision and 54
the lag behind changing harvest rates limit their applicability. Alternatively, MTFWP can use baited barbed wire corrals to collect hair DNA samples during the summer and compare hair from bears harvested in the same area in a mark-recapture design. For the same cost as collecting harvest data per year, this DNA sampling could be completed in, at most, 1 bear management unit, taking at least 25 years to cover the entire state. One rotation through every bear management unit can be used to estimate harvest rates, but two cycles would be required to assess population trend. If the monitoring goal was truly to cover the entire state, harvest data would have the advantage of estimating harvest rate and population trend over this wide area more quickly than DNA. If the goal is to have the greatest confidence that decision-making reflects the current status of the population, an investment in a more widespread demographic study within the state would be ideal.
55
Figure Legends
Figure 3.1. Black bear hunter days in Montana by season from 1996 to 2003 based on hunter surveys.
Figure 3.2. Proportion of the Montana black bear harvest, 1985-2005, at each age that is composed of females.
Figure 3.3. The (a) proportion of females in the harvest and the (b) total harvest by age in a simulated population in which female vulnerability decreases by 50% at the age of primiparity, and the (c) actual proportion of females in Montana’s spring and fall harvests,
1985-2005.
Figure 3.4. Estimated harvest rates for male and female black bears in Montana as a function of the assumed ratio of natural male survival to natural female survival.
Figure 3.5. The (a) proportion of females in the harvest and the (b) total number harvested at each age in a simulated population in which male black bear non-harvest mortality is
96% of female non-harvest mortality.
Figure 3.6. Estimates of harvest rate and associated confidence intervals for a simulated black bear population as more years of data are combined in the estimation.
Figure 3.7. Annual and 5 pooled year estimates of female black bear harvest rate in
Montana, 1985-2005, assuming an initial sex ratio of 1:1 and equal male and female non- harvest mortality rates.
Figure 3.8. Estimates of (a) annual harvest rate and the (b) age structure of the harvest through time as the harvest rate in a simulated population declines.
Figure 3.9. Estimates of black bear population size in Montana, 1985-2005, calculated from total reported black bear harvest divided by estimated harvest rate.
56
Figure 3.10. Proportion of simulated populations in which a statistically significant negative trend was identified in the harvest data given stochastic or deterministic population growth.
Figure 3.11. Number of years of harvest data required to identify statistically significant declines in 90% of simulated populations given the deterministic population growth rate.
57
70,000
60,000
50,000
40,000
30,000 Fall
Hunter Days Hunter 20,000 Spring
10,000
0 1996 1997 1998 1999 2000 2001 2002 2003 Year
Figure 3.1
58
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
Proportion Females in the Harvest the in Females Proportion 0 0 5 10 15 20 25 Age of Harvested Bears
Figure 3.2.
59
0.8 a) 0.7 0.6
0.5 0.4
Harvest 0.3 0.2
Proportion Females in in Females Proportion 0.1 0 0 10 20 30 Age b) 4000
3500
3000 2500 2000 Female 1500 Male
1000 Number Harvested Number 500 0 0 5 10 15 20 25 30 Age c)
0.8 0.7 0.6 0.5 0.4 Fall 0.3 Spring 0.2 0.1
Proportion Females in Harvest in Females Proportion 0 0 5 10 15 20 25 Age
Figure 3.3.
60
0.12
0.1
0.08
0.06 Male
0.04 Female Harvest Rate Harvest
0.02
0 0.925 0.95 0.975 1 Male/Female Survival
Figure 3.4.
61
0.9 a) 0.8 0.7
0.6 0.5 0.4 Harvest 0.3 0.2
Proportion Females in in Females Proportion 0.1 0 0 10 20 30 Age
4500 b) 4000 3500 3000 2500 2000 Female 1500 Male 1000 Number Harvested Number 500 0 0 10 20 30 Age
Figure 3.5.
62
0.14
0.12
0.1
0.08
Males 0.06 Females
0.04 Estimated Harvest Rate Harvest Estimated 0.02
0 0 5 10 15 20 Years of Data Included
Figure 3.6.
63
0.09 0.08 0.07 0.06 0.05
Rate 0.04 Annual 0.03 5 year 0.02
0.01 Estimated Female Harvest Female Estimated 0 1985 1990 1995 2000 2005 Year
Figure 3.7.
64
a) 0.14
0.12 Male Estimate 0.1 Male Simulated 0.08 Rate 0.06 Female Estimate
0.04 Female Simulated Harvest Rate Harvest 0.02 Rate 0 0 5 10 15 20 Year b) 100%
90%
80% Age Class 70% 1-5 Years 60% 6 to 10 50% 11 to 15 40% 16 to 20 30%
21 to 25 Each Age GroupAge Each
20% 26 to 30
Proportion Harvest of Harvest Proportion 10% 0% 1 4 7 10 13 16 19 Year
Figure 3.8.
65
60000
50000
40000
30000
20000
Population Size Size Population 10000 (Harvest/Harvest Rate) (Harvest/Harvest 0 1985 1990 1995 2000 2005 Year
Figure 3.9.
66
1 Initial Population Sizes 0.8
(Stochastic Simulations)
0.6 10000
0.4 30000 Declines
0.2 50000 Proportion of Harvest of Proportion Series with Significant Significant with Series 0 Deterministic 0 5 10 15 20 25 30 Population Growth Years of Data
Figure 3.10.
67
70
60
50
40
30
20
10
of Detecting Decline (Years) Decline Detecting of 0 Time to Achieve 90% Probability Probability 90% Achieve to Time 0.95 0.96 0.97 0.98 0.99 1 Population growth rate (λ)
Figure 3.11.
68
CHAPTER 4
SPATIAL HETEROGENEITY AND POPULATION VIABILITY OF AMERICAN BLACK
BEARS
Abstract
Variation has important consequences for population dynamics, but it is often difficult to assess how spatial heterogeneity affects population status. For American black bears, recent demographic meta-analysis indicated that the average population growth rate of studied bear populations in the western US is less than 1. However, evidence from harvest data in Montana suggests that the population is stable or increasing. We use discrete and continuous models of spatial heterogeneity to explore whether movement of bears among habitat types can explain the apparent discrepancy between the demographic and harvest data. The discrete space model, in which subadult bears disperse among a source and sink habitat, revealed that for most combinations of source and sink, about 20% of the habitat needed to be source to sustain the entire population in the worst case scenario in which all subadults disperse. When fewer subadults disperse, less than 10% source habitat is sufficient. In the continuous space models, movement rates of 20.6% or less resulted in a stable or increasing total population. Both models reveal that population growth rates increase with decreasing movement rates, due to retention of bears in good quality habitats.
These results are reasonable expectations for black bears and could explain why the average population growth rate is less than 1 while the actual population is stable or increasing. Even in a closed population, movement can create a discrepancy between the average growth rate and the actual total growth rate. This type of modeling exercise could be useful for other large or rare animals, for which obtaining sufficient sample sizes to estimate vital rates may necessitate pooling across spatial variation. 69
Introduction
Demographic studies of vital rates are often used to estimate asymptotic population growth rate and its variability to understand how the growth and reproduction of individuals translate into long-term population dynamics (Wisdom et al. 2000, Waples et al.
2010). Demographic studies can improve the accuracy of population growth estimates and allow researchers to analyze the effects of individual vital rates on overall population trajectory (Caswell and Fujiwara 2004, Sandercock 2006). Variation in vital rates has important effects on realized population growth, and much work has been devoted to the effect of temporal variation. In general, the more variable the population growth rate is from one year to the next, the lower the realized population growth rate will be relative to a deterministic population (Boyce et al. 2006). Fluctuations in vital rates themselves have a similar effect, assuming they are uncorrelated. The effect of spatial variation in population growth rate, on the other hand, is less consistent and less well understood (Ylikarjula et al.
2000).
We know that spatial variation can have important consequences for population dynamics. For example, Etterson and Nagy (2008) found that, even with modest sample sizes to estimate movement, a spatially explicit model of migratory songbird population dynamics usually provided a more accurate estimate of population growth than the average across space. In contrast, one study found that a general population model with density- dependent dispersal among 25 patches produced dynamics more similar to a single patch than to a model with 2 patches (Ylikarjula et al. 2000). More recently, Shima et al. (2010) used a metapopulation model to explore the effect of spatial variation on recruitment in a marine system. They determined that variation in habitat quality in the matrix between patches increased spatial variability in recruitment compared to a model where the entire matrix was equally poor (Shima et al. 2010). Therefore, population data without spatial 70
context can be misleading. In one case, information on population size over time would have led to the conclusion that a population of migrant birds within Illinois woodlots was stable, but in reality reproductive rate had decreased dramatically and the population was being subsidized by recruits from other areas (Brawn and Robinson 1996).
The variety of consequences found in these studies likely reflects both the actual variety of spatial situations and the fact that ecologists tend to deal with spatial variation in idiosyncratic ways. We often consider space when (1) the populations being studied are disjoint (e.g. Johnson, H. E., et al. 2010) or (2) the history or management regime differs dramatically between areas (e.g. Iverson and Esler 2010). When space is explicitly modeled, it is usually modeled as discrete categories. For instance, metapopulation studies consider patches which are homogenous within themselves (Levins 1969), and source-sink studies divide the landscape into two distinct habitat types (Pulliam 1988). Griffin and
Mills (2009) generalize to animals moving through a landscape with patches of varying quality. In other cases, we do not explicitly model space, but we assume that study areas are representative either because they are considered good habitat or because we are specifically targeting suboptimal or heavily managed populations (e.g. Hunter et al. 2010).
Applying spatial population models to natural systems is difficult, not necessarily because they are inappropriate, but because estimating the parameters is difficult (Battin 2004,
Bowler and Benton 2005). For large and/or rare species, achieving sufficient sample sizes for vital rate or population growth rate estimation often necessitates pooling across space.
This paper was motivated by results from recent analyses of black bear vital rates
(Chapter 2 of this dissertation) and Montana harvest data (Chapter 3 of this dissertation).
One of us (J. Beston) analyzed black bear demographic studies across their range, using
Bayesian hierarchical meta-analysis to partition variance in vital rates. Vital rates of black bears in western North America differed from those in eastern North America, and the 71
posterior distribution of the western population growth rate, λ, suggested population decline (Chapter 2 of this dissertation). However, manager perceptions and evidence from harvests in Montana indicate a stable or increasing population (Garshelis and Hristienko
2006, Chapter 3 of this dissertation). This apparent contradiction could result from a bias in populations selected for demographic analysis, if researchers tend to focus on heavily harvested or peripheral populations.
Alternatively, the demography could correctly represent black bear populations but the average could be an inappropriate measure to characterize overall population dynamics because of space. Specifically, we know from source-sink models that populations can persist in heterogeneous landscapes consisting of areas with growing and declining populations (e.g., Holt 1985). A classic result from source-sink theory is that abundance and population trends do not always reflect the quality of the habitat. Due to movement among different habitat types, populations can be increasing or stable where they should be declining and vice versa (Pulliam 1988, Donovan and Thompson 2001). Based on this general phenomenon, we hypothesized that it might be possible for a population to persist in a landscape in which the growth rate, averaged across habitat heterogeneity, is less than one, but some portion of the landscape has growing populations. Our hypothesis was that these growing habitat patches could be sufficient to subsidize the declining areas, leading to overall population growth on the landscape. If our hypothesis is correct, the apparently contradictory demography and harvest data sets from black bears could both be right, depending on movement of individuals among habitat types.
Unfortunately, as is often the case, we have limited data with which to assess this hypothesis. We approached this problem by taking the information that we do have and using it in models that incorporate space. Our goal was to use available data and theory to determine if movement patterns are a reasonable way to marry the disparate results of the 72
demographic and harvest data. The aim was not to model a specific population, but to ask whether habitat heterogeneity could result in source-sink dynamics given what we know about black bears. By using the data we have and exploring over unknown parameters, we determined whether these models are plausible or if the importance of spatial dynamics could be ruled out. This modeling approach is important for large and/or rare animals in general because we often cannot achieve sufficient sample sizes to estimate all the parameters for spatially explicit models and researchers often have to pool samples across habitat heterogeneity. As with any model, black bear movement and demography are surely more complex than these models. Rather than capturing all of the unknown details of behavior and population dynamics, our goal was to explore a range of models that are sufficiently broad to span expectations for black bear populations and yet simple enough to allow straightforward interpretation and sensitivity analyses to unknown parameters.
Methods
We use two approaches to explore the potential effects of space for Montana black bears: a discrete-space model and a continuous-space model. Both models are relatively simple, allowing us to apply information we have, and explore consequences of uncertainty in unknown parameters, without having to guess values for a large number of variables.
The discrete-space model assumes habitats fall into one of two types: source (good) and sink
(bad). This model easily accommodates population stage structuring and allows dispersal to be limited to a specific stage in the life history. Using this model, we can determine how much source habitat is needed to support a population based on the vital rates of both habitat types, and compare this proportion to the estimated proportion of populations that are growing, based on our past analyses of the distribution of population growth rates in
Montana (Chapter 1 of this dissertation). We also explore the consequences of different 73
assumptions about dispersal, using a continuous-space model that reflects a probability distribution of habitat quality, as defined by habitat-specific population growth rates, across the landscape. This model allowed us to explore consequences of different kinds of movement behavior, and ask how sensitive our conclusions were to general behaviors such as local dispersal and habitat preference.
Discrete Space Model
The discrete-space model used vital rates estimated from our hierarchical Bayesian meta-analysis of demographic studies in western North America. The output of that analysis included a posterior probability distribution for each vital rate across studies.
Here we ask if, assuming these posterior distributions represent spatial variation in vital rates, black bear populations could be increasing, even though the average population growth rate (λ) across sites is < 1 (see Figure 4.1 and Chapter 2 of this dissertation). The posterior probability distribution of λ (Figure 4.1) was obtained by randomly sampling each of these vital rate distributions and plugging the values into a stage-structured matrix model to estimate the asymptotic population growth rate. Thus, each value of λ in the posterior distribution is associated with a particular matrix composed of vital rates randomly sampled from their own posterior distributions (see Chapter 2 of this dissertation). To obtain vital rates for source and sink habitat types, we split these sample matrices into a source group that produced λ>1 and a sink group with λ<1. We then randomly selected a matrix from each group and constructed a single stage and habitat structured matrix model describing population processes within each habitat and dispersal between them. The matrix for this model can be written
74
[ ]
for
for where for { for
is the survival of bears in habitat h (g and b for source (good) and sink (bad), respectively)
from age i to age i+1 given stage specific survival of cubs (c), yearlings (y), subadults (s),
and adults (a),
for { for for
is the proportion of i aged bears in habitat h that will survive and be mature at age i+1, fh is
fecundity (number of female cubs per female per year) in habitat h, pi is the probability that
the mean age at primiparity is i or younger, and ag is the proportion of source (good) habitat
on the landscape. The values for survival and fecundity varied based on the selected
matrices, but the probability of primiparity was constant across all habitat types (see
Chapter 2 of this dissertation).
We used this model to explore the minimum proportion of source habitat that could
support a growing (λ<1) population, given these demographic rates. To calculate this
proportion, we assumed all bears dispersed during their third summer and the probability
75
of settling in the source or sink was equivalent to the proportion of each habitat on the landscape. Survival of the dispersing year was set to the value for the starting habitat and fecundity was set to the value for the habitat in which a bear settled. For each of 5000 randomly chosen sets of vital rates, we calculated the proportion of source habitat that resulted in an asymptotic total λ of 1.
We also calculated the average population growth rate when the proportion of source and the proportion of subadults dispersing each varied independently between 0 and 1. For each combination of amount source and dispersal rate, we calculated the average growth rate of 1000 combinations of source and sink vital rates. We then described what combinations of habitat distribution and dispersal probabilities resulted, on average, in growing or declining populations.
Finally, we calculated sensitivity of λ to the vital rates in the source and sink, the proportion of source habitat, and the dispersal rate for 1000 source-sink combinations. We calculated the sensitivities using matrices with 34% source habitat and 10% dispersal.
These represent the proportion of the posterior distribution of λ greater than 1 (i.e. the amount of source habitat) in the meta-analysis (Chapter 2 this dissertation) and a rough upper bound for dispersal by subadult females (5%, Rogers 1987; 8%, Elowe and Dodge
1989; 3%, Schwartz and Franzmann 1992; 0%, Lee and Vaughan 2003), respectively. To evaluate the choice of parameter space for sensitivity calculation, we also found sensitivities with 100% movement rate and 20% source habitat, the most common amount needed for persistence when all subadult females disperse.
Continuous-Space Model
We used a continuous-space model without explicit population structure to examine the consequences of continuous variation in population growth rate across the landscape, and to explore consequences of a wider range of dispersal behaviors, in which movement is 76
a function of habitat quality. In this model, we assumed the distribution of habitat quality across the landscape was equal to the posterior probability distribution of λ in western
North America from the meta-analysis (Chapter 2 of this dissertation). We had three general models of movement which are explained below: one in which the proportion of individuals moving was the same for all habitats, a second in which movement rate varied linearly with local population growth rate, and a third in which movement was restricted to similar habitats (e.g. from source to source). This third model would result if habitat quality were spatially correlated on the landscape, so that animals were more likely to disperse to similar habitat types, or if animals were selecting habitat similar to their natal habitat. As with the two habitat matrix model, we assumed that moving bears would settle in proportion to the habitat availability.
In the continuous-space model, the population size, Nh,t, in any habitat, h, at time t can be written
∫
Where λh is the local population growth rate, mh is the local movement rate, ah is the proportion of habitat h on the landscape, and the integral is over all H habitat types. Recall that in our model, ah is equal to the probability density function for λh in the posterior distribution of population growth rate from the meta-analysis. In practice, this model is analogous to an integral projection model, in which a large discrete matrix is used to approximate continuous variation in a trait that affects fitness, such as size (Easterling et al. 2000, Childs et al. 2003). In the same way that stage-structured matrix models can be adapted to reflect spatial structure, we adapted this integral projection approach to represent continuous variation in local population growth rate. Transitions in the matrix therefore refer to movement between patches with different intrinsic growth rates.
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We used this model with a constant movement rate across habitats to find the movement rate that resulted in a total population growth rate, the first eigenvalue of the projection matrix used to approximate the continuous variation in habitat, equal to one.
We call this value the critical movement rate, and movement rates higher than this value resulted in population declines. We also calculated population growth as movement rate varied between 0 and 0.3 and the mean overall growth rate varied within its 95% credible interval (analogous to 95% confidence intervals in frequentist statistics, Gelman et al.
2004). Allowing the growth rate to vary between 0 and 0.3 is analogous to allowing 0 to
100% of subadults disperse, assuming subadults make up no more than 30% of the population. Changing the mean growth rate shifted how much of the habitat distribution was greater and less than 1. As in the discrete model, we calculated the sensitivity of population growth rate to the parameters of the model (the mean and standard deviation of
λ and the movement rate) while holding the movement rate at 3% and 30% and randomly sampling the mean and standard deviation of λ from their posterior distributions. We also calculated the critical movement rate across the 95% credible intervals of mean and standard deviation of λ from the meta-analysis to determine how our conclusions might change across the plausible values for these parameters.
This model assumes individuals in all habitats have the same movement rates and range, but individuals may be more likely to move from one habitat than another depending on a variety of factors, from perceived quality to availability of home ranges (Lee and
Vaughan 2003, Costello et al. 2008). Therefore we also explored two scenarios in which movement depended on the local population growth rate of the starting habitat. These models allowed habitat selectivity by making it more or less likely that animals will leave a particular habitat type. In one scenario, we examined the population-wide λ when movement rate varied linearly with the local population growth rate. We allowed 78
movement rate in the best and worst habitats to vary independently between 0 and 1, with a straight line between these end values determining the movement rate in intermediate habitats. Lines with high movement at low local λ and low movement at high λ represent situations where individuals are selecting for good habitat. Conversely, lines with low movement rates at low local λ and high movement rate at high λ are analogous to an ecological trap, where bears are leaving good habitats and staying in poor ones.
In the final scenario, all individuals moved, but they were limited in movement range and tended to settle in habitat similar to their starting habitat. This model probably best represents female movement, which tends to include movements within the home range of adult females and short-distance dispersal of young females (Larivière 2001). We varied the range of movement, measured as the difference in population growth rates between the starting and stopping habitats, to determine the range at which total λ was 1.
In this scenario, moving individuals settled in proportion to availability of habitat within their movement range.
Results
Discrete-Space Model
In the simplest situation, where all subadults dispersed and distributed themselves according to the proportion of source and sink on the landscape, most combinations of source and sink vital rates required about 20% source habitat to achieve a total population growth rate of 1 (Figure 4.2a, solid line). The mean amount of source needed was 37.5%, and the median was 32% with a right-skewed distribution. When only 10% of subadults dispersed, most combinations of source and sink required less than 10% source habitat with a median of only 1% (Figure 4.2a, dotted line). In the meta-analysis, 34% of the posterior distribution of λ was greater than 1, which is more than the amount of source needed in 79
most situations. The variation in the critical proportion of source habitat was high when large proportions of subadults dispersed due to the high variability in both source and sink vital rates. If the sink habitat was very poor and the growth rate in the source was close to
1, the landscape sometimes had to be entirely source to maintain a population.
As the proportion of source on the landscape decreases or the movement rate increases, the average population growth rate declines (Figure 4.2c). The exact growth rate depended on the vital rates of the source and the sink, but the trend was the same for each combination of source and sink vital rates.
In general, the growth rate of the entire population was more sensitive to the vital rates of the source than those of the sink (Figure 4.3a). The relative sensitivity of sink vital rates was greater when more subadults dispersed, but the source vital rates, especially adult survival, still had higher sensitivity.
Continuous-Space Model
In the continuous-space model with random movement, annual movement rates less than 20% produced asymptotic population growth rates greater than or equal to 1. When movement rates exceeded this critical value, individuals produced in high quality habitats immigrated to lower-quality habitat at too great a rate to maintain populations. The total population growth rate is most sensitive to the standard deviation of λ when the movement rate is low but to mean λ when relatively large portions of the population move (Figure
4.3b). The critical movement rate itself is relatively insensitive to differences in the standard deviation of population growth rate at any given mean growth rate, and remains in the 20-30% range for most of the credible interval of the mean (Figure 4.2b). The same pattern of higher growth rate with lower movement rates that was evident in the discrete- space model was found in the continuous-space model (Figure 4.2d).
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When individuals are more likely to move from bad habitat and stay in good (Figure
4.4a, solid lines), population growth rate is generally above unity. If individuals are more likely to leave good habitat and settle in poor areas (Figure 4.4a, dashed lines), then the poor habitats act as an ecological sink and the overall population declines. However, when the preference is not extreme, some situations are exceptions to this rule (Figure 4.4a, bold lines). In general, when the probability of movement varies linearly with the local population growth rate, fewer than 20.7% of animals can move from the best habitat for the total population growth rate to remain above 1 (Figure 4.4b). It does not matter how much movement occurs in the worst habitat, and any line falling entirely within the shaded area
(Figure 4.4b) produces positive total population growth.
In the final scenario, when all animals move but their range is restricted, a difference between starting and ending local population growth rates of less than 0.036 allows the total population to have a growth rate of at least 1. This is small compared to the total range of local population growth rates, which is 0.613. In other words, bears must stay relatively close to their original habitat in order for the area-wide growth rate to be greater than 1. This could occur if bears choose to settle in habitats similar to their natal habitat or if the landscape exhibits high spatial autocorrelation.
Discussion
Overall, the range of models we explored suggests that our hypothesis is plausible: bears may persist in spatially heterogeneous landscapes where the average population growth rate is less than one, with modest amounts of movement among habitat types.
Black bear reserves and conservation areas are often established with the goal to provide source habitats that will support surrounding harvested populations (Powell et al. 1996) and create linkages for small populations (Larkin et al. 2004). Indeed, our results are 81
encouraging because they may suggest that bear populations are more viable than has been assumed. For example, Powell et al. 1996 calculated population growth using the combined average survival of bears living in and out of the Pisgah Bear Sanctuary, and concluded that populations were nonviable because the average growth rate was less than one. A spatially explicit model separating bears into residents and nonresidents may have produced a viable population.
In the discrete-space model, most combinations of source and sink vital rates required only about 20% source to sustain populations in the least likely situation where all subadults dispersed. This is within our reasonable parameter space because 34% of the posterior distribution of population growth rate from the meta-analysis was above 1
(Chapter 2 of this dissertation). Assuming the sample of populations studied is representative of the distribution of populations across the state, we can expect Montana to have enough source area to offset sink habitats. The continuous space model indicated that fewer than 20% of animals can disperse from the best habitats in order to maintain a population growth rate larger than 1. This rate represents the proportion of the total population that is moving, but we know that black bears usually disperse as subadults and remain in their adult home range for the rest of their lives (Larivière 2001). Typically more than 90% of subadult females remain near their mothers’ home ranges (Rogers 1987,
Schwartz and Franzmann 1992, Lee and Vaughan 2003), and subadults usually make up only 15-30% of the population in the western US (Jonkel and Cowan 1971, Schwartz and
Franzmann 1991, Cunningham and Ballard 2004). Thus, dispersal of subadults, and movement of individuals in general, is unlikely to exceed the estimated critical movement rate.
While these models simplify the complex processes of dispersal and movement, they provide insight into situations in which individuals are moving randomly with respect to 82
habitat and theory alone does not tell us what to expect. We know from theory that if individuals choose good habitats, populations will persist, and if they select poor habitat, populations will decline. When animals are good at choosing the highest quality available habitat, they theoretically follow an ideal free or ideal despotic distribution (Brown 1969,
Oro 2008). For example, yellow-legged gulls were observed attempting to disperse from a poor to a good patch but not in the opposite direction (Oro 2008). There is also evidence that bears follow an ideal-despotic distribution in some habitats (Beckmann and Berger
2003). As long as sufficient good habitat is available, ideal distributions can prevent declines by maintaining populations in the best habitats. At the opposite extreme, animals sometimes actually choose degraded habitats due to mismatched cues of habitat quality.
For instance, black bears are attracted by garbage and other food sources into urban areas in Nevada, but these areas tend to have much lower survival and population growth rate
(Beckmann and Lackey 2008). Consistent movement towards such ecological traps will drive population decline (Battin 2004). When individuals effectively sample and choose habitats, we can predict population response based on the type of decisions they make.
However, there are many situations in which these two theoretical extremes do not apply, and simple modeling exercises such as ours can help produce predictions of necessary habitat distribution or movement rates for population viability. Often species do not perceive differences in habitat quality due to degradation by humans – things like increased road mortality, harvest pressure, pesticides, etc. – and they therefore do not move in a directed way from one habitat quality to another (Doak 1995). Additionally, individuals may make imperfect habitat selection decisions due to imperfect knowledge about available habitats (Lima and Zollner 1996), conflicting benefits offered by different habitats (Kokko and Sutherland 2001), or unavailability of reliable cues during the time decisions are being made (Arlt and Part 2007). If any of these situations occur, the simple 83
models with random movement that we use can be more informative than models that assume animals are choosing good habitat (or bad). Moreover, our results indicate that some situations where individuals prefer good habitats result in declines and even some trap-like scenarios allow populations to persist. Differences in habitat quality would have to be large, and preference strongly mismatched, for traps to drive declines. These results set bounds that could be tested in a targeted way with dispersal data.
Movement in heterogeneous landscapes has both benefits and, as our modeling demonstrated, costs for organisms and populations (Bowler and Benton 2005). However, in human-dominated landscapes with increasing fragmentation, we often focus on the benefits of movement and what we might be losing. Habitat fragmentation was associated with reduced fitness and reduced genetic diversity in common frogs (Rana temporaria;
Johansson et al. 2007). Likewise, while none of the current reintroduction sites for Arabian
Oryx (Oryx leucoryx) in the Israeli Negev can support a viable population, connectivity between them would create a viable metapopulation (Gilad et al. 2008). In cougars, population growth rate estimated from demography underestimated the actual growth rate because movement from surrounding populations boosted the local population (Robinson et al 2008). Movement and connectivity are important goals for many conservation organizations, both to support small, nonviable local populations and to prevent inbreeding depression (Johnson, W. E. et al. 2010). Indeed, populations in poor habitats in our models would be unable to persist without immigration from populations in high quality habitat.
However, this work reminds us that too much movement can jeopardize source populations.
Movement homogenizes a landscape and brings the overall population growth rate closer to the average of the local population growth rates. Similar results were achieved with a density-dependent model of reef fish in which local demography became more important as dispersal became more limited (Figueira 2009). 84
The potential for a mismatch between the actual population status and the results of an analysis of average vital rates make it clear that space is an important consideration, even when we cannot measure its effects directly. Many studies rely on average vital rates or population growth rate to assess population status. For example, assessments of the population viability of northern spotted owl (Strix occidentalis caurina) used a weighted average of λ across 13 study areas representing 12% of the total range of the subspecies
(Noon and Blakesley 2006). In this case, only one of these 13 populations was increasing, so their conclusion of overall decline was probably robust, although limited movement could mean the rate of decline would be slower than expected from the average growth rate.
Averaging across space also occurs when we pool individuals for estimation of vital rates.
Information from critically endangered Mexican axolotl salamanders (Ambystoma mexicanum) in 62 channels and 8 lakes was combined to estimate survival and growth rates for a matrix model (Zambrano et al. 2007). Before averaging across space, we should consider the level of connectivity and realize that sometimes our confidence in having a well-mixed population may be misplaced. Bearded vultures (Gypaetus barbatus) in the
Alps dispersed long distances after reintroduction, and researchers therefore justified the consideration of the entire Alpine population as a single demographic unit (Schaub et al.
2009). However, newly released animals regularly make long distance movements from release sites (Stamps and Swaisgood 2007), and a closer consideration of actual dispersal may reveal a more geographically structured population.
The sensitivity values and their consistency among simulations of the discrete-space model suggest it is more useful to improve parameter estimates for sources than sinks.
This is consistent with other studies that have found source vital rates to have higher sensitivity than those of sinks (Pulliam and Danielson 1991, Doak 1995). It may also be more useful to monitor sources than sinks, if they can be reliably identified. Monitoring is 85
most critical when it would change our management decision (Hauser et al. 2006), and for black bears in Montana, manipulating harvest in source areas may be the most efficient strategy to maintain overall population persistence. While Jonzen et al. (2005) found that it was more efficient to monitor the sink to detect reproductive declines in the source in many situations, in this situation it may be more useful to monitor sources because we are likely most interested in adult survival in the source, which has high sensitivity and can be directly affected through harvest management.
Spatial variation is potentially important for population dynamics, but we often cannot assess its effects directly. In this work, we demonstrate that average population growth rate can be an inaccurate descriptor of overall population status, even for a closed population. Modeling can help determine whether likely movement rates and habitat distributions result in stable or growing populations. Combining intense but less extensive data (e.g. demography), less intense but more extensive data (e.g. harvest data), and models can give insight into potential consequences of spatial heterogeneity that are not obvious with either data source alone.
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Figure Legends
Figure 4.1. Posterior probability density of black bear population growth rate in western North America (from Ch 2 this dissertation).
Figure 4.2. The critical amounts of (a) source habitat in the discrete-space model and (b) movement in the continuous-space model that result in population growth rate greater than 1 as the habitat distribution varies, and the overall average population growth rate in (c) the discrete-space model and (d) the continuous-space model as the habitat distribution and the movement rate varies. The star (b) represents the best estimate of the mean and standard deviation of population growth rate.
Figure 4.3. Sensitivity of total black bear population growth rate (a) in the discrete space model to changes in the vital rates of the source and sink, the proportion of source habitat, and the proportion of subadults dispersing calculated for 1000 sample pairs of source and sink vital rates with 34% source habitat and 10% or
100% of subadults dispersing and (b) in the continuous space model to changes in the mean or standard deviation of overall population growth rate and movement rate calculated for 1000 samples of mean and standard deviation from their posterior distributions with 3% and 30% of all animals moving.
Figure 4.4. Total population growth rate in the continuous space model given local movement rates that vary linearly with local population growth rate. Solid lines in panel (a) show preferences for good habitat, and dotted lines are when individuals prefer to remain in poor habitat. When the preference is not extreme, as in the bold
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lines of panel (a), populations do not necessarily grow or decline as we would expect based on free distributions or ecological traps, respectively. Whenever local movement rates are within the shaded area of panel (b), total population growth remains greater than or equal to 1.
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7
6
5
4
3
2
1 Posterior Probability Density 0 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 Population Growth Rate
Figure 4.1.
89
Population Population Growth Rate
12 Standard Deviation of
0.081
10 Proportion of 0.072 8 Subadults Moving 0.063 6 1 4 0.1 0.054 2
Probability Density Probability 0.045
0.98 0.93 0.94 0.95 0.96 0.97 0.99 1
0 0 0.5 1 Critical Proportion of Source Mean Population Growth Rate
Critical Movement Rate
0.1-0.2 0.2-0.3 0.3-0.4 0.4-0.5 0.5-0.6 0.6-0.7
0.7-0.8 0.8-0.9 0.9-1 Proportion Proportion of Source Habitat 1 1 0.9 0.99 0.8 Overall Mean 0.7 0.98 0.6 0.97 0.5 0.4 0.96
0.3 0.95 λ 0.2 0.94 0.1
0.93
0.3 0.05 0.1 0.15 0.2 0.25
0 0
0.1 0.5 0.9 0 0.2 0.3 0.4 0.6 0.7 0.8 1
Proportion Subadults Dispersing Proportion Population Moving
Average Resulting λ Average Resulting λ 0.95-0.96 0.96-0.97 0.97-0.98 0.9-0.95 0.95-1 1-1.05 0.98-0.99 0.99-1 1-1.01 1.05-1.1 1.1-1.15 1.15-1.2 1.01-1.02 1.02-1.03 1.03-1.04 1.2-1.25 1.25-1.3
Figure 4.2.
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Source Cub Survival a) Source Yearling Survival Source Subadult Survival
Source Adult Survival Source Fecundity Proportion of Subadult Sink Cub Survival Females Sink Yearling Survival Dispersing Sink Subadult Survival 0.1 Sink Adult Survival 1 Sink Fecundity Proportion Source Proportion Subadults Dispersing
-0.2 0 0.2 0.4 0.6 0.8 1 Sensitivity
b) Proportion Mean λ of Females Moving St Dev λ 0.05 0.5 Movement Rate
-2 -1 0 1 2 3 4 5 Sensitivity
Figure 4.3.
91
a)
1 λ = 0.96
0.9 0.8 0.7 λ = 0.97 0.6 0.5 0.4 0.3 λ = 0.98 0.2 λ = 1.01 λ = 1.13 0.1 Local Movement Probability Movement Local λ = 1.26 0 0.65 0.85 1.05 1.25 Local Population Growth Rate
Select Good Habitat Prefer Poor Habitat b)
1
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 Total Population Growth ≥ 1
0.1 Local Movement Probability Movement Local 0 0.65 0.95 1.26 Local Population Growth Rate
Figure 4.4.
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CHAPTER 5
POPULATION RESPONSE OF BROWN BEARS TO SALMON ESCAPEMENT AND
HARVEST
Abstract
Food resources affect different vital rates differently. Large carnivores often respond to changes in food with changes in reproduction, but the sensitivity of population growth to this vital rate is expected to be low for these long-lived species. Though some studies point to food resources as vitally important for carnivore conservation, others have concluded that human-caused adult mortality is of greater concern. I used meta-analysis to synthesize brown bear (Ursus arctos) vital rates and assess their population status. I simulated changes in salmon abundance and bear harvest rate using a suite of 4 structural models to explore the effects of fishing and hunting on the central coastal British Columbia population. Under current salmon conditions without harvest, the average female population growth rate is 1.01, and 95% of simulations fell between
0.93 and 1.06. Twenty and 50% reductions in salmon affected population growth under some models but not others, but complete salmon failure reduced population growth in all models.
Harvest rates of 2 and 5% reduced population growth significantly in all models. If the goal is to maintain or increase the brown bear population, the only truly robust strategy is to maintain high salmon escapement and low brown bear harvest. More work on the relationship between salmon and brown bear population processes would be valuable in precisely predicting the population response of brown bears to changes in salmon escapement.
93
Introduction
The fates of numerous mammal species are often tightly bound with those of their food resources. For example, grasses regulate wildebeest (Connochaetes taurinus) populations on the
Serengeti (Mduma et al. 1999), and lynx (Lynx canadensis) famously cycle with snowshoe hare
(Lepus americanus; Elton and Nicholson 1942). Dependence on food can be especially critical for animals at the top of the food chain, like the lynx. In general, carnivores are limited by food
(Karanth et al. 2004; Carbone and Gittleman 2002) and sensitive to changes in food abundance
(Ward et al. 2009). However, because food affects species and vital rates differently, it is not always clear how changes in food resources will translate into changes in population dynamics.
Relatively large-bodied, long-lived carnivores respond to food resources through changes in reproduction. Higher fecundity with higher food availability has been found in wolves (Canis lupus; Boertje and Stephenson 1992), black bears (U. americanus; Elowe and Dodge 1989), wolverines (Gulo gulo; Persson 2005), and a variety of other large and small carnivores (Fuller and Sievert 2001). In addition to fluctuating food resources, large carnivores face human-caused adult mortality from harvest, poaching, road kill, and nuisance control. Legal and illegal hunting is the leading cause of adult mortality in many carnivore populations, including some populations of black bears (Czetwertynski et al. 2007; Koehler and Pierce 2005), brown bears
(Knight et al. 1988), and lynx (Andren et al. 2006). Conflict with neighboring humans is a major mortality source even for carnivores in protected reserves (Woodroffe and Ginsberg 1998).
Moreover, recent research has shown that poaching is more important to the short-term persistence of tiger (Panthera tigris) populations than prey (Chapron et al. 2008). Interpreting whether changes in fecundity or adult survival are more important influences on population growth requires consideration of both the sensitivity of population growth to each vital rate and the magnitude of changes (Mills 2007). 94
Though they are generalists, brown bears in coastal British Columbia (BC) rely heavily on seasonally available spawning salmon (Oncorhynchus spp). Salmon-fed bears are significantly larger and more productive than their terrestrially-feeding counterparts (Hilderbrand et al. 1999; Mowat and Heard 2006; Ben-David et al. 2004). Salmon are also a favorite food of many humans, and some salmon runs have been heavily impacted by fishing activities at sea
(Ludwig et al. 1993; Schwindt et al. 2003). Brown bears’ ecological and cultural significance have made them a key species for conservation and management, but potentially critical salmon resources are managed independently for commercial fisheries. Additionally, brown bears themselves are a game species in BC. Brown bear population growth is more sensitive to adult survival than reproduction, but reproduction can be more important in determining population growth because of its higher variability (Garshelis et al. 2005; Schwartz et al. 2006). It remains unclear how changes in these rates due to management of salmon and harvest affect brown bear population growth.
In this study, I use meta-analysis and population projection models to achieve two objectives. The first objective is to synthesize brown bear vital rates presented in previous studies and assess the general population status. I then incorporate information about BC salmon escapement (i.e. the adult fish that escape the fishery and return to spawn) and bear harvest to project brown bear populations under different scenarios. Modeling across a range of reasonable structural models and parameter values for salmon and harvest provides insight into the effects of salmon and harvest on brown bear population persistence.
95
Methods
Meta-analysis
I collected demographic data from published studies that measured brown bear vital rates and studies that presented tables of vital rates when the original source could not be accessed (Table 5.1, see Simulations for an explanation of variables). Only the most recent study available from a given population was included. I combined the survival rates from the various studies using a meta-analysis approach.
I used the package R2WinBUGS to call WinBUGS 1.4.3 (MRC Biostatistics Unit,
Cambridge, United Kingdom, www.mrc-bsu.cam.ac.uk/bugs) from R (R Core Development
Team, www.r-project.org) to estimate the posterior distribution for each survival rate given the available studies and uninformative priors. I used a simple beta model weighted by study standard error to combine survival rates, while taking into account whether a population was harvested:
2 si ~ (i , i )
i a hi 2 2 2 i SE(si )
th th where si is the survival estimate of the i study, i is the mean of the i study, is the overall mean, a is the difference in survival rate between harvested and unharvested populations, hi is an indicator variable set to 0 if the ith study population is not hunted and
2 th 2 1 otherwise, i is the variance of the i study, is the overall variance, and SE(si ) is the standard error of the ith study. Studies with larger standard error were allowed to vary farther from the mean, giving them less weight in the fitting. The means and variances were converted into shape parameters α and β in the estimation routine. I checked for
96
convergence by ensuring the Rˆ statistic, the potential scale reduction factor, was within
0.01 of 1 (Gelman et al. 2004).
Fecundity Function
I quantified salmon escapement using information from 1976 to 2000 on BC salmon escapement levels provided by the province to the Nature Conservancy (R. Jeo, the Nature
Conservancy, personal communication). I then used the response of brown bears to salmon density (Quinn et al. 2003) and the relationship between brown bear productivity and meat consumption (Hilderbrand et al. 1999) to relate salmon escapement to fecundity, measured as the number of female cubs produced per adult female per year.
I converted the raw estimates of salmon escapement for five species of salmon from streams in central coastal BC into an index of salmon escapement. Salmon species included were Chinook (O. tshawytscha), chum (O. keta), coho (O. kisutch), pink (O. gorbuscha), and sockeye (O. nerka). I only used streams with at least 3 nonzero entries and complete data for a species for all years. This subset of streams did not appear biased, but any likely bias would exclude small runs or runs where salmon are not readily visible. These streams would be less important for bears (Boulanger et al. 2004), and the purpose of the index is to establish a baseline and variability, not measure actual numbers or biomass of fish.
Therefore the exclusion of streams with few salmon or unreliable counts in this analysis should not affect the results. I used a weighted average of the total numbers of each salmon species over all included streams for each year: x [(8Chinook 6chum 4.5coho 3.5sockeye 2 pink)/ 24]106 , where the weights are based on relative biomass of each species and the average is divided by one million to rescale.
97
I quantified the relationship between this salmon escapement index and fecundity based on information from Hilderbrand et al. (1999), Quinn et al. (2003), and Mowat and
Heard (2006). Hilderbrand and colleagues (1999) measured the dietary contributions of marine and terrestrial meat and vegetation to brown bear diets in several populations by using stable isotope analysis. They provided estimates of percent salmon in diet as well as litter size for several brown bear populations. I converted the mean litter sizes to fecundity for each population in Hilderbrand et al. 1999 by dividing by 2×mean interbirth interval. I then performed a regression of fecundity on the percent salmon in diet to estimate the relationship between salmon consumption and productivity.
I then related the index of salmon escapement to the percent of salmon in brown bear diets. Quinn and colleagues (2003) found an asymptotic relationship between numbers of salmon killed by bears and salmon density. I used their asymptotic function, y a(1 exp(bx)) , where y is the number of salmon killed and x is the salmon density and a and b are shape parameters, as a guideline. Alternatively, the relationship between salmon availability and salmon consumption could follow an s-shaped curve, with bears ignoring salmon until they reach some critical density which makes them profitable. I fit both Quinn’s function and the logistic growth function heuristically to the variables of interest, setting y as the percent salmon in diet, x as the salmon escapement index. The minimum of percent salmon in diet is necessarily 0, and I set the asymptote at 95%, which was the highest value within the confidence intervals measured by Hilderbrand et al.
(1999). The diet of coastal BC bears probably contains about 70% salmon (Mowat and
Heard 2006) at the current mean salmon escapement levels. Fixing this point allowed the calculation of b in Quinn’s equation and the rate of increase in the logistic equation. I
98
coupled each of these functions with the linear relationship between percent salmon in diet and fecundity to relate the salmon escapement index to fecundity.
Simulations
I conducted stochastic simulations of population growth of female brown bears using the information and estimates gathered above. I constructed a density independent, age based, post birth pulse matrix model using the vital rates from the meta-analysis and the equation relating salmon and fecundity. The population growth is described by the 30×30 matrix
0 0 0 0 0 ss f sa f sa f sa f s 0 0 0 0 0 0 0 0 c
0 s y 0 0 0 0 0 0 0 0 0 ss 0 0 0 0 0 0 0 0 0 s 0 0 0 0 0 s 0 0 0 0 ss 0 0 0 0 0 0 0 0 0 s 0 0 0 s 0 0 0 0 0 0 sa 0 0 0 0 0 0 0 0 0 s 0 a where f is fecundity and si is the survival of bears in the ith class: cubs, c, yearlings, y, subadults, s, and adults, a. Because salmon may affect the carrying capacity instead of directly reducing fecundity, I also performed simulations with this matrix where the carrying capacity varied with salmon escapement but fecundity varied independently of salmon. The relationship between escapement and carrying capacity was linear, with the current mean escapement equal to a carrying capacity of 3000 bears and complete salmon failure reducing the carrying capacity by 50%. I implemented this carrying capacity in two ways. One model used ceiling density dependence with subadults perishing first, then cubs, and finally adults until the total population did not exceed the carrying capacity. This
99
model would be representative if alternative foods were sufficiently dispersed to induce territoriality in the population. The second model linked fecundity with salmon and also reduced survival of all stage classes as the population exceeded the carrying capacity, which could be a worst case scenario as reductions in survival can overcompensate for reduced carrying capacity.
I randomly selected values for the mean and variance of each survival rate from their joint posterior distribution at the beginning of each run. I calculated the mean matrix and set the initial population of 2000 bears to the stable stage distribution of the mean matrix for each run. I generated random survival values each year from the beta distribution determined by the mean and variance for that stage and run. This method incorporates uncertainty in the actual distribution of survival rates by selecting a different distribution for each run, and then incorporates environmental stochasticity by selecting a random value from that distribution for each year of the run. Note that these methods substitute spatial variation (among studies) for temporal variation (among years), which probably overestimates variance due to differences in management regimes among populations. I then incorporated demographic stochasticity using a random binomial with p equal to the survival rate for that year and n equal to the number of bears at the beginning of the year.
I used salmon escapement to calculate the value for mean fecundity or carrying capacity each year. Salmon escapement was increasing before 1985, but leveled off from
1985 to 2000 (Figure 5.1). I only used this more recent trend-free section for simulations. I randomly selected values for salmon escapement each year from a lognormal distribution with mean and variance corresponding to this time period. I modified the index to examine four scenarios: current salmon escapement levels, a 20% reduction in salmon escapement, a
50% reduction in salmon escapement, and complete collapse of the salmon population. I 100
used salmon escapement to calculate the mean fecundity value for each year. I simulated environmental stochasticity due to factors other than variation in salmon escapement by drawing the actual fecundity value from a lognormal distribution with the variance equal to the residual variance of the regression of fecundity on percent salmon in diet. Demographic stochasticity was included by generating the number of new cubs from a Poisson distribution with shape parameter equal to fecundity times the adult population size.
I incorporated harvest by setting an annual additive harvest rate of 0%, 2% or 5% for subadult and adult bears. Although the current harvest rate of the coastal BC population is unknown, it was estimated at 2% in the late 1980s (Banci et al. 1994), and other populations face harvest rates between 1 and 6% (Banci et al. 1994; Poole et al. 2001).
Assuming the harvest is additive will give conservative results representing a population unable to compensate. I simulated the number of each age harvested using a random binomial with p equal to the harvest rate and subtracted them from the population. This resulted in 12 combinations of harvest rate and salmon escapement level for each of the 4 models, with 2000 replicate populations each. For each run, I generated 48 populations subject to the same sequence of base survival values but different salmon and harvest levels and different structural models relating salmon to population dynamics. I calculated the geometric mean growth rate, λ, over a 20 year time horizon for each population and the paired differences between λ for populations with the same model but changed salmon or harvest compared to those with unchanged salmon or no harvest, respectively.
Results
In the meta-analysis, the mean difference (95% credible interval) in survival between unharvested and harvested populations was not different from 0 for cubs, -0.032 (-
0.189, 0.122), yearlings, 0.010 (-0.110, 0.123), or subadults, 0.030 (-0.095, 0.136). Adult survival decreased by 0.029 (-0.054, -0.001) in harvested populations and was the only 101
survival rate statistically different between management regimes. This confirms that, on average, harvest adds about 3% mortality for females. The posterior distributions of the survival rates used in population models represent unharvested populations (Figure 5.2).
The linear relationship between salmon and fecundity based on data from
Hilderbrand et al. 1999 accounted for more than half the variation among the studies included (r2 = 0.59, Figure 5.3a). I combined this with the asymptotic and logistic functions relating salmon escapement to percent salmon in diet to produce the final functions used to calculate fecundity based on salmon escapement index (Figure 5.3b),
Quinn’s asymptotic function: f (x) 0.3245 0.0807(1 exp(0.988x))
0.0008 Logistic function: f (x) 0.3245 . 0.01 0.94 exp(4.125x)
Fecundity values calculated these ways were within the range observed in the studies from the meta-analysis.
Under current salmon escapement levels and no harvest, the population growth rate was 1.01 (0.93, 1.06) and the average population was stable (Figure 5.4). Considerable variation existed among simulated populations due to variation or uncertainty in vital rates. All models produced the same pattern of changes in population growth rate from baseline scenarios of current salmon escapement or no harvest (Figure 5.5). Reductions in salmon escapement did not greatly reduce the population growth rate unless salmon failed completely (Table 5.2), but harvest of 2 and 5% reduced the population growth rate by an average of 0.013 and 0.040, respectively (Figure 5.5). The λ values for populations with low harvest rates were within the range of observed values from the studies. However, increasing harvest rates rapidly pushed the population growth rate below most reported values from the literature.
102
Discussion
The grizzly bear population occupying central coastal British Columbia is probably stable under current conditions, though considerable uncertainty remains. A substantial proportion of the simulated populations decreased, even in the baseline scenario. This high variability most likely reflects high uncertainty in the measurement of parameter values rather than the true process variation. My simulations suggest that population changes are mediated to some extent by both salmon availability and additive harvest of adult female bears, but harvest has a relatively larger effect than salmon.
Adult female survival was lower in harvested populations, representing an average additive harvest of 3% for adult female bears. While some researchers have found this to be a sustainable additive harvest rate (Miller 1990; Swenson et al. 1994), adding even a 2% harvest reduced the mean growth rate below 1 in the simulated populations. Part of this inconsistency may be due to the fact that most reports of sustainable harvest rate include both sexes, with the assumption that males are more vulnerable to harvest and the harvest rate for females will be considerably less than the total harvest rate. Given the proximity of the population growth rate to 1 and the large amount of uncertainty, monitoring of hunted populations would be a valuable measure if population stability or increase is a management goal.
Relatively low levels of additive harvest affected population growth more than large changes in salmon escapement in all models. While we expect population growth of long- lived species to be more sensitive to changes in adult survival, reproduction often has a greater impact in reality due to its higher variability (Saether and Bakke 2000). Indeed,
Garshelis et al. (2005) found that although adult brown bear survival had the highest elasticity, variability in other rates was more important in determining annual population 103
growth. Though my results appear to contradict their conclusion, it is important to note that the changes imposed in adult survival due to harvest go beyond the natural variation in this rate. The posterior distribution of adult survival demonstrated that the natural variation in this rate is quite low, and we might expect changes in the growth of unharvested populations to be largely due to changes in other, more variable vital rates.
Salmon escapement, as included, was of less importance than harvest in determining a population’s fate. Only the scenario with complete elimination of salmon caused average population decline in the absence of harvest, but the variation in vital rates meant that some populations declined in all scenarios. Previous research has found that grizzly bear abundance in southern British Columbia tracked salmon escapement well
(Boulanger et al. 2004). However, the study sampled only the population at the stream, and bears are only expected to be using streams in years where salmon are available (Ben-
David et al. 2004; Boulanger et al. 2004). Even though the effects of salmon were not large, the population growth rate is so close to 1 that such small variations could tip the scales toward population decline.
Furthermore, decreases in salmon escapement could have detrimental transient effects on populations. Salmon-fed bears are larger than other bears (Hilderbrand et al.
1999), and they may not be able to support their own size on less rich foods. In a similar scenario, Craighead et al. (1974) observed a drop in survival of female grizzly bears after open pit garbage dumps in Yellowstone were closed. Reduction in salmon runs could lead to starvation of large bears or force them into conflicts with humans. This reduction in survival may be transient if bears subsequently raised without salmon did not grow as large, but the reduced population size would make them more vulnerable to overharvest.
While the density dependent models examined changes caused by reduced habitat quality, they still describe a situation in which bears are able to secure alternate food. Alternative 104
foods may be insufficient to support a viable population, although this seems unlikely given that some BC populations exist with little to no salmon (Mowat and Heard 2006).
Several other factors that I did not include could buffer bear population dynamics from changes in salmon escapement. Years with high salmon escapement may be more likely to be those with high water flow (Jager and Rose 2003), which reduces the accessibility of salmon to bears (Quinn et al. 2003; Boulanger et al. 2004). Thus the variation in salmon availability may be reduced because accessibility is inversely related to salmon numbers. My models also assume that the percent salmon in diet is directly proportional to the number of salmon killed. However bears eat less of each carcass as salmon availability increases (Gende et al. 2001), so their actual diet composition may be less responsive to changes in escapement. Finally, subordinate bears and mothers with cubs may avoid salmon streams to reduce conflict with dominant or infanticidal bears, reducing the salmon in their diet even when salmon are available (Ben-David et al. 2004;
Quinn et al. 2003). All of these situations reduce the responsiveness of percent salmon in diet to salmon escapement.
Incorporation of uncertainty through Bayesian meta-analysis and stochastic population simulations reveals that brown bears in the central coast of British Columbia may not have a secure future. Even with unchanged levels of salmon escapement, there is a risk of decline. Collapse of salmon runs increases the risk of population decline and may lead to detrimental transient effects. Additive harvest plays a significant role in determining whether the population grows or declines. Important gaps remain in our knowledge of brown bear vital rates and their response to human interventions, especially with regard to process variation. If managers and conservationists want greater precision in assessing this population, more work needs to be done to estimate vital rates and their annual variation for this specific population. 105
Table 5.1. Demographic studies used in brown bear meta-analysis (see Methods for explanation of variables).
Location sc sy ss sa F λ Harvest
Banff and Kananaskis, 0.79 0.91 0.92 0.95 0.239 1.039 No
Albertaa
Black Lake, Alaskab 0.57 0.9 0.407 Yes
Cabinet-Yaak, Montanac 0.679 0.875 0.771 0.929 0.287 0.964 No
Denali NP, Alaskab 0.34 0.97 0.333 No
Flathead Valley, BCd 0.867 0.944 0.931 0.946 0.422 1.085 Yes
Katmai NP, Alaksae 0.34 0.79 1.00 0.91 0.25 0.98 No
Kenai Peninsula, Alaskaf 0.683 0.587 0.919 0.342 Yes
Kuskokwim Mountains, 0.482 0.724 0.862 0.91 0.38 0.996 Yes
Alaskag
McNeil River, Alaskah 0.53 0.93 0.34 Yes
Noatak River, Alaskai 0.874 0.887 0.94 0.329 Yes
a Garshelis et al. 2005 b Miller et al. 2003 c Wakkinen and Kasworm 2004 d Hovey and McLellan 1996 e Sellers et al. 1999, from a f Farley 2005 g Kovach et al. 2006 h Sellers and Aumiller 1994 i Ballard et al. 1991
106
Location sc sy ss sa F λ Harvest
N Continental Divide, 0.887 0.863 0.398 No
Montana and Wyomingj
Nunavut, Northwest 0.737 0.683 0.979 0.40 1.033 No
Territoriesk
Selkirk Mountains, 0.875 0.784 0.9 0.936 0.288 1.019 No
Washingtonc
Susitna River, Alaskal 0.64 0.88 0.86 0.92 0.36 1.02 Yes
Swan Mountains, Montanam 0.785 0.906 0.629 0.899 0.261 0.977 No
Yellowstone, Wyomingn 0.64 0.817 0.95 0.95 0.318 1.076 No
Note: Fecundity for the Black Lake and Denali populations was calculated from the litter size presented in the study and the mean interbirth interval for the other studies.
j Aune et al. 1994 k McLoughlin et al. 2003 l Miller 1997, from a m Mace and Waller 1998 n Schwartz et al. 2006
107
Table 5.2. Average population growth rate of brown bears in British Columbia under four structural models (see Methods for explanation), three harvest rates with current salmon escapement, and four salmon escapement levels with no harvest.
Harvest Rate Salmon Escapement
Model 0 0.02 0.05 1 0.8 0.5 0
Ceiling 0.997 0.988 0.963 0.997 0.995 0.993 0.986
Combo 0.987 0.979 0.955 0.987 0.987 0.985 0.983
Logistic 1.007 0.988 0.961 1.007 1.004 1.000 0.999
Quinn 1.009 0.991 0.963 1.009 1.008 1.005 0.999
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Figure Legends
Figure 5.1. Central coastal British Columbia salmon (Oncorhynchus spp) escapement index, 1976-2000; the section after the dashed line, 1985-2000, is the portion used in simulations.
Figure 5.2. Posterior distributions of the means of female brown bear survival rates based on meta-analysis of demographic studies.
Figure 5.3. Functions relating (a) brown bear fecundity to the proportion of their diet comprised of salmon and (b) fecundity to the index of salmon escapement with arrows indicating the observed range of salmon escapement in the focal population. Data for (a) from Hildebrand et al. (1999); see additional details in Methods.
Figure 5.4. Female brown bear population size over a 20 year time horizon under current salmon escapement and no harvest using Quinn’s asymptotic model; dashed lines indicate the upper 75% and lower 25% of simulated populations.
Figure 5.5. Change in female brown bear population growth rate due to changes in salmon escapement or bear harvest from current escapement or no harvest, respectively.
109
2.5
2
1.5
1
0.5 Salmon Escapement Index Escapement Salmon 0 1975 1980 1985 1990 1995 2000 Year
Figure 5.1.
110
40
35
30
25
20
15
Probability Density Probability 10
5
0 0.4 0.5 0.6 0.7 0.8 0.9 1 Survival
Cub Survival Yearling Survival Subadult Survival Adult Survival
Figure 5.2.
111
a) 0.44
0.42
0.4
0.38
0.36 Fecundity y = 0.0849x + 0.3245 R² = 0.5909 0.34
0.32
0.3 0 0.2 0.4 0.6 0.8 1 Proportion Salmon in Diet
0.42 b) 0.4
0.38
0.36 Quinn's Asymptotic
Fecundity 0.34 Logistic
0.32
0.3 0 1 2 3 4 Salmon Escapement Index
Figure 5.3.
112
4000 3500 3000 2500 2000 1500
Population Size Population 1000 500 0 0 5 10 15 20 Year
25% Median 75%
Figure 5.4.
113
Salmon Harvest
0.8 0.5 0 0.02 0.05 0
-0.005
-0.01
-0.015 Quinn
-0.02 Logistic Ceiling -0.025 Combo
Scenario -0.03
-0.035
-0.04
-0.045 Difference in Lambda from Baseline Baseline from in Lambda Difference -0.05
Figure 5.5.
114
BIBLIOGRAPHY
Allendorf, F. W., and J. J. Hard. 2009. Human-induced evolution caused by unnatural
selection through harvest of wild animals. Proceedings of the National Academy of
Science 106:9987-9994.
Andren, H., J. D. Linnell, O. Liberg, R. Andersen, A. Danell, J. Karlsson, J. Odden, P. F.
Moa, P. Ahlqvist, T. Kvam, R. Franzen, and P. Segerstrom. 2006. Survival rates and
causes of mortality in Eurasian lynx (Lynx lynx) in multi-use landscapes. Biological
Conservation 131:23-32.
Arlt, D. and T. Part. 2007. Nonideal breeding habitat selection: a mismatch between
preference and fitness. Ecology 88: 792-801.
Atkinson, S. N., and M. A. Ramsay. 1995. The effects of prolonged fasting of the body
composition and reproductive success of female polar bears (Ursus maritimus).
Functional Ecology 9:559-567.
Aune, K. E., R. D. Mace, and D. W. Carney. 1994. The reproduction biology of female grizzly
bears in the Northern Continental Divide Ecosystem with supplemental data from
the Yellowstone Ecosystem. International Conference on Bear Research and
Management 9:451-458.
Bailey, R. G. 1998. Ecoregions Map of North America Explanatory Note. P. 10 Washington,
DC: USDA Forest Service.
Baldwin, R. A., and L. C. Bender. 2009. Survival and productivity of a low-density black
bear population in Rocky Mountain National Park, Colorado. Human-Wildlife
Conflicts 3:271-281.
115
Bales, S. L., E. C. Hellgren, D. M. Leslie, and J. Hemphill. 2005. Dynamics of a recolonizing
population of black bears in the Ouachita Mountains of Oklahoma. Wildlife Society
Bulletin 33:1342-1351.
Ballard, W. B., L. A. Ayres, S. G. Fancy, D. J. Reed, and K. E. Roney. 1991. Demography of
Noatak grizzly bears in relation to human exploitation and mining development.
Federal Aid in Wildlife Restoration Program Report, Alaska Department of Fish and
Game, Juneau, USA.
Banci, V., D. A. Demarchi, and W. R. Archibald. 1994. Evaluation of the population status
of grizzly bears in Canada. International Conference on Bear Research and
Management 9:129-142.
Battin, J. 2004. When good animals love bad habitat: Ecological traps and the conservation
of animal populations. Conservation Biology 18: 1482-1491.
Beckmann, J. P. and J. Berger. 2003. Using black bears to test ideal-free distribution
models experimentally. Journal of Mammalogy 84: 594-606.
Beckmann, J. P., and C. W. Lackey. 2008. Carnivores, urban landscapes, and longitudinal
studies: a case history of black bears. Human-Wildlife Conflicts 2:77-83.
Beecham, J. 1980. Some population characteristics of two black bear populations in Idaho.
Ursus 4:201-204.
Beecham, J. J. 1983. Population characteristics of black bears in west central Idaho.
Journal of Wildlife Management 47:405-412.
Beecham, J. J., D. G. Reynolds, and M. G. Hornocker. 1983. Black bear denning activities and
den characteristics in west-central Idaho. Ursus 5:79-86.
116
Ben-David, M., K. Titus, and L. R. Beier. 2004. Consumption of salmon by Alaskan brown
bears: a trade-off between nutritional requirements and the risk of infanticide?
Oecologia 138:465-474.
Benson, J. F., and M. J. Chamberlain. 2007. Space use, survival, movements, and
reproduction of reintroduced Louisiana black bears. Journal of Wildlife Management
71:2393-2403.
Beringer, J., S. G. Seibert, S. Reagan, A. J. Brody, M. R. Pelton, and L. D. Vangilder. 1998.
The influence of a small sanctuary on survival rates of black beras in North
Carolina. Journal of Wildlife Management 62:727-734.
Bertram, M. R., and M. T. Vivion. 2002. Black bear monitoring in eastern interior Alaska.
Ursus 13:69-77.
“Black Bear in New Jersey: Status Report 2004.” 2004. New Jersey Department of
Environmental Protection.
Boertje, R. D., and R. Stephenson. 1992. Effects of ungulate availability on wolf
reproductive potential in Alaska. Canadian Journal of Zoology 70:2441-2443.
Boulanger, J., S. Himmer, and C. Swan. 2004. Monitoring of grizzly bear population trends
and demography using DNA mark-recapture methods in the Owikeno Lake area of
British Columbia. Canadian Journal of Zoology 82:1267-1277.
Bowler, D. E. and T. G. Benton. 2005. Causes and consequences of animal dispersal
strategies: relating individual behavior to spatial dynamics. Biological Reviews 80:
205-225.
Boyce, M. S., C. V. Haridas, C. T. Lee, and the NCEAS Stochastic Demography Working
Group. 2006. Demography in an increasingly variable world. TRENDS in Ecology
and Evolution 21: 141-148.
117
Boyd, I. L., J. P. Croxall, and N. J. Lunn. 1995. Population demography of Antarctic fur
seals - the costs of reproduction and implications for life-histories. Journal of Animal
Ecology 64:505-518.
Brawn, J. D. and S. K. Robinson. 1996. Source-sink population dynamics may complicate
the interpretation of long-term census data. Ecology 77: 3-12.
Brongo, L. L., M. S. Mitchell, and J. B. Grand. 2005. Long-term analysis of survival,
fertility, and population growth rate of black bears in North Carolina. Journal of
Mammalogy 86:1029-1035.
Brown, J. L. 1969. Territorial behavior and population regulation in birds. Wilson Bulletin
81: 293-329.
Brown, K. M. 1985. Intraspecific life history variation in a pond snail: The roles of
population divergence and phenotypic plasticity. Evolution 39:387-395.
Bunnell, F. L., and D. E. N. Tait. 1980. Bears in models and in reality: Implications to
management. Ursus 4:15-23.
Carbone, C., and J. L. Gittleman. 2002. A common rule for the scaling of carnivore density.
Science 295:2273-2276.
Caswell, H. 2001. Matrix Population Models: Construction, Analysis, and Interpretation.
Sinauer Associates, Sunderland, Massachusetts.
Caswell, H. and M. Fujiwara. 2004. Beyond survival estimation: mark-recapture, matrix
population models, and population dynamics. Animal Biodiversity and Conservation
27(1): 471-488.
Chapron, G., D. G. Miquelle, A. Lambert, J. M. Goodrich, S. Legendre, and J. Clobert. 2008.
The impact on tigers of poaching versus prey depletion. Journal of Applied Ecology
45:1667-1674.
118
Childs, D. Z., M. Rees, K. E. Rose, P. J. Grubb, and S. P. Ellner. 2003. Evolution of complex
flowering strategies: an age- and size-structured integral projection model.
Proceedings of the Royal Society of London B 270: 1829-1838.
Clark, J. D., and R. Eastridge. 2006. Growth and sustainability of black bears at White
River National Wildlife Refuge, Arkansas. Journal of Wildlife Management 70:1094-
1101.
Clark, J. D., and K. G. Smith. 1994. A demographic comparison of two black bear
populations in the interior highlands of Arkansas. Wildlife Society Bulletin 22:593-
603.
Clutton-Brock, T. H., F. E. Guinness, and S. D. Albon. 1983. The cost of reproduction to red
deer hinds. Journal of Animal Ecology 52:367-383.
Coltman, D. W., P. O'Donoghue, J. T. Jorgenson, J. T. Hogg, C. Strobeck, and M. Festa-
Bianchet. 2003. Undesirable evolutionary consequences of trophy hunting. Nature
426:655-658.
Conn, P. B., D. R. Diefenbach, J. L. Laake, M. A. Ternent, and G. C. White. 2008. Bayesian
analysis of wildlife age-at-harvest data. Biometrics 64:1170-1177.
Cooley, H. S., R. B. Wielgus, G. M. Koehler, H. S. Robinson, and B. T. Maletzke. 2009. Does
hunting regulate cougar populations? A test of the compensatory mortality
hypothesis. Ecology 90:2913-2921.
Costello, C. M., D. E. Jones, K. A. Green Hammond, R. M. Inman, K. H. Inman, B. C.
Thompson, R. A. Deitner, and H. B. Quigley. 2001. “A study of black bear ecology in
New Mexico with models for population dynamics and habitat suitability.” Federal
Aid in Wildlife Restoration Project W-131-R Final Report, New Mexico Game and
Fish.
119
Costello, C. M., S. R. Creel, S. T. Kalinowski, N. V. Vu, and H. B. Quigley. 2008. Sex-biased
natal dispersal and inbreeding avoidance in American black bears as revealed by
spatial genetic analyses. Molecular Ecology 17: 4713-4723.
Craft, M. E., E. Volz, C. Packer, and L. A. Meyers. 2009. Distinguishing epidemic waves
from disease spillover in a wildlife population. Proceedings of the Royal Society B
276: 1777-1785.
Craighead, J. J., J. R. Varney, and F. C. J. Craighead. 1974. A population analysis of the
Yellowstone grizzly bears. Montana Forest and Conservation Experiment Station
Bulletin 40:1-20.
Cunningham, S. C., and W. B. Ballard. 2004. Effects of wildfire on black bear demographics
in central Arizona. Wildlife Society Bulletin 32:928-937.
Czetwertynski, S. M., M. S. Boyce, and F. K. Schmiegelow. 2007. Effects of hunting on
demographic parameters of American black bears. Ursus 18:1-18.
Darimont, C. T., S. M. Carlson, M. T. Kinnison, P. C. Paquet, and T. E. Relmchen. 2009.
Human predators outpace other agents of trait change in the wild. Proceedings of
the National Academy of Sciences 106:952-954.
Diefenbach, D. R., and G. L. Alt. 1998. Modeling and evaluation of ear tag loss in black
bears. Journal of Wildlife Management 62:1292-1300.
Diefenbach, D. R., J. L. Laake, and G. L. Alt. 2004. Spatio-temporal and demographic
variation in the harvest of black bears: implications for population estimation.
Journal of Wildlife Management 68: 947-959.
Doak, D. F. 1995. Source-sink models and the problem of habitat degradation: general
models and applications to the Yellowstone grizzly. Conservation Biology 9: 1370-
1379.
120
Dobson, F. S., and J. O. Murie. 1987. Interpretation of intraspecific life history patterns:
Evidence from Columbian Ground Squirrels. The American Naturalist 129:382-397.
Donovan, T. M. and F. R. Thompson III. 2001. Modeling the ecological trap hypothesis: A
habitat and demographic analysis for migrant songbirds. Ecological Applications 11:
871-882.
Easterling, M. R., S. P. Ellner, and P. M. Dixon. 2000. Size-specific sensitivity: applying a
new structured population model. Ecology 81: 694-708.
Eberhardt, L. L. 1990. Survival rates required to sustain bear populations. Journal of
Wildlife Management 54:587-590.
Eiler, J. H., W. G. Wathen, and M. R. Pelton. 1989. Reproduction in black bears in the
southern Appalachian Mountains. Journal of Wildlife Management 53:353-360.
Elowe, K. D., and W. E. Dodge. 1989. Factors affecting black bear reproductive success and
cub survival. Journal of Wildlife Management 53:962-968.
Elton, C., and M. Nicholson. 1942. The ten-year cycle in numbers of the lynx in Canada.
Journal of Animal Ecology 11:215-244.
Ericsson, G. 2001. Reduced cost of reproduction in moose (Alces alces) through human
harvest. Alces 37:61-69.
Etterson, M. A. and L. R. Nagy. 2008. Is mean squared error a consistent indicator of
accuracy for spatially structured demographic models? Ecological Modelling 211:
202-208.
Farley, S. 2005. Ecological studies of the Kenai Peninsula brown bear. Federal Aid Final
Research Report, Alaska Department of Fish and Game, Juneau, USA.
Figueira, W. F. 2009. Connectivity or demography: Defining sources and sinks in coral reef
fish metapopulations. Ecological Modelling 220: 1126-1137.
121
Fraser, D. 1984. A simple relationship between removal rate and age-sex composition of
removals for certain animal populations. Journal of Applied Ecology 21:97-101.
Freedman, A. H., K. M. Portier, and M. E. Sunquist. 2003. Life history analysis for black
bears (Ursus americanus) in a changing demographic landscape. Ecological
Modelling 167:47-64.
Fryxell, J. M., C. Packer, K. McCann, E. J. Solberg, and B.-E. Saether. 2010. Resource
management cycles and the sustainability of harvested wildlife populations. Science
328:903-906.
Fuller, T. K., and P. R. Sievert 2001. Carnivore demography and the consequences of
changes in prey availability. Pages 161-178 in John L Gittleman, Stephan M Funk,
David Macdonald, and Robert K Wayne, editors. Carnivore Conservation.
Cambridge University Press, United Kingdom.
Gaillard, J.-M., M. Festa-Bianchet, and N. G. Yoccoz. 1998. Population dynamics of large
herbivores: variable recruitment with constant adult survival. Trends in Ecology
and Evolution 13:58-63.
Garrison, E. P., J. W. McCown, and M. K. Oli. 2007. Reproductive ecology and cub survival
of Florica black bears. Journal of Wildlife Management 71:720-727.
Garshelis, D. L. 1994. Density dependent population regulation of black bears. Pp. 3-14 in
M Taylor, editor. Density-dependent population regulation in black, brown, and
polar bears. International Conference on Bear Research and Management
Monograph Series 3.
Garshelis, D. L., and H. Hristienko. 2006. State and provincial estimates of American black
bear numbers versus assessments of population trend. Ursus 17:1-7.
Garshelis, D. L., P. L. Coy, and K. V. Noyce. 2005. “Ecology and population dynamics of
black bears in Minnesota.” 122
http://files.dnr.state.mn.us/publications/wildlife/research2004/forest.pdf, Forest
Wildlife Populations and Research Group, Grand Rapids, MN.
Garshelis, D. L., M. L. Gibeau, and S. Herrero. 2005. Grizzly bear demographics in and
around Banff National Park and Kananaskis country, Alberta. Journal of Wildlife
Management 69:277-297.
Gelman, A., J. B. Carlin, H. S. Stern, and D. B. Rubin. 2004. Bayesian Data Analysis.
Chapman & Hall/CRC, New York.
Gende, S. M., T. P. Quinn, and M. F. Willson. 2001. Consumption choice by bears feeding on
salmon. Oecologia 127:372-382.
Gilad, O., W. E. Grant, and D. Saltz. 2008. Simulated dynamics of Arabian Oryx (Oryx
leucoryx) in the Israeli Negev: Effects of migration corridors and post-reintroduction
changes in natality on population viability. Ecological Modelling 210: 169-178.
Ginsberg, J. R., and E. J. Milner-Gulland. 1994. Sex-biased harvesting and population
dynamics in ungulates: Implications for conservation and sustainable use.
Conservation Biology 8:157-166.
Gove, N. E., J. R. Skalski, P. Zager, and R. L. Townsend. 2002. Statistical models for
population reconstruction using age-at-harvest data. Journal of Wildlife
Management 66:310-320.
Griffin, P. C. and L. S. Mills. 2009. Sinks without borders: snowshoe hare dynamics in a
complex landscape. Oikos 118:1487-1498.
Gusset, M., and D. W. Macdonald. 2010. Group size effects in cooperatively breeding
African wild dogs. Animal Behaviour 79:425-428.
Hammond, F. M. 2002. “The effects of resort and residential development on black bears in
Vermont.” Final Report, Vermont Agency of Natural Resources, Department of Fish
and Wildlife. 123
Harris, R. B., and L. H. Metzgar. 1987. Estimating harvest rates of bears from sex ratio
changes. Journal of Wildlife Management 51:802-811.
Hauser, C. E., A. R. Pople, and H. P. Possingham. 2006. Should managed populations be
monitored every year? Ecological Applications 16: 807-819.
Hebblewhite, M., M. Percy, and R. Serrouya. 2003. Black bear (Ursus americanus) survival
and demography in the Bow Valley of Banff National Park, Alberta. Biological
Conservation 112:415-425.
Hellgren, E. C., and M. R. Vaughan. 1989. Demographic analysis of a black bear population
in the Great Dismal Swamp. Journal of Wildlife Management 53:969-977.
Heppell, S. S., H. Caswell, and L. B. Crowder. 2000. Life histories and elasticity patterns:
Perturbation analysis for species with minimal demographic data. Ecology 81:654-
665.
Hersey, K. R., and K. Bunnell. 2006. “Utah Black Bear Annual Report.” Annual
Performance Report for Federal Aid Project W-65-M-54, Utah Department of
Natural Resources, Division of Wildlife Resources.
Hilderbrand, G. V., C. C. Schwartz, C. T. Robbins, M. E. Jacoby, T. A. Hanley, S. M. Arthur,
and C. Servheen. 1999. The importance of meat, particularly salmon, to body size,
population productivity, and conservation of North American brown bears. Canadian
Journal of Zoology 77:132-138.
Holt, R. D. 1985. Population dynamics in two-patch environments: some anomalous
consequences of an optimal habitat distribution. Theoretical Population Biology 28:
181-208.
Hone, J. and T. H. Clutton-Brock. 2007. Climate, food, density and wildlife population
growth rate. Journal of Animal Ecology 76: 361-367.
124
Hovey, F. W., and B. N. McLellan. 1996. Estimating population growth of grizzly bears from
the Flathead River drainage using computer simulations of reproduction and
survival rates. Canadian Journal of Zoology 74:1409-1416.
Hristienko, H., and J. E. McDonald, Jr. 2007. Going into the 21st century: a perspective on
trends and controversies in the management of the American black bear. Ursus
18:72-88.
Hristienko, H., D. Pastuck, K. J. Rebizant, B. Knudsen, and M. L. Connor. 2004. Using
reproductive data to model American black bear cub orphaning in Manitoba due to
spring harvest of females. Ursus 15:23-34.
Hunter, C. M., H. Caswell, M. C. Runge, E. V. Regehr, S. C. Amstrup, and I. Stirling. 2010.
Climate change threatens polar bear populations: a stochastic demographic analysis.
Ecology 91: 2883-2897.
Iverson, S. A. and D. Esler. 2010. Harlequin Duck population injury and recovery dynamics
following the 1989 Exxon Valdez oil spill. Ecological Applications 20: 1993-2006.
Jackson, A. L., A. C. Broderick, W. J. Fuller, F. Glen, G. D. Ruxton, and B. J. Godley. 2008.
Sampling design and its effect on population monitoring: How much monitoring do
turtles really need? Biological Conservation 141: 2932-2941.
Jager, H. I., and K. A. Rose. 2003. Designing optimal flow patterns for fall Chinook salmon
in a Central Valley, California, river. North American Journal of Fisheries
Management 23:1-21.
Johansson, M., C. R. Primmer, and J. Merila. 2007. Does habitat fragmentation reduce
fitness and adaptability? A case study of the common frog (Rana temporaria).
Molecular Ecology 16: 2693-2700.
125
Johnson, H. E., L. S. Mills, T. R. Stephenson, and J. D. Wehausen. 2010. Population-specific
vital rate contributions influence management of an endangered ungulate.
Ecological Applications 20: 1753-1765.
Johnson, J. B., and J. J. Zuniga-Vega. 2009. Differential mortality drives life-history
evolution and population dynamics in the fish Brachyrhaphis rhabdophora. Ecology
90:2243-2252.
Johnson, W. E., D. P. Onorato, M. E. Roelke, E. D. Land, M. Cunningham, R. C. Belden, R.
McBride, D. Jansen, M. Lotz, D. Shindle, J. Howard, D. E. Wildt, L. M. Penfold, J. A.
Hostetler, M. K. Oli, and S. J. O’Brien. 2010. Genetic restoration of the Florida
panther. Science 329: 1641-1645.
Jolicoeur, H., F. Goudreault, and M. Crete. 2006. “Etude de la dynamique de deux
populations d'ours noirs de l'Outaouais fortement exploitees par la chasse et le
piegeage, 1992-1995.” Ministere des Ressources naturelles et de la Faune.
Jonkel, C. J., and I. M. Cowan. 1971. The black bear in the spruce-fir forest. Wildlife
Monographs 27:3-57.
Jonzen, N., J. R. Rhodes, and H. P. Possingham. 2005. Trend detection in source-sink
systems: When should sink habitats be monitored? Ecological Applications 15: 326-
334.
Jorgensen, C., B. Ernande, and O. Fiksen. 2009. Size-selective fishing gear and life history
evolution in the Northeast Arctic cod. Evolutionary Applications 2:356-370.
Karanth, K. U. and R. Chellam. 2009. Carnivore conservation at the crossroads. Oryx 43:1-
2.
Karanth, K. U., J. D. Nichols, N. S. Kumar, W. A. Link, and J. E. Hines. 2004. Tigers and
their prey: Predicting carnivore densities from prey abundance. Proceedings of the
National Academy of Science 101:4854-4858. 126
Kasbohm, J. W., M. R. Vaughan, and J. G. Kraus. 1996. Effects of gypsy moth infestation
on black bear reproduction and survival. Journal of Wildlife Management 60:408-
416.
Kasworm, W. F., and T. J. Thier. 1994. Adult black bear reproduction, survival, and
mortality sources in Northwest Montana. Bears: Their Biology and Management
9:223-230.
Kemp, G. A. 1972. Black bear population dynamics at Cold Lake, Alberta, 1968-70. Bears:
Their Biology and Management 23:26-31.
Kendall, K. C., J. B. Stetz, D. A. Roon, L. P. Waits, J. B. Boulanger, and D. Paetkau. 2008.
Grizzly bear density in Glacier National Park, Montana. Journal of Wildlife
Management 72:1693-1705.
Klenzendorf, S. A. 2002. Population dynamics of Virginia's hunted black bear population. in
Dissertation. Blacksburg, Virginia: Virginia Polytechnic Institute and State
University.
Knight, R. R., B. M. Blanchard, and L. L. Eberhardt. 1988. Mortality patterns and
population sinks for Yellowstone grizzly bears, 1973-1985. Wildlife Society Bulletin
16:121-125.
Koehler, G. M., and D. J. Pierce. 2005. Survival, cause-specific mortality, sex, and ages of
American black bears in Washington state, USA. Ursus 16:157-166.
Kokko, H. and W. J. Sutherland. 2001. Ecological traps in changing environments:
ecological and evolutionary consequences of a behaviourally mediated Allee effect.
Evolutionary Ecology Research 3: 537-551.
Kolenosky, G. B. 1990. Reproduction biology of black bears in east-central Ontario. Bears:
Their Biology and Management 8:385-392.
127
Kovach, S. D., G. H. Collins, M. T. Hinkes, and J. W. Denton. 2006. Reproduction and
survival of brown bears in southwest Alaska, USA. Ursus 17:16-29.
Lambert, C. M. S., R. B. Wielgus, H. S. Robinson, D. D. Katnik, H. S. Cruickshank, R.
Clarke, and J. Almack. 2006. Cougar population dynamics and viability in the
Pacific Northwest. Journal of Wildlife Management 70:246-254.
Larivière, S. 2001. Ursus americanus. Mammalian Species 647: 1-11.
Larkin, J. L., D. S. Maehr, T. S. Hoctor, M. A. Orlando, and K. Whitney. 2004. Landscape
linkages and conservation planning for the black bear in west-central Florida.
Animal Conservation 7: 23-34.
LeCount, A. L. 1982. Characteristics of a central Arizona black bear population. Journal of
Wildlife Management 46:861-868.
LeCount, A. L. 1987. Causes of black bear cub mortality. Bears: Their Biology and
Management 7:75-82.
Lee, D. J. and M. R. Vaughan. 2003. Dispersal movements by subadult American black
bears in Virginia. Ursus 14: 162-170.
Lee, D. J., and M. R. Vaughan. 2005. Yearling and subadult black bear survival in a hunted
Virginia population. Journal of Wildlife Management 69:1641-1651.
Levins, R. 1969. Some demographic and genetic consequences of environmental
heterogeneity for biological control. Bulletin of the Entomological Society of America
71: 237-240.
Lima, S. L. and P. A. Zollner. 1996. Towards a behavioral ecology of ecological landscapes.
Trends in Ecology and Evolution 11: 131-135.
Litvaitis, J. A., and D. M. Kane. 1994. Relationship of hunting technique and hunter
selectivity to composition of black bear harvest. Wildlife Society Bulletin 22:604-606.
128
Ludwig, D., R. Hilborn, and C. Walters. 1993. Uncertainty, resource exploitation, and
conservation: Lessons from history. Science 260:17, 36.
Lunn, D. J., A. Thomas, N. Best, and D. Spiefelhalter. 2000. WinBUGS - a Bayesian
modelling framework: concepts, structure, and extensibility. Statistics and
Computing 10:325-337.
Mace, R. D., and J. S. Waller. 1998. Demography and population trend of grizzly bears in
the Swan Mountains, Montana. Conservation Biology 12:1005-1016.
Maehr, D. S., T. S. Hoctor, L. J. Quinn, and J. S. Smith. 2001. Black bear habitat
management guidelines for Florida. Technical Report No. 17. Florida Fish and
Wildlife Conservation Commission, Tallahassee, Florida, USA.
Mattson, D. J. and T. Merrill. 2002. Extirpations of grizzly bears in the contiguous United
States, 1850-2000. Conservation Biology 16:1123-1136.
Mattson, D. J., S. Herrero, and T. Merrill. 2005. Are black bears a factor in the restoration
of North American grizzly bear populations? Ursus 16: 11-30.
McLoughlin, P. D., M. K. Taylor, H. D. Cluff, R. J. Gau, R. Mulders, R. L. Case, S. Boutin,
and F. Messier. 2003. Demography of barren-ground grizzly bears. Canadian
Journal of Zoology 81:294-301.
McLoughlin, P. D., M. K. Taylor, and F. Messier. 2005. Conservation risks of male-selective
harvest for mammals with low reproductive potential. Journal of Wildlife
Management 69:1592-1600.
McConnell, P. A., J. R. Garris, E. Pehek, and J. L. Powers. 1997. “Black bear management
plan.” New Jersey Department of Environmental Protection, Division of Fish, Game
and Wildlife.
McDonald, J. E., and T. K. Fuller. 2001. Prediction of litter size in American black bears.
Ursus 12:93-102. 129
McDonald, J. E., and T. K. Fuller. 2005. Effects of spring acorn availability on black bear
diet, milk composition, and cub survival. Journal of Mammalogy 86:1022-1028.
McLaughlin, C. R. 1998. Modeling effects of food and harvests on female black bear
populations. in Dissertation. University of Maine.
McLean, P. K., and M. R. Pelton. 1994. Estimates of population density and growth of black
bears in the Smoky Mountains. Bears: Their Biology and Management 9:253-261.
McLellan, B. 2005. Sexually selected infanticide in grizzly bears: the effects of hunting on
cub survival. Ursus 16:141-156.
Mduma, S., A. R. E. Sinclair, and R. Hilborn. 1999. Food regulates the Serengeti
wildebeest: A 40-year record. Journal of Animal Ecology 68:1101-1122.
Millar, J. S., E. M. Derrickson, and S. T. P. Sharpe. 1992. Effects of reproduction on
maternal survival and subsequent reproduction in northern Peromyscus
maniculatus. Canadian Journal of Zoology 70:1129-1134.
Miller, S. D. 1990. Population management of bears in North America. International
Conference on Bear Research and Management 8:357-373.
Miller, S. D. 1994. Black bear reproduction and cub survivorship in south-central Alaska.
Bears: Their Biology and Management 9:263-273.
Miller, S. D., R. A. Sellers, and J. A. Keay. 2003. Effects of hunting on brown bear cub
survival and litter size in Alaska. Ursus 14:130-152.
Mills, L. S. 2007. Conservation of Wildlife Populations: Demography, Genetics and
Management. Blackwell Publishing, Malden, Massachusetts, USA.
Milner-Gulland, E. J., and J. M. Rowcliffe. 2007. Conservation and Sustainable Use. Oxford
University Press, Oxford, England.
Mitchell, M. S., L. B. Pacifici, J. B. Grand, and R. A. Powell. 2009. Contributions of vital
rates to growth of a protected population of American black bears. Ursus 20:77-84. 130
Monson, D. H., J. A. Estes, J. L. Bodkin, and D. B. Siniff. 2000. Life history plasticity and
population regulation in sea otters. Oikos 90:457-468.
Morris, W. F., and D. F. Doak. 2002. Quantitative Conservation Biology. Sinauer Associates
Inc., Sunderland, MA, USA.
Mowat, G., and D. C. Heard. 2006. Major components of grizzly bear diet across North
America. Canadian Journal of Zoology 84:473-489.
Murie, J. O., and F. S. Dobson. 1987. The costs of reproduction in female Columbian ground
squirrels. Oecologia 73:1-6.
Nilsen, E. B., J.-M. Gaillard, R. Andersen, J. Odden, D. Delorme, G. van Laere, and J. D. C.
Linnell. 2009. A slow life in hell or a fast life in heaven: Demographic analyses of
contrasting roe deer populations. Journal of Animal Ecology 78:585-594.
Noon, B. R. and J. A. Blakesley. 2006. Conservation of the Northern Spotted Owl under the
Northwest Forest Plan. Conservation Biology 20: 288-296.
Noyce, K. V., and D. L. Garshelis. 1997. Influence of natural food abundance on black bear
harvests in Minnesota. Journal of Wildlife Management 61:1067-1074.
Obbard, M. E., and E. J. Howe. 2008. Demography of black bears in hunted and unhunted
areas of the boreal forest of Ontario. Journal of Wildlife Management 72:869-880.
Oro, D. 2008. Living in a ghetto within a local population: an empirical example of an ideal
despotic distribution. Ecology 89: 838-846.
Paloheimo, J. E., and D. Fraser. 1981. Estimation of harvest rate and vulnerability from
age and sex data. Journal of Wildlife Management 45:948-958.
Pasitschniak-Arts, M. 1993. Ursus arctos. Mammalian Species 439:1-10.
Persson, J. 2005. Female wolverine (Gulo gulo) reproduction: reproductive costs and winter
food availability. Canadian Journal of Zoology 83:1453-1459.
131
Pfister, C. A. 1998. Patterns of variance in stage-structured populations: Evolutionary
predictions and ecological implications. Proceedings of the National Academy of
Sciences 95:213-218.
Poole, K. G., G. Mowat, and D. A. Fear. 2001. DNA-based population estimate for grizzly
bears Ursus arctos in northeastern British Columbia, Canada. Wildlife Biology
7:105-115.
Powell, R. A., J. W. Zimmerman, D. E. Seaman, and J. F. Gilliam. 1996. Demographic
analyses of a hunted black bear population with access to a refuge. Conservation
Biology 10:224-234.
Powell, R. A., J. W. Zimmerman, D. E. Seaman, and J. F. Gilliam. 1996. Demographic
analyses of a hunted black bear population with access to a refuge. Conservation
Biology 10:224-234.
Promislow, D. E. L. 1992. Costs of sexual selection in natural populations of mammals.
Proceedings of the Royal Academy of Science B. 247:203-210.
Promislow, D. E. L., R. Montgomerie, and T. E. Martin. 1992. Mortality costs of sexual
dimorphism in birds. Proceedings of the Royal Academy of Science B. 250:143-150.
Pulliam, H. R. 1988. Sources, sinks, and population regulation. American Naturalist 132:
652-661.
Pulliam, H. R. and B. J. Danielson. 1991. Sources, sinks, and habitat selection – a
landscape perspective on population-dynamics. American Naturalist 137: S50-S66.
Quinn, T. P., S. M. Gende, G. T. Ruggerone, and R. D. E. 2003. Density-dependent
predation by brown bears (Ursus arctos) on sockeye salmon (Oncorhynchus nerka).
Canadian Journal of Fisheries and Aquatic Science 60:553-562.
R Development Core Team 2009. R: A Language and Environment for Statistical
Computing. Vienna: R Foundation for Statistical Computing. 132
Reynolds, D. G., and J. J. Beecham. 1980. Home range activities and reproduction of black
bears in west-central Idaho. Bears: Their Biology and Management 4:181-190.
Robbins, C. T., C. C. Schwartz, and L. A. Felicetti. 2004. Nutritional ecology of ursids: a
review of newer methods and management implications. Ursus 15: 161-171.
Robinson, H. S., R. B. Wielgus, H. S. Cooley, and S. W. Cooley. 2008. Sink populations in
carnivore management: Cougar demography and immigration in a hunted
population. Ecological Applications 18:1028-1037.
Rogers, L. L. 1987. Effects of food supply and kinship on social behavior, movements, and
population growth of black bears in northeastern Minnesota. Wildlife Monographs
97:3-72.
Roseberry, J. L., and A. Woolf. 1991. A comparative evaluation of techniques for analyzing
white-tailed deer harvest data. Wildlife Monographs 117:3-59.
Rossell, C. R., and J. A. Litvaitis. 1994. Application of harvest data to examine responses of
black bears to land-use changes. Bears: Their Biology and Management 9:275-281.
Rupp, S. P., W. B. Ballard, and M. C. Wallace. 2000. A nationwide evaluation of deer hunter
harvest survey techniques. Wildlife Society Bulletin 28:570-578.
Ryan, C. W. 1997. Reproduction, survival, and denning ecology of black bears in
southwestern Virginia. in Thesis. Blacksburg, Virginia: Virginia Polytechnic
Institute and State University.
Saether, B.-E., and O. Bakke. 2000. Avian life history variation and contribution of
demographic traits to the population growth rate. Ecology 81:642-653.
Sandercock, B. K. 2006. Estimation of demographic parameters from live-encounter data: a
summary review. Journal of Wildlife Management 70: 1504-1520.
Sargeant, G. A., and R. L. Ruff. 2001. Demographic response of black bears at Cold Lake,
Alberta, to the removal of adult males. Ursus 12:59-68. 133
Sasaki, K., S. F. Fox, and D. Duvall. 2008. Rapid evolution in the wild: Changes in body
size, life-history traits, and behavior in hunted populations of the Japanese
mamushi snake. Conservation Biology 23:93-102.
Schaub, M., R. Zink, H. Beissmann, F. Sarrazin, and R. Arlettaz. 2009. When to end
releases in reintroduction programmes: demographic rates and population viability
analysis of bearded vultures in the Alps. Journal of Applied Ecology 46: 92-100.
Schwartz, C. C., and A. W. Franzmann. 1991. Interrelationship of black bears to moose and
forest succession in the northern coniferous forest. Wildlife Monographs 113:1-58.
Schwartz, C. C. and A. W. Franzmann. 1992. Dispersal and survival of subadult black bears
from the Kenai Peninsula, Alaska. Journal of Wildlife Management 56: 426-431.
Schwartz, C. C., M. A. Haroldson, G. C. White, R. B. Harris, S. Cherry, K. A. Keating, D.
Moody, and C. Servheen. 2006. Temporal, spatial, and environmental influences on
the demographics of grizzly bears in the Greater Yellowstone Ecosystem. Wildlife
Monographs 161:1-68.
Schwindt, R., A. R. Vining, and D. Weimer. 2003. A policy analysis of the BC salmon
fishery. Canadian Public Policy 29:73-94.
Seamans, M. E. and R. J. Gutierrez. 2007. Sources of variability in spotted owl population
growth rate: testing predictions using long-term mark-recapture data. Oecologia
152: 57-70.
Sellers, R. A., and L. D. Aumiller. 1994. Brown bear population characteristics and McNeil
River, Alaska. International Conference on Bear Research and Management 9:283-
293.
Shima, J. S., E. G. Noonburg, and N. E. Phillips. 2010. Life history and matrix
heterogeneity interact to shape metapopulation connectivity in spatially structured
environments. Ecology 91: 1215-1224. 134
Sokal, R. R., and F. J. Rohlf. 1995. Biometry. Third edition. W.H. Freeman and Company,
New York.
Sorci, G., J. Clobert, and S. Belichon. 1996. Phenotypic plasticity of growth and survival in
the common lizard Lacerta vivpara. Journal of Animal Ecology 65:781-790.
Sorensen, V. A., and R. A. Powell. 1998. Estimating survival rates of black bears. Canadian
Journal of Zoology 76:1335-1343.
Stamps, J. A. and R. R. Swaisgood. 2007. Someplace like home: experience, habitat
selection and conservation biology. Applied Animal Behaviour Science 102: 392-409.
Stetz, J. B., K. C. Kendall, and C. Servheen. 2010. Evaluation of bear rub surveys to
monitor grizzly bear population trends. Journal of Wildlife Management 74:860-870.
Sturtz, S., U. Ligges, and A. Gelman. 2005. R2WinBUGS: A package for running WinBUGS
from R. Journal of Statistical Software 12:1-16.
Swenson, J. E., F. Sandegren, A. Bjarvall, A. Soderberg, P. Wabakken, and R. Franzen.
1994. Size, trend, distribution and conservation of the brown bear Ursus arctos
population in Sweden. Biological Conservation 70:9-17.
Sweson, J. E., F. Sandegren, A. Soderberg, A. Bjarvall, R. Franzen, and P. Wabakken. 1997.
Infanticide caused by hunting of male bears. Nature 386:450-451.
Ternent, M. A., and D. Sittler. 2007. “Black Bear Reproduction in Northcentral
Pennsylvania.” Project Annual Job Report, Bureau of Wildlife Management,
Pennsylvania Game Commission, Harrisburg, PA.
Timmins, A. 2008. “Black bear research and management.” Performance Report Grant W-
89-R-8, New Hampshire.
Trauba, D. R. 1996. Black bear population dynamics, home range, and habitat use on an
island in Lake Superior. in Dissertation. Stevens Point, Wisconsin: University of
Wisconsin. 135
Vaughan, M. R. and M. R. Pelton. 1995. Black bears in North America. Our Living
Resources – Mammals. p 100-103.
Verbruggen, H., C. A. Maggs, G. W. Saunders, L. L. Gall, H. S. Yoon, and O. D. Clerck.
2010. Data mining approach identifies research priorities and data requirements for
resolving the red algal tree of life. BMC Evolutionary Biology 10:16.
Wakkinen, W. L., and W. F. Kasworm. 2004. Demographics and population trends of grizzly
bears in the Cabinet-Yaak and Selkirk Ecosystems of British Columbia, Idaho,
Montana, and Washington. Ursus 15:65-75.
Waples, R. S., D. W. Jensen, and M. McClure. 2010. Eco-evolutionary dynamics:
fluctuations in population growth rate reduce effective population size in Chinook
salmon. Ecology 91: 902-914.
Ward, E. J., E. E. Holmes, and K. C. Balcomb. 2009. Quantifying the effects of prey
abundance on killer whale reproduction. Journal of Applied Ecology 46:632-640.
Weaver, K. M. 1999. The ecology and management of black bears in the Tensas River Basin
of Louisiana. in Dissertation. Knoxville, Tennessee: University of Tennessee.
Wiegand, T., E. Revilla, and F. Knauer. 2004. Dealing with uncertainty in spatially explicit
population models. Biodiversity and Conservation 13:53-78.
Wielgus, R. B., F. Sarrazin, R. Ferriere, and J. Clobert. 2001. Estimating effects of adult
male mortality on grizzly bear population growth and persistence using matrix
models. Biological Conservation 98:293-303.
Williams, B. K., J. D. Nichols, and M. J. Conroy. 2002. Analysis and Management of Animal
Populations. Academic Press, San Diego, CA.
Wisdom, M. J., L. S. Mills, and D. F. Doak. 2000. Life stage simulation analysis: Estimating
vital-rate effects on population growth for conservation. Ecology 81:628-641.
136
Wooding, J. B., and T. S. Hardisky. 1994. Home range, habitat use, and mortality of black
bears in north-central Florida. Bears: Their Biology and Management 9:349-356.
Wooding, S., and R. Ward. 1997. Phylogeography and pleistocene evolution in the North
American black bear. Molecular Biology and Evolution 14:1096-1105.
Woodroffe, R., and D. W. Macdonald. 1995. Costs of breeding status in the European
badger, Meles meles. Journal of Zoology 235:237-245.
Woodroffe, R., and J. R. Ginsberg. 1998. Edge effects and the extinction of populations
inside protected areas. Science 280:2126-2128.
Ylikarjula, J., S. Alaja, J. Laakso, and D. Tesar. 2000. Effects of patch number and
dispersal patterns on population dynamics and synchrony. Journal of Theoretical
Biology 207: 377-387.
Yodzis, P., and G. B. Kolenosky. 1986. A population dynamics model of black bears in
eastcentral Ontario. Journal of Wildlife Management 50:602-612.
Zambrano, L., E. Vega, L. G. Herrera M., E. Prado, and V. H. Reynoso. 2007. A population
matrix model and population viability analysis to predict the fate of endangered
species in highly managed water systems. Animal Conservation 10: 297-303.
Zedrosser, A., B. Dahle, O.-G. Stoen, and J. E. Swenson. 2009. The effects of primipartiy on
reproductive performance in the brown bear. Oecologia 160:847-854.
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APPENDIX
R AND WINBUGS CODE FOR BAYESIAN META-ANALYSIS IN CHAPTER 2
##### BEGIN FILE ##### # Demography meta-analysis for black bears library("BRugs") library("R2WinBUGS") vr <- read.csv("BBVitalRates.csv") #read in the data #Each row is one study and includes means and variance estimates for vital #rates as well as columns indicating the location of the study
# Format data for use by WinBUGS # Cub Survival cs <- na.omit(cbind(vr$cs, vr$csv2, vr$Hunted, vr$Half, vr$Ecor, vr$Ecop)) # Yearling Survival ys <- na.omit(cbind(vr$ys, vr$ysv2, vr$Hunted, vr$Half, vr$Ecor, vr$Ecop)) # Subadult Survival ss <- na.omit(cbind(vr$ss, vr$ssv2, vr$Hunted, vr$Half, vr$Ecor, vr$Ecop)) # Adult Survival as <- na.omit(cbind(vr$as, vr$asv2, vr$Hunted, vr$Half, vr$Ecor, vr$Ecop)) # Primiparity p <- na.omit(cbind(vr$p, vr$pv2, vr$Hunted, vr$Half, vr$Ecor, vr$Ecop)) # Fecundity m <- na.omit(cbind(vr$m, vr$mv2, vr$Hunted, vr$Half, vr$Ecor, vr$Ecop))
# Prepare to run all models for a selected vital rate x<-cs #which vital rate J <- nrow(x) #how many samples are there mu <- x[,1] #means from studies var <- x[,2] #variance for each one eco <- as.numeric(factor(x[,5], labels=c(1:nlevels(as.factor(x[,5]))))) #provinces ecop <- as.numeric(factor(x[,6], labels=c(1:nlevels(as.factor(x[,6]))))) #divisions K <- nlevels(as.factor(eco)) #number of provinces N <- nlevels(as.factor(ecop)) #number of divisions half <- as.numeric(factor(x[,4],labels=c(1:nlevels(as.factor(x[,4]))))) halfr <- rep(0, K) halfp <- rep(0, N) for(i in 1:J){ for(k in 1:K){ if(eco[i]==k) halfr[k]<- half[i] #which half is each province in } for(n in 1:N){ if(ecop[i]==n) halfp[n]<- half[i] #which half is each division in } }
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# Prep inputs for bugs command data1 <- list("mu", "var", "J") data2 <- list("mu", "var", "J", "half") data3 <- list("mu", "var", "J", "ecop", "N") data4 <- list("mu", "var", "J", "eco", "K") data5 <- list("mu", "var", "ecop", "halfp", "J", "N") data6 <- list("mu", "var", "eco", "halfr", "J", "K")
# Functions to create initial values for SURVIVAL and PRIMIPARITY rates inits1 <- function(){ list(mu.c = runif(1,0.1,0.99), var.c = runif(1,0.001,0.5)) } inits2 <- function(){ list(a.c = runif(1,0,10), b.c = runif(1,0,10), mu.half = runif(2, 0.25, 0.95), stdev.half=runif(2,0.005, 0.015)) } inits3 <- function(){ list(a.c = runif(1,0,10), b.c = runif(1,0,10), mu.ecop = runif(N, 0.25, 0.95), stdev.ecop=runif(N,0.005, 0.015)) } inits4 <- function(){ list(a.c = runif(1,0,10), b.c = runif(1,0,10), mu.eco = runif(K, 0.25, 0.95), stdev.eco=runif(K,0.005, 0.015)) } inits5 <- function(){ list(a.c = runif(1,0,10), b.c = runif(1,0,10), mu.ecop = runif(N, 0.25, 0.95), stdev.ecop=runif(N,0.005, 0.015), mu.half = runif(2, 0.25, 0.95), stdev.half=runif(2,0.005, 0.015)) } inits6 <- function(){ list(a.c = runif(1,0,10), b.c = runif(1,0,10), mu.eco = runif(K, 0.25, 0.95), stdev.eco=runif(K,0.005, 0.015), mu.half = runif(2, 0.25, 0.95), stdev.half=runif(2,0.005, 0.015)) }
# Parameter lists for SURVIVAL and PRIMIPARITY rates parameters1 = c("mu.c", "var.c") parameters2 = c("mu.c", "var.c", "mu.half", "stdev.half") parameters3 = c("mu.c", "var.c", "mu.ecop", "stdev.ecop") parameters4 = c("mu.c", "var.c", "mu.eco", "stdev.eco") parameters5 = c("mu.c", "var.c", "mu.ecop", "stdev.ecop", "mu.half", "stdev.half") parameters6 = c("mu.c", "var.c", "mu.eco", "stdev.eco", "mu.half", "stdev.half")
# Call Bugs for SURVIVAL and PRIMIPARITY rates # Files “Beta_.bug” contain the WinBugs code for each survival model sim1 <- openbugs(model.file="Beta1.bug", data=data1, inits=inits1, n.iter=100000, n.burnin=1000, n.thin=2, parameters.to.save = parameters1) sim2 <- openbugs(model.file="Beta2.bug", data=data2, inits=inits2, 139
n.iter=300000, n.burnin=1000, n.thin=2, parameters.to.save = parameters2) sim3 <- openbugs(model.file="Beta3.bug", data=data3, inits=inits3, n.iter=100000, n.burnin=1000, n.thin=2, parameters.to.save = parameters3) sim4 <- openbugs(model.file="Beta4.bug", data=data4, inits=inits4, n.iter=100000, n.burnin=1000, n.thin=2, parameters.to.save = parameters4) sim5 <- openbugs(model.file="Beta5.bug", data=data5, inits=inits5, n.iter=100000, n.burnin=1000, n.thin=2, parameters.to.save = parameters5) sim6 <- openbugs(model.file="Beta6.bug", data=data6, inits=inits6, n.iter=100000, n.burnin=1000, n.thin=2, parameters.to.save = parameters6)
# Functions to set initial values for FECUNDITY inits1 <- function(){ list(mu.c = runif(1,0.4,0.9), var.c = runif(1,0.01,0.5)) } inits2 <- function(){ list(mu.c = runif(1, 0.4, 0.9), tau.c = runif(1, 0, 2), mu.half = runif(2, 0.4, 0.9), var.half = runif(2, 0.01, 0.5)) } inits3 <- function(){ list(mu.c = runif(1, 0.4, 0.9), tau.c = runif(1, 0, 2), mu.ecop = runif(N, 0.4, 0.9), var.ecop = runif(N, 0.01, 0.5)) } inits4 <- function(){ list(mu.c = runif(1, 0.4, 0.9), tau.c = runif(1, 0, 2), mu.eco = runif(K, 0.4, 0.9), var.eco = runif(K, 0, 0.5)) } inits5 <- function(){ list(mu.c = runif(1, 0.4, 0.9), tau.c = runif(1, 0, 2), mu.ecop = runif(N, 0.4, 0.9), var.ecop = runif(N, 0.01, 0.5), mu.half = runif(2, 0.4, 0.9), tau.half = runif(2, 0, 2)) } inits6 <- function(){ list(mu.c = runif(1, 0.4, 0.9), tau.c = runif(1, 0, 2), mu.eco = runif(K, 0.4, 0.9), var.eco = runif(K, 0.01, 0.5), mu.half = runif(2, 0.4, 0.9), tau.half = runif(2, 0, 2)) }
# Parameter lists for FECUNDITY parameters1 = c("mu.c", "var.c") parameters2 = c("mu.c", "var.c", "mu.half", "var.half") parameters3 = c("mu.c", "var.c", "mu.ecop", "var.ecop") parameters4 = c("mu.c", "var.c", "mu.eco", "var.eco") parameters5 = c("mu.c", "var.c", "mu.ecop", "var.ecop", "mu.half", "var.half") parameters6 = c("mu.c", "var.c", "mu.eco", "var.eco", "mu.half", "var.half")
# Call Bugs for FECUNDITY # Files “M_.bug” contain the WinBugs code for fecundity models sim1 <- openbugs(model.file="M1.bug", data=data1, inits=inits1, n.iter=100000, 140
n.burnin=1000, n.thin=2, parameters.to.save=parameters1) sim2 <- openbugs(model.file="M2.bug", data=data2, inits=inits2, n.iter=100000, n.burnin=1000, n.thin=2, parameters.to.save=parameters2) sim3 <- openbugs(model.file="M3.bug", data=data3, inits=inits3, n.iter=100000, n.burnin=1000, n.thin=2, parameters.to.save=parameters3) sim4 <- openbugs(model.file="M4.bug", data=data4, inits=inits4, n.iter=100000, n.burnin=1000, n.thin=2, parameters.to.save=parameters4) sim5 <- openbugs(model.file="M5.bug", data=data5, inits=inits5, n.iter=100000, n.burnin=1000, n.thin=2, parameters.to.save=parameters5) sim6 <- openbugs(model.file="M6.bug", data=data6, inits=inits6, n.iter=100000, n.burnin=1000, n.thin=2, parameters.to.save=parameters6)
# Summarize Results s1 <- sim1$summary #study~overall s2 <- sim2$summary #study~half~overall s3 <- sim3$summary #study~division~overall s4 <- sim4$summary #study~province~overall s5 <- sim5$summary #study~division~half~overall s6 <- sim6$summary #study~province~half~overall
##### END FILE #####
The WinBUGS code files describe the hierarchical structures used to estimate vital rates. For example, the file “Beta6.bug” is as follows:
##### BEGIN FILE ##### model { for(j in 1 : J) { mu[j] ~ dbeta(a.study[j],b.study[j]) a.study[j] <- max(0.01, (pow(mu.eco[eco[j]],2)- pow(mu.eco[eco[j]],3))/var.study[j]-mu.eco[eco[j]]) b.study[j] <- max(0.01, (mu.eco[eco[j]]*var.study[j]- var.study[j]+pow(mu.eco[eco[j]],3)- 2*pow(mu.eco[eco[j]],2)+mu.eco[eco[j]])/(var.study[j])) var.study[j] <- pow(stdev.eco[eco[j]],2)+var[j] } for(k in 1 : K) { mu.eco[k] ~ dbeta(a.eco[k], b.eco[k]) stdev.eco[k] ~ dunif(0.001, 0.9) a.eco[k] <- max(0.01, (pow(mu.half[halfr[k]],2)- pow(mu.half[halfr[k]],3))/var.half[halfr[k]]-mu.half[halfr[k]]) b.eco[k] <- max(0.01, (mu.half[halfr[k]]*var.half[halfr[k]]- var.half[halfr[k]]+pow(mu.half[halfr[k]],3)- 2*pow(mu.half[halfr[k]],2)+mu.half[halfr[k]])/(var.half[halfr[k]])) } for(m in 1 : 2) { mu.half[m] ~ dbeta(a.c, b.c) var.half[m] <- pow(stdev.half[m],2) stdev.half[m] ~ dunif(0.001, 0.9) 141
} mu.c <- a.c/(a.c+b.c) var.c <- (a.c*b.c)/(pow((a.c+b.c),2)*(a.c+b.c+1)) a.c ~ dgamma(1, 0.1) b.c ~ dgamma(1, 0.1) }
##### END FILE #####
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