Implementation of Bayesian Inference Techniques To

Implementation of Bayesian inference technique to address data limited problems in ecology: A case study with Peary caribou in Canadian Arctic Archipelago

Samarth Kaluskar

A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Department of Physical and Environmental Science University of Toronto

Implementation of Bayesian inference technique to address data limited problems in ecology: A case study with Peary caribou in Canadian Arctic Archipelago

Samarth Kaluskar

Doctor of Philosophy

Department of Physical and Environmental Science University of Toronto

2021

Abstract:

In the present era, rates of decline in species’ abundance provide some of the most compelling evidence of biodiversity loss rates globally. To address the problem of biodiversity loss, a critical piece of knowledge is the understanding of species interactions with their environment, because environmental variables are generally better predictors of population integrity than intrinsic biological traits. Peary caribou (Rangifer tarandus pearyi), the smallest of all caribou subspecies, are endemic to the Canadian Arctic Archipelago (CAA) and a characteristic example of species at risk. Climate change can affect their habitat availability, as well as the makeup of the entire Arctic ecosystem. Logistical and financial constraints in the CAA often compromise the frequency and the spatial extent of Peary caribou surveys, and therefore inconsistent sampling, errors in measurements, or faults in data acquisition encumber the robust assessment of their population status. To remedy such data gaps in surveys and, improve the robustness of any modelling exercise, I first developed a regression-based imputation framework to reconstruct the Peary caribou time series. The model was able to capture more than 65% of the variability in the dataset. To date, little work has been done to evaluate the net impact of changes from the climate on Peary caribou population dynamics, as it has been argued that the net balance of limited forage accessibility due to severe weather conditions relative to that of increased forage biomass due to prolonged growing season will depend on local climate, floral abundance and composition, and iii

landscape characteristics. Using a two-pronged modelling approach, I characterized the year-to- year variability of the habitat conditions across the CAA, using meteorological variables, landscape features, and resource competition. My dissertation also introduced a spatially explicit modelling framework to examine the strength and nature of the relationships of snow density and vegetation with Peary caribou populations. My dissertation concludes by identifying critical augmentations of the available scientific knowledge that necessitate to design the optimal management actions of Peary caribou populations across the Canadian Arctic Archipelago.

Acknowledgement I would love to thank my ever loving, wife Akshata for her assurances and advices which helped me in good stead. Her enthusiasm and encouragement helped me get through the toughest part of my academic career. I express my whole hearted thanks to my family for their generosity, unwavering support and encouragement. Thank you for helping me to flourish. Thank you for supporting me through trying times, always believing in me, and for giving me strength. Siddharth, thank you for being my best friend.

I would like to express deep sense of gratitude to Dr. George Arhonditsis. He is like a candle who has lit up my career path, so I can achieve my goals. Without his inspiring and instrumental role, this research would not have been possible. I consider myself very fortunate to have him as my supervisor. His dynamic approach and encouraging guidance boosted my moral which helped me to complete this research work to a great extent. I am very grateful for all the support that the supervisory committee (Dr. George Arhonditsis, Dr. Agnes Richards, Dr. William

Gough and Dr. Péter K. Molnár) have extended to me during my time here at UofT. I deeply appreciate how you have been continuously encouraging and guiding me, and also how you have always been so friendly and supportive of all of my efforts and struggles. With immense pleasure,

I take this opportunity to express my deep sense of gratitude and respect to my parents, professors, colleagues, friends & well-wishers. A very special gratitude goes out to all Ecological Modelling lab members. They have made time that spent working in the lab a much enjoyable and memorable experience.

I also thank Dr. Cheryl-Ann Johnson for sharing meteorological and landscape feature dataset and habitat suitability estimates. I am highly indebted to her for the guidance and for providing necessary information regarding the project and also for the support in completing the v

project. I would like to express my special gratitude and thanks to Dr. Johnson for giving me such attention and time. With gratitude, I would like to thank Dr. Alexander Langlois, who gave me the opportunity to learn SNOWPACK model and for his support in this project. I am grateful for the experience. Special thanks to Dr. Yuhong He from University of Toronto, Mississauga for sharing

NDVI data. I am sincerely grateful for their contribution.

This project was undertaken with the financial support of the Government of

Canada provided through the Department of the Environment. I would also like to acknowledge the contributions with respect to data sharing and empirical/technical input from the Communities of Nuvanut (Resolute Bay, Grise Fiord, Gjoa Haven, Kugaaruk, Taloyoak, Cambridge Bay) and

Northwest Territories (Sachs Harbour, Ulukhaktok, Paulatuk).

Samarth Kaluskar

Dedication

I dedicate this dissertation to my wonderful family:

To my parents, Rachna & Ramesh Kaluskar, and brother, Siddharth Kaluskar

Who believe in the pursuit of academic excellence. Thanks for supporting me and encouraging me!

To my wife, Akshata (A.K.A Bestie) …

Life is NOT beautiful but you try to make it joyful. For that I dedicate this work to you

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Table of Contents Acknowledgement ...... iv List of Tables ...... ix List of Figures ...... xi List of Appendices Figures ...... xiv List of Appendices Tables ...... xvi Chapter 1 Introduction ...... 1 1.1 Ecological services and importance of biodiversity ...... 1 1.2 Species extinction risk ...... 2 1.3 Introduction to Peary caribou ...... 7 Chapter 2 Research Objectives ...... 11 Chapter 3 Connecting the Dots in Databases of Endangered Species: A Bayesian Hierarchical Imputation Strategy for Missing Peary caribou (Rangifer tarandus pearyi) Population Data ...... 15 3.1 Introduction ...... 15 3.2 Methods...... 18 3.2.1 Peary caribou population ...... 18 3.2.2 Study area ...... 19 3.2.3 Modelling Framework...... 22 3.3 Results-Discussion ...... 28 3.3.1 Data imputation and island-specific population sizes ...... 28 3.3.2 Delineation of local population units and inter-island migration ...... 32 3.3.3 Peary caribou population trends across the Canadian Arctic Archipelago ...... 35 Chapter 4 A stochastic modelling framework to accommodate the inter-annual variability of habitat conditions for Peary caribou (Rangifer tarandus pearyi) populations ...... 54 4.1 Introduction ...... 54 4.2 Methods...... 56 4.2.1 Case Study-Dataset ...... 56 4.2.2 Modelling framework ...... 59 4.3 Results-Discussion ...... 62 4.3.1. Mapping the habitat variability in the Canadian Arctic Archipelago ...... 62 4.3.2. Predicting the likelihood of Peary caribou presence given the prevailing habitat conditions . 63 4.3.3. Characterizing the Peary caribou population trends in the Canadian Arctic Archipelago ..... 65 4.3.4. Future augmentations of the Peary caribou habitat modelling framework ...... 68 viii

Chapter 5 Development of a Bayesian ensemble of empirical models to predict Peary caribou (Rangifer tarandus pearyi) populations in the Canadian Arctic Archipelago ...... 82 5.1 Introduction ...... 82 5.2 Methods...... 85 5.2.1 Study area-Dataset ...... 85 5.2.2 Modelling framework ...... 87 5.3 Results-Discussion ...... 91 5.3.1 Model Performance...... 91 5.3.2 Identification of the role of snow and vegetation on the year-to-year variability of Peary caribou populations ...... 93 5.3.3 Bayesian ensemble modelling and Peary caribou population predictions ...... 95 5.3.4 Assessing the relationship between Peary caribou population predictions and observation/imputation errors...... 98 Chapter 6 Conclusions and Future Perspectives ...... 115 6.1 Purpose of the Dissertation ...... 115 6.1.1 Purpose and Key Findings of Chapter 3 ...... 115 6.1.2 Purpose and Key Findings of Chapter 4 ...... 116 6.1.3 Purpose and Key Findings of Chapter 5 ...... 117 6.2 Future work ...... 118 Bibliography ...... 121 Appendix A1 ...... 141 Appendix A2 ...... 156

List of Tables

Table 3-2 Posterior mean and standard deviation (SD) values of the imputation model parameter estimates...... 43

Table 3-3 Three estimates of the Peary caribou population rates of change across the Canadian Arctic Archipelago. The first estimate (λ1) is derived by linear least-squares fitting against the original dataset, according to the method presented by Dennis et al. (1991). The second estimates (λ2) correspond to the same method after data imputation. The third set of rates of change (λ3) are derived by the hierarchical formulation of the exponential growth model using both imputed values and survey data. NA denotes locations with sample size ≤ 4. Numbers in parenthesis correspond to the standard error of the corresponding linear regression models...... 44

Table 4-1 General interpretation and ecological reasoning of the explanatory variables used in the present modelling framework...... 73

Table 4-2 Estimates of the Peary caribou population rates of change on the six island complexes of the Canadian Arctic Archipelago, as derived by the hierarchical formulation of the exponential growth model parameterized against population data from a 45-yr (1970- 2015) time period (Kaluskar et al., 2020). The latter term determines the degree of the population rate of change between two consecutive years t and t − 1 (or between year t and the initial year t0 of our study). The nature of this change (growth or decline) is also determined by the corresponding habitat suitability estimates and the degree to which a critical threshold c* (=33 or 50% probability of the location i to be favorable for Peary caribou in year t) is exceeded...... 74

Table 4-3 Posterior estimates of the island-complex specific parameters and performance of the logistic regression models developed to connect the binary Peary caribou dataset (presence/absence) for the summer (July to October) period against meteorological factors, landscape features, and muskoxen density. Model fit represent the percentage of the cases where the logistic regression correctly predicts the presence or absence of Peary caribou. N ...... 75

Table 5-1 Classification of the Canadian Arctic Archipelago into six island groups along with x

the years surveyed and imputed (Kaluskar et al., 2020) for each island complex. Because of the NDVI data availability the study period (1985-2007)...... 104

Table 5-2 Performance of the four models examined to reproduce the year-to-year Peary caribou variability within the six island groups of the Canadian Arctic Archipelago...... 105

Table 5-3 Posterior parameter estimates (mean ± standard deviation) of the four models developed to examine the spatiotemporal Peary caribou density trends across. Subscripts 1 to 6 corresponds to Banks, Axel Heiberg, Melville, Boothia and Mackenzie King island complexes ...... 106

Table 5-4 Euclidean distances of model predictions against the mean empirical population estimates (top) and the latent "true" Peary caribou population (bottom), based on one-at-a- time sensitivity analysis exercise. The “Reference” scenario corresponds to the current observation and imputation error values...... 107

List of Figures

Figure 1-1 Map of the study area (Canadian Arctic Archipelago) ...... 10

Figure 2-1 Structural overview demonstrating the modelling approaches taken for addressing limited data problem for Peary caribou population across CAA ...... 14

Figure 3-1 Map of the Canadian Arctic Archipelago and application of the Bayesian hierarchical framework to allow the transfer of information across the six island complexes...... 45

Figure 3-2 Peary caribou population trends across all of the (a) McKenzie King, (b) Axel Heiberg, (c) Banks, (d) Boothia, (e) Melville, and (f) Bathurst spatial complexes. White and black dots represent recorded and imputed population (number of animals) estimates, respectively...... 47

Figure 3-3 Predicted weights expressing the likelihood for the Peary caribou populations to be higher in a secondary/satellite location relative to the primary one within each of the spatial complexes of the Canadian Arctic Archipelago. Black and white dots represent probabilistic weights that correspond to recorded and imputed population estimates, respectively...... 49

Figure 3-4 Comparison between the annual recorded/imputed and predicted Peary caribou populations on the six island groups of the Canadian Arctic. Solid and dashed lines correspond to the median predictions and the associated 95% credible intervals of the Bayesian hierarchical exponential model...... 50

Figure 3-5 Predictive distributions (solid lines) of Peary caribou populations across the Canadian Arctic Archipelago for the year 2018 based on the exponential growth model. Log- normal distributions denoted in dashed lines correspond to the most recent Peary caribou populations recorded on each of the six spatial complexes, after accounting for both sampling and imputation error...... 53

Figure 4-1 Logic of modelling framework. The first step uses a Bernoulli-logistic model to characterize the habitat conditions in different locations of the study domain, based on the prevailing local weather conditions, landscape features, resource competition, and predation. The predicted probabilities from this resource-selection function exercise are subsequently used to guide the stochastic algorithms, which in turn delineate the potential range of population growth/decline. The magnitude of the quasi-random walk method in each habitat and time step is determined by the uncertainty of the Peary caribou population rates of change on the six island complexes of the Canadian Arctic Archipelago, as derived xii

by the parameterization of the exponential growth model against population data from a 45- yr (1970-2015) time period (Table 4-2; see also Kaluskar et al., 2020)...... 76

Figure 4-2 Predicted mean probabilities (and associated standard deviations) of summer habitat suitability for Peary caribou across the Canadian Arctic Archipelago during the 2000-2013 period, as predicted by the Bernoulli-logistic models presented in Table 4-3. ... 77

Figure 4-3 Uncertainty envelope of the Peary caribou population trends across the Canadian Arctic Archipelago, as derived by the four random-walk models designed to accommodate site- and year-specific rates of change. The median trend over the course of the 14-yr (2000- 2013) study period was calculated for each grid cell and model, which were then used to determine the corresponding minimum and maximum rates of change...... 78

Figure 4-4 Spatial distribution of the probability of Peary caribou to be reduced by 10% relative to their 2000 population level across the Canadian Arctic Archipelago in 2002, 2005, 2009 and 2013. The projected population trends represent the average predictions by the four configurations of the exponential growth model...... 79

Figure 4-5 Spatial distribution of the probability of Peary caribou to be reduced by 25% relative to their 2000 population level across the Canadian Arctic Archipelago in 2002, 2005, 2009 and 2013. The projected population trends represent the average predictions...... 80

Figure 4-6 Spatial distribution of the probability of Peary caribou to be reduced by 50% relative to their 2000 population level across the Canadian Arctic Archipelago in 2002, 2005, 2009 and 2013. The projected population trends represent the average predictions by the four configurations of the exponential growth model...... 81

Figure 5-1 Map of the Canadian Arctic Archipelago and application of the Bayesian hierarchical framework to allow the transfer of information across the six island complexes...... 108

Figure 5-2 Observed versus median predicted Peary caribou areal population values. The diagonal line represents a perfect fit between predicted and observed median values. The coefficient of determination (r2) values were 0.481, 0.632, 0.373, and 0.614 for Models 1 to 4, respectively...... 109

Figure 5-3 Temporal variability of the conditional autoregressive terms φt terms (Left panel). Coefficients of variation (CV) values associated with the regression coefficient of the temporal-trend term across the Canadian Arctic Archipelago using Models 2, 3, and 4 (Right panel). Check and cross marks indicate positive and negative relationships between Peary caribou density and time, respectively...... 110 xiii

Figure 5-4 Predicted Peary caribou levels on Banks (2005), Axel Heiberg (2007), Boothia (2006), Melville (1997), Bathurst (2002) and McKenzie King (1997) island complexes for the last year of the study period when population records were available. Predictive distributions are based on the four models examined and the two Bayesian ensembles formulated. Percentages represent the probability of exceedance of 1,000 animals in each island complex according to the two ensemble predictions...... 113

Figure 5-5 Posterior distributions of the regression coefficient associated with the snow effect on Peary caribou across the six island complexes of the Canadian Arctic Archipelago (Model 2). Black solid, black dashed, and gray lines correspond to scenarios where the observation error variance is assigned the reference (R), half (H), and double (D) of the values associated with the Peary caribou populations dataset (Kaluskar et al., 2020), respectively...... 114

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List of Appendices Figures

Figure S1: Average and standard deviation of air temperature (oC) and precipitation (mm day-1), surface snowmelt rates (mm day-1), wind speed (m s-1), muskox density (density of muskoxen/100 km2) and rockland fraction (%) across the Canadian Arctic Archipelago from 2000 to 2013...... 143

Figure S2: Relationship between Peary caribou population growth rates and habitat suitability in Axel Heiberg island complex, as reproduced by the four random-walk models. Dots represent the growth rates on the 1841 cells of this island complex averaged over our 13-year (2001-2013) study period...... 144

Figure S3 Relationship between Peary caribou population (expressed in the natural logarithmic scale) growth rates and habitat suitability in Melville island complex, as reproduced by the four random-walk models. Dots represent the growth rates on the 680 cells of this island complex averaged over our 13-year (2001-2013) study period...... 145

Figure S4 Histograms of the Peary caribou population (expressed in the natural logarithmic scale) growth rates in Axel Heiberg island complex during the years 2004 (top panels) and 2013 (bottom panels). Left and right panels correspond to the random-walk model that postulates the location-specific population growth rates to be a function of their counterparts in 2000 (initial year of our study) and the preceding year, respectively. In all cases, the probability threshold c* is set equal to 33%...... 146

Figure S5 Histograms of the Peary caribou population (expressed in the natural logarithmic scale) growth rates in Melville island complex during the years 2004 (top panels) and 2013 (bottom panels). Left and right panels correspond to the random-walk model that postulates the location-specific population growth rates to be a function of their counterparts in 2000 (initial year of our study) and the preceding year, respectively. In all cases, the probability threshold c* is set equal to 33%...... 147

Figure S6 Relationships among longitude (oW), air temperature (oC) or time (2001-2013), and habitat suitability for Peary caribou populations in grid cells of the Ellesmere island with latitude lower than 77o 0’N (top panels). Year-to-year variability of the Pear caribou population rates of change in the same grid cells, according to the random-walk models that postulate the location-specific population growth rates to be a function of their counterparts in 2000 (initial year of our study) and the preceding year, respectively. The corresponding probability thresholds c* are set equal to 33% (middle panels) or 50% (bottom panels). .. 148

Figure S7 Time series of Normalized Difference Vegetation Index (NDVI) for Axel Heiberg, Banks, Boothia, Melville, Bathurst and McKenzie King island complexes standardized xv

relative to a mean of 0.119 and standard deviation of 0.096 over the entire Canadian Arctic Archipelago during the 1985-2007 study period...... 151

Figure S8 Time series of Snopack Water Equivalent Intensity (SWEI) for Axel Heiberg, Banks, Boothia, Melville, Bathurst, and McKenzie King island complexes standardized relative to a mean of 19.96 and standard deviation of 5.69 cm day-1 over the entire Canadian Arctic Archipelago during the 1985-2007 study period...... 153

Figure S9 Coefficients of variation (CV) associated with the slope of SWEI across the Canadian Arctic Archipelago using Models 2, 3, and 4. Check and cross mark indicate positive and negative relationships between Peary caribou density and SWEI, respectively...... 154

Figure S10 Coefficients of variation (CV) associated with the slope of NDVI across the Canadian Arctic Archipelago using Models 2, 3, and 4. Check and cross marks indicate positive and negative relationships between Peary caribou density and NDVI, respectively...... 155

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List of Appendices Tables

Table S1 Time series of Normalized Difference Vegetation Index (NDVI) for Banks, Axel Heiberg, Boothia, Melville, Bathurst, and McKenzie King island complexes over the entire Canadian Arctic Archipelago during the 1985-2007 study period...... 156

Table S2 Time series of Snow Water Equivalent Intensity (cm day-1) for Banks, Axel Heiberg, Boothia, Melville, Bathurst, and McKenzie King island complexes over the entire CAA during the 1985-2007 study period...... 157 1

Chapter 1 Introduction 1.1 Ecological services and importance of biodiversity Biodiversity supports many critical ecological services that are intricately linked with both humans and living organisms on Earth. Biodiversity represents the variation at the genetic, species, and ecosystem level and can be simply defined as the abundance of different species of plants and animals (Moinuddin, 2018). Plants and animals depend upon each other to perform their role in the production of goods (e.g., meat, fuelwood, timber, and pharmaceutical products) from which critical ingredients of our agricultural, pharmaceutical and, industrial enterprises are derived (Daily, 1997). Human overconsumption of natural resources, climate change, environmental pollution, and other human-induced ecosystem disturbances are responsible for species extinction, the prevalence of non-native species, and ultimately the degradation of biodiversity. The causal link between anthropogenic activities and the diversity of organisms found in ecosystems above- and below-ground is critical for the integrity of biotic assemblages (Moinuddin, 2018), and thus the identification of the “sweet spot” where we can effectively balance economic development with the sustenance of biodiversity is essential. The logic is that if certain species are affected by pollution, climate change, or other human activities, the socio-ecological system as a whole must adapt to avoid non-linear regime shifts and the establishment of new (and likely undesirable) states. Of the four billion species that supposedly evolved on the planet over the last 3.5 billion years, around 99% are extinct (Barnosky et al., 2011). The majority of species extinction can be attributed to five events -known as the “Big Five” mass extinctions- that occurred near the end of the Ordovician, Devonian, Permian, Triassic, and Cretaceous periods. Scientists are currently observing the sixth mass extinction due to anthropogenic activities, such as co-opting of resources (i.e., a degree of power given to humans in designing or implementing changes that directly or indirectly impact resource availability), habitat fragmentation, the introduction of non-native species, spreading of pathogens, selective killing of species, and global climate change (Daily, 1997). The recent loss of species is serious and, if current threats are not resolved, it is believed that earth may be subjected to an extreme diversity loss comparable to those experienced by the “Big Five” (Barnosky et al., 2011). Conservation efforts should focus on ameliorating the impact of the major direct threats to species loss, such as biological resource overutilization; natural system modifications; residential and commercial development; farming activities; energy

production and mining; construction of transportation and service corridors; habitat destruction; climate change; invasive species and pathogens; environmental pollution; and catastrophic geological events.

1.2 Species extinction risk In predicting species’ extinction risk and make their protection and conservation planning more efficient, it is essential to understand which biological/ecological traits make them more vulnerable. For example, mammals going through a hibernating phase are less prone to becoming extinct, due to a greater capacity to avoid harsher seasonal conditions (Liow et al., 2009). According to Chichorro et al., (2019), there are two ways that species diet can influence in predicting their extinction. First, species restricted to fewer dietary options have shown to be more threatened (Basset et al., 2015; Jeppsson and Forslund, 2014; González-Suárez et al., 2013; Matsuzaki et al., 2011; Mattila et al., 2008), probably due to lower flexibility in switching to other food options when the availability of their preferred food source decreases (Purvis et al., 2000). Secondly, the diet type of a species across a food chain is important in predicting extinction risk. So, the species at higher trophic levels tend to be more threatened (Chessman, 2013; Bender et al., 2013; Cardillo et al., 2004; Purvis et al., 2000) and often provide early warnings about the broader food web integrity (Cardoso et al., 2010). Higher‐level consumers are less diverse, less abundant, and under stronger anthropogenic pressure on average than wild plants, and thus face greater risk of extinction (Duffy, 2002). Migration is another significant predictor of extinction risk. The main reasons are that long-distance migrants tend to be at higher risk due to either phenological mismatch caused by climate change (Amano and Yamaura, 2007; Jiguet et al., 2010; Thaxter et al., 2010; Flousek et al., 2015), or due to increased competition with resident species, or due to the earlier thinning or breaking of ice caused by climate change (Jiguet et al., 2010; Amano and Yamaura, 2007; Johnson et al., 2016). Also, traits related to geographic range size are important for quantifying extinction risk for mammals (Purvis et al., 2000; González-Suárez et al., 2013; Bland et al., 2015; Verde Arregoitia, 2016). The mechanism behind this relationship is that species with larger geographic range size have a higher chance to escape from multiple pressure types and are consistently less threatened across taxa and spatial settings (Davidson et al., 2009). Habitat breadth is another trait that could be useful in predicting extinction risk. Ecological niche theory predicts a worldwide decline in habitat specialist species (Clavel et al., 2011). Species with greater

habitat breadth (habitat generalists) are less prone to becoming extinct compared to specialists, who have been regarded as losers in the current extinction crisis (McKinney and Lockwood, 1999). Other traits that could be useful in predicting extinction risk includes the duration of life cycle and reproductive outputs: fecundity, egg/neonatal size, and generation length. These traits usually correlate with each other: larger, longer-lived species often have lower fecundity, larger egg/neonatal sizes and longer generation lengths (Chichorro et al., 2019). Threat status has been positively related to species with decreased fecundity (Cardillo, 2003; González-Suárez and Revilla, 2013; Böhm et al., 2016; Ribeiro et al., 2016; Pinsky and Byler, 2015; Sreekar et al., 2015), larger egg/neonatal sizes (Cardillo et al., 2005; Jones et al., 2006; González-Suárez and Revilla, 2013; Pinsky and Byler, 2015) and longer generation lengths (Anderson et al., 2011; Hanna and Cardillo, 2013; Jeppsson and Forslund, 2014; Comeros-Raynal et al., 2016; Chessman, 2013) because these traits reduce the capability of species to compensate for high mortality rates (Pimm et al., 1988; Purvis et al., 2000; González-Suárez et al., 2013).

Since humans first arrived in North America, mammalian species’ diversity dropped by 15-42% compared to the previous normal diversity baseline that existed for millions of years (Carrasco et al, 2009). Carrasco et al (2009) confirmed quantitatively that the decline in mammal diversity can be attributed to human presence. Over the years, many studies have linked human population density to the number of threatened species, demonstrating a strong correlation between the two (McKee et al, 2013). McKee et al (2013) found that human population density is a key cause of mammal and bird species becoming threatened. Species’ habitats that overlaps with human’s population are at higher risk of extinction (Stefanaki et al., 2015; Powney et al., 2014). In Greece, flowering plants occurring in coastal or rural habitats, under pressure from urbanization and tourism, were at higher risk than flowering plants occurring on cliffs or high-mountain vegetation (Stefanaki et al., 2015).

Human activities have directly impacted species extinction risk through habitat modification and destruction. Perhaps the most profound impact is the human’s role on climate change, which increases the susceptibility of high-risk species (Sodhi et al., 2008). Climate change impacts such as increases in temperature, changes in precipitation patterns, and changes in the occurrence of floods and droughts are predicted to have a large influence on forest and agricultural systems (Álvaro-Fuentes et al., 2012; Anaya-Romero et al., 2015; Conant et al., 2011; Lal, 2004;

Muñoz-Rojas et al., 2013). Previous studies suggested that continued rises in atmospheric

CO2 would entail increased photosynthetic rates and plant productivity (Muñoz-Rojas et al., 2017). Recent studies have shown that this phenomenon might be actually less significant than initially expected (Muñoz-Rojas et al., 2017). Rising levels of CO2 may lead to reduced plant productivity (Camarero et al., 2015; Long et al., 2006). Moreover, through changes in climate, land use and management, many of the soils worldwide are expected to become more sensitive to soil erosion by water and wind due to increases in runoff (Anaya-Romero et al., 2015; Cerdá and Doerr, 2005, Cerdá et al., 2010; Panagos et al., 2015). In the humid tropics, increased intensities of rainfall events could cause an increased occurrence of temporary flooding or water-saturation, whereas in other areas, such as arid or semiarid environments, it could lead to further land degradation or desertification (Martttínez-Casasnovas et al., 2002). According to Marine Mammal Commission (https://www.mmc.gov/priority-topics/arctic/climate-change/), the impacts of climate change are being observed earlier in the Arctic, and with more immediate and severe consequences, than in most of the rest of the world. Researchers believe that the changes in the Arctic are worrisome because they could lead to feedback loops that trigger further warming (Corell, 2014; Serreze and Barry 2011). For instance, when the sea ice melts in summer, areas of dark open water are exposed which can absorb more heat from the sun, which in turn can further accelerate ice melt. Permafrost may also be involved in positive feedback. As permafrost thaws, plants and animals that were frozen in the ground begin to decay. When they decay, they release carbon dioxide and methane back to the atmosphere that contributes to further warming (Dean et al., 2018).

In predicting species’ extinction risk and make their protection and conservation planning more efficient, it is essential to understand which biological/ecological traits make them more vulnerable. For example, mammals going through a hibernating phase are less prone to becoming extinct, due to a greater capacity to avoid harsher seasonal conditions (Liow et al., 2009). According to Chichorro et al., (2019), there are two ways that species diet can influence in predicting their extinction. First, species restricted to fewer dietary options have shown to be more threatened (Basset et al., 2015; Jeppsson and Forslund, 2014; González-Suárez et al., 2013; Matsuzaki et al., 2011; Mattila et al., 2008), probably due to lower flexibility in switching to other food options when the availability of their preferred food source decreases (Purvis et al., 2000).

Secondly, the diet type of a species across a food chain is important in predicting extinction risk. So, the species at higher trophic levels tend to be more threatened (Chessman, 2013; Bender et al., 2013; Cardillo et al., 2004; Purvis et al., 2000) and often provide early warnings about the broader food web integrity (Cardoso et al., 2010). Higher‐level consumers are less diverse, less abundant, and under stronger anthropogenic pressure on average than wild plants, and thus face greater risk of extinction (Duffy, 2002). Migration is another significant predictor of extinction risk. The main reasons are that long-distance migrants tend to be at higher risk due to either phenological mismatch caused by climate change (Amano and Yamaura, 2007; Jiguet et al., 2010; Thaxter et al., 2010; Flousek et al., 2015), or due to increased competition with resident species, or due to the earlier thinning or breaking of ice caused by climate change (Jiguet et al., 2010; Amano and Yamaura, 2007; Johnson et al., 2016). Also, traits related to geographic range size are important for quantifying extinction risk for mammals (Purvis et al., 2000; González-Suárez et al., 2013; Bland et al., 2015; Verde Arregoitia, 2016). The mechanism behind this relationship is that species with larger geographic range size have a higher chance to escape from multiple pressure types and are consistently less threatened across taxa and spatial settings (Davidson et al., 2009). Habitat breadth is another trait that could be useful in predicting extinction risk. Ecological niche theory predicts a worldwide decline in habitat specialist species (Clavel et al., 2011). Species with greater habitat breadth (habitat generalists) are less prone to becoming extinct compared to specialists, who have been regarded as losers in the current extinction crisis (McKinney and Lockwood, 1999). Other traits that could be useful in predicting extinction risk includes the duration of life cycle and reproductive outputs: fecundity, egg/neonatal size, and generation length. These traits usually correlate with each other: larger, longer-lived species often have lower fecundity, larger egg/neonatal sizes and longer generation lengths (Chichorro et al., 2019). Threat status has been positively related to species with decreased fecundity (Cardillo, 2003; González-Suárez and Revilla, 2013; Böhm et al., 2016; Ribeiro et al., 2016; Pinsky and Byler, 2015; Sreekar et al., 2015), larger egg/neonatal sizes (Cardillo et al., 2005; Jones et al., 2006; González-Suárez and Revilla, 2013; Pinsky and Byler, 2015) and longer generation lengths (Anderson et al., 2011; Hanna and Cardillo, 2013; Jeppsson and Forslund, 2014; Comeros-Raynal et al., 2016; Chessman, 2013) because these traits reduce the capability of species to compensate for high mortality rates (Pimm et al., 1988; Purvis et al., 2000; González-Suárez et al., 2013).

consequences, than in most of the rest of the world. Researchers believe that the changes in the Arctic are worrisome because they could lead to feedback loops that trigger further warming (Corell, 2006; Serreze and Barry 2011). For instance, when the sea ice melts in summer, areas of dark open water are exposed which can absorb more heat from the sun, which in turn can further accelerate ice melt. Permafrost may also be involved in positive feedback. As permafrost thaws, plants and animals that were frozen in the ground begin to decay. When they decay, they release carbon dioxide and methane back to the atmosphere that contributes to further warming (Dean et al., 2018).

1.3 Introduction to Peary caribou Life in the planet’s polar regions can be difficult due to barren landscape, bitterly cold winds, low temperatures can reach deep into the negatives, and the winter night can last for months. These seemingly barren landscapes are home to a rich diversity of wildlife, undersea surface, and land. Considering the impact of life history, ecological, behavioral, physiological and genetic traits (e.g., species with small geographic ranges, low fecundity, and specialized habitats) on species- extinction risk, climate change could have profound implications for the diversity of Arctic ecosystems (Descamps et al., 2017). One such characteristic example of species at risk in the Canadian Arctic Archipelago is the Peary caribou (Rangifer tarandus pearyi) (See fig. 1-1). Peary Caribou are found in small groups on the Arctic islands of the Northwest Territories (NWT) and Nunavut, excluding Baffin Island. In the NWT, Peary caribou live on Banks Island, northwest Victoria Island, and the western Queen Elizabeth Islands. Peary caribou are the smallest of all caribou subspecies with several adaptations to the Arctic environment, such as compact body size for conserving heat, hooves that allow them to walk on and dig through wind-driven snow, and pelage that provides camouflage (Johnson et al., 2016). They have shorter faces and legs and are lighter in colour than barren-ground caribou. In winter, Peary caribou have a mostly white coat. Their summer coat is slate-gray with white legs and underparts. Both males and females have antlers. Antlers on adult males are larger than those on females and juvenile males. The velvet covering the antlers is gray, unlike the dark brown velvet of barren-ground caribou. They are adapted to limited plant growth with a highly compressed growing season and long periods of snow-covered frozen standing vegetation (Johnson et al., 2016). Peary caribou live in small groups and maintain a wide dispersion across the landscape, even during calving and rutting. They are

thought to live for approximately 15 years in the wild. Cows usually produce their first offspring by 3 years of age, and may even calve every year under conditions of high forage availability. On the other hand, they cope with occasional years of restricted forage access either by not becoming pregnant or by weaning a calf prematurely. For Peary caribou, repeated yearly migration between winter and summer ranges and seasonal rutting and calving grounds is critical. Nonetheless, anthropogenic activities are pushing caribou herds into isolation and cutting off their seasonal migration, which poses threats to their ability to access seasonal forage. Arrival to calving areas when highly nutritious, digestible forage plants emerge is highly critical to calf-provisioning by female caribou. The onset of the growing season has advanced in the Arctic, while the timing of caribou migration and calving has largely remained constant as they are cued by day length (Post and Forchhammer, 2008). This mismatch in timing has been causally connected to reduced calf production and survival in Arctic caribou in western Greenland (Post and Forchhammer, 2008; Kerby and Post 2013). Compared to mainland populations, island populations often exhibit reduced genetic diversity (Jenkins et al., 2018). Such examples include island red fox, Vulpes vulpes (Lade et al., 1996); various Australian macropodids (Eldridge et al., 2004); North American gray wolf, Canis lupus (Carmichael et al., 2008); Ornithorhynchus anatinus (Furlan et al., 2012); and Svalbard reindeer (Côté et al., 2002). The genetic diversity within a species (e.g., many discrete populations with different life-history strategies rather than a single homogenized population) allows the population to withstand variable conditions. By having that variation built-in, species can minimize their risk of complete extirpation. In the Canadian Arctic Archipelago (CAA), it is critical to facilitate connectivity between island populations and reduce genetic isolation by facilitating the flow of genes (Geffen et al., 2007; Jenkins et al., 2016). For terrestrial animals, like Peary caribou, sea ice is a platform for dispersal, seasonal inter-island and island–mainland migrations and sporadic long-distance movements (Johnson et al., 2016). Peary caribou use sea ice as a corridor between islands to migrate between winter and summer ranges and to access traditional calving areas. Sea ice thickness and early sea ice breaking caused by climate change may decrease or prevent Peary caribou migration, thereby impacting reproductive success, foraging efficiency, and leading to genetic isolation. Peary caribou are an essential staple in the traditional, subsistence-based way of life in Canadian High Arctic communities (Thomas and Gray, 2002). Peary caribou and muskoxen

(Ovibos moschatus) provide food and raw materials for clothing and artwork (Taylor, 2005). Their survival is especially vital to Indigenous communities living in High Arctic Resolute Bay (Qausuittuq) and Grise Fiord (Aujuittuq) (Miller, 2001; Taylor, 2005; Festa-Bianchet et al., 2011). Nonetheless, the Committee on the Status of Endangered Wildlife in Canada (COSEWIC) added Peary caribou to the endangered-species list (Miller, 1991; Gunn and Dragon, 2002) in 1991 due to population decline caused by natural and anthropogenic factors (Miller, 2001; Wolf, 2010) over the past four decades in the CAA (Festa-Bianchet et al., 2011). With climate change occurring at an accelerated rate in the Arctic relative to trends in other regions (IPCC, 2013), it is considered to be one of the greatest threats to Peary caribou (COSEWIC, 2015). Prolonged and severe weather events have been linked to poor body condition, malnutrition, high adult and calf mortality, and significant population die-offs (Miller and Gunn, 2003; Canadian Wildlife Service, 2015). While evidence to date has linked climate change to the Peary caribou population declines, impacts have been spatially and temporally inconsistent due to significant survey gaps (Miller, 1991; Gunn, 1998). Also, few individuals are aware of caribou and muskoxen population trends and distributions across the CAA (Audlaluk and Audlaluk, 1998). Given the extinction risks faced by Peary caribou, this dissertation aims to develop a methodological framework that will allow the delineation of their spatiotemporal distribution across the Canadian Arctic Archipelago, and also offer guidance on essential management actions to protect their population integrity.

Figure 1-1 Map of the study area (Canadian Arctic Archipelago)

Chapter 2 Research Objectives To date, little work has been done to evaluate the impact of changes in climate on Peary caribou population dynamics (Tews et al., 2007a). This dissertation aims to use statistical models in conjunction with Bayesian inference techniques to delineate the distribution of Peary caribou under changing environmental conditions across the CAA (Figure 2-1). One of the novel features of this research lies in the development of a method that facilitates the integration of Indigenous Knowledge to identify critical habitats. Founded upon the use of Bayesian techniques, the project design explicitly accommodates quantitative and qualitative knowledge (expert elicitation, interviews, and anecdotal historical data), thereby allowing empirical evidence and theoretical knowledge to interact in a complementary fashion. Existing evidence from other disciplines suggests that the proposed modelling approach can be particularly useful for constraining input parameters within realistic ranges and may increase the articulation level of management-oriented modelling (Van Putten et al., 2013; Bélisle et al., 2018; Girondot and Rizzo 2015; Kaluskar et al. 2019b). This dissertation comprises three main chapters (chapters 3-5), followed by a concluding section in which I also provide a few pointers for future research (Chapter 6). The third chapter focuses on infilling Peary caribou populations to detect spatiotemporal trends across the CAA. Studying rare and endangered species can be particularly challenging due to monetary and logistic constraints. A logical way to remedy data gaps and thus improve the robustness of any given modelling exercise is through imputation schemes, which are typically selected according to missing data patterns. Based on a novel regression-based imputation method, this framework infills data gaps wherever necessary while capturing complex Peary caribou abundance patterns. One of the fundamental assumptions of the imputation model is that there is a subset of primary islands that act as the core areas from where the Peary caribou populations migrate to secondary or satellite islands. Specifically, six distinct geographic clusters (Banks, Axel Heiberg, Bathurst, Boothia, Melville, and Mackenzie King) have been delineated across the CAA, within which Peary caribou population movements take place in any given year. Parameterized with Bayesian inference technique, the imputation modelling strategy has a flexible structure that can accommodate non-monotonic spatiotemporal patterns within each of the six geographic regions. The robustness of the outputs of the proposed approach is examined with the exponential growth model by comparing the derived spatiotemporal trends with and without imputed data. Lastly, this

study also aims to develop a Bayesian hierarchical configuration to estimate region-specific growth rates with the observed and infilled dataset. The objectives are (i) to illustrate how hierarchical structure can assist in sharing information among different complexes; (ii) to obtain predictions along with uncertainty bounds that take into account the insufficient amount of information in less studied spatial complexes, as well as the variability, observed across complexes in the CAA; and (iii) to explicitly propagate the importance of the imputation error on the population estimates derived. Building upon the previous empirical estimates of the Peary caribou population rates of change, the fourth chapter introduces a two-pronged approach aiming to characterize year-to-year variability of habitat conditions across the CAA from 2000 to 2013. Johnson et al. (2016) integrated the available scientific information and local community knowledge to identify Peary caribou critical habitat for maintaining healthy, self-sustaining populations, so animals can able move freely across the land and sea. Based on four general categories of predictor variables (human disturbance, forage availability, climate and competition with other species), and available georeferenced datasets, Johnson et al. (2016) developed three seasonal models using Maxent (version 3.3.3k, 2011; Phillips et al., 2006) to describe seasonal shifts in habitat preferences across the species’ distribution and to inform important locations for local populations of Peary caribou within the species distribution. The predictive power of each of the seasonal models was assessed based on expert input collected during technical meetings, geographically referenced observations of Peary caribou collected during surveys and, limited locations from collared animals on the models’ abilities to accurately predict areas of known use by Peary caribou. My study extends Johnson et al.’s (2016) habitat identification framework. First, using logistic regression, the year- to-year variability of the habitat conditions across the CAA are characterized using meteorological variables, landscape features, and resource competition with muskoxen. The predicted estimates of the habitat suitability (or forage accessibility) are used to determine the population rate of change by sampling over the uncertainty associated with the Peary caribou population rate of change from the exponential model derived from a 45-yr study period. Daily data, from 2000 – 2013, for climatological and landscape variables, were taken from the Canadian Regional Climate Model (CanRCM4) from the Canadian Centre from Climate Modelling and Bolin Centre, Stockholm University.

The fifth chapter also builds upon the Bayesian hierarchical exponential model by developing three new spatially explicit models to examine the strength and nature of the relationships of snow density (Snowpack Water Equivalent Intensity or SWEI) and vegetation abundance (Normalized Difference Vegetation Index or NDVI) with Peary caribou populations while propagating observation and imputation uncertainties. Recognizing the uncertainty typically associated with the selection of the best subset of explanatory variables and their optimal functional relationship with the response variable, four models across six island complexes (Banks, Axel Heiberg, Melville, Bathurst, Mackenzie King, and Boothia) were examined. Additionally, this study formulates two ensembles to synthesize their predictions into averaged Peary caribou population distributions. The latter exercise will be based on the use of Bayesian Model Averaging (BMA), which is a technique designed to explicitly account for the uncertainty inherent in the model selection process. By averaging over many different competing models, BMA incorporates the uncertainty about the optimal model for any given exercise into the inference drawn about parameters and prediction (Raftery et al., 2005). Therefore, rather than picking the single "best- fit" model to predict future system responses, the use of Bayesian model averaging provides a weighted average of the forecasts from different models (Hoeting et al., 1999). BMA has been applied successfully to many model classes, including linear regression, generalized linear, exponential decay, discrete graphical, and dynamic models (Lamon and Clyde, 2000; Stow et al., 2004; Sloughter et al., 2007; Azim et al., 2011).

Figure 2-1 Structural overview demonstrating the modelling approaches taken for addressing limited data problem for Peary caribou population across CAA

Chapter 3 Connecting the Dots in Databases of Endangered Species: A Bayesian Hierarchical Imputation Strategy for Missing Peary caribou (Rangifer tarandus pearyi) Population Data1 3.1 Introduction Peary caribou (Rangifer tarandus pearyi) are endemic to the Canadian Arctic Archipelago with the smallest population size among the caribou subspecies. These light-color, nearly white, ungulates occupy the northernmost extent of all caribou in North America, due to physical and behavioral characteristics that allow them to regulate their body temperature and facilitate their survival in cold winter conditions (Festa-Bianchet et al., 2011; Madsen, 2018). Peary caribou are opportunistic feeders and use a wide-variety of plants in a given season (Miller and Gunn, 2003). In particular, the diet of Peary caribou varies seasonally in proportion to forage availability and nutritional quality (Larter and Nagy, 2004, Drucker et al., 2012). From June to August they feed on willow (Salix spp.) which replenishes fat reserves, followed by grass, forbs, and sedges. In the winter (September to May), legumes are an important dietary component owing to their high protein content and digestibility (Larter et al., 2002), while lichens provide high carbohydrate content and promote rapid digestibility (Thomas et al., 1999). Peary caribou are an important staple in the traditional way of life in Canadian High Arctic communities because they provide food and raw materials for clothing and artwork (Hummel and Ray, 2008; Festa-Bianchet et al., 2011). Nonetheless, the increasing Arctic temperatures and precipitation along with the higher frequency of extreme weather events are responsible for spatiotemporal changes in plant phenology, shifts in species distributions and overlap (including predators such as wolves and potential competitors like muskoxen), which in turn impact Peary caribou migration, foraging, and calving processes (Vors and Boyce, 2009; Johnson et al., 2016). Moreover, a wide range of anthropogenic activities including hunting, ship traffic/ice breaking, oil/gas development on calving grounds, mining and exploration, and other disturbances (snow machines, automobiles, and aircrafts) could interfere with instinctive maternal behaviors,

1 Kaluskar, S., Blukacz-Richards, E.A, Johnson, C., Kim, D.K., Arhonditsis, G.B., 2020. Connecting the Dots in Databases of Endangered Species: A Bayesian Hierarchical Imputation Strategy for Missing Peary Caribou (Rangifer tarandus pearyi) Population Data

functional integrity of habitats, migratory patterns, and life history traits (Johnson et al., 2016). Thus, the changing Arctic environment may jeopardize the Peary caribou survival, with the potential for greater impact in areas where their numbers are already low (Miller and Gunn, 2003; Festa-Bianchet et al., 2011). Given this ominous context, Peary caribou has been listed as Endangered under Canada's Species at Risk Act (2011)1, and was assigned a Threatened status after a recent assessment by the Committee on the Status of Endangered Wildlife in Canada (COSEWIC, 2015). The latter decision was driven by an estimated decline of over 35% over the last three generations (Johnson et al., 2016). Population and distribution objectives for the Peary Caribou Recovery Strategy are intended to promote healthy, self-sustaining populations across their current geographical domain, where the animals will be able to maintain their natural patterns of habitat use, even under the pressure occasionally exerted by various stressors, e.g., extreme weather events or harvest by the local Indigenous communities. In this regard, Johnson et al. (2016) presented a knowledge assessment framework to inform the identification of critical habitats for the survival or recovery of Peary caribou, which comprised the following steps: (i) identification of the current species distribution of Peary caribou in Canada; (ii) delineation of local populations based on empirical evidence for inter-island movements, genetic analysis, and expert input regarding the spatial variation in biogeographic attributes; (iii) assessment of population threats and factors influencing habitat use and population conditions; (iv) analysis of habitat attributes at different spatiotemporal scales to inform the identification of critical habitat across Peary caribou distribution; and (v) use of demographic data from surveys along with modelling to evaluate the range of demographic and environmental conditions that would support a self-sustaining population of Peary caribou. Modelling rare and endangered species can be particularly challenging given the constraints posed by missing or incomplete datasets due to poor weather conditions, lack of technology, organizational deficiencies, and high survey costs in remote areas (Hebblewhite and Haydon, 2010; Beniston et al., 2012). Logistical and financial constraints in the Arctic Archipelago often compromise the frequency and spatial extent of Peary caribou surveys, and therefore inconsistent sampling, errors in measurements or faults in data acquisition encumber the robust assessment of their population status. In particular, the databases on northern local population estimates are insufficient for detecting both short- and long-term spatiotemporal trends

in the Arctic Archipelago. Furthermore, the lack of data on the direction/frequency of movement routes, as well as the movement of Peary caribou outside of the boundaries of surveyed areas represent a major source of uncertainty with partial population surveys. Namely, it is difficult to assess whether an increase in one area of a local population's range is related to a decrease in another due to movement or if the increase reflects actual population growth, especially when islands or island groups that make up a local population are surveyed after multi-year gaps (Johnson et al., 2016). A potential approach to quantify this uncertainty and to improve the robustness of any given modelling exercise is through imputation schemes, which are typically selected on the basis of missing data patterns. Single imputation methods (i.e., linear interpolation, cubic-spline interpolation, and nearest-neighbor interpolation) can effectively fill only short data gaps. Performance of single imputation methods decline as the gap length increases, and can introduce artefacts in the analysis. According to Junninen et al. (2004), linear interpolation methods are a good choice amongst other single imputation methods but their performance decreases as the complexity in missing data patterns increases. Time series data that are derived from complex, non-linear processes are better captured by multivariate methods, i.e., regression- based imputation, multivariate nearest-neighbor methods, and artificial neural networks (Silva- Ramírez et al., 2011). Hence, the credibility of an imputation strategy depends on both the amount and patterns of the missing data (Junninen et al., 2004). The aim of this chapter is to introduce an infilling method to support the Peary caribou knowledge-assessment framework and associated conservation practices across the Canadian Arctic Archipelago. First, a regression-based imputation framework was developed to reconstruct the Peary caribou time series. Parameterized with Bayesian inference techniques (Pritchard et al., 2000; Fukasawa et al., 2013), the imputation model has a flexible structure that can accommodate non-monotonic spatiotemporal patterns within each of the geographic regions of the Canadian Arctic Archipelago. The explicit consideration of several important covariates to capture co- dependencies in time and space offers an opportunity to understand the patterns underlying the Peary caribou population data. The robustness of the imputation outputs and the likelihood to introduce artifacts into Peary caribou population assessment is examined by comparing the spatiotemporal trends delineated with and without imputed data. The latter modelling exercise is based on a hierarchical configuration of the exponential growth model to derive region-specific population rates of change. In doing so, following ability of hierarchical formulations can be

illustrated: to share information among the different island complexes; to propagate both imputation and sampling/observation error on the population estimates; and to obtain predictions along with realistic uncertainty bounds for less-studied island groups across the Canadian Arctic Archipelago.

3.2 Methods 3.2.1 Peary caribou population Since the early 1960s, more than 150 aerial surveys have been conducted in the Canadian Arctic to estimate Peary caribou populations (see Appendix VI in Johnson et al., 2016). Studies with questionable data quality, due to the poor sightability conditions prevailing in Banks Island (McLean, 1992) and Northwest Victoria Island (Heard, 1992) during the time of the surveys, were removed from the analysis. Similarly, when multiple surveys within a single year and island were available, the summer surveys were selected over spring records to maintain consistency across years. For each survey included in the dataset, animal counts from transects were used to derive densities (number of caribou per area surveyed). In an effort to standardize population estimates, the reported calf estimates were added to the non-calf estimates to estimate total population size (i.e., all age classes). For the surveys where calf estimates were not reported, the reported productivity index (proportion of calves in total count) was used to adjust non-calf estimates. All raw caribou density estimates from aerial surveys were adjusted using standardized areas (Table 3- 1), calculated with a land mask generated from the CanVec dataset (an open source digital cartographic reference from Natural Resources Canada), to ensure that estimates of total caribou numbers per island or per island group were comparable among years. The Canada Albers Equal Area Conic projection was used to estimate areas that were consistently surveyed. This process was repeated for each time series and the standardized population estimates were used in all subsequent calculations (Detailed information about the procedures followed during the selection and standardization of survey data can be found in Johnson et al., 2016).

Standard error or confidence intervals to bracket survey estimates were available for only 60% of the abundance data (Gunn and Poole, 2014). Nonetheless, even when the sampling error was reported, the different survey methods used to derive the population estimates represented an additional source of uncertainty across sampling years and island groups. To obtain consistency in terms of the population data uncertainty, the margins of error was standardized by expressing probabilistically each population estimate with lognormal distributions. Specifically, each

distribution was parameterized such that the probability mass lying between the originally reported lower and upper bounds was readjusted in order to confine the coefficients of variation (CV) within a plausible range (10%≤CV≤70%) across the areas/years surveyed and/or methods used (Arhonditsis et al., 2007). When uncertainty estimates were not available, a global coefficient of variation (32.5%) from all the existing records across the Canadian Arctic Archipelago was used to assign uncertainty brackets to the rest of the population data. These uncertainty intervals are not meant as an absolute measure of the confidence on the population size, but rather offer a realistic range for each data point, encompassing all the potential sampling/calculation biases. In doing so, the data themselves are not treated as “perfectly” measured values, and instead an intermediate latent variable, specified probabilistically by the empirical population estimates and associated uncertainty brackets (as the corresponding first- and second-order moments), is used to determine the Peary caribou trends in time and space (see description of hierarchical modelling framework).

3.2.2 Study area The Arctic Archipelago, also known as the Canadian Arctic Archipelago, is a group of islands north of the Canadian mainland. Situated in the northern extremity of North America and covering about 1,424,500 km2, this group of 36,563 islands in the Arctic Sea comprises much of the territory of Northern Canada – most of Nunavut and part of the Northwest Territories. The Archipelago spans across two Ecozones: (i) the Arctic Cordillera which covers the northeastern fringe of Nunavut and is composed of the deeply dissected mountain ranges and (ii) the Northern Arctic which is known as a polar dessert and represents the harshest environment in Canada (Jenkins et al., 2011). One fundamental assumption of the imputation modelling exercise is that there is a subset of core areas known as primary islands from which the Peary caribou populations migrate to secondary or satellite islands. This fundamental assumption is supported by scientific literature (Gauthier, 1996; Gunn and Dragon, 2002; Zittlau, 2004; Miller et al., 2005; Gunn et al., 2006, Miller and Barry, 2009; Jenkins et al., 2011), empirical evidence from Indigenous Knowledge, and expert input (Johnson et al., 2016). Four local populations are recognized based on genetic evidence, spatial extent of inter-island movements, and expert knowledge: 1) Banks/Northwest Victoria Islands, 2) Prince of Wales-Somerset-Boothia, 3) Western Queen Elizabeth Islands, and 4) Eastern Queen Elizabeth Islands. These local populations were used to identify six (6) island complexes with primary and secondary islands (Table 3-1 and Fig. 3-1).

For the Banks island complex, Banks Island served as the primary island from where Peary caribou move from to Northwest Victoria Island (Miller, 1986; Johnson et al., 2016). Both of these islands are within the Inuvik Region in the Northwest Territories and separated by the Prince of Wales Strait. Zittlau (2004) found genetic similarities in samples collected between Banks and Victoria Islands (Minto Inlet) compared to the rest of the Canadian range of Peary caribou. The Prince of Wales-Somerset-Boothia population was identified as the Boothia island complex which included the islands of Prince of Wales, Somerset, and Russel, where Peary caribou have been shown to migrate among the islands and the Boothia peninsula (Gunn and Dragon, 1998). For example, Miller et al. (1982) showed the Peary caribou left Somerset Island in the spring, when ground-fast ice depths were relatively unfavourable, to forage on Prince of Wales, where snow cover was shallow and retreated quickly. In a 2004 survey of Prince of Wales and Somerset Islands, Dumond (2006) observed only one Peary caribou. The Boothia Peninsula has been surveyed more frequently compared to the other islands and it is where a substantial portion of Peary caribou overwinters, relative to the tundra-covered Prince of Wales Island, or Somerset and Russell Islands (Jenkins et al., 2011). Genetic analysis suggests that caribou from Prince of Wales are more similar to those on Somerset than caribou on either island are to those on Boothia (Johnson et al., 2016), and thus some uncertainty exists in the literature whether the Boothia Peninsula should be considered as part of the same local population (Gunn et al., 2006). The Western Queen Elizabeth Islands population was represented by three island complexes: Melville, Bathurst, and Mackenzie King. Melville Island was selected as the primary island with Prince Patrick, Byam-Martin, Emerald, and Eglinton as secondary islands. This specification is supported by studies that show high proportion of migration between Melville Island and the secondary islands (Miller et al., 1977; Gunn and Fournier, 2000). Vegetation is relatively more diverse on islands south of Ellesmere Island, consisting of hummocks of mosses, lichens, sedges, as well as dwarf willows (Salix herbaceae), and consequently Peary caribou experience higher survival rates compared to other islands (Miller et al., 1977; Johnson et al., 2016 and references therein). The Bathurst cluster included the Bathurst Island Complex (BIC) (Cameron, Ile Vanier, Marc, Massey, Alexander, Bathurst islands), Cornwallis, Little Cornwallis, Helena, Devon, and Lougheed islands. Over the past 50 years, BIC and some of the surrounding islands have been surveyed more frequently compared to other Western Queen Elizabeth Islands (COSEWIC, 2015).

The vegetation cover in this area is sparse to moderate with forbs, prostrate dwarf shrubs, sedges and grasses (Poole et al., 2010). BIC has been an area of interest highlighted by Tener's (1961) survey, which identified this island complex as an important habitat for Peary caribou as well as a critical site for mining exploration and hunting ground (Jenkins et al., 2011). BIC was considered as the primary group of islands (Jenkins et al., 2011), whereas Helena, Little Cornwallis, Devon, and Lougheed were classified as the secondary/satellite islands (Table 1) (see distribution and movement reports in Miller et al., 1977; Miller, 1990; Johnson et al., 2016). The landscape of Devon Island (55,534 km2) is predominantly a polar desert characterized by several mountain ranges and extensive glaciers, while the coastal lowlands are dominated by prostrate shrubs (Salix arctica, Dryas integrifolia) and sedges (Edlund and Alt, 1989; Johnson et al., 2016). The Mackenzie King cluster of islands comprises Mackenzie King and Brock Islands and was last surveyed in 1997 (Gunn and Dragon, 2002). Surveys throughout the years consistently showed that Mackenzie King Island has the highest estimates of caribou and thus served as the primary island. Studies have documented inter-island caribou movements from Mackenzie King to Borden Island (Tener, 1963; Johnson et al., 2016). The Eastern Queen Elizabeth Islands population was represented by the Axel Heiberg cluster, comprising the Axel Heiberg and Ellesmere Islands. Axel Heiberg was considered as the primary island and Ellesmere Island was the secondary one (Jenkins et al., 2011). Axel Heiberg Island is separated from Ellesmere Island by Nansen and Eureka Sound. This island is characterized by a central mountain range (Princess Margaret Range), two large ice caps (Müller and Stacie), several smaller highland ice caps, and many glaciers that dominate the interior. East of the Princess Margaret Range, vegetation progresses from an herb-shrub transition zone at higher elevations to an enriched prostrate shrub zone along the low-lying coast. The plant flora can be diverse and dense, dominated by shrubs and sedge meadows (Edlund and Alt, 1989). West of the Princess Margaret Range, vegetation is less diverse with large areas of sparse herbaceous communities (Edlund and Alt, 1989). Ellesmere Island (197,577 km2) is Canada's third largest island and the most northerly one in the Arctic Archipelago. Glaciers and the Arctic Cordillera mountain range cover most of Ellesmere Island. Vegetation is sparse, but the coastal regions such as the Truelove Lowlands and portions of the Grinnell Peninsula, support a greater diversity of vegetation dominated by prostrate shrubs and sedges (Edlund and Alt, 1989). Recent surveys

(Jenkins et al., 2011; Anderson, 2014; Anderson and Kingsley, 2015) have recorded Peary Caribou on Ellesmere and Axel Heiberg islands on all non-glacier-covered areas.

3.2.3 Modelling Framework 3.2.3.1 Imputation Modelling Data-infilling method is based upon a multiple regression model that aims to identify the linkages among available population records in time and space. Peary caribou population estimates in secondary/satellite islands are predicted from the population of the corresponding primary islands, the areal ratio of the pair of islands considered, and the year. Bayesian inference was used to estimate the model parameters based on the value of information contained in the dataset. The governing equation for predicting population estimates in secondary/satellite islands is given by:

̂ 2 푙푛(푃퐶푖(푗),푡) ~ 푁(푙푛 (푃퐶푖(푗),푡), 휎푖푚푝)

푙푛 (푃퐶̂ 푖(푗),푡) = 휃1 + 휃2 ∙ 푙푛(훿푖(푗)) + 휃3 ∙ 푡 + 휃4 ∙ 푝푖(푗),푡 ∙ 푙푛(푃퐶푗,푡)

+휃5 ∙ (1 − 푝푖(푗),푡) ∙ 푙푛(푃퐶푗,푡)

̂ −2 휃 ~ 푀푉푁(휃, ∑휃), 휎푖푚푝 ~ 퐺푎푚푚푎(0.001, 0.001)

i=1,…,22 j=1,…,6 t=1,…,45 where 푃퐶̂푖(푗),푡 and 푃퐶푖(푗),푡 represent the predicted and recorded population within a secondary/ 2 satellite island i for a given spatial complex j and year t, respectively; 휎푖푚푝 represents the associated structural error of the imputation model drawn from an uninformative gamma prior distribution; 푝푖(푗),푡 denotes the probabilistic weight, varying from 0 to 1, that expresses the likelihood for the population to be higher in the secondary/satellite island i relative to the primary one of a given spatial complex j and year t. Thus, this parameter can also be perceived as an indirect attempt to characterize the degree of movement within each island group of the Canadian Arctic Archipelago. The imputation model also explicitly considers the nearly monotonic decline of the Peary caribou population over time by introducing a linear term (in the natural logarithmic scale),

푃퐶푗,푡 represents the population recorded in the primary island of a given spatial complex j and year t, 훿푖(푗) is the ratio of the area of the secondary/satellite islands i relative to the area of the primary island of a given spatial complex j. The parameter vector θ was drawn from a multivariate normal

distribution, with mean values provided by the vector 휃̂ = [0,0,0,0,0] and covariance matrix Σθ drawn from a Wishart prior as follows:

−1 훴휃 ~W𝑖푠ℎ푎푟푡(푅 , 푛)

1 0 0 0 0 0 1 0 0 0 푅 = 0 0 1 0 0 0 0 0 1 0 (0 0 0 0 1)

where R is the prior covariance matrix of the Wishart distribution, representing an assessment of the order of magnitude of the covariance matrix, specified as 5 x 5 elementary matrix, and n was assigned the minimum possible degrees of freedom (5), suggesting vague prior knowledge on the parameter covariance. It is important to tote that except from very small sample sizes, the choice of R has little effect on the posterior estimate of Σθ.

After the Bayesian updating, the posterior predictive distribution of the model was used to infill data in secondary/satellite islands using as predictors the observed estimates in primary locations along with the rest variables. There were also instances where the data gaps existed in primary islands, while the secondary/satellite locations did have population records. In the latter cases, by rearranging the previously described governing equation, the populations on the primary islands, 푃퐶̂푗,푡 , is infilled as follows:

푙푛(푃퐶푖(푗),푡) − 휃2 ∙ 푙푛(훿푖(푗)) − 휃3 ∙ 푡 − 휃1 푙푛(푃퐶̂푗,푡 ) = (휃4 − 휃5) ∙ 푝푖(푗),푡 + 휃5

The infilling model has an additional layer that specifies the probabilistic weight, 푝푖(푗),푡, associated with the relative Peary caribou population size between the secondary/satellite island i and the primary island of a given spatial complex j and year t. In order to quantify the likelihood of the secondary/satellite island population to be greater than the primary island in a particular year, logistic regression model was used as follows:

훾푖(푗),푡 ~ 퐵푒푟푛표푢푙푙𝑖(푝푖(푗),푡)

푙표푔𝑖푡(푝푖(푗),푡) = 푎1푖(푗) + 푐푖(푗) ∙ 푎2푡 ∙ 푡

2 2 2 푎1푖(푗)~훮(휇푎1, 휎푎1), 푐푖(푗)~훮(휇푐, 휎푐 ), 푎2푡~훮(휇푎2, 휎푎2),

−2 −2 −2 휎푎1 ~ 퐺푎푚푚푎(0.001, 0.001), 휎푐 ~ 퐺푎푚푚푎(0.001, 0.001), 휎푎2 ~ 퐺푎푚푚푎(0.001, 0.001)

휇푎1~훮(0,10000), 휇푐~훮(0,10000), 휇푎2~훮(0,10000)

i=1,…,22 j=1,…,6 t=1,…,45 where 푎1푖(푗) represents the intercept of the logistic model assigned to the secondary/satellite island i within a given spatial complex j, 푎2푡 is a year-specific coefficient connecting the year t of the study period with the probability 푝푖(푗),푡, 푐푖(푗) is an island-specific coefficient that shapes the relationship between time and probability 푝푖(푗),푡. The vectors 푎1, 푎2, and 푐 are draws from normal 2 2 2 distributions with mean and variance of 휇푎1, 휇푎2, 휇푐, and 휎푎1, 휎푎2, 휎푐 , respectively, while the corresponding parameters are constrained to have zero sum to make the model identifiable; 훮(0,10000) is the normal distribution with mean 0 and variance 10000; 퐺푎푚푚푎(0.001, 0.001) is the gamma distribution with shape and scale parameters equal to 0.001. The latter prior distributions are considered “non-informative” or vague. It is also worth noting that the sensitivity of the model outputs to the gamma prior distribution assigned to the variance terms was tested with uniform and half-Cauchy priors and the results were practically identical (Gelman,

2006). 훾푖(푗),푡 is a binary variable (0 or 1) that characterizes the relative Peary caribou abundance between the secondary/satellite island i and the primary location of the spatial complex j for a given year t. For example, when the secondary island has greater population than the primary one in the training dataset, γ will be equal to 1; otherwise, γ will be equal to 0. Because of the likelihood of co-dependence between 푃퐶푖(푗),푡 and 훾푖(푗),푡, the introduction of the latter auxiliary variable could lead to an underestimation of the underlying uncertainty.

The Bayesian inference was used to estimate model parameters because of its ability to include prior information (e.g., literature reviews, expert knowledge, metadata, past parameter estimates) in the modelling analysis and to explicitly deal with model structural/parametric uncertainty as well as missing data and measurement errors (Gelman et al., 2013). Bayesian inference treats each element of the parameter vector ω as a random variable and uses the likelihood function to express the relative plausibility of different parameter values given the available data from the system:

푃(휔)푃(푑푎푡푎|휔) 푃(휔|푑푎푡푎) = 푃(휔)푃(푑푎푡푎|휔)푑휔 ∫휔 where P(ω) represents the prior distribution of the model parameter ω, P(data|ω) indicates the likelihood of the data observation given the different ω values, and P(ω|data) is the posterior probability representing the updated beliefs on the ω values, contingent upon empirical knowledge from the system. The denominator is often refered to as the marginal distribution of the available data and acts as a scaling constant that normalizes the integral of the area under the posterior probability distribution (Gelman et al., 2013).

Sequences of realizations from the model posterior distribution were obtained using Markov-chain Monte Carlo (MCMC) simulations (Gilks et al., 1998). Specifically, the general normal-proposal Metropolis algorithm is used as it is implemented in the WinBUGS software (Lunn et al., 2000); this algorithm is based on a symmetric normal proposal distribution, whose standard deviation is adjusted over the first 4,000 iterations such as the acceptance rate ranges between 20% and 40%. Using an ordered over-relaxation multiple samples per iteration were generated and then this method selects one that is negatively correlated with the current value of each stochastic node (Neal, 1998). The latter option resulted in an increased time per iteration but reduced within-chain correlations. with the modified Gelman–Rubin convergence statistic (Brooks and Gelman, 1998), convergence was assessed for 50,000 iterations. The accuracy of the posterior estimates was inspected by assuring that the Monte Carlo error (an estimate of the difference between the mean of the sampled values and the true posterior mean; see Lunn et al., 2000) for all the parameters was less than 5% of the sample standard deviation.

3.2.3.2 Trend Analysis of Peary caribou populations The Peary caribou population temporal trends were determined across the different islands of the Canadian Arctic Archipelago using the exponential growth model (Dennis et al., 1991):

푁푃퐶푡+1 = 휆 ∙ 푁푃퐶푡 ∙ 휑 where 푁푃퐶푡 is the number of individuals in the population in year t, λ is the population growth rate, or the amount by which the population multiplies each year, and φ is a lognormal random variable with a mean of 1 and a shape parameter σ2. The latter parameter accommodates the idea that the possible realizations of population growth in a stochastic environment diverge over time and gradually become skewed, with a few high-abundance realizations outweighed by a large number of low-abundance realizations (Dennis et al., 1991). Despite its frequent use in the ecological

modelling practice, this simple conceptual model is founded upon three major assumptions that may not necessarily hold true when reproducing population dynamics of endangered species in extreme environments, like the Canadian Arctic Archipelago (see also following Discussion): (i) the population growth rate is not influenced by the variations of the population density; (ii) the environmentally-driven variability is not extreme, and thus there are no years with catastrophic (e.g., icing) events or unusually favorable conditions; (iii) the year-to-year variability in the population growth rate is primarily modulated by the environmental stochasticity, whereas the contribution of the observation/ sampling error to the variation in the animal counts is negligible and represents a constant fraction of the entire population over time (Morris et al., 1999).

The exponential growth model was first used to examine the impact of data imputation by evaluating the temporal trends independently in each of the twenty two (22) islands (Table 1) with sample size n greater than 4. To do so, a simple approach presented by Dennis et al. (1991) was used to estimate the mean estimate of the population rate of change and the uncertainty/error surrounding this rate from a series of population censuses in each island surveyed. The method involves the following simple steps: (i) first select pairs of animal counts, 푁푃퐶푖(푗), in each island i of the spatial cluster j from adjacent censuses conducted in years ta and tb; (ii) then calculate the transformed variables 푥 = √(푡푎 − 푡푏) and 푦 = 푙푛 (푁̂푃퐶푖(푗),푡푎/푁̂푃퐶푖(푗),푡푏)/푥 for each pair; and (iii) all the resulting pairs of x and y were then used to perform a linear regression of y on x, forcing the regression line to have a y-intercept of zero. The slope of the resulting regression line is a mean estimate of the population rate of change, while the mean square root residual is an estimate of the uncertainty/variability surrounding this mean estimate. This process was conducted before and after the imputation exercise to examine the robustness of the inference drawn.

This trend analysis was repeated using a Bayesian hierarchical formulation that has two distinguishing features: first, the data were classified according to the island complex collected; and the model itself had its own hierarchical configuration, with the spatial cluster-specific population growth rates at the first level, controlled by the hyper-parameters at a second (upper) level that capture the population variability over the entire Canadian Arctic Archipelago. With the hierarchical model structure, significant sources of variability that differentially modulate the Peary caribou population trends within each spatial complex can be explicitly accommodated, while overcoming problems of insufficient group-specific data by “borrowing strength” from well-

studied modelled units (Zhang and Arhonditsis, 2009; Cheng et al., 2010). The latter issue is particularly important for the case study, as the Peary caribou populations are inconsistently recorded over time and differ in terms of their accuracy among the different locations. The data uncertainty was accounted for by postulating that the population data represent a random draw from a probability distribution with an expected value, the true (or error-free) value of the Peary caribou population modelled, and the variance comprising both imputation model error and observational (sampling) uncertainty (Carroll et al., 2006; Ramin and Arhonditsis, 2013; Shimoda and Arhonditsis, 2015). The mathematical notation for the hierarchical formulation of the exponential growth model is summarized as follows:

2 푙푛 (푁푃퐶푗,푡)~훮(푙푛 (푁푃퐶푡푟푢푒푗,푡), 훿푗푡)

2 푙푛 (푁푃퐶푡푟푢푒푗,푡)~훮(푙푛 (푁̂푃퐶푗,푡), 휎푚표푑)

푙푛 (푁̂푃퐶푗,푡) = (푡 − 푡0푗) ∙ 휆푗 + 푙푛 (푁푃퐶푗,0)

2 2 2 2 훿푗푡 = 휎푖푚푝푗,푡 + 휎표푏푠푗,푡 휆푗~훮(휆퐺, 휎휆푗)

2 −2 휆퐺~훮(휇휆, 휎휆 ), 휎휆푗 ~ 퐺푎푚푚푎(0.001, 0.001), j=1,…,6

−2 휇휆~훮(0,10000), 휎휆 ~ 퐺푎푚푚푎(0.001, 0.001) −2 휎푚표푑~ 퐺푎푚푚푎(0.001, 0.001) where 푁̂푃퐶푗,푡, and 푁푃퐶푗,푡 represent the predicted and measured population within the spatial complex j and year t, respectively; 푁푃퐶푡푟푢푒푗,푡 is a latent variable representing the “true” or error-free Peary caribou 2 2 abundance and 훿푗푡 is pre-specified error term, which in turn is the sum of the observation, 휎표푏푠푗,푡, and 2 2 imputation, 휎푖푚푝푗,푡, errors for the spatial complex j and year t; 휎푚표푑 represents the associated structural error of the hierarchical model drawn from an uninformative gamma prior distribution with shape and scale parameters equal to 0.001; 푁푃퐶푗,0 represent the initial measured population in the spatial complex j and year 푡0푗; 휆푗 is the island complex-specific population growth rate, which is drawn from a normal distribution with a global population growth rate, 휆퐺, and island complex-specific 2 2 variance, 휎휆푗; 휇휆 and 휎휆 are the mean and variance of the hyperparameter, respectively.

3.3 Results-Discussion 3.3.1 Data imputation and island-specific population sizes The imputation model displayed satisfactory performance with a posterior standard error of 1.919±0.205, i.e., median model error of 6.814 caribou bracketed by a 95% credible interval (or 95% CI) between 4.559 and 10.183 (Table 3-2), while the coefficient of determination (r2) between mean predicted and empirical population estimates was equal to 0.65. The signal-to-noise ratio of the regression coefficient θ2 (0.857±0.064) suggests that the areal ratio between secondary/satellite and primary islands within a given spatial complex is a strong predictor variable of the Peary caribou population at the secondary/satellite islands, and so is the corresponding population at the primary islands. Interestingly, the signal-to-noise ratios of the associated parameters were indicative of a strong relationship between the Peary caribou counts at the two locations, whether the number of animals is higher at the secondary/satellite location relative to the primary one (θ4 =

0.949 ± 0.016) or not (θ5 = 0.741 ± 0.075). The updated model also considers a distinct monotonic decline of the Peary caribou population over time (θ3 = -0.021 ± 0.002 or number of animals ∝ 0.979t) across the Canadian Arctic Archipelago. Because of the distance from human settlements as well as the adverse prevailing weather conditions, the Mackenzie King complex does not favor systematic aerial surveys and therefore only six (6) surveys were conducted since the 1970s. The highest animal count on Brock Island (24 animals) was reported in 1973, and the same is true for the Mackenzie Island in year 1974 (60 animals). In 1997, the total population size including both actual records and imputed data remained lower than 100 animals (Fig. 3-2a), which suggests a dramatic decline relative to the population size (≈4,000 animals) registered in the 1961 survey (Tener, 1963). More recently, Miller et al. (2005) conducted a bootstrap analysis of Tener's (1963) survey dataset and adjusted the mean estimate to 4,260±767 animals with an areal density of 0.514 caribou per km2. The same study surmised that the Mackenzie King complex has served on occasions as a “spillover area” when the caribou on southern eco-units reached high densities. However, Miller et al. (2005) also noted that this eco-unit is unlikely to offer a hospitable habitat for a sustainable Peary caribou population, given that it is characterized by sparse vegetation and lies beyond the northern limit of prostrate shrubs and sedges. Only five (5) surveys with partial coverage were conducted in the two islands of the Axel Heiberg complex over the past four decades, which posed challenges to the standardization of the population data and the delineation of temporal trends with realistic uncertainty. The imputation

exercise allowed to obtain estimates of the total Peary caribou counts over the entire island complex for the years 1989, 2005, 2006, 2007, and 2015 (Fig. 3-2b). Consistent with total population mean estimate (≈470 caribou) for the late 1980s, empirical information from this eco- unit was suggestive of a fairly stagnant population until the early 2000s (Case and Ellesworth, 1991; Manseau et al., 2004). Nonetheless, the most recent surveys in 2005 and 2006 indicated that the mean local population estimates are greater than 1,200 caribou with reported densities from surveys on southern and northern Ellesmere of 9.1 and 8.3 per 1000 km2, respectively. These trends are on par with contemporary reports of healthier and more stable population on Ellesmere and Axel Heiberg Islands; especially, on some well-vegetated sections (Miller et al., 2005). In 2007, Jenkins et al. (2011) reported the highest Peary caribou abundance of 2,255 on Axel Heiberg Island, which led to an imputed value of 7,115 on Ellesmere Islands. The latter value though should be viewed with caution, as it is nearly seven times higher than the caribou counts registered in 2005 and 2006 on the same island. It is also interesting to note that the predicted total population size for the entire island complex in 2015 (≈1,240 caribou) was comparable to the 2005 and 2006 estimates (Anderson and Kingsley, 2015). The detected population patterns on Banks island complex have been identified as benchmark to evaluate the potential for long-term Peary caribou fluctuations, as the local community information is indicative of several wax-and-wane cycles since the 1920s (Canadian Wildlife Service, 2013; Johnson et al., 2016). After adding the imputed data, the Banks and Northwest Victoria population displayed an overall decrease from the 1970s onwards, but again the surveys conducted after the 2000s indicate that the population has increased since the minimum estimates registered in the 1990s (Fig. 3-2c). Specifically, the total population was well above the level of 10,000 caribou over the entire island complex during the early 1970s, but ranged between 367 and 2,595 during the 1990s. After including the imputed value on Northwest Victoria Island, the most recent survey in 2014 suggests an exceedance of the level of 3,000 caribou. Among the variety of factors that can conceivably modulate population dynamics, the recent increase could be driven by the increased harvesting of wolves and reduced caribou hunting by the Inuvialuit hunters (Gunn et al., 2006), as well as the earlier snowmelt and associated increase of the growing season by 7.1 days in the sedge-shrub tundra on Banks island complex (Jia et al., 2009), which may be resulting in an increased summer fat accumulation and subsequently increased reproductive rates and winter survival (Johnson et al., 2016).

Based on the available information, the Peary caribou population on the Boothia Island complex (Boothia, Prince of Wales, Somerset, and Russell Islands) has experienced a dramatic decline over the course of the past 30 years (Fig. 3-2d). Specifically, the sum of imputed and survey data suggests that their population ranged anywhere between 4,900 to 6,500 during the mid-1970s, while the 1980 estimate raises the Peary caribou abundance up to 8,900 after adding an imputed value of 2,661 for Boothia Island. The 1985 survey estimate on the same island was 4,738 caribou (see area-corrected value by Johnson et al., 2016), which according to the logic of the imputation model (i.e., the abundance of secondary/satellite sites is strongly dependent upon the magnitude of the population on the primary island) led to a population size of over 16,000 caribou over the entire Boothia Island complex. Nonetheless, given that anecdotal evidence by Inuit hunters during the late 1980s/early 1990s had suggested a decrease in the abundance of caribou that posed challenges for harvesting (Gunn et al., 2006), it is believe that the latter value is likely an overestimate. Indeed, the subsequent total population estimates showed a dramatic decline to lower than 3,500 caribou in the mid-1990s (Miller, 1997; Gunn and Dragon, 1998), and critically low numbers, near to extirpation, in the mid-2000s (Dumond, 2006; Jenkins et al., 2011). While the significant gaps among the surveys make it difficult to unequivocally identify the causes for this significant decline through the 1980s and 1990s, it has been hypothesized that it could be attributed to reduced survival rates for breeding females and calves (in the first year of life), excessive harvesting, and increased forage competition and/or wolf predation stemming from the contemporary increase in muskoxen abundance (Gunn et al., 2006). Other plausible factor could be the prevailing weather conditions in the area and, in particular, the severe winters of 1989-90 and 1994-95 (Jenkins et al., 2011; Langlois et al., 2017). According to Tener's (1963) survey data, the Melville island complex appeared to be a preferable forage habitat, as this eco-unit represented a major fraction of the caribou population with a mean areal density of 0.272 caribou km−2 (see Table 2 in Miller et al., 2005). In the mid- 1970s, the total population size varied between 2,385 and 5,240 (Fig. 3-2e), but was reduced down to 480-1,460 during the mid-1980s (Miller, 1988; Johnson et al., 2016) and remained within the same range according to a subsequent survey in 1997 (Gunn and Dragon, 2002). Interestingly, the most recent survey in 2012 exhibited an increased abundance amounting to 6,700 caribou over the entire complex (Davison and Williams, 2012). While the long intervals between surveys represent a major challenge in determining the current population trends, the prolongation of the growing

season along with the less extreme winter conditions over time could have contributed to an increased availability of vascular plant forage, and consequently to higher survival and productivity in caribou (Zeng and Epstein, 2011). On the other hand, Tews et al. (2007b) used data from Bathurst island complex and climate simulations to show that Peary caribou die-offs are dependent on projected aboveground biomass levels and the degree of forage accessibility. In particular, the underlying simulations suggested that Peary caribou may experience significantly lower population die-offs during disturbance years if biomass increases by 50% as projected within the next 100 years and if the currently estimated proportion of inaccessible caribou forage during such disturbance events does not change with climate change (Tews et al., 2007b). Given that there is very little to no harvest pressure in this area and minimal human activity (e.g., mineral exploration or other development) on the landscape, this area could also be an excellent opportunity to understand the causal linkages between climate and Peary caribou population dynamics. Earlier work on Queen Elizabeth Islands highlighted the Bathurst island complex as an important eco-unit for Peary caribou (Tener, 1963), and as such this area has been subjected to extensive investigation over the past four decades. Other reasons for the focus on this eco-unit are related to its importance as a caribou hunting area for the community of Resolute Bay (Miller, 1995), the activities related to oil and gas exploration and development, as well as the lead-zinc deposits on Bathurst and Little Cornwallis (Taylor, 2005). After the addition of the imputed data, the 1974 population estimate of 385 caribou suggests a nearly 70% decline from the previous year (Fig. 3-2f), which was attributed to widespread mortality and minimal reproductive success due to adverse weather conditions in 1973 (Miller et al., 1977). Peary caribou populations gradually rebounded after the mid-1980s (≈1,100 caribou) and reached a maximum level in 1993 (>4,000), but demonstrated a steep decline immediately after which resulted in an all-time low of about 100 caribou in 1997 (Jenkins et al., 2011). This decline was again associated with the increased caribou mortality caused by the exceedingly severe winter and spring conditions during those years (Miller and Gunn, 2003). Counter to Jenkins et al.’s (2011) projection, Peary caribou dataset does not provide any evidence of recovery until the early 2000s, but the most recent survey in 2013 does suggest a discernible increase with a mean total population estimate higher than 1,450 caribou. Although evaluation of trends in abundance is quite uncertain when having multi-year data gaps, the latter result may render support to Jenkins et al.’s (2011) assertion that Peary caribou

population on Bathurst island complex could return to levels experienced in the early 1960s and early 1990s, if there are no major setbacks by severe weather events (deep snow cover, icing), excessive harvesting, or other environmental conditions. 3.3.2 Delineation of local population units and inter-island migration In the context of Peary caribou ecology, the identification of the appropriate units of spatial analysis is critical for the current recovery objective of self-sustaining local populations across their current distribution (Canadian Wildlife Service, 2015). According to Johnson et al. (2016), a local population is a group of animals occupying a well-delineated area such that the demography of the animals (e.g., birth and death rates) is driven primarily by the prevailing environmental and climatic conditions that influence resource availability, rather than immigration and emigration. While methods for delineating local populations for land use planning, conservation, and management can vary significantly, the definition of Peary caribou demographic units used in the present study, largely following the Johnson et al.’s (2016) scheme, was primarily based on island groupings, as defined by the territorial jurisdictions (SARC, 2012), coupled with three additional lines of evidence: (i) the degree of genetic similarity of individuals from different areas; (ii) inter- island migration routes to characterize the degree of demographic separation of a group of animals inhabiting a given island; and (iii) expert input. The latter two sources of information have been based on direct sightings of animals, tracks on sea ice, or on assumptions regarding movement to smaller, satellite islands which are used as shorter-term refugia for Peary caribou. Thus, given the lack of concrete quantitative information, the imputation modelling framework used the probabilistic weights p as an indirect proxy to characterize the degree of movement within each island group of the Canadian Arctic Archipelago, although they were originally designed to simply express the likelihood for the populations to be higher in secondary/satellite islands relative to the primary ones of any given spatial complex and year. It is important to note though that this interpretation could be confounded by the areal ratio of the examined (secondary/satellite versus primary) islands. Furthermore, as a pragmatic alternative to the lack of data to predict the spatiotemporal movement trends, the logistic equation used to derive these probabilistic weights considered time (year) as the sole predictor along with a multitude of parameters, i.e., intercepts specifically assigned to each secondary/satellite island within a given spatial complex, year-specific coefficients connecting each year of the study period with the corresponding probability p, and island-specific coefficients that shape the relationship between time and probability p. In the following section, some of the posterior p estimates are used

to draw inference about inter-island movements, but it should also be noted that this parameterization resulted in considerable (and practically uninformative) uncertainty in several instances (Fig. 3-3). Thus, in light of the emerging evidence of Peary caribou movement patterns in time and space, the next iteration of the modelling framework should consider additional predictors that will augment the mechanistic foundation of the logistic regression model and consequently reduce the problem of overparameterization and inflated uncertainty. One of the clear distinctions in the spatial structure of Peary caribou populations is the divide between the groups inhabiting the Queen Elizabeth island complex and those occupying areas further south. Existing evidence is suggestive of little genetic interchange between the Prince of Wales/Somerset (Zittlau, 2004; COSEWIC, 2004) or Banks/Northwest Victoria island groups (McFarlane et al., 2014) and those living around the Queen Elizabeth Islands. Except from the North-South breakdown, the minimal gene flows and movement records indicate a split between the eastern and western Queen Elizabeth Islands (Johnson et al., 2016). Specifically, Ellesmere and Axel Heiberg Islands form the eastern local population unit mainly due to their similarities in geomorphology, vegetation patterns, and climatic conditions. Within this spatial cluster, the imputation model suggests that more than 70% of the local population is located in Ellesmere Island (posterior p→1) with only exception being the estimate for 2015 (Fig. 3-3). Regular seasonal movements have also been documented within the Melville island complex, whereby Peary caribou are moving from summer ranges on Melville and Byam Martin Islands to winter ranges on Prince Patrick and Eglinton Islands, or even transitional ranges on Emerald Island for smaller caribou numbers, mainly during spring and autumn (Miller et al., 2005; Mallory and Boyce, 2019). In particular, Prince Patrick was characterized by higher p values during the earlier years of the study period but less so during the 1997 and 2012 surveys, and the same pattern generally held true for the rest of the islands of this complex (see corresponding panels in Fig. 3- 3). Consistent with the expert input presented by Johnson et al. (2016) and, Mallory and Boyce's (2019) flow-centrality projections, the posterior p values suggest high degree of movement among the islands (Mackenzie King, Borden, and Brock) of the Mackenzie King complex (Fig. 3-3). Peary caribou within the Bathurst island complex also make seasonal inter-island migrations, although existing empirical evidence suggests that a fraction of the local population remains year-round on Bathurst Island and on other smaller islands (Miller et al., 2005). The primary linkage appears to be among Bathurst, Cornwallis, and Little Cornwallis (Gunn and

Dragon, 2002, Johnson et al., 2016), and the corresponding posterior p values (>0.50) are on par with these observations. Cameron Island has also been identified as a major migration route for Peary caribou moving between Bathurst and Melville Islands (Johnson et al., 2016) or even to Lougheed Island (Miller, 1998; Mallory and Boyce, 2019). Nonetheless, the low p estimates (<0.02) associated with the relative population size between Lougheed and Bathurst islands cannot be used to infer the origin of the animals, but rather reflect the lower likelihood of exceedance of its population size relative to the primary one (Fig. 3-3). Peary caribou behavior generally suggests periodic movements from Bathurst to Devon Islands (see Inuit knowledge shared in Johnson et al., 2016). Geomorphological characteristics, vegetation/productivity patterns, and temperature regime of the western unglaciated portion of Devon Island resemble to those of the rest islands of the Bathurst Island complex (Edlund and Alt, 1989; Johnson et al., 2016), while the corresponding p posteriors were consistently greater than 0.70. Microsatellite DNA analyses, aerial surveys, and community knowledge suggest that Banks and Northwest Victoria Islands are occupied by Peary caribou with similar genetic makeup with active seasonal movement between the two islands (Johnson et al., 2016; Mallory and Boyce, 2019). According to the imputation model, the median p values ranged from 0.47 to 0.68 during the study period but with no apparent trend over time (Fig. 3-3). Nonetheless, most of the survey reports indicate that movement was more common in the 1970s and 1980s and less so during the most recent years (SARC, 2012). While the identification of the actual causes of this change in the migration patterns is beyond the scope of the present study, it is interesting to note that community knowledge suggests the inter-island movements and use of smaller islands become less frequent as the population size declines (COSEWIC, 2004). Moreover, the increased likelihood of connectivity loss across sea ice (owing to a warmer climate or increased ice-breaking activities) highlights the importance of maintaining the linkages and consequently facilitating the flow of genes among the local Peary caribou populations on Banks, Bathurst, and Melville island complexes (Mallory and Boyce, 2019). The grouping of Boothia island complex is characterized by greater uncertainty relative to the rest of the local populations considered in the present analysis. Aerial surveys documenting trails on the sea ice and community knowledge have linked summer ranges on Prince of Wales and Russell Islands with winter ranges on Somerset Island and the Boothia Peninsula (Gunn et al., 2006). Nonetheless, recent empirical evidence has identified Peary caribou migration routes

towards the southern areas of Boothia Peninsula, which is also consistent with genetic analysis showing that caribou from Prince of Wales are more similar to those on Somerset than caribou on either island are to those on Boothia (McFarlane et al., 2014). Interestingly, the derived p values varied considerably (0.32-0.99) during the study period probably reflecting the substantial year- to-year variability in the relative population abundance among the islands (Boothia, Russell, Somerset, and Prince of Wales) of this spatial cluster (Fig. 3-3). 3.3.3 Peary caribou population trends across the Canadian Arctic Archipelago In the context of animal population modelling, various techniques have been used (population viability analysis, agent-based, or stochastic simulation models) for understanding the dynamics of a wide range of species (Boyce et al., 2002; Tews et al., 2007a). These models aim to shed light on the role of both top-down (i.e., predation, hunting, and other anthropogenic disturbances) and bottom-up (i.e., forage accessibility, climate) factors that can potentially control animal populations. Nonetheless, steep data requirements put constraints on the applicability of complex age-structured simulation models (Dennis et al., 1991), and thus simple stochastic models, like the hierarchical exponential growth model, might serve as useful approximations to tease out general population patterns. In this chapter, before assessing the temporal trends of Peary caribou with the hierarchical formulation over the entire Canadian Arctic Archipelago, the impact of data imputation by using the simple approach presented by Dennis et al. (1991) was first examined.

The mean estimates of the island-specific population rate of change remained practically unaltered after the introduction of the imputed data (Table 3-3). Specifically, the two islands of the Banks island complex displayed an average rate of change of 0.970 yr−1 or 3% population decline per year. The decreasing population trends were distinctly more pronounced on Boothia island complex, where the rates of change varied from 0.780±0.121 yr−1 on Prince of Wales Island or 0.831±0.353 yr−1 on Boothia Island to 0.921±0.236 yr−1 on Russell Island. The population of Peary caribou remained fairly steady on Bathurst island complex with rates of changes varying anywhere from 0.942±0.208 yr−1 (Helena Island) to 1.053±0.246 yr−1 (Helena Island). Similar evidence of a steady trend was registered on the Melville island complex, where Peary caribou displayed weakly decreasing rates of change on Emerald Island (0.975±0.165 yr−1) but weakly positive trends on the rest constituent islands (1-7% per year), regardless of the consideration of imputed data or not. Positive rates of change were derived for Axel Heiberg (1.058±0.649 yr−1) and Ellesmere

(1.033±0.594 yr−1) islands. Given that the sample size in this spatial cluster is small (n=5) even after the inclusion of the imputed data, a caution must be taken.

The mean predicted Peary caribou population levels, NPCj,t, from the hierarchical model satisfactorily matched the observed values, NPCj, t, on Banks island group, but with a tendency to under-predict the most recent population records during the 2010s, while the opposite was true for the 1990s (Fig. 3-4). On the other hand, the exponential model displayed poor performance in reproducing caribou abundance on Boothia and Bathurst island complexes (Fig. 3-4). The model structural error, σmod2, characterizing the mean discrepancy between the latent “true” Peary caribou abundance, NPCtruej, t, after accounting for the pre-specified observation/imputation error, and the predicted population estimates, NPCj,t, was equal to 0.633±0.233 (i.e., median model error of 1.844 caribou bracketed by a 95% credible interval between 1.270 and 3.196). On the top of this error, the residual variability between measured, NPCj, t, and “true” Peary caribou abundance was equal to 1.515 ± 0.176. The posterior mean estimate of the global population rate of −1 change, λG = 0.983±0.099 yr , is suggestive of an overall declining trend across the Canadian Arctic Archipelago over the past four decades. In terms of the island group-specific rates of change, Boothia (0.905±0.031 yr−1) and Banks (0.935±0.010 yr−1) displayed the stronger decline, followed by Bathurst (0.972±0.044 yr−1) and Melville (0.982±0.020 yr−1), whereas Axel Heiberg (1.072±0.057 yr−1) and Mackenzie King (1.026 ± 0.087 yr−1) were characterized by weakly increasing trends over the course of the study period (Table 3-3). Based on the aforementioned posterior estimates of the rates of change, the Peary caribou population on each island complex by the year 2018 was projected (Fig. 3-5). Having as a reference point the total population size of 4,074 (2,742 recorded on Banks Island and 1,332 imputed on Northwest Victoria Island) from the most recent survey in 2014, the median number of caribou on Banks Island complex is projected to be 3,113 animals bracketed by a 95% credible interval between 2,854 and 3,412. To put this estimation into perspective, it is important to note that the caribou numbers on Banks Island indeed declined by 90% between 1982 and 1998, likely due to the combined effects of overharvesting, increased wolf predation in response to increased muskox abundance, and lack of forage availability caused by adverse snow and ice conditions in some years in the 1970s and 1980s (Nagy et al., 1996). This dramatic declining trend prompted the implementation of recovery actions that curtailed caribou hunting, which consequently led to a distinct increase of their population size during the 2000s (Gunn et al., 2006). In particular, the

Peary caribou counts increased from 727 to 2,014 animals between 1998 and 2001, and varied anywhere between 1,350 and 1,650 during the 2005 and 2010 surveys. Bearing in mind the potential influence of factors (low calf-to-cow ratio of the local population, recurring freezing rain events) that could moderate the recovery rate (Gunn et al., 2006), it is important to note that the model projections suggest that the caribou numbers would have been much lower (i.e., 677 in 2014 and 520 in 2018) if the recovery actions had not been in place. A declining trend is also estimated on Bathurst island complex, where the 2013 population estimate of 2,651 over the entire spatial cluster (see Table 3.1) is projected to be reduced down to a median number of 2,276 caribou (95 CI%: 1,449-3,518). Likewise, the 6,703 animals recorded after the 2012 survey on Melville Island group are expected to decline to a median number of 5,972 caribou (95 CI%: 4,666-7,598). Similar to Banks Island complex though, the corresponding posterior rates of change are 40-yr average estimates and thus cannot effectively capture the recent population increase on the two island complexes. In fact, according to Jenkins et al. (2011) assertions, if the weather or other environmental conditions are not prohibitive in the area, the strongly female-dominated Peary caribou population on Bathurst island complex could return to levels experienced in the early 1960s in the foreseeable future. This positive trajectory may be even more pronounced in Melville Island, where the absence of harvest pressure and human activities could conceivably allow the realization of a Malthusian rate of increase for caribou (i.e., intrinsic natural rate of population growth in the absence of all density- dependent effects). On the other hand, the total population size of 1,242 on Axel Heiberg Island complex (918 area-corrected estimate on Ellesmere Island and 324 imputed on Axel Heiberg) from the most recent survey in 2015 is projected to increase up to 1,516 caribou (95 CI%: 1,125-2,058). This estimation is on par with Jenkins et al.’s (2011) findings, who attributed the recent population increase to a favorable combination of rich vegetation, climate, and topography that is likely beneficial for Peary caribou; especially if the current accelerated climate change trends continue. In particular, it was hypothesized that the eastern portion of Axel Heiberg and the western coast of Ellesmere Island may be natural refugia for Peary caribou, given that they are almost completely surrounded by mountains which provide protection from cyclonic activities and lead to a rain shadow effect, characterized by low precipitation and a wide temperature range (Maxwell, 1981). Finally, Peary caribou abundance on Mackenzie and Boothia Island complexes is projected to

remain at very low levels, although their number on the former spatial cluster will likely increase (≈150 animals) if the current positive rate of change persists in the near future. Regarding the dramatic decline of Peary caribou abundance on Boothia Island complex, Gunn et al. (2006) identified as plausible culprits the excessive caribou harvesting and/or increased wolf predation which may be responsible for the reduced long-term survival rates of breeding females and calves in their first year of life. Given the extremely low number of caribou in the area, the same study also argued that the recovery of Peary caribou will likely be lengthy, at best, and the prospect of extirpation may be unavoidable without the development of an ecologically sound management plan (Gunn et al., 2006). A regression-based imputation framework was presented to reconstruct the Peary caribou time series within each of the island complexes of the Canadian Arctic Archipelago. The explicit consideration of several important covariates to account for co-dependencies in time and space offers an opportunity to understand the patterns underlying the Peary caribou population data. Founded upon a multitude of evidence that there is a subset of primary islands that act as the core areas from where the Peary caribou populations migrate to secondary (or satellite) islands, the imputation model was able to capture more than 65% of the variability in the Peary caribou dataset. Importantly, the mean estimates of the island-specific population rates of change were particularly robust, regardless of the consideration or not of imputed data. The two islands (Banks and Northwest Victoria) of the Banks island complex exhibited an average decline rate of 6% per year over the past four decades, which collectively reflects the dramatic population decrease from the early 1970s until the late 1990s, as well as the distinct recovery after the early 2000s. Similar “wax- and-wane” cycles characterize the Peary caribou population patterns on Melville and Bathurst island complexes. The analysis provides evidence of positive rate of change of the population trends on Axel Heiberg and Ellesmere Islands, which likely stems from pockets on those islands (eastern portion of Axel Heiberg and western coast of Ellesmere Island), where favorable climatic/geomorphological conditions, and rich vegetation prevail. In stark contrast, a wide array of climatic/environmental factors (e.g., overharvesting, higher predation, adverse climatic conditions, human-induced forage unavailability) has led to a dramatic decline, nearing their extirpation, on the Boothia island complex. In conclusion, this chapter presented a regression-based imputation framework to reconstruct the Peary caribou time series within each of the island complexes of the Canadian

Arctic Archipelago. The explicit consideration of several important covariates to account for co- dependencies in time and space offers an opportunity to understand the patterns underlying the Peary caribou population data. Founded upon a multitude of evidence that there is a subset of primary islands that act as the core areas from where the Peary caribou populations migrate to secondary (or satellite) islands, the imputation model was able to capture more than 65% of the variability in the dataset. Importantly, the mean estimates of the island-specific population rates of change were particularly robust, regardless of the consideration or not of imputed data. The two islands (Banks and Northwest Victoria) of the Banks island complex exhibited an average decline rate of 6% per year over the past four decades, which collectively reflects the dramatic population decrease from the early 1970s until the late 1990s, as well as the distinct recovery after the early 2000s. Similar “wax-and-wane” cycles characterize the Peary caribou population patterns on Melville and Bathurst island complexes. This analysis provides evidence of positive rate of change of the population trends on Axel Heiberg and Ellesmere Islands, which likely stems from pockets on those islands (eastern portion of Axel Heiberg and western coast of Ellesmere Island), where favorable climatic/geomorphological conditions, and rich vegetation prevail. In stark contrast, a wide array of climatic/environmental factors (e.g., overharvesting, higher predation, adverse climatic conditions, human-induced forage unavailability) has led to a dramatic decline, nearing their extirpation, on the Boothia island complex.

Island complex-specific estimates of population rates of change were also derived using a hierarchical augmentation of the exponential growth model, which enables sharing information among the different island complexes, and thus obtaining predictions along with realistic uncertainty bounds for less-studied island groups across the Canadian Arctic Archipelago. Nonetheless, the rigid structure of the exponential model posed constraints on its ability to accommodate the non-monotonic patterns typically characterizing natural populations. A characteristic case in point was its failure to consider the recent Peary caribou increase in Banks, Melville, and Bathurst island complexes. An alternative strategy could have been to use the double exponential growth model that can -in theory- capture the oscillatory population patterns, but is also particularly prone to poor parameter identification (Azim et al., 2011); especially when basing the trend analysis on datasets with significant gaps. In a next chapter (Kaluskar et al., 2019a), I will introduce a new stochastic framework that will extend the potential application of the exponential growth model by drawing projections that explicitly consider the degree of uncertainty

pertaining to the long-term population rates of change, as well as the year-to-year variability of the climatic and other environmental factors that shape habitat suitability across the Canadian Arctic Archipelago.

Table 3-1 Classification of the Canadian Arctic Archipelago into six island groups with their corresponding primary and secondary/satellite islands. Primary islands are considered core areas from where Peary caribou populations migrate to secondary and/or satellite islands. Areas sampled, years surveyed and imputed (numbers in bold font) are provided for each island. Island Primary Secondary/Satellite Average Area Years surveyed and imputed Complex Island Island Sampled (km2) Banks Banks 71,013 1970, 1971, 1972, 1980, 1982, 1985, 1987, 1989, 1991, 1992, 1993, 1994, 1998, 2001, 2005, 2010, 2014

Northwest Victoria 35,760 1970, 1971, 1972, 1980, 1982, 1985, 1987, 1989, 1991, 1992, 1993, 1994, 1998, 2001, 2005, 2010, 2014

Axel Axel Heiberg 30,390 1989, 2005, 2006, 2007, 2015

Ellesmere 111,580 1989, 2005, 2006, 2007, 2015

Boothia Boothia 32,085 1974, 1975, 1976, 1980, 1985, 1995, 1996, 2004, 2006

Prince of Wales 33,771 1974, 1975, 1976, 1980, 1985, 1995, 1996, 2004, 2006

Somerset 24,517 1974, 1975, 1976, 1980, 1985, 1995, 1996, 2004, 2006

Russell 963 1974, 1975, 1976, 1980, 1985, 1995, 1996, 2004, 2006

Melville Melville 42,776 1972, 1973, 1974, 1986, 1987, 1997, 2012

Prince Patrick 16,316 1972, 1973, 1974, 1986, 1987, 1997, 2012

Byam Martin 1,181 1972, 1973, 1974, 1986, 1987, 1997, 2012

Emerald 556 1972, 1973, 1974, 1986, 1987, 1997, 2012

Eglinton 1,557 1972, 1973, 1974, 1986,

1987, 1997, 2012

Bathurst Bathurst 19,939 1973, 1974, 1985, 1988, 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 2001, 2002, 2013

Cornwallis 7,148 1973, 1974, 1985, 1988, 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 2001, 2002, 2013

Helena 330 1973, 1974, 1985, 1988, 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 2001, 2002, 2013

Little Cornwallis 422 1973, 1974, 1985, 1988, 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 2001, 2002, 2013

Devon 38,764 1973, 1974, 1985, 1988, 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 2001, 2002, 2013

Lougheed 1,329 1973, 1974, 1985, 1988, 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 2001, 2002, 2013

Mackenzie King Mackenzie King 5,100 1973, 1974, 1997

Borden 2,700 1973, 1974, 1997

Brock 790 1973, 1974, 1997

Table 3-2 Posterior mean and standard deviation (SD) values of the imputation model parameter estimates.

Parameter Predictor Variable Mean SD

θ1 Intercept 1.183 0.058 Areal ratio between secondary/satellite and primary islands θ2 within a given spatial complex 0.857 0.064

θ3 Trend in time -0.021 0.002 Peary caribou abundance at the primary island, when the θ4 number of animals is higher on the secondary location 0.949 0.016 Peary caribou abundance at the primary island, when the θ5 0.741 0.075 number of animals is lower on the secondary location σ Standard Error 1.919 0.205

Table 3-3 Three estimates of the Peary caribou population rates of change across the

Canadian Arctic Archipelago. The first estimate (λ1) is derived by linear least-squares fitting against the original dataset, according to the method presented by Dennis et al. (1991). The second estimates (λ2) correspond to the same method after data imputation. The third set of rates of change (λ3) are derived by the hierarchical formulation of the exponential growth model using both imputed values and survey data. NA denotes locations with sample size ≤ 4. Numbers in parenthesis correspond to the standard error of the corresponding linear regression models.

Name Island λ1 λ2 λ3 Banks Banks 0.970±0.061 0.969±0.119 0.935±0.010 (1.484) (2.140) Northwest Victoria 0.912±0.164 0.976±0.132 (2.309) (2.312) Boothia Boothia 0.821±0.491 0.831±0.353 0.905±0.031 (4.047) (6.194) Prince of Wales 0.751±0.141 0.780±0.121 (2.019) (2.158) Somerset 0.833±0.282 0.853±0.168 (2.821) (2.604) Russell 0.839±0.293 0.921±0.236 (3.014) (3.349) Axel Heiberg Axel Heiberg NA 1.058±0.649 1.072±0.057 (4.329) Ellesmere NA 1.033±0.594 (4.123) Bathurst Island Bathurst 1.013±0.143 1.006±0.155 0.972±0.044 (2.251) (2.480) Little Cornwallis 0.947±0.089 0.942±0.208 (1.525) (3.554) Cornwallis NA 0.898±0.212 (3.838) Helena 1.013±0.442 1.053±0.246 (5.020) (3.798) Devon NA 0.978±0.140 (2.327) Lougheed NA 0.976±0.269 (4.690) Melville Melville 1.006±0.103 1.006±0.173 0.982±0.020 (1.621) (2.466) Prince Patrick 1.034±0.164 1.077±0.161 (1.968) (2.333) Eglinton 1.024±0.579 1.025±0.285 (4.609) (4.019) Emerald 1.004±0.232 0.975±0.165 (2.547) (2.440)

Byam Martin 1.014±0.685 1.017±0.322 (5.138) (4.551) Mackenzie King McKenzie King NA NA 1.026 ± 0.087

Figure 3-1 Map of the Canadian Arctic Archipelago and application of the Bayesian hierarchical framework to allow the transfer of information across the six island complexes.

Figure 3-4 Comparison between the annual recorded/imputed and predicted Peary caribou populations on the six island groups of the Canadian Arctic. Solid and dashed lines

correspond to the median predictions and the associated 95% credible intervals of the Bayesian hierarchical exponential model.

Figure 3-5 Predictive distributions (solid lines) of Peary caribou populations across the Canadian Arctic Archipelago for the year 2018 based on the exponential growth model. Log-normal distributions denoted in dashed lines correspond to the most recent Peary caribou populations recorded on each of the six spatial complexes, after accounting for both sampling and imputation error.

Chapter 4 A stochastic modelling framework to accommodate the inter-annual variability of habitat conditions for Peary caribou (Rangifer tarandus pearyi) populations2 4.1 Introduction Climate change is occurring at an accelerated rate in the Canadian Arctic Archipelago (CAA) relative to global trends. According to Derksen et al. (2012), the surface air temperatures across the Canadian Arctic have warmed at twice the global rate in all seasons over the past four decades, and these trends are manifested as warming permafrost, reduction in summer sea-ice extent, increased mass loss from glaciers, reduction in snow-cover extent and duration, thinning or even break-up of ice shelves (Anisimov et al., 2007; Rinke and Dethloff, 2008; Vors and Boyce, 2009; IPCC, 2019). In particular, the annual mean extent of Arctic sea ice experienced a decrease at a rate of 3.5–4.1% per decade from 1979 to 2012, and this trend was more pronounced during the late summer and autumn at 11% per decade (Post et al., 2013). As a result, the length of the ice-free season increased from 109 to 148 days (rate of 1.5 days per year) in the Canadian Arctic during the 1979–2006 period (Rodrigues, 2009). Future climate projections suggest a nearly 50% decrease in summer ice extent from 2041 to 2060, along with a prolongation of the ice-free season by 1–3 months (Miller et al., 2005; Sou and Flato, 2009). Ice thickness is also projected to decrease by over 30% in summer in the CAA region (Sou and Flato, 2009). However, the common denominator of all these projections is that climate models appear to underestimate the rapid decline in summer Arctic sea ice registered over the past few decades, and therefore the future changes in ice phenology may be even more dramatic (Derksen et al., 2012). Climate warming shapes the dynamics of resource availability in time and space, and may have discernible effects on the functional and structural integrity of biotic communities in the seasonal CAA environment. Warmer spring (March to June) temperatures are strongly correlated with earlier snowmelt, shorter duration and reduced extent of snow cover in the Canadian Arctic (Brown et al., 2007; Brown and Robinson, 2011; Liston and Hiemstra, 2011), which collectively result in a protracted growing season. The latter trend may confer a competitive advantage on

2 Kaluskar. S, Johnson, C., Blukacz-Richards, E.A, Kim, D.K., Arhonditsis, G.B., 2019a. A stochastic modelling framework to accommodate the inter-annual variability of habitat conditions for Peary Caribou (Rangifer tarandus pearyi) populations

herbivorous animals by increasing forage availability and plant productivity (Jia et al., 2009; Kingsolver et al., 2002; Xu et al., 2013). A characteristic example is the Peary caribou (Rangifer tarandus pearyi), an endemic caribou subspecies that is particularly important to Indigenous communities living in the Arctic (Festa-Bianchet et al., 2011; Taylor, 2005). Peary caribou selectively graze on protein-rich flowers of louseworts (Pedicularis spp.), arctic poppy (Papaver radicatum), white mountain avens (Dryas integrifolia), and purple saxifrage (Saxifraga oppositofolia), the catkins, stems and leaves of arctic willow (Salix arctica), and the seed heads of snow saxifrage (Saxifraga nivalis) during the growing season (Johnson et al., 2016). Longer growing seasons and warmer summers across the Arctic are predicted to increase the aboveground biomass by up to 70% or even trigger vegetation growth in areas currently characterized by limited productivity that could have a positive effect on population dynamics (Pearson et al., 2013). Nonetheless, Johnson et al. (2016) cautioned that the positive effects of climate change on Peary caribou populations may be moderated by two factors: (i) the likelihood of a spatiotemporal trophic mismatch, whereby the timing of important life-history events (migration, calving), cued by day length, may not follow the seasonality changes in forage availability (Post et al., 2008, Post et al., 2013; Post and Forchhammer, 2008); and (ii) the nutritional quality of the increased vegetation abundance (e.g., evergreen shrubs) may not be on par with the physiological requirements of Peary caribou (Turunen et al., 2009). Other authors have suggested that the severe winter weather along with the higher frequency of extreme events (e.g., freezing rain) can hinder the forage accessibility and may represent the primary threat of climate change to the sustainability of Peary caribou populations (Miller and Barry, 2009). In fact, one popular hypothesis about the role of severe weather conditions involves the creation of locked pastures, whereby the forage becomes practically unavailable (or “locked”) under excessive ice or snowpack, causing malnutrition, starvation, and ultimately high adult mortality and calf losses (Stien et al., 2010; Vors and Boyce, 2009). Deep, hard-packed, or frozen-over snow may significantly increase the energy expenditure during cratering (Fancy and White, 1985) or locomotion (Fancy and White, 1987), and may be responsible for massive die-offs; especially, if extreme weather events increase in severity and frequency (Stien et al., 2010). The loss of sea ice predicted with climate change could also have deleterious effects on Peary caribou by curtailing the animal's ability to move between winter and summer ranges in CAA (Mallory and Boyce, 2019; Post et al., 2013). The loss of sea ice deprives Peary

caribou of the ability to reach areas of high quality and easily accessible forage during the season of highest reproductive costs. Inter-island movements not only increase foraging efficiency and reproductive success, but also allow escaping severe weather or environmental conditions and minimizing the likelihood of genetic isolation or local extirpation in small islands (Post et al., 2013). Without the option to exploit among-island ranges, Miller et al. (2005) asserted that viable Peary caribou population will only be sustained on Victoria and Ellesmere Islands. To date, little work has been done to evaluate the net impact of changes from climate on Peary caribou population dynamics (Tews et al., 2007 a,b). It has been argued that the net balance of limited forage accessibility due to severe weather conditions relative to that of increased forage biomass due to prolonged growing season will depend on local climate, floral abundance and composition, and landscape characteristics (Turunen et al., 2009). Advancing the understanding of the net influence of climate-induced changes on Peary caribou is essential, given their critical importance to Indigenous communities in the Arctic. The main objective of the present study is to delineate the relative importance of meteorological variables and local habitat conditions on Peary caribou population growth rates. Founded upon Bayesian inference techniques, this study presents two-pronged approach to characterize the year-to-year variability of the habitat conditions across the Canadian Arctic Archipelago, using meteorological (surface snowmelt rate, precipitation, temperature, wind speed) variables, landscape features (fraction of rockland), and resource competition with muskoxen (Ovibos moschatus). These proxies for habitat suitability (or forage accessibility) are then used to predict the population growth rates and to identify locations where Peary caribou could experience >10%, 25%, or 50% decrease relative to the population level determined at the beginning of the study period (i.e., 2000). The ultimate goal is to develop an empirical modelling framework with quasi-mechanistic foundation that can be used for drawing inference on the implications of climate change for the integrity of Peary caribou populations in any location of the Canadian Arctic.

4.2 Methods 4.2.1 Case Study-Dataset The Canadian Arctic Archipelago is a group of islands, which lies north of the Canadian mainland, comprising 94 major islands (>130 km2) and 36,469 minor islands covering about 1,424,500 km2. The major islands in the eastern Arctic are mountainous, with peaks over 2000 m, and occupied by ice caps that correspond to nearly the one-third of the volume of land ice

worldwide. By contrast, the central and western islands are generally flat with low relief (<200– 250 m). The floral diversity gradually decreases north of the mainland, with close to 270 vascular plant species, 325 mosses, around 100 liverworts and over 550 lichens. Similarly, the number of animal species decreases north from the mainland, with close to 20 species of land mammals live on the High Arctic islands. Aside from Peary caribou, other mammals include the muskox, Arctic fox (Vulpes lagopus), Arctic wolf (Canis lupus arctos), Arctic hare (Lepus arcticus), brown (Lemmus sibiricus) and collared lemmings (Dicrostonyx groenlandicus complex). The surrounding sea is home to the polar bear (Ursus maritimus), the walrus (Odobenus rosmarus), the narwhal (Monodon monoceros) and the beluga (Delphinapterus leucas). According to expert judgment (Johnson et al., 2016), the relationship between the patterns of Peary caribou habitat use and environmental conditions could be divided into the historic (1970– 1999) and present (2000−2013) time stanzas. Three distinct seasons have also been identified to characterize the within-year Peary caribou ecology and habitat use: (i) April to June, representing the period of spring migration and calving; (ii) July to October, approximating the period of summer foraging and rut; and (iii) November to March, associated with fall migration and winter foraging (COSEWIC (Committee on the Status of Endangered Wildlife in Canada), 2004; Johnson et al., 2016). This chapter focused on the summer (July–October) season of the recent (2000–2013) time stanza, owing to its critical importance for Peary caribou to replenish and accumulate fat reserves, thereby influencing reproduction, overwinter survival, and expected population trends in the future. The variables used to assess the impact of climate on the accessibility of forage and the distribution of Peary caribou were the precipitation, near-surface air temperature, daily-mean near- surface wind speed, and surface snow melt (Table 4-1), which were obtained from the 0.22 degree Arctic CORDEX simulations of the CanRCM4 regional climate model created by the Canadian Centre for Climate Modelling and Analyses (http://modelisation- climatique.canada.ca/climatemodeldata/cgcm4/CanCM4/decadal2017/mon/ index.shtml). Daily values for climatic predictors were retrieved from the historical climate scenario between 1991 and 2005, and the RCP 4.5 scenarios from 2006 to 2013. The RCP 4.5 scenario reflects a moderate trajectory with greenhouse gas emissions reaching a maximum around 2040 and declining thereafter (See Fig. 4-1). The percentage of area dominated by rocks and the density of muskoxen as surrogate variables of the landscape features and resource competition were used to characterize Peary

caribou habitat use, respectively (Table 4-1). Rockland percentage averaged over the 14 yr study period were obtained from the Bolin Centre, Stockholm University (http://bolin.su.se/data/ncscd/). Muskoxen average density at 5 km2 from 2000 to 2013 was estimated from survey information provided by the territorial governments (Johnson et al., 2016). The intent with the inclusion of the latter variable was to examine the hypothesis that Peary caribou would avoid areas with high muskoxen densities, given that existing evidence suggests little overlap in habitat use throughout the annual cycle and distribution of Peary caribou (Schaefer et al., 1996). Other potential influential predictor variables of the habitat characteristics (Normalized Difference Vegetation Index or NDVI, percentage cover of glaciers, distance-to-water) or climate (sea ice, snow depth, rain-on-snow) were not included because they either displayed high collinearity with the aforementioned variables or their spatial/temporal extent was not adequate to describe the observed habitat and vegetation variability in time and space. Unlike the “global” character of the Johnson et al. (2016) modelling analysis, this work is designed to accommodate the spatiotemporal variability within each of the six distinct geographic clusters (Banks, Axel Heiberg, Bathurst, Boothia, Melville and Mackenzie King) delineated by the recent work (Kaluskar et al., 2020), and therefore predictors with a strong relative signature over the entire CAA domain were not necessarily the strongest causative factors within individual spatial complexes. All predictor variables were re-sampled to a 10 × 10 km cell resolution to match the grid size selected to represent observations of Peary caribou. Several different sources of information were combined to characterize “used” (i.e. presence) locations for the habitat suitability analysis (COSEWIC (Committee on the Status of Endangered Wildlife in Canada), 2004; SARC (Species at Risk Committee), 2012; IUCN (International Union for Conservation of nature), 2014). Georeferenced Peary caribou locations (observed animals only, including carcasses) from aerial surveys conducted across different areas of the Arctic Archipelago during 2000–2013 were provided by the territorial governments of the Northwest Territories and Nunavut, as well as Parks Canada (Johnson et al., 2016). Monetary and logistical constraints often limit the timing and extent of Peary caribou surveys, which are often conducted at specific times of year when Peary caribou are segregated spatially from Barren- ground caribou or Dolphin and Union caribou. Because the latter potentially introduces a seasonal bias in available presence data, information from 7 female Peary caribou fitted with GPS collars within the Bathurst Island Complex from 2003 to 2006 were also included (Jenkins and Lecomte,

2012). The database was further augmented with observations of Peary caribou from members of local communities from the Canadian Arctic (Taloyoak, Ulukhaktok, Sachs Harbour, Cambridge Bay, Kugaaruk, Resolute Bay, Grise Fiord, Paulatuk and Gjoa Haven). Indigenous Knowledge (IK)1 was used to delineate areas and current Peary caribou movement routes, as well as month or season of use, on maps ranging in scale from 1:250,000 to 1:3 million. The areas were digitized and georeferenced for the analysis. All information on Peary caribou presence was combined. The study area was divided into 1 km2 grids and assigned “Peary caribou present” or “not present” to each grid. Information on frequency of use by animals was removed to increase the complementarity among the sources of information and to avoid problems of pseudoreplication and autocorrelation (see Johnson et al., 2016 for more details on Peary caribou location data). Over 3000 presence locations were available for the analysis based on the 1 km2 grids. “Present/not present” data were rescaled to 10 × 10 km resolution to match the spatial resolution for the aforementioned covariates and support the logistic regression modelling.

4.2.2 Modelling framework A two-step strategy aiming to characterize the year-to-year variability of the habitat conditions across the Canadian Arctic Archipelago, based on meteorological variables, landscape features (fraction of rockland), and resource competition with muskoxen was designed. The first step of the analysis bears resemblance to a resource-selection function exercise, whereby a family of models was developed to examine which habitat characteristics are important to Peary caribou, by assessing the probability of the animals to be present within a particular location to vary with the degree of prevalence of certain environmental conditions or the availability of essential resources (Boyce et al., 2002; Manly et al., 2002). Specifically, the first statistical model (Bernoulli-logistic model) examines the likelihood of presence of Peary caribou within a particular habitat, given different combinations of climatic conditions, surface snowmelt rate (SnowMelt), precipitation (Prec), temperature (Temp), wind speed (WindSp), percentage of rockland (Rockland), and muskoxen density (MuskDen). This model postulates that the presence of Peary caribou resembles a Bernoulli process, such that the occurrence of Peary caribou in a given location i and year t represent a sequence of independent identically distributed Bernoulli trials (Mahmood et al., 2014; Shimoda et al., 2016). For every data point (presence/non-presence) in time and space, the model calculates the likelihood of Peary caribou presence independently from the previous or subsequent location i and year t, while the probability p of presence is determined by the

explanatory variables considered. The causal relationship between the probability Peary caribou presence and climatic/environmental conditions was modelled using logistic regression:

푃퐶푖,푡|푝푖,푡(휃0, 휃푥, 푥푖,푡)~퐵푒푟푛표푢푙푙𝑖(푝푖,푡) (1)

푙표푔𝑖푡(푝푖,푡) = 휃0 + ∑ 휃푥 ∙ 푥푖,푡 (2)

휃0, 휃푥~푁(0, 10000) (3) 𝑖 = 1 … 훭, 푡 = 1 … 푁, 푥 = 푆푛표푤푀푒푙푡, 푃푟푒푐, 푇푒푚푝, 푊𝑖푛푑푆푝, 푅표푐푘푙푎푛푑, 푀푢푠푘퐷푒푛 where PCi, t denotes the presence or not of Peary caribou (1 or 0) in the location i and year t; xi, t corresponds to the value of each of the (standardized) predictors in the same location and year; and θ0 and θx are the regression coefficients which were assigned flat (or diffuse) normal prior distributions with mean 0 and variance 10,000; M is the number of cells in each of the six distinct geographic clusters (Banks, Axel Heiberg, Bathurst, Boothia, Melville and Mackenzie King), and N (=14) is the number of years. For each island complex, the most parsimonious model was identified to assess the probability of presence of Peary caribou given the prevailing conditions in a particular location, using the deviance information criterion (DIC); a Bayesian measure of model fit and complexity (Spiegelhalter et al., 2002). DIC is measured by:

̅̅̅̅̅̅̅ 퐷퐼퐶 = 퐷(휃) + 푝퐷 (4) where 퐷̅̅̅(̅휃̅̅̅) is the posterior mean of the deviance, a measure of residual variance in data conditional on the parameter vector θ. The deviance is defined as -2log(model likelihood); 푝퐷 is a measure of the “effective number of parameters” and is specified as the posterior mean deviance of the model 퐷̅̅̅(̅휃̅̅̅) minus the point estimate of the model deviance when using the means of the ̅̅̅̅̅̅̅ posterior parameter distributions, i.e., 푝퐷 = 퐷(휃)- 퐷(휃̅). Thus, this Bayesian model comparison ̅̅̅̅̅̅̅ first assesses model fit or model “adequacy”, 퐷(휃), and then penalizes complexity, 푝퐷.

In the next step, the predicted estimates of the habitat suitability (or forage accessibility) are used to determine the population rates of change in each location i and year t. Specifically, formulated random-walk process informed by the posterior 푝푖,푡 values samples over the uncertainty of Kaluskar et al.’s (2020) Peary caribou population rates of change on the six island complexes of the Canadian Arctic Archipelago. The latter rates of change were derived by the exponential population growth (or decline) model, which postulated an island complex-specific

monotonic pattern and was parameterized against population data from a 45-yr (1970-2015) time period. The mathematical notation of random-walk algorithm is summarized as follows:

푁푃퐶푖,푡+1 = 휆푖,푡 ∙ 푁푃퐶푖,푡 (5)

휆푖,푡 = 휆푖,0 ∙ 휓푖,푡 ⨁ 휆푖,푡 = 휆푖,푡−1 ∙ 휓푖,푡 (6)

∗ 휓푖,푡 = 1 + 푠푔푛(푝푖,푡 − 푐 )|1 − 휑푖,푡| (7)

2 휎푐 휇푐+ 휆푖,0 = 푒 2 (8)

2 휑푖,푡~퐿훮(0, 휎푐 ) (9) where 푁푃퐶푖,푡 represents the predicted population within the location (or cell size) i and year t; 휇퐶 2 and 휎푐 denote the mean values and associated variances of the Peary caribou population rates of change on the six island complexes of the Canadian Arctic Archipelago (Table 4-2; see also

Kaluskar et al., 2020); 휆푖,푡 is the location-specific population growth rate in year 푡, which is specified either as a function of the population growth rate of the previous year, 휆푖,푡−1, on the same location i or the corresponding rate of change, 휆푖,0, during the initial year (푡0= 2000); 2 휎푐 휑푖,푡 represents a lognormal random variable with mean and variance parameters equal to 푒 2 and 2 2 (푒휎푐 − 1)푒휎푐 , respectively. The latter term determines the ratio of the population rate of change between years 푡 and 푡 − 1 (or 푡0), while the nature of this ratio (increase or decrease), and ultimately the value of the stochastic term 휓푖,푡, is determined by the corresponding habitat ∗ suitability estimate, 푝푖,푡, and the degree to which a critical threshold 푐 (=33 or 50% probability of Peary caribou to be present in location 𝑖 and year 푡) is exceeded. Simply put, four (two specifications of the Peary caribou annual rate of change × two critical probability thresholds of presence in a particular habitat) random-walk models were formulated to relax the rigid structure of the exponential population growth model by allowing to assign site- and year-specific rates of change, which in turn are determined by the prevailing conditions within each grid cell, such as landscape features, meteorological factors, and muskoxen density. The four random-walk configurations differed with respect to the potential magnitude of the year-to-year shifts on Peary caribou growth rates, as modulated by the specification of the expected value for a particular year and the probability thresholds used to determine whether the prevailing conditions habitat favor a

population increase or decrease. In doing so, the four models collectively provide an uncertainty envelope that delineates the (likely) lower and upper bounds of the Peary caribou population rates of change across the Canadian Arctic Archipelago from 2000 to 2013.

4.3 Results-Discussion 4.3.1. Mapping the habitat variability in the Canadian Arctic Archipelago The warmest average summer (July–October) temperatures, varying from 1 to 4 °C, were recorded in Victoria, Banks, Prince of Wales Islands, and Boothia Peninsula during the 2000–2013 study period (Fig. S1). Surface air temperatures consistently >0 °C are also registered in the southernmost parts of Melville, Cornwallis, and Devon Islands. Interestingly, the Axel Heiberg and Ellesmere Islands displayed the greatest year-to-year variability, with standard deviation values that ranged from 1 to 2.5 °C. The highest levels of precipitation were recorded in the Bathurst, Melville, and Mackenzie King island complexes with values >0.4 mm day−1, while fairly high precipitation levels also characterized the northwestern section of Boothia Peninsula. In terms of the surface snowmelt, there were extensive areas with rates faster than 0.05 mm day−1 along the coastlines of the Prince Patrick, Eglington, Melville, Cameron, and Bathurst Islands, as well as smaller pockets on Axel Heiberg and Ellesmere Islands where relatively fast snowmelt occurs (Fig. S1). Regarding the wind speed, values higher than 5.5 m s−1 were recorded on Boothia Peninsula and on several pockets in Banks and Melville Islands. Likewise, the Mackenzie and Bathurst island complexes along with the rest of the islands forming the Melville spatial cluster were characterized by wind speeds >4.5 m s−1. Consistent with the work by Nagy and Gunn (2009), areas of high muskoxen density can be found on Banks Islands (>9 animals per 100 km2), although the documented number (≈4700 animals) by the latter study was the lowest recorded on Banks Island since 1992. On the other hand, Jenkins et al. (2011) reported a total abundance of 17,500 muskoxen (aged one year or older) in Nunavut's High Arctic Islands with variable abundance trends among islands. In particular, 2086 muskoxen were estimated on Prince of Wales Island, 1910 on Somerset Island, 456 on southern Ellesmere, 8115 on northern Ellesmere, and 4237 on Axel Heiberg Islands (Jenkins et al., 2011). Some of these recorded estimates are also manifested as pockets of high muskoxen areal density in Fig. S1. Extensive fractional areas of rockland (30– 75%) can be found on Devon, Bathurst, and Melville Islands, as well as on Ellesmere and Axel Heiberg Islands.

4.3.2. Predicting the likelihood of Peary caribou presence given the prevailing habitat conditions The Bernoulli-logistic regression models identified distinct linkages between the binary Peary caribou dataset (presence/non-presence within a particular location) and precipitation, surface air temperature, snow melt, wind speed, fractional area of rockland, and muskoxen density across the different island complexes of the Canadian Arctic Archipelago (Table 4-3). The performance of the best model selected for each island complex was satisfactory with the likelihood of either false positives (>50% probability for Peary caribou to be present within a particular site, even though they were never observed) or negatives (<50% probability for Peary caribou to be present, although existing empirical evidence suggests the opposite) varying from nearly 30% (Boothia, Melville) to 10% (Axel Heiberg, Banks) of their cell sizes. In terms of the habitat suitability patterns, the spatial predictions are consistent with existing evidence that Peary caribou tend to summer in the north and northwest coast of Banks Island (Fig. 4-2), after spending their winter on the southwest coast (Johnson et al., 2016). Likewise, the southern part of Melville Island (Dundas Peninsula) represents another favorable summer range, with high predicted probabilities of occurrence (Fig. 4-2), from where they tend to migrate to winter ranges on Prince Patrick and Eglinton Islands (Miller et al., 1977). Bathurst, Little Cornwallis, and Cornwallis Islands similarly provide favorable forage with significant inter-island migration, although the available empirical evidence has not addressed unequivocally which is the actual summer and winter range (Johnson et al., 2016; Miller, 1992; Miller and Gunn, 1978). The southern Ellesmere Island represents an area where favorable forage is accessible (Taylor, 2005), as does the northern Devon Island (Fig. 4-2). The model predictions are also conceptually on par with existing empirical evidence that Boothia Peninsula provides a winter range for Prince of Wales, Somerset and lesser satellite islands from where the majority of Peary caribou annually migrate across sea ice in spring (May–June) before break-up and return back in autumn after freeze-up; hence, the corresponding low (Boothia Peninsula) and high (Prince of Wales and Somerset Islands) probabilities of summer habitat suitability are plausible (Miller et al., 2005; Miller and Gunn, 1978; Taylor, 2005). According to the Bernoulli-logistic regression models, when the predictor variables in Table 3 are set equal to their average values for the corresponding island complexes, the posterior intercept estimates suggest higher odds ratios (or probability of Peary caribou presence relative to the likelihood of non-presence) in Mackenzie King (3.82:1), Bathurst (1.99:1), and Melville (1.47:1). Given that binary Peary caribou dataset heavily relies on IK, it is worth

noting that the latter finding is consistent with the reported population trends during the post-2000 period, as derived by field-survey data (Kaluskar et al., 2020). Precipitation appears to have a strong negative relationship with the likelihood of Peary caribou presence on various locations within the Banks, Melville, and Mackenzie island complexes (Table 4-3), which is consistent with their tendency to select areas with less precipitation and avoid wet habitats to forage throughout their annual life cycle (Larter and Nagy, 2001a). Surface air temperature has a strong positive association with the likelihood of presence of Peary caribou on various sites in the Axel Heiberg island complex, which reinforces the notion that the mountains of its constituent islands create barriers that effectively shelter the local population from Arctic storms with higher mean July temperatures and longer melt season duration, thereby creating areas of high vegetation biomass and diversity (Hill and Henry, 2011; Hudson and Henry, 2009; Jia et al., 2009; Xu et al., 2013). In the latter island complex, the fractional area of rockland was another important predictor of Peary caribou habitat use, and the corresponding positive relationship reflects the tendency of snow to be shallower or melt faster in areas with rugged topography, such as rocky outcrops and beach ridges, and therefore to facilitate Peary caribou foraging (Canadian Wildlife Service, 2015; Miller et al., 1982). The negative association with muskoxen density in Melville and Axel Heiberg provides support to the hypothesis of the Peary caribou propensity to avoid muskoxen. The results suggest that processes governing habitat selection at larger spatial scales are likely responsible for the limited overlap in micro-habitat selection (1 m2 to 1 ha) between Peary caribou and muskoxen (Schaefer et al., 1996). Muskoxen may support higher wolf densities which could, in turn, result in higher predation rates on Peary caribou (Nagy et al., 1996; Gunn, 2005). More studies are required to elucidate the mechanism(s) affecting patterns of space use and population dynamics between muskoxen and Peary caribou. As indicated in Table 4-1, the negative relationship between surface snowmelt rate and habitat suitability on Axel Heiberg and Mackenzie King may suggest that faster snowmelt rates combined with temperatures hovering around zero lead to ice formation, thereby posing challenges to forage accessibility. Alternatively, it could stem from the temporary presence of extensive wet areas that are being avoided by Peary caribou (Johnson et al., 2016). Interestingly, a negative relationship between the likelihood of Peary caribou presence and air temperature manifests itself within the Banks and Boothia island complexes (Table 4-3). The latter result could reflect a behavioral tactic at reducing exposure to insects in warmer areas. Alternatively, it may be driven by the role of other important

confounding factors, such as the vegetation abundance which appear to drive the summer movements of Peary caribou (e.g., higher abundance on the north/ northwestern Banks Island, where the surface air temperature is somewhat lower than the rest area). The negative relationship between habitat suitability and wind speed is again consistent with the tendency of Peary caribou to avoid areas with the highest near surface wind speeds during April through the end of October (Jenkins et al., 2018). In particular, Johnson et al. (2016) surmised that the combination of high precipitation, high winds, and freezing temperatures during this period likely trigger the formation of ice layers in the snow profile, thereby impeding the accessibility to desirable forage. 4.3.3. Characterizing the Peary caribou population trends in the Canadian Arctic Archipelago The predicted trends from the four configurations of the exponential growth model collectively allowed to derive an uncertainty range (or lower and upper bounds) of the Peary caribou population rates of change across the Canadian Arctic Archipelago from 2000 to 2013 (Fig. 4-3). In the Banks island complex, the median population rate of change varied from 0.92 to 0.94 year−1. On a comparative scale, the lower bound lies within the medium range of minimum rates of change derived across the Canadian Arctic Archipelago, while the upper bound represents one of the lowest maximum estimates (Fig. 4-3). Given that the starting values of the rates of change for the random-walk search were derived by population data from a 45-yr (1970–2015) time period, these conservative predictions partly reflect the dramatic decline (≈90%) of the Peary caribou population on Banks and Northwest Victoria Islands between 1982 and 1998. This trend was conjectured to be the cumulative effect of a wide array of factors, such as hunting, extreme snow and icing events, inter-island migration, competition from the increasing muskox population or increased wolf predation (Nagy et al., 1996). Interestingly, the study period coincides with the implementation of voluntary restrictions established by Hunters and Trappers organizations in the area in response to small population sizes that may have been responsible for the moderate increase of the Peary caribou population size during the 2000s (Gunn et al., 2006; Kaluskar et al., 2020). The moderate declining trends of the present modelling analysis indicate that the caribou numbers would have been distinctly lower in the Banks island complex, if the Indigenous co-management actions had not been in effect. In particular, the reference growth rate estimate for this region (Table 4-2; see also Kaluskar et al., 2020), as modulated by the year-to-year variability of weather conditions, suggests that the probability for Peary caribou to have been reduced by 10% and 25% relative to their 2000 population level would have been almost certain by the year 2005 (Fig. 4-

4, Fig. 4-5). Interestingly, the likelihood of the Peary caribou population to be halved remained low (29%) until the year 2009, but became very likely by the end of the study period (Fig. 4-6). Similar declining trends were also registered in Boothia island complex with very low (0.87 to to 0.91 year−1) median population rates of change (Fig. 4-3). The same area was the first with predicted probabilities consistently >80–90% for Peary caribou to be reduced by 10% and 25% relative to their 2000 population level (Fig. 4-4, Fig. 4-5), as well as one of the regions with high probability of their population to be halved (Fig. 4-6). While the reasons for this dramatic decline are not qualitatively different from those identified for the Banks island complex, the fact that only few caribou remain on Prince of Wales, Somerset, and Russell Islands suggests that a critical point may have been reached, where the occurrence of episodic weather-related events, future disease outbreaks, or even elevated incidental predation could trigger a population collapse and ultimate extirpation from these locations; the so-called Allee effect (Caughley and Gunn, 1996; Drake and Kramer, 2011). In stark contrast, the uncertainty envelope of the projected trends in Mackenzie King island complex was much wider (1.05–1.25 year−1), albeit consistently positive with practically no discernible evidence of population decline during the study period (Fig. 4-3, Fig. 4- 4, Fig. 4-5, Fig. 4-6). Because of the weak identification of the corresponding rate of change

(coefficient of variation>350%; see Table 4-2), the stochastic term φi, t was amenable to longer random walks over the uncertainty space, and therefore the wider population range is not surprising. The interesting finding with this modelling analysis is that the explanatory variables (i.e., precipitation, snowmelt, and fraction of rockland) selected in the Bernoulli-logistic regression model for that spatial cluster provided consistently favorable predictions about the likelihood of

Peary caribou presence (i.e., pi, t greater than the 33 or 50% probability thresholds), and consequently the values sampled for ψi, t were predominantly suggestive of geometric growth (>1 year−1). In a similar manner, owing to the weakly identified growth rate in the Axel Heiberg island complex (see noise-to-signal ratio in Table 2), the projected uncertainty envelope for the corresponding population rates of change was much wider, 0.95 to 1.05 year−1, but also inconclusive with respect to the overall trend over the course of the 2001–2013 period (Fig. 4-3). Nonetheless, based on the averaged predictions of the four configurations of the exponential growth model, the likelihood of population decline was projected to be fairly low in the area (Fig. 4-4, Fig. 4-5, Fig. 4-6). Even though the Axel Heiberg island complex makes up a significant

portion of Nunavut's Peary caribou range, the historical surveys in the area are infrequent and limited in their spatial coverage. Weather conditions are typically identified as the most influential factor that shapes their spatial distribution in the area, as caribou tend to avoid deep snow conditions and seek refuge in high-elevation areas or rugged terrains, where they can find favorable microenvironments with reduced precipitation and more exposed vegetation that facilitate their survival (Jenkins et al., 2011). In line with this evidence, this analysis does reproduce the inherent spatiotemporal variability of the habitat suitability and annual population rates of change in Axel Heiberg island complex; especially when using the algorithm that postulates the location-specific population growth rates to be a function of their counterparts in the previous year (Figs. S2–S6; see also discussion in the following section). Similar to Axel Heiberg, the derived ranges of the Peary caribou population rates of change in Melville, 0.98 to 1.01 year−1, and Bathurst island complexes, 0.98 to 1.07 year−1, were not conclusive in regard to the nature of the overall trend during the 2001–2013 period (Fig. 4-3). Even more so, the projected population trends based on the average predictions of the four configurations of the exponential model identified pockets of negative growth that could lead to 10% (Fig. 4-4), 25% (Fig. 4-5) or even 50% (Fig. 4-6) reduction relative to the 2000 population levels, but also extensive areas with high likelihood of increase. According to Kaluskar et al. (2020), Peary caribou on both spatial clusters displayed interannual fluctuations since the early 1970s, and recent trends are indicative of a population increase. In the same context, Jenkins et al. (2011) argued that if the weather is not prohibitive, the absence of hunting pressure and human disturbances could allow the realization of a Malthusian rate of increase (λ = 1.35 year−1) for caribou on Melville Island. Similar predictions could be made for the strongly female-dominated Peary caribou population on Bathurst Island complex (Jenkins et al., 2011). This analysis does not render support to Jenkins et al.'s (2011) assertions, as the predicted growth rates were nowhere near to the intrinsic natural rate of population growth in the absence of density-dependent effects, but it does suggest that the consideration of weather-related explanatory variables (precipitation, wind speed) to guide the random-walk search could partly explain the recent Peary caribou population increase in several pockets of the two broader regions (Fig. 4-6; Figs. S3 and S5). The habitat-modelling framework did a satisfactory job in predicting Peary caribou space- use patterns, and subsequently recreating their response to changing forage accessibility conditions. The primary focus here was on the summer-foraging (July–October) period, which

tends to be a critical time to ameliorate their nutritional status and build essential fat reserves for pregnancy rates, body growth, and winter survival (Taylor, 2005). An important next augmentation will be to extend the present modelling analysis to the winter-foraging (November–March) period, when Peary caribou migrate in order to increase foraging options but extreme weather conditions can lead to starvation/die-offs, and to the spring-calving (April–June) period, when limited access to forage can undermine adult survival and calf production/survival (Johnson et al., 2016). 4.3.4. Future augmentations of the Peary caribou habitat modelling framework In terms of the structural uncertainties of this modelling framework, there are four potential areas for further consideration and potential future improvement:

(i) Given the limited number of meteorological stations in the Canadian Arctic Archipelago, it was practically impossible to account for the regional climate variability in the area. While their granularity is still not entirely adequate to capture the regional variations in topography and vegetation, CanRCM4 regional climate model predictions with coarse resolution (25 × 25 km) were used instead. An interesting future exercise will be to quantify the error introduced from using simulated climatic predictors, by comparing them against the existing meteorological records and subsequently propagating the derived residual variability through the modelling framework with an errors-in- variables formulation (Carroll et al., 2006). (ii) This analysis did not consider a proxy variable for the vegetation abundance, which in some instances was identified as a likely reason for the counterintuitive signs of the explanatory variables used. Recent modelling work by Johnson et al. (2016) indicated that the NDVI data or other available land-cover classifications for the Arctic may not be adequate to describe the habitat and vegetation differences observed in the field, and therefore it was concluded that the role of forage abundance was generally underrepresented in their habitat models. Thus, an essential augmentation of the modelling framework should revolve around the elucidation of the net effects of climate change on the causal linkages between floral phenology and Peary caribou population dynamics. In the same context, it is important to bear in mind that the prospect of longer growing seasons and warmer

summers could not only provide additional forage for Peary caribou throughout their range, but may also affect the forage type and quality. The evolving paradigm of the climate-induced increases in vegetation biomass in the Arctic suggests a compositional shift towards evergreen shrubs and bryophytes and less so towards deciduous shrubs, forb flowers, and lichens (Hudson and Henry, 2009). The former vegetation type is considered to be of inferior nutritional quality relative to the forage typically selected by Peary caribou during their calving stage (Larter and Nagy, 2001a). Similar predictions of reduced nutritional quality under a changing climate can be generalized for all Arctic plants due to decreasing protein

concentrations, as a result of higher temperatures and CO2 concentrations, and increasing phenolics, driven by higher UV-B levels in the Arctic (Turunen et al., 2009). Given the limited capacity of the digestive physiology and rumen microflora of Peary caribou to adapt to variations of the nutritional quality forage, the latter scenario may influence the inter-specific competition for resource procurement with other herbivores (Turunen et al., 2009). (iii) Another unaccounted factor involves the impact of past and present human infrastructure and development in the Arctic. While many sources may have information on these human activities, supporting information on timing, duration, location is often incomplete. Nonetheless, the effects of resource extraction (mining and oil and gas) activities on Peary caribou health, behavior and movement are believed to have caused changes in local population sizes and distribution; especially in areas such as the Prince of Wales, Somerset and Bathurst Islands (Johnson et al., 2016). The construction and operation of pipelines has been identified as a likely culprit for the loss of important breeding grounds and calving areas on Somerset and Boothia Islands, as well as a potential disruptor of the Peary caribou migratory movement (Russell et al., 1979; Dumond et al., 2013). Finally, inter-island migration and movements could also be influenced by ice-breaking from shipping activities (Miller et al., 2005). Shipping traffic increased by 75% from 1990 to 2012, and is expected to increase even more in the future, given projections of ice-free Arctic waters by 2030 (Prowse et al., 2009). This prospect could lead to the loss of ecologically critical corridors that may prevent inter-island

crossings and consequently increase the isolation of local populations (Pizzolato et al., 2014). Seasonal connectivity provided by sea ice are essential for protecting genetic diversity and facilitating dispersal and recolonization of areas from which caribou have been extirpated (Jenkins et al., 2018; Mallory and Boyce, 2019). Improvement in the pertinent dataset would be helpful in reducing some of the uncertainty underlying the habitat model predictions. (iv) This analysis represents one of the first attempts to use modelling in order to integrate the disparate pieces of knowledge regarding the Peary caribou population spatiotemporal trends and ecology. Two stochastic algorithms were used to relax the rigid structure of exponential population growth model that postulates a constant rate of change over the time period examined. The first random-walk considered the year-specific population rates of change to be a function of their counterparts in 2000 (initial year of the study), while the second one conditioned the year-specific population rates of change upon those derived for the preceding year. This analysis showed that the latter strategy can lead to a distinct bimodal pattern and wider range of population rates of change among the cells within any island group (e.g., see histograms for Axel Heiberg in Fig. S4); especially, if there are locations with consistently favorable/unfavorable habitat conditions over time, the corresponding rates of change display a nearly monotonic increasing/decreasing trend. The patchiness of the projected population rates of changes (e.g., horizontal stripes in Fig. 4-4, Fig. 4-5, Fig. 4-6) was a reflection of the dynamics recreated by the second random-walk model, through which neighboring locations with distinct differences in their habitat suitability classification over time experienced a gradual divergence of the corresponding population trajectories. A characteristic example that reinforces the latter pattern is shown when examining the relationship among longitude, air temperature, and habitat suitability or the year-to-year variability of the Peary caribou population rates of change in grid cells of the Ellesmere island with latitude lower than 77° 0′N (Fig. S6). Thus, the modelling framework in its present form should be primarily used to delineate “hot-spots”, where the prevailing conditions could pose higher risks for the survival of local Peary caribou populations, and less so as a

predictive tool to estimate the actual animal numbers on any locations within the Canadian Arctic Archipelago. As such, the present results offer an overview of the prevailing habitat conditions in the Canadian Arctic Archipelago and could be used to generate hypotheses about favorable and/or problematic areas for the sustainability of Peary caribou populations. The coarse-scale predictions of the framework cannot single-handedly guide the local management decisions, but rather represent first approximations that can be evaluated by empirical studies with finer granularity. Peary caribou is an endangered species with varying habitat needs depending on season and forage availability (Festa-Bianchet et al., 2011; Taylor, 2005). It represents an important staple in the traditional, subsistence-based way of life of Indigenous communities living on High Arctic Resolute Bay (Qausuittuq) and Grise Fiord (Aujuittuq) (Thomas and Gray, 2002). Using empirical estimates of the Peary caribou population rates of change from previous chapter (Kaluskar et al., 2020), a two-pronged approach aiming to characterize the year-to-year variability of the habitat conditions across the Canadian Arctic Archipelago from 2000 to 2013 was presented. Among the explanatory (climatic, landscape, and biologic) variables selected, this analysis showed that precipitation, surface air temperature, and wind speed appear to have a strong signature on the Peary caribou habitat conditions and forage preferences during their life cycle. The habitat suitability estimates, as derived by the Bernoulli-logistic regression modelling framework, formed the basis of a stochastic algorithm used to recreate the population growth rates and identify locations, where Peary caribou could experience >10%, 25%, or 50% decrease relative to the population levels at the beginning of the study period. This analysis identified the Boothia island complex as a high-risk area, where the likelihood of a strong Allee effect could lead to extinction after episodic weather-related events or elevated incidental predation. This study also provide evidence that the prevailing habitat conditions in Melville and Bathurst island complexes were generally favorable and could partly explain the recently increasing Peary caribou population trends. In Banks island complex, this analysis suggests that the pre-2000 declining trends would have led to distinctly lower Peary caribou numbers without the voluntary restrictions on harvesting suggested and adopted by the Indigenous communities out of concern for low population numbers. Other unaccounted factors, such as the vegetation quantity/quality, human disturbance, and higher predation could further improve the fidelity of the modelling framework in representing the year-

to-year forage accessibility in the Arctic environment. Of equal importance is the elucidation of the effects of human- and climate-induced changes on the connectivity for both island-dwelling and mainland-migratory populations in the dynamic landscape of the Canadian Arctic Archipelago. Connectivity is critical for the colonization of suitable habitats, the support of gene flow between populations, the alleviation of inbreeding, and thus the enhancement of local genetic diversity and long-term persistence of populations (Jenkins et al., 2018; Mallory and Boyce, 2019).

Table 4-1 General interpretation and ecological reasoning of the explanatory variables used in the present modelling framework. Predictors Explanation Precipitation1 Peary caribou avoid using wet habitats to forage. Precipitation influences indirectly through changes in the timing of plant growth and may increase the likelihood of trophic mismatch between forage availability and critical life stages of Peary caribou. High precipitation, high winds, and below freezing temperatures play a key role in the formation of ice layers over the snow profile that can hinder the ability of caribou to access forage through the snow. Air Temperature2 Warmer surface temperatures prolong the growing season and increase vegetation productivity. Increased biomass could provide additional forage for Peary caribou. Declines in sea ice from rising temperatures could affect migratory patterns. Surface snowmelt 3 Snowmelt represents a critical factor that determines forage accessibility in a period of the year (early or mid-summer), when Peary caribou have lost weight and are in need to replenish energy reserves for reproduction. With temperatures hovering around zero, faster snowmelt rates may instead create ice, thereby making it harder for Peary caribou to feed. Wind speed4 Peary caribou tend to avoid areas where surface wind speeds are above 6.0 m s-1 Muskox5 Contrasting physiology and foraging strategies between muskoxen and Peary caribou reduce the likelihood of competition for habitat use and diet. Peary caribou avoidance of muskoxen is widely reported in IK, due to the unpleasant odor of muskoxen and damage to forage resources. Muskox-supported wolf populations could increase predation rates on Peary caribou due to increased probability of wolf- caribou encounters and/or their selective preference for caribou, i.e., apparent competition. Rockland6 The preferable fraction of rockland is either areas of low-intermediate (20%) or high (70%). During the winter, Peary caribou inhabit areas where the snow is shallower, such as rugged uplands, beach ridges, and rocky outcrops. Peary caribou are frequently found on the upper slopes of river valleys and uplands in the summer months where the vegetation is richest. 1Gunn and Skogland (1997), Post et al. (2008), Festa-Bianchet et al. (2011); 2,4,6Johnson et al. (2016); 3Jenkins et al. 2018, Malory and Boyce (2019); 5Staaland et al. (1997), Larter et al. 1994.

Complex Islands μc±σc Banks Banks, Northwest Victoria -0.067±0.010

Boothia Boothia, Prince of Wales, -0.101±0.034 Somerset, Russell Axel Heiberg Axel Heiberg, Ellesmere 0.068±0.053

Bathurst Bathurst, Little -0.029±0.045 Cornwallis, Cornwallis, Helena, Devon, Lougheed Melville Melville, Prince Patrick, -0.019±0.020 Eglinton, Emerald, Byam Martin Mackenzie King McKenzie King, Brock, 0.022±0.084 Borden

Air Snow Wind Model Precipitation Muskox Rockland Intercept Temperature melt speed fit Banks (N=1074) -3.073±0.206 -4.901±0.095 0.207±0.094 -3.089±0.115 87.7% Axel Heiberg 3.545±0.202 -4.056±0.679 -1.109±0.493 0.033±0.103 -4.561±0.235 90.0% (N=1841) Bathurst 1.837±0.193 0.691±0.096 80.7% (N=730) Boothia -1.416±0.156 -1.898±0.181 -1.224±0.095 71.4% (N=944)

Complexes Melville -0.961±0.131 -1.134±0.186 -0.106±0.087 0.385±0.085 71.9% (N=680) Mackenzie King -0.992±0.892 -2.320±0.836 0.581±0.375 1.334±0.292 80.0% (N=95)

3The classification scheme of the minimum population rates of change (year-1) distinguishes among very low (λ<0.85), low (0.85<λ<0.87), medium (0.87<λ<0.98), high (0.98<λ<1.09), and very high (λ>1.09). 4The classification scheme of the maximum population rates of change (year-1) distinguishes among very low (λ<0.97), low (0.97<λ<0.99), medium (0.99<λ<1.01), high (1.01<λ<1.27), and very high (λ>1.27).

Chapter 5 Development of a Bayesian ensemble of empirical models to predict Peary caribou (Rangifer tarandus pearyi) populations in the Canadian Arctic Archipelago 5 5.1 Introduction Biodiversity enhances ecological services and may significantly modulate the magnitude and efficiency of ecosystem functioning (Jeffers, 1992; Diaz et al., 2006; Gamfeldt et al., 2008). Protecting biodiversity through conservation/management programs represents a multifaceted endeavor that is shaped by socio-economic, political, scientific, and traditional factors (Grace and Ratcliffe, 2002). Prevention of biodiversity loss and ecosystem degradation through biological conservation programs requires ascertaining the nature of the driving forces of species extinction (Perrings et al., 2011). Hence, successful biological conservation programs should be founded upon: (i) an in-depth understanding of the biology of the organism at hand, e.g., genetic strains, species, and ecological assemblages present; (ii) a robust delineation of the population abundance and distribution over time and space; (iii) a reliable characterization of the causal linkages between population integrity and human or natural disturbances; (iv) a rigorous assessment of the organism’s proven or potential utility for human benefits and its broader functional role in ecological processes (Wheeler et al., 2012). In this context, Canada has proclaimed the Species at Risk Act (2002)6 with the mandate to prevent the disappearance of wildlife species, empower the recovery of wildlife species that are extirpated, endangered, or threatened because of human activity, and manage species of special concern in order to prevent them from becoming endangered or threatened.

Peary caribou (Rangifer tarandus pearyi) is species at risk that plays an important role to the traditional, subsistence-based way of life in Canadian High Arctic communities (Thomas and Gray, 2002). Peary caribou provide food and raw materials for clothing and artwork, and their survival is particularly important to Indigenous communities living in High Arctic Resolute Bay (Qausuittuq) and Grise Fiord (Aujuittuq) (Miller, 2001; Taylor, 2005; Festa-Bianchet et al., 2011). Owing to an estimated decline of over 35% during the last three generations (27 years), the most

5 Kaluskar. S., Blukacz-Richards, E.A, Johnson, C., He .Y, Langlois. A, Kim, D.K., Arhonditsis, G.B., 2019b. Development of a model ensemble to predict Peary caribou populations in the Canadian Arctic Archipelago 6https://laws.justice.gc.ca/eng/acts/S-15.3/

recent assessment by the Committee on the Status of Endangered Wildlife in Canada (COSEWIC) assigned a Threatened status to Peary caribou (COSEWIC, 2015). The decline of Peary caribou has been causally associated with a series of severe weather (snow, icing) events in the Canadian Arctic that can profoundly affect their seasonal forage availability/accessibility, and consequently lead to malnutrition, desperation long-distance movements in response to low-resource availability, adult mortality, and loss of calves (Festa-Bianchet et al., 2011). Peary caribou population decline could also be related to the occurrence of irregular winter conditions, when more frequent rain-on-snow and thaw-freeze events can seal vegetation under thick ice (Langlois et al., 2017). Sea-ice thickness and early sea-ice break up may also decrease or prevent Peary caribou migration, whereby reproductive success, foraging efficiency, and genetic diversity can be severely compromised (Jenkins et al., 2018; Malory and Boyce, 2019). Other factors (e.g., hunting, competition with muskoxen, predation by wolves, petroleum exploration, and shipping activity) have contributed to the decline, with the potential for greater impact when population numbers are low (Jenkins et al., 2011).

In the field of biological conservation and sustainability, ecological modelling has been at the forefront of the efforts to advance our understanding of population dynamics. The appeal of models mainly stems from their ability to synthesize among different types of information reflecting our best understanding of species ecology, to identify the key relationships and feedback loops from an inconceivably wide array of intertwined ecophysiological processes, and to probe their relative role on animal behavior using different levels of model granularity (Grimm and Railsback, 2005). Building upon this “bottom-up” strategy, mechanistic, agent- and matrix-based models aim to characterize growth/metabolic rates and resource-consumer-predator interactions at the individual level, and then reproduce the emergence of population-level patterns related to particular management actions (Grimm et al., 2005; Tews et al., 2007a). Nonetheless, modelling rare and endangered species with complex mechanistic tools can be particularly challenging due to the constraints posed by the increased data requirements. Missing or incomplete dataset are repeatedly encountered due to poor weather conditions, lack of technology, organizational deficiencies, and high survey costs in remote areas (Beniston et al., 2012). This mismatch between what we are trying to tease out from a complex model and the available empirical knowledge and data undermines our ability to parameterize individual processes and subsequently make inference about the collective population behavior (Garamszegi, 2006). Thus, mathematical modelling may

not be the best way to reliably predict population dynamics of species at risk, and instead the most prudent strategy could be to maximize the use of information of the existing data and build simple empirical (statistical) models.

To this end, Kaluskar et al. (2020) presented a regression-based imputation method to reconstruct the Peary caribou population data across the Canadian Arctic Archipelago (CAA). Founded upon the assumption that there is a subset of primary islands that act as the core areas from where the Peary caribou populations migrate to secondary (or satellite) islands. Peary caribou population estimates in secondary/satellite islands were predicted from the population of the corresponding primary islands, the areal ratio of the pair of islands considered, and the year we are trying to infill. This imputation model was able to capture co-dependencies in time and space and reproduce more than 65% of the variability from 1970 to 2015. In a follow-up study, Kaluskar et al. (2019b) showed that the rigid structure of the exponential growth model posed constraints on its ability to accommodate the non-monotonic patterns typically characterizing Peary caribou populations. The present study builds upon the data and lessons learned from our recent work and develops a spatially explicit modelling framework in order to evaluate the hypotheses of the presence of a distinct negative relationship between Peary caribou population size and snow and a positive one with vegetation abundance. Specifically, this analysis will examine the relationship between the Snowpack Water Equivalent Intensity (SWEI) (snowpack water equivalent divided by the number of days the snow was on the ground), and the Advanced High Resolution Radiometer (AVHRR) Normalized Difference Vegetation Index (NDVI) with the year-to-year variability of the Peary caribou populations in different islands of the CAA. Recognizing the uncertainty typically associated with the selection of the subset of predictors and their optimal functional relationship with the response variable (Hoeting et al., 1999), this analysis examines multiple models and subsequently integrate them into one averaged prediction of the Peary caribou populations. The latter exercise is based on model averaging, which is a technique designed to explicitly account for the uncertainty inherent in the model selection process. By averaging over many different competing models, our strategy incorporates the uncertainty about the optimal model for any given exercise into the inference drawn about parameters and predictions (Raftery et al., 2005). Therefore, rather than picking the single “best-fit” model to recreate Peary caribou population spatio-temporal trends, model averaging will be used to provide a weighted average of the predictions from different models. Alongside the parametric and structural uncertainty, this study

considers the role of the observation/imputation error associated with the Peary caribou dataset and illustrates the influence of the assumptions made about its magnitude.

5.2 Methods 5.2.1 Study area-Dataset The Canadian Arctic Archipelago, is a group of 36,563 islands that cover about 1,424,500 km2 north of the Canadian mainland, and comprises a significant portion of the territory of Northern Canada- most of Nunavut and part of the Northwest Territories (Fig. 5-1). The area lies within the Arctic Cordillera and Northern Arctic Ecozones of Canada (Jenkins et al., 2011). The major (e.g., Ellesmere, Axel Heiberg, Devon) islands in the eastern Arctic Archipelago are mountainous with most of their area occupied by ice caps (ESWG, 1995). The eastern islands represent the northern extent of the Canadian Shield, which is extensively covered by flat-lying Paleozoic rocks. The central and western islands have generally low relief and consist of sedimentary rocks, whereas the northern islands consist of heavily folded sedimentary rocks that produce mountains on Axel Heiberg and partly on Devon and Ellesmere islands. This geological variety produces variations in the landscape, with rugged mountains, high and low plains of various ages and rock types, and steep-sided fjords. Based on scientific literature7, evidence from Indigenous Knowledge, and expert input, Kaluskar et al. (2020) delineated six geographic clusters within larger scale metapopulations, or conservation units, which were explicitly considered by our modelling analysis to accommodate the spatial patterns of Peary caribou across the CAA; namely, the Banks, Axel Heiberg, Melville, Bathurst, Mackenzie King, and Boothia island complexes (Table 5-1). The latter spatial classification was further reinforced by the differentiation in the genetic make-up of samples from Peary caribou collected in different areas of the Arctic, evidence of regular movement between islands, and expert input (scientific and community) on proposed delineations (Johnson et al., 2016). More than 150 aerial surveys have been conducted in the Canadian Arctic to estimate Peary caribou counts since the early 1960s (see Appendix VI in Johnson et al., 2016). For each survey included in the dataset, caribou animal counts from transects were used to derive densities (number of caribou per area surveyed). All raw caribou density estimates from aerial surveys were adjusted using standardized areas, calculated with a land mask

7 Gauthier, 1996; Gunn and Dragon, 2002; Zittlau, 2004; Miller et al., 2005; Gunn et al., 2006, Miller and Barry 2009; Jenkins et al., 2011.

generated from the CanVec dataset (an open source digital cartographic reference from Natural Resources Canada), to ensure that estimates of total caribou numbers per island or per island group were comparable among years. The abundance counts included different life stages of the animals (e.g., one-year olds, calf and non-calf estimates), which were summed up to derive the total population size per year and islands. For surveys that did not record calf estimates, corrections were implemented based on the reported fecundity index, i.e., proportion of calves in total count (Johnson et al., 2016). Margins of error to bracket survey estimates were available for only 60% of the existing surveys (Gunn and Poole, 2014), which were then adjusted probabilistically to obtain consistency in terms of the population data uncertainty (Kaluskar et al., 2020). When uncertainty estimates were not available, a global coefficient of variation (32.5%) was calculated from all the existing records across the CAA, which provided the uncertainty bounds for the rest of the population data. These error estimates do not represent an absolute measure of confidence on the population size, but rather offer a realistic range for each data point when considering all the potential sampling/calculation biases.

The causal linkage between vegetation response and environmental change as well as the associated trophic interactions with wildlife, e.g., timing of spring vegetation with calving and rutting of red deer (Cervus elaphus), could be captured by NDVI as a proxy variable (Pettorelli et al., 2005). This study investigated the relationship between vegetation and Peary caribou population dynamics using 10-day AVHRR composite images at 1 km spatial resolution for the entirety of CAA from 1985 to 2007 (He et al., 2012). The 10-day length of a composite period was selected as it could provide reduced or no cloud-contaminated images with sufficient temporal resolution to catch vegetation variations during the growing season. Because the resulting AVHRR 10-day composite products contained contaminated pixels, they were subsequently processed by the Cloud Elimination from Composites using Albedo and NDVI Trend (CECANT) technique (Adair et al., 2002). After processing the 10-day AVHRR composite images, the maximum value for each growing season and CAA location was used as the annual NDVI predictors across our study domain. Regarding the second explanatory variable, Maher et al. (2012) showed that the development of remotely sensed indices of snow cover could further enhance our understanding of how Arctic ungulates may adapt to climate change. Likewise, Snow Water Equiavalent Intensity was calculated by dividing the snowpack water equivalent by the number of days the snow was on the ground (SWEI), as derived by the SNOWPACK model version 3.4 with 25 km2 resolution

(https://models.slf.ch/p/snowpack/). SNOWPACK is a multi-purpose snow and land-surface model that depicts the mass and energy exchange among snow, atmosphere, vegetation, and soil (Lehning et al., 2002a,b). A particular feature of the model is the treatment of soil and snow as a continuum with a resolution that can vary from a few up to several hundred layers. SNOWPACK features a very detailed description of snow properties including weak layer characterization (Stossel et al., 2010), as well as phase changes and water transport in snow (Hirashima et al., 2010). Standardized time series for the two predictor variables across the six island complexes of the CAA are provided in the supporting Information (Figs. S7-S8), while their raw values are shown in Tables S1 and S2.

5.2.2 Modelling framework Four models were used to describe the Peary caribou population temporal trends across the different CAA islands. The first model does not explicitly consider any explanatory variables (vegetation, snow) and simply postulates an exponential monotonic growth/decline of the population over time (Dennis et al., 1991). In its classical form, this simple conceptual model is founded upon three major assumptions that may be violated to a variant degree when reproducing population dynamics of endangered species in extreme environments, like the Canadian Arctic Archipelago: (i) the population growth rate is not influenced by the variations of the population density; (ii) the environmentally-driven variability is not extreme, and thus there are no years with catastrophic (e.g., icing) events or unusually favorable conditions; (iii) the year-to-year variability in the population growth rate is primarily modulated by the environmental stochasticity, whereas the contribution of the observation/sampling error to the variation of animal counts is negligible and represents a constant fraction of the entire population over time (Morris et al., 1999). The parameter estimation was based on a Bayesian hierarchical formulation, whereby the data are classified according to the island complex collected; and the model itself has its own hierarchical configuration (Kaluskar et al., 2019a, b). The spatial cluster-specific population rates of change at the first level are controlled by the hyper-parameters at a second (upper) level that capture the population variability over the entire CAA. With the hierarchical model structure, significant sources of variability that differentially determine the Peary caribou population trends within each spatial complex can be explicitly accommodated, while overcoming problems of insufficient group-specific data by “borrowing strength” from well-studied modelled units (Ellison, 2004; Zhang and Arhonditsis, 2009; Cheng et al., 2010; Shimoda and Arhonditsis, 2015). The latter issue

is particularly relevant to our modelling exercise, as the Peary caribou populations are inconsistently recorded over time and differ in terms of their amount and accuracy among the different locations. The data uncertainty was accounted for by postulating that our population data represent a random draw from a probability distribution with an expected value, the true (or error- free) value of the Peary caribou population modelled, and the variance comprising both the imputation model error and the observational (sampling) uncertainty (Carroll et al., 2006; Ramin and Arhonditsis, 2013). The mathematical notation for the hierarchical formulation of the exponential growth model is summarized as follows:

2 푙푛 (푁푃퐶푗,푡)~훮(푙푛 (푁푃퐶푡푟푢푒푗,푡), 훿푗푡)

2 푙푛 (푁푃퐶푡푟푢푒푗,푡)~훮(푙푛 (푁̂푃퐶푗,푡), 휎푚표푑)

푙푛 (푁̂푃퐶푗,푡) = (푡 − 푡0푗) ∙ 휆푗 + 푙푛 (푁푃퐶푗,0) (Model 1)

2 2 2 2 훿푗푡 = 휎푖푚푝푗,푡 + 휎표푏푠푗,푡 휆푗~훮(휆퐺, 휎휆푗)

2 −2 휆퐺~훮(휇휆, 휎휆 ), 휎휆푗 ~ 퐺푎푚푚푎(0.001, 0.001), j=1,…,6

−2 휇휆~훮(0,10000), 휎휆 ~ 퐺푎푚푚푎(0.001, 0.001) −2 휎푚표푑~ 퐺푎푚푚푎(0.001, 0.001) where 푁̂푃퐶푗,푡, and 푁푃퐶푗,푡 represent the predicted and measured population within the spatial complex j and year t, respectively; 푁푃퐶푡푟푢푒푗,푡 is a latent variable representing the “true” (or error- 2 free) Peary caribou population when we account for the pre-specified error 훿푗푡, which in turn is 2 2 the sum of the observation, 휎표푏푠푗,푡, and imputation, 휎푖푚푝푗,푡, errors for the spatial complex j and 2 year t; 휎푚표푑 represents the associated structural error of the hierarchical model drawn from an uninformative gamma prior distribution with shape and scale parameters equal to 0.001; 푁푃퐶푗,0 represent the initial measured population in the spatial complex j and year 푡0푗; 휆푗 is the island complex-specific population growth rate, which is drawn from a normal distribution with a global 2 2 population growth rate, 휆퐺, and island complex-specific variance, 휎휆푗; 휇휆 and 휎휆 are the mean and variance of the hyperparameter, respectively.

The second model expresses the log-transformed Peary caribou population levels as a linear function of the annual vegetation abundance (NDVI), the snowpack intensity (SWEI), and time. When the population is expressed in the original scale, the latter term is the equivalent of a monotonic exponential change over time. Thus, the second model builds upon the first one by simply adding two explanatory variables for the variability unaccounted for by the exponential growth model. Likewise, the third model considers the causal linkages between Peary caribou and the two predictor variables, but does not include the term that represents the population change over time. The fourth model introduces the Conditional Autoregressive (CAR) term aiming to relax the rigid assumption of a monotonic trend over time, and thus accommodate the non-monotonic patterns (e.g., interannual fluctuations) frequently characterizing Peary caribou populations. Similar to the first model, the slopes of the two explanatory variables along with the intercepts of the rest three models have been subjected to a hierarchical configuration conducive to deriving island complex-specific parameter estimates. The mathematical notation for the rest three models is as follows:

2 푙푛 (푁푃퐶푘(푗),푡)~훮(푙푛 (푁푃퐶푡푟푢푒푘(푗),푡), 훿푘(푗)푡)

2 푙푛 (푁푃퐶푡푟푢푒푘(푗),푡)~훮(푙푛 (푁̂푃퐶푘(푗),푡), 휎푚표푑)

푙푛 (푁̂푃퐶푘(푗),푡) = 휃1,푗 ∙ 푁퐷푉퐼푘(푗),푡 + 휃2,푗 ∙ 푆푊퐸퐼푘(푗),푡 + 휃3,푗 ∙ (푡 − 푡0푘(푗)) + 휃0,푗 (Model 2)

푙푛 (푁̂푃퐶푘(푗),푡) = 휃1,푗 ∙ 푁퐷푉퐼푘(푗),푡 + 휃2,푗 ∙ 푆푊퐸퐼푘(푗),푡 + 휃0,푗 (Model 3)

푙푛 (푁̂푃퐶푘(푗),푡) = 휃1,푗 ∙ 푁퐷푉퐼푘(푗),푡 + 휃2,푗 ∙ 푆푊퐸퐼푘(푗),푡 + 휑푡 + 휃0,푗 (Model 4)

2 푁(휑푡+1, 휔 ) 푓표푟 푡 = 1 2 2 휑푡−1 + 휑푡+1 휔 푝(휑푡|휑−푡, 휔 )~ 푁 ( , ) 푓표푟 푡 = 2, … , 푇 − 1 2 2 2 { 푁(휑푡−1, 휔 ) 푓표푟 푡 = 푇

2 2 2 2 훿푗푡 = 휎푖푚푝푗,푡 + 휎표푏푠푗,푡 휃푖,푗~훮(휃푖,퐺, 휎휃푖푗)

2 −2 휃푖,퐺~훮(휇휃푖, 휎휃푖), 휎휃푖푗 ~ 퐺푎푚푚푎(0.001, 0.001)

−2 휇휃푖~훮(0,10000), 휎휃푖 ~ 퐺푎푚푚푎(0.001, 0.001) i=0,…3 j=1,…,6

−2 휎푚표푑~ 퐺푎푚푚푎(0.001, 0.001)

where 푁̂푃퐶푘(푗),푡, 푁푃퐶푘(푗),푡, 푁푃퐶푡푟푢푒푘(푗),푡 represent the predicted, measured, and latent “true” Peary caribou population within the island k of the spatial complex j and year t, respectively; NDVIk(j),t and SWEIk(j),t denote the annual vegetation abundance and snowpack intensity on the island k of the spatial complex j and year t, respectively; 휃0,푗, 휃1,푗, 휃2,푗, and 휃3,푗 represent the intercept and slopes of the relationships between Peary caribou and vegetation, snowpack water equivalent, and time within the spatial complex j, respectively. The island complex-specific parameters are drawn from normal distributions with mean values, 휃푖,퐺, and island complex-specific variances, 2 2 휎휃푖푗; 휇휃푖 and 휎휃푖 are the mean and variance of the corresponding hyperparameters, respectively. In regards to the conditional autoregressive term 휑푡 assumed a first-order random walk prior where 2 휑−푡 denotes all elements of 휑푡 except from the error associated with a particular year t, 휔 is the conditional variance and the prior densities 푝(휔2) were based on conjugate inverse-gamma (0.001, 0.001) distributions. The conditional autoregressive approach implies that the first-order differences of the annual population levels are smooth in particular area, and that the probability of sudden jumps between consecutive years is unlikely (Shaddick and Wakefield, 2002; Azim et al., 2011; Sadraddini et al., 2011). It is also worth noting that the sensitivity of model outputs to the gamma prior distribution assigned to the variance terms was tested with uniform and half- Cauchy priors and the results were practically identical (Gelman, 2006).

The implementation of Bayesian framework was based on Markov-chain Monte Carlo (MCMC) simulations (Gilks et al., 1998). Specifically, the general normal-proposal Metropolis algorithm was used to obtain sequences of realizations from the model posterior distributions using the WinBUGS software (Lunn et al., 2000). This algorithm is based on a symmetric normal proposal distribution, whereby standard deviation is adjusted over the first 4,000 iterations such as the acceptance rate ranges between 20% and 40%. An ordered over-relaxation was used, which generates multiple samples per iteration and then selects one that is negatively correlated with the current value of each stochastic node (Neal, 1998). The latter option resulted in an increased time per iteration but reduced within-chain correlations. I used 50,000 iterations and convergence was assessed with the modified Gelman–Rubin convergence statistic (Brooks and Gelman, 1998). The accuracy of the posterior estimates was examined by assuring that the Monte Carlo error (an estimate of the difference between the mean of the sampled values and the true posterior mean;

see Spiegelhalter et al., 2003) for all the parameters was less than 5% of the sample standard deviation.

Recognizing that each of the four models used to detect the spatiotemporal trends of Peary caribou population density has different assumptions, one of the key messages that the present study aims to convey is the importance of adopting conceptually integrative modelling frameworks. Rather than selecting the “best” of the four modelling configurations examined and then basing the delineation of the trajectories on that single “best-fit” model, I developed a weighted average description from all four approaches (Azim et al., 2011). Because one of the four models has the conditional autoregressive term that does not allow to implement a full Bayesian averaging scheme (at least, in the sense that was originally presented by Hoeting et al., 1999), I adopted a post-hoc strategy that is based on the calculation of the root mean square error (or RMSE)8 between posterior predicted median and observed values (Ramin et al., 2012; Arhonditsis et al., 2018). While this approach deviates from the typical statistical ensemble strategies presented in literature, it is a straightforward way to assess the performance of the four models and assign weights accordingly. Two ensemble strategies were developed to evaluate the performance of the four models. The first ensemble considers the performance of the four models within each of the six island complexes and then assigns region-specific weights for each model. A second ensemble considers the overall performance of each model and then assigns model-specific weights across the entire CAA.

5.3 Results-Discussion 5.3.1 Model Performance Considering the lack of causal foundation, the exponential growth model (Model 1) displayed satisfactory performance with a posterior structural error, 휎푚표푑, of 0.633±0.233, i.e., median model error of 1.883 caribou bracketed by a 95% credible interval (or 95% CI) between 1.181 and 3.001 (Table 5-2). It is important to note though that the structural error term characterizes the mean discrepancy between the latent true Peary caribou size, 푁푃퐶푡푟푢푒푗,푡, after accounting for the pre-specified observation/imputation error, and the predicted population estimates, 푁̂푃퐶푗,푡, whereas the (most commonly used) residual variability between recorded, 푁푃퐶푗,푡,

∑(ln(푃표푠푡푒푟푖표푟 푝푟푒푑푖푐푡푒푑 푚푒푑푖푎푛)−ln (푂푏푠푒푟푣푒푑))2 8 Root Mean Squared Error or RMSE=√ 푆푎푚푝푙푒 푠푖푧푒

and predicted, 푁̂푃퐶푗,푡, Peary caribou population was equal to 1.348 ± 0.162, i.e., median model error of 3.849 caribou bracketed by a 95% credible interval (or 95% CI) between 2.784 and 5.322. Likewise, the coefficient of determination (r2) between mean predicted and empirical areal population estimates was equal to 0.481 (Figure 5-2). In terms of the island complex-specific performance of the exponential growth model, the lowest error values were registered on Banks (RMSE=0.872±0.072), Mackenzie King (RMSE=0.852±0.128), and Axel Heiberg (RMSE= 0.954±0.104), whereas the highest error was found against the Peary caribou population data from Boothia island complex (RMSE=5.589±0.184). By contrast, the consideration of the role of vegetation and snow without a temporal component (Model 3) did not allow recreating the population time-series in a satisfactory manner, as the 휎푚표푑 and RMSE statistics were equal to 1.627±0.153 and 1.689±0.165, respectively. Similar to the exponential growth model, the lowest error values were registered on Mackenzie King (RMSE=0.568±0.097), Banks (RMSE=1.077±0.101), Axel Heiberg (RMSE=1.337±0.114), whereas the highest error was again registered on Boothia island complex (RMSE=6.549±0.358). Based on the overall performance, the model configurations that comprised the two explanatory variables and also included temporal- trend terms (Models 2 and 4) displayed the highest performance. In terms of their deviance information criterion (DIC) values9, Models 2 (322.3) and 4 (330.1) were also identified as the most parsimonious constructs. Moreover, the assumption of a monotonic trend over time (Model 2) led to a somewhat higher performance relative to the term designed to accommodate non- monotonic patterns (Model 4), in regards to both 휎푚표푑 (1.269±0.132 versus 1.391±0.125) and RMSE (1.310±0.133 versus 1.404±0.145) values. In particular, not only did Model 2 improve the reproduction of Peary caribou trends on areas where the performance was already satisfactory (Banks, Axel Heiberg, Maxkenzie King), but also on Boothia (RMSE=1.645±0.148) and Bathurst (RMSE=2.552±0.187) island complexes. It is also interesting to note the remarkably low error

9 ̅̅̅̅̅̅̅ ̅̅̅̅̅̅̅ 퐷퐼퐶 = 퐷(휃) + 푝퐷 where 퐷(휃) is the posterior mean of the deviance, a measure of residual variance in data conditional on the parameter vector θ. The deviance is defined as -2log(likelihood); pD is a measure of the “effective number of parameters” and corresponds to the trace of the product of Fisher’s information and the posterior covariance. It is specified as the posterior mean deviance of the model 퐷̅̅̅(̅휃̅̅̅) minus the point estimate of the model ̅̅̅̅̅̅̅ deviance when using the means of the posterior parameter distributions, i.e., 푝퐷 = 퐷(휃) − 퐷(휃̅). Thus, this Bayesian model comparison first assesses model fit or model “adequacy” (sensu Spiegelhalter et al., 2002), 퐷̅̅̅(̅휃̅̅̅), and then penalizes complexity, 푝퐷. A smaller DIC value indicates a “better” model.

values registered on Banks (RMSE=0.729±0.068), Melville (RMSE=0.951±0.101), Mackenzie King (RMSE=0.555±0.098) with Model 2 (see also following discussion).

5.3.2 Identification of the role of snow and vegetation on the year-to-year variability of Peary caribou populations In a recent knowledge assessment pertaining to Peary caribou, Johnson et al. (2016) showed that the critical ecological factors shaping the optimal habitat conditions differ depending on the season considered. Aboveground plant biomass and associated phenology appear to be critical determinants during the snow-free season, whereas snow and ice conditions are the primary drivers during the snow-covered period. Snow depth, density, and hardness influence the energetic cost of cratering through snow to access forage, and therefore Peary caribou select winter habitats with shallow snow cover that are easily cratered and rapidly melted with the rise of spring temperatures (Gunn and Dragon, 1998; Larter and Nagy, 2001a, b). Greater forage accessibility and lower energetic expenditures can compensate for the lower forage quantity and inferior nutritional quality available in the winter. Consequently, prolonged and severe winter conditions with deep snowpack have been causally associated with poor body condition, malnutrition, calf and adult mortality, and major Peary caribou population die-offs (Miller and Gunn, 2003). Interestingly, the negative relationship between snow and Peary caribou populations did manifest itself with the models examined (Table 5-3), but the noise-to-signal (standard deviation-to-mean) ratios were generally high and there were instances where the regression coefficients were practically not distinguishable from zero (Figs S9 and S10). In particular, the negative signature of the snow water equivalent was strong on Melville (odds ratios10 for a negative snow effect varying from 1.3-20.2:1 depending on the model examined), Axel Heiberg (2.9-3.7:1), and Banks (1.5-4.7:1), but less so on Boothia (1.1-5.3:1), Bathurst (1.2-2.0:1), and MacKenzie King (≈1.8:1) island complexes. One plausible explanation for the moderate degree of identification of the slopes related to the snow effect on the year-to-year population variability could have been the introduction of the observation/imputation error, which taxes our modelling exercise with an additional stochastic

10 The odds ratio of a regression coefficient to be negative/positive is the ratio of the probability mass below/above zero to the mass above/below zero. In the present study, the magnitude of the causal relationships examined are classified such that odd ratios >4 (>80% probability of a negative/positive regression coefficient value), 2-4 (66-80% probability), and 1-2 (50-66% probability) were indicative of a strong, medium, and weak negative/positive relationship, whereas odds ratios <1 (<50% probability of a negative/positive regression coefficient value) are suggestive of the opposite sign from that examined for a particular relationship.

node and reduces the amount of information allocated to parameter estimation (Ramin and Arhonditsis, 2013; Wellen et al., 2014). Nonetheless, the noise-to-signal ratios did not change significantly, when the Peary caribou data is treated as “perfectly” measured values without the consideration of the associated errors (see also additional discussion about the data error terms in Section 5.3.4).

Based on their digestive physiology (high metabolism, rapid rate of passage) and morphology (small body, relatively low gut capacity), Peary caribou are usually classified as mixed feeders (intermediate between grazers and concentrate selectors) with an aptitude to select the most nutritious parts of seasonally available forage with high content in crude protein and energy, such as winter-green leaves, flower and seed heads (Staaland et al., 1997). During the snow-free season, Peary caribou habitat selection is primarily influenced by forage availability in order to maximize food intake for reproduction, growth, and winter survival (Miller and Barry, 2003). Thus, plant phenology (i.e., timing of “greening”, flowering of forage) is an essential determinant of the ability of Peary caribou populations to recover from their winter nutritional stress and replenish their fat reserves (Larter and Nagy, 2004), which in turn can positively influence their pregnancy rates during rut (Gunn and Dragon, 1998). Nonetheless, the positive causal association between vegetation abundance (using NDVI as a proxy variable) and Peary caribou population size was not consistently evident with the parameter posteriors of modelling framework (Table 3). In particular, the positive effect of vegetation was strong on Melville (odds ratios for a positive NDVI effect varying from 2.7-125.8:1) and Bathurst (2.1-11.5:1), but less so on Axel Heiberg (2.0-2.7:1), Banks (≈2.2:1), and MacKenzie King (≈1.1:1) island complexes. In stark contrast, the relationship between vegetation abundance and Peary caribou switched to negative (odds ratios for a negative relationship varying from 1.1-2.9:1) on Boothia island complex and the same result held true on Banks and Axel Heiberg with Models 2 and 4. The absence of a consistently strong positive relationship is on par with Johnson et al.’s (2016) findings, who asserted that NDVI as well as the available land cover classifications for the Arctic may not be able to depict habitat and vegetation patterns at the scale that is appropriate to delineate Peary caribou habitat selection. Although there are alternative data sets available, such as the vegetation mapping done for Aulavik National Park on Banks Island (Larter et al., 2009) or the Quttinirpaaq National Park on the northern portion of Ellesmere Island, they do not cover the spatial extent required for our modelling analysis.

The posterior estimates of the island complex-specific population rates of change remained fairly consistent between Models 1 and 2 (Figure 5-3 and Table 5-3). Specifically, according to the hierarchical exponential growth model (Model 1), Boothia (0.91±0.03 yr-1) and Banks (0.94±0.01 yr-1) displayed the stronger decline, followed by Bathurst (0.97±0.04 yr-1) and Melville (0.98±0.02 yr-1), whereas Axel Heiberg (1.07±0.06 yr-1) and Mackenzie King (1.03±0.09 yr-1) were characterized by weakly increasing trends over the course of our study period. Likewise, after parsing out the role of vegetation abundance and snow, Model 2 suggests a strong declining trend on Melville (-0.33±0.05 ln[number of animals∙km-2]∙yr-1) and Boothia (-0.23±0.07 ln[number of animals∙km-2]∙yr-1), followed by Banks (-0.11±0.05 ln[number of animals∙km-2]∙yr-1) and Bathurst (-0.09±0.06 ln[number of animals∙km-2]∙yr-1) island complexes. The same pattern was also recreated by the conditional autoregressive (휑푡) term (Model 4) with a nearly monotonic decline until the early 2000s, but also an increasing trend over the last 4-5 years of our study period (Figure 5-3). Alongside the increasing trends on Axel Heiberg and Mackenzie King island complexes, the latter result may also reflect the distinct increase of the Peary caribou population size on Banks Island during the 2000s, after the implementation of recovery actions that curtailed caribou hunting in the area (Gunn et al., 2006). In fact, Kaluskar et al. (2019a) presented projections that reinforced the success of the recovery measures, as the population would have been nearly five times lower from the population levels recorded in 2014, given the low calf-to-cow ratio of the local population and the recurring local freezing rain events. Similar recent empirical evidence is available on Melville and Bathurst island complex, where either the strongly female-dominated Peary caribou population (Bathurst) or the absence of harvest pressure and human activities (Melville) could conceivably favour the realization of high rates of increase and a potential return to levels experienced in the early 1960s (Jenkins et al., 2011). On a final note, the emergence of non- monotonic population patterns towards the end of our study period and their establishment during the subsequent years suggest that the monotonic trend term postulated by Model 2 may not have been the optimal one if our study had extended beyond 2007, thereby rendering support to the structure introduced by Model 4.

5.3.3 Bayesian ensemble modelling and Peary caribou population predictions Being primarily a reflection of current level of understanding and existing limitations of measurement technologies, the fact that many different model structures (or even many different

parameter sets within a chosen model structure) can reproduce the dynamics of a modelled unit (e.g., environmental system, species populations) with a similar degree of fidelity has long been discussed in the literature (Beven and Freer, 2001; Christakos, 2003; Arhonditsis et al., 2018). Most notably, Neuman (2003) asserted that the practise of basing forecasts on a single model implies that a valid alternative model may be rejected from the decision making process (Type I model error), but also that projections may be the result of an erroneous construct that we failed to reject in an earlier stage (Type II model error). In the present study, the conceptual differences of the four models developed along with their variant degree of performance depending on the time or island complex modelled underscore the uncertainty of any forecasting exercise pertaining to Peary caribou population trends that is based on a single model. As an appealing alternative to the latter practice, two ensembles were formulated that were designed to provide integrated predictions after weighting each of the four models according to either its performance within a particular island complex (Ensemble 1) or its overall performance across the entire Canadian Arctic Archipelago (Ensemble 2). Based on the RMSE values reported in Table 5.2, the latter ensemble was primarily influenced by Models 2, 1, and 4, whereas the weights assigned to the four models varied significantly among the island complexes examined with the former one. For example, Boothia was primarily based on Model 2, Melville on Models 2 and 4, and Axel Heiberg on Models 1 and 2. Overall, the first ensemble strategy with region-specific weights resulted in the highest r2 (=0.734) and low RMSE (1.394±0.122) values as well as the most balanced error across the six island complexes of the Canadian Arctic Archipelago (Table 5.2). In particular, Ensemble 1 was ranked as the second highest performing model (Axel Heiberg, Bathurst, Banks, Melville) and there was one instance where it outcompeted all the available modelling constructs (Boothia). Assigning model-specific weights was proven to be a somewhat less effective ensemble strategy, but still maintained a balanced error across the six island complexes and resulted in fairly high r2 (=0.673) and low RMSE (1.589±0.131) values (Table 5.2).

The differences between individual and ensemble predictions are illustrated for each island complex for the last year of our study period (1985-2007) when Peary caribou population records were available (Figure 5.4). According to Kaluskar et al. (2020), the Peary caribou population was approximately 1,400 animals on Banks island complex in 2005, which was fairly close to the median prediction of 1,240 (90% CI: 799-1,957) from Model 1, followed by the prediction of 1,373 (90% CI: 587-3,460) from Model 4. By contrast, Models 2 and 3 profoundly overestimated

the empirical estimate on Banks island complex suggesting population levels of 2,882 (90% CI: 1,310-7,005) and 3,270 (90% CI: 1,380-6,089), respectively. Building upon these predictions and the corresponding island complex-specific or overall model performances, Ensembles 1 and 2 moderated the degree of overestimation of the latter two models, suggesting population levels of 2,377 (90% CI: 1,612-3,792) and 2,328 (90% CI: 1,608-3,607). Consequently, the predicted probability of exceedance of 1,000 Peary caribou on Banks Island was nearly 100% during the year of 2005. To put these predictions into perspective, the populations registered on the same island complex from subsequent surveys in 2010 and 2014 were 1,654 and 4,074, respectively (Kaluskar et al., 2020). In the same context, the empirical estimates on Axel Heiberg during the 2005-2006 period were approximately 1,300 animals (Kaluskar et al., 2020), which was also corroborated by the Peary caribou numbers presented by Jenkins et al. (2011). Nonetheless, Kaluskar et al. (2020) projected more than 9,000 Peary caribou in 2007, stemming from Jenkins et al.’s (2011) report of 2,255 animals on Axel Heiberg Island and an imputed value of over 7,000 on Ellesmere Islands. Even though it has been included for the training exercise of the four models, the latter value should be viewed with caution, given that it is nearly seven times higher than the caribou counts registered in 2005 and 2006 on the same island complex. The predictions of the four models ranged from 1,586 (90% CI: 475-5,366; Model 1) to 5,616 (90% CI: 2,202-14,796; Model 2), while the two mean ensemble predictions were 3,516 (90% CI: 2,009-6,617) and 3,775 (90% CI: 2,206-6,923), respectively. Interestingly, data from a subsequent survey by Anderson and Kingsley (2015) in 2015 combined with Kaluskar et al.’s (2020) imputed estimates led to population numbers that were comparable to the lower bounds of the two ensemble predictions.

The Peary caribou population on Boothia island complex (Boothia, Prince of Wales, Somerset, and Russell Islands) has experienced a dramatic decline over the course of the past 30 years (Gunn et al., 2006; Johnson et al., 2016). Specifically, the sum of imputed and survey data suggested that their population varied anywhere between 4,900 to 6,500 during the mid-1970s (Kaluskar et al.’s 2020), but reached critically low numbers, near to extirpation, in the early 2000s (Dumond, 2006; Jenkins et al., 2011). Among the four models developed, only Models 1 (261 and 90% CI of 61-950) and 2 (26 and 90% CI of 12-57) provided similar ominous predictions in 2006, and so did the Ensemble 1 (390 and 90% CI of 232-733). On the other hand, Ensemble 2 was more influenced by the overestimation bias of Model 4, and therefore the predicted range was somewhat higher (685 and 90% CI of 414-1,238). In Melville island complex, the total population size varied

between 2,385 and 5,240 during the mid-1970s, but was reduced down to 480-1,460 during the mid-1980s (Miller, 1988; Johnson et al., 2016) and remained within the same range (≈900) according to a subsequent survey in 1997 (Gunn and Dragon, 2002). Models 2 (891 and 90% CI: 418-1,894) and 4 (1,043 and 90% CI: 498-2,243) provided predictions that were close to the 1997 empirical population estimate. Being primarily influenced by the same models (see corresponding RMSE values in Table 5.2), Ensemble 1 predicted a median population size of 1,741 (90% CI: 1,206-2,519), whereas Ensemble 2 distinctly overestimated the population levels (2,163 and 90% CI: 1,458-3,260) mainly due to the greater influence of Model 1. Interestingly, the most recent survey in 2012 amounted to 6,700 caribou over the entire complex (Davison and Williams, 2012), indicative of the recent Peary caribou increased population size in that area.

The Bathurst island complex is an important eco-unit for Peary caribou due to its importance as a caribou hunting area for the community of Resolute Bay (Miller, 1995), the lead-zinc deposits on Bathurst and Little Cornwallis, and the activities related to oil and gas exploration and development (Taylor, 2005). According to Jenkins et al. (2011), their populations displayed a steep decline after the early 1990s and reached an all-time low of about 100 caribou in 1997, which was attributed to the increased caribou mortality caused by the severe winter and spring conditions during those years (Miller and Gunn, 2003). Consistent with Jenkins et al.’s (2011) projections though, this analysis provides evidence of recovery after the early 2000s, as even the most conservative Models 1 (1,580 and 90% CI of 309-8,209) and 4 (1,544 and 90% CI of 781-3,072) were suggestive of the likelihood of a recent increase. Interestingly, the range delineated by the two median ensemble predictions 2,968-3,262 was on par with the Peary caribou number (≈2,700) registered in a subsequent survey on the same island complex (Anderson, 2014; Johnson et al., 2016; Kaluskar et al., 2020). Consistent with the available population record (<100) on Mackenzie King island complex during the last survey year (1997) of the study period, the four models coalesced with respect to their individual and ensemble median predictions (<200-250).

5.3.4 Assessing the relationship between Peary caribou population predictions and observation/imputation errors. To put these results into perspective, the robustness of the predictions of the four models 2 2 were evaluated against the sampling/observation (휎표푏푠) and imputation (휎푖푚푝) errors of the Peary caribou dataset. With a simple one-at-a-time (OAT) sensitivity analysis exercise, I double/halved the observation and imputation error variance and then calculated the Euclidean distances between

the median values of model predictions (푁̂푃퐶) from the empirical population estimates (푁푃퐶) and the latent "true" Peary caribou population (푁푃퐶푡푟푢푒) sizes (Table 5-4). The first important result from this exercise was that the influence of the magnitude of the imputation error 2 (휎푖푚푝=3.881±0.789; see also Table 2 in Kaluskar et al. 2020) on the Euclidean distance values was relatively minor, relative to the model sensitivity displayed after modulating the observation/sampling error of the Peary caribou dataset (Gunn and Poole, 2014; Johnson et al., 2016; Kaluskar et al., 2020). That is, increasing the degree of confidence to our dataset is more impactful with respect to the model training and posterior patterns derived, relative to the gains from the development of a better imputation model.

In the same context, higher fidelity data (or reduced observation error) decreased the distance between model predictions and observations without any discernible difference among the responses of the four models. In stark contrast, the distance between model predictions and “true” population size increases when a reduced observation error is assigned to characterize the uncertainty of the Peary caribou data. This finding reinforces earlier work (Ramin and Arhonditsis, 2013; Wellen et al., 2014) that higher confidence (or lower error) to the data reduces the leeway of the latent variable “true” population to divert from the mean observation values, and therefore most of the information contained in the dataset is used to guide the parameter estimation exercise and improve the model fit. On the other hand, higher observation error allows greater excursions of the stochastic node “true” values from the observed data, and consequently reduces the amount of information that is allocated to optimize the model structure. In particular, the degree of change of the first and second order moments of the posterior distributions of the regression coefficient associated with the snow effect on Peary caribou population size was calculated (Figure 5-5). Reducing by half the observation error variance assigned to our dataset resulted in an average reduction of 6% of the posterior standard deviation and anywhere between 1 to 30% of the corresponding posterior mean values. In a similar manner, doubling the observation error variance increased on average the posterior standard deviation by 8% and led to the posterior means that varied anywhere from 1 to 45%. Thus, while it is important to explicitly consider the errors associated with the available Peary caribou population data and avoid overinflating their value of information, it is equally critical to not misleadingly underestimate their fidelity by assigning

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unrealistically high error estimates that can hinder the identification of important cause-effect relationships.

Forage availability and accessibility are the primary factors that determine habitat selection of Peary caribou. Given that the ground in the Canadian Arctic Archipelago is covered by snow for nearly ten months of the year, the key habitat requirement involves the terrain and vegetation features that offer options to maximize access to forage, whereas plant phenology is likely the key determinant of forage availability during the short snow-free period. In this study, I examined two hypotheses related to the presence of a distinct negative relationship between Peary caribou population size and snow and a positive one with vegetation abundance. Using SWEI as a surrogate variable of the snow severity in the Canadian Arctic Archipelago on an annual basis, our analysis was successful to tease out a strong negative signature on Melville, Axel Heiberg, and Banks, but less so on Boothia, Bathurst, and MacKenzie King island complexes. Likewise, the positive relationship NDVI (proxy for vegetation abundance) and Peary caribou was evident on Melville and Bathurst, but was weaker on the rest island complexes and there were even instances where the sign of that relationship switched to negative. Possible explanations for the moderate degree of identification of the slopes related to the snow effect and vegetation abundance on the year-to- year caribou variability is likely the fidelity of the explanatory variables used in approximating their role, as well as the presence of other confounding factors that could potentially modulate their signal (Johnson et al., 2016; Kaluskar et al., 2020). In the next iteration of our modelling framework, it is thus critical to explicitly account for the role of the following factors that can demonstrably shape the integrity and behavioral patterns of Peary caribou populations.

 Forage accessibility in winter is not only affected but the amount and duration of snow, but also from the occurrence of rain-on-snow and thaw-freeze events, which cause ice formation on top or within the snow pack and are expected to increase in frequency and severity with warmer and wetter winters (Hansen et al., 2011; Larsen et al., 2014). Recent work by Langlois et al. (2017) has shown that three or four rain-on-snow and one or two icing events can have a significant negative impact on Peary caribou numbers, and can be a critical predictor variable for any forecasting exercise. In the same context though, Hansen et al. (2019) offered a somewhat different perspective suggesting that extreme rain-on-snow events mainly suppress vital rates of vulnerable ages at high population densities, resulting in the emergence of a new

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population state with resilient ages and reduced population sensitivity to subsequent severe winters. Thus, more frequent rain-on-snow events may actually reduce extinction risks and stabilize population dynamics due to the buffering capacity of internal density-dependent feedbacks.  Peary caribou use sea ice as a corridor between islands to migrate between winter and summer ranges and to access traditional calving areas. Inter-island movements can also be beneficial on occasions to escape severe weather conditions. Physical or human-related barriers that prevent movements between islands could reduce foraging efficiency and reproductive success, with dire repercussions for the genetic flow and diversity (Jenkins et al., 2018; Malory and Boyce, 2019). Changes in the ice phenology, such as delays to ice formation and decreased thickness, can elevate the mortality risks from drowning during migration but may also increase the energetic expenditures in their effort to access desirable forages (Miller et al. 2005). Improvement in the dataset pertinent to the extent, duration and thickness of sea ice would be helpful in reducing some of the uncertainty of habitat model predictions.  The prospect of a prolonged growing season with a warmer climate is projected to increase vegetation productivity/biomass and forage availability during a critical time of the Peary caribou life-cycle (Hudson and Henry, 2009; Jia et al., 2009; Xu et al., 2013), and can therefore increase summer fat accumulation and consequently improve reproductive rates and winter survival. However, while increased biomass could provide additional forage for Peary caribou, empirical evidence and theoretical predictions suggest that the increases in vegetation biomass in the Arctic will occur in favor of evergreen shrubs and bryophyte biomass expansion and less so through an increase of more nutritionally desirable staples of their diet, such as deciduous shrubs, forbs, lichens or graminoids (Hudson and Henry, 2009; Fauchald et al., 2017). With the prospect of shrub expansion, caribou will likely have to cope with their greater structural and chemical defense mechanisms against herbivores along with a lower protein intake, which are likely to offset the projected benefits of increased vegetation biomass (Thompson and Barboza, 2014). It is thus critical to establish a suitable proxy variable that will account for the role of forage quality on the integrity and sustainability of Peary caribou populations alongside with the forage quantity. From a technical standpoint, this modelling framework had three distinct features (hierarchical structure, consideration of the observation/imputation error, ensemble formulations)

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in order to account for different facets of the year-to-year variability of Peary caribou in the Canadian Arctic Archipelago. (i) The hierarchical configuration not only allowed accommodating the differences of the habitat conditions among the different island complexes, but also facilitated the modelling of areas that are understudied (e.g., Axel Heiberg, Mackenzie) by borrowing information from neighboring locations (e.g., Banks, Bathurst), where adequate population data exist, on the basis of global (Arctic-wide) parameters (Ellison, 2004; Cheng et al., 2010; Shimoda and Arhonditsis, 2015). (ii) The explicit consideration of the observation/imputation errors pertaining to the Peary caribou dataset is a conceptually sound approach to recognize that the information used to guide the parameter estimation is based on imperfect empirical population estimates. However, our analysis showed that the error values assigned must be assigned with caution, as the assumptions regarding the data credibility may impede the delineation of cause- effect relationships and could influence the degree of parameter identification. (iii) Considering that this study is based on simple empirical models, which by designation represent drastic simplifications of the natural population dynamics, the adoption of an ensemble strategy represents an effective way to capitalize upon the structural strengths and overcome the weaknesses of multiple competing models. A characteristic example of the necessity to consider multiple models with distinct structural features was the fact that the highest-performing Model 2, postulating monotonic population change over time, may not have been the most favorable, if our study had included the most recent survey data. In fact, given the tendency of Peary caribou populations to display wax-and-wane cycles, the evolving structure of Model 4 that allows accommodating non- monotonic patterns makes it an essential member of any future ensemble exercise. The evolving nature of the interplay between the environment and population dynamics provides the best evidence that we cannot base ecological forecasts on a single model.

The decision-making process admittedly gravitates towards mechanistic, bottom–up simulation models, when addressing complex problems like the recovery of natural animal populations and protection of species-at-risk. After all, their foundation upon the mathematical description of ecophysiological processes and behavioral patterns pertaining to their life cycles (e.g., calving, foraging, migration) provides assurance that these models are better equipped to draw predictions and formulate theories about the interplay among human disturbances, climate variability, inter-specific competition, and higher predation (Tews et al., 2007a). However, the presence of an empirical modelling framework is a worthwhile activity and can assist the on-going

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recovery efforts of Peary caribou populations in a meaningfully way. Data-driven models not only provide predictive statements confined within the bounds of data-based parameter estimation, but also delineate critical consumer-resource/abiotic environment relationships and pinpoint areas where field-scale experimentation can allow the characterization of critical ecophysiological processes (Elmendorf et al., 2012 a, b). Thus, they can be used as complementary tools to complex mathematical models to constraint their processes or improve parameterizations, and put the ecological forecasts drawn into perspective.

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Table 5-1 Classification of the Canadian Arctic Archipelago into six island groups along with the years surveyed and imputed (Kaluskar et al., 2020) for each island complex. Because of the NDVI data availability the study period (1985-2007).

Island Islands Years surveyed Complex and imputed Banks Banks, 1970, 1971, 1972, 1980, 1982, Northwest 1985, 1987, 1989, 1991, 1992, Victoria 1993, 1994, 1998, 2001, 2005, 2010, 2014 Axel Axel Heiberg, 1989, 2005, 2006, 2007, Ellesmere 2015 Boothia Boothia, Prince 1974, 1975, 1976, 1980, of Wales, 1985, 1995, 1996, 2004, Somerset, 2006 Russell Melville Melville, Prince 1972, 1973, 1974, 1986, Patrick, Byam 1987, 1997, 2012 Martin, Emerald, Eglinton Bathurst Bathurst, 1973, 1974, 1985, 1988, Cornwallis, 1990, 1991, 1992, 1993, Helena 1994, 1995, 1996, 1997, 2001, 2002, 2013 Mackenzie King Mackenzie King, 1973, 1974, 1997 Borden, Brock

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Table 5-2 Performance of the four models examined to reproduce the year-to-year Peary caribou variability within the six island groups of the Canadian Arctic Archipelago.

Measures Location Model 1 Model 2 Model 3 Model 4 Ensemble 1 Ensemble 2 of fit Overall σmod 0.633±0.233* 1.269±0.132 1.627±0.153 1.391±0.125 r2 0.481 0.632 0.373 0.614 0.738 0.673 DIC 274.1±12.6* 322.3±11.8 336.8±13.6 330.1±12.1 RMSE 1.348±0.162 1.310±0.133 1.689±0.165 1.404±0.145 1.394±0.122 1.589±0.131 RMSE Banks 0.872±0.072 0.729±0.068 1.077±0.101 0.887±0.085 0.885±0.082 0.892±0.081 RMSE Axel Heiberg 0.954±0.104 1.225±0.135 1.337±0.114 2.761±0.122 1.099±0.102 1.206±0.118 RMSE Boothia 5.589±0.184 1.645±0.148 6.549±0.358 3.588±0.201 1.515±0.136 2.232±0.185 RMSE Melville 1.471±0.108 0.951±0.101 1.864±0.171 0.995±0.112 1.361±0.115 1.610±0.114 RMSE Bathurst 1.274±0.085 2.552±0.187 2.755±0.168 2.005±0.126 1.580±0.116 1.575±0.118 RMSE Mackenzie King 0.852±0.128 0.555±0.098 0.568±0.097 0.737±0.099 0.946±0.109 0.922±0.103 *Based on annual population data lumped per island complex, whereas the rest of the measures of fit refer to individual islands.

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Parameter Model 1 Parameter Model 2 Parameter Model 3 Parameter Model 4 SWEI λ1 0.94±0.01 β1,1 -0.15±0.60 β1,1 -0.72±0.77 β1,1 -0.18±0.67 λ2 1.07±0.06 β2,1 -0.43±0.54 β2,1 -0.41±0.51 β2,1 -0.35±0.53 λ3 0.98±0.02 β3,1 -0.06±0.36 β3,1 -0.77±0.46 β3,1 -0.40±0.41 λ4 0.91±0.03 β4,1 -0.01±0.29 β4,1 -0.33±0.33 β4,1 -0.14±0.31 λ5 0.97±0.04 β5,1 -0.04±0.30 β5,1 -0.15±0.34 β5,1 -0.06±0.31 λ6 1.03±0.09 β6,1 -0.66±1.81 β6,1 -0.57±1.54 β6,1 -0.44±1.32 NDVI β1,2 -0.06±0.47 β1,2 0.26±0.55 β1,2 -0.01±0.52 β2,2 -0.06±0.29 β2,2 0.02±0.32 β2,2 -0.15±0.29 β3,2 0.41±0.65 β3,2 2.39±0.99 β3,2 1.27±0.98 β4,2 -0.22±0.33 β4,2 -0.03±0.40 β4,2 -0.15±0.36 β5,2 0.42±0.43 β5,2 0.59±0.42 β5,2 0.16±0.36 β6,2 1.38±2.88 β6,2 1.31±2.18 β6,2 0.85±1.97 Time β1,3 -0.11±0.05 β2,3 0.03±0.08 β3,3 -0.33±0.05 β4,3 -0.23±0.07 β5,3 -0.09±0.06 β6,3 -0.14±0.38 Intercept β1,0 -3.04±0.67 β1,0 -4.54±0.64 β1,0 -4.48±0.58 β2,0 -4.21±1.80 β2,0 -4.19±0.78 β2,0 -3.67±0.92 β3,0 -2.45±0.73 β3,0 -6.09±0.65 β3,0 -6.04±0.63 β4,0 -3.19±0.52 β4,0 -4.49±0.47 β4,0 -5.04±0.52 β5,0 -2.73±0.52 β5,0 -3.38±0.40 β5,0 -3.86±0.38 β6,0 -3.34±4.42 β6,0 -4.73±1.24 β6,0 -4.67±1.15

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풍풏 (푵푷푪풋,풕) Model 1 Model 2 Model 3 Model 4 − 풍풏 (푵̂ 푷푪풋,풕) 흈ퟐ 0.011 0.012 0.008 0.010 풐풃풔 ퟐ 흈ퟐ 0.025 0.029 0.028 0.027 풊풎풑 ퟐ Reference 0.031 0.034 0.028 0.029

ퟐ ퟐ ∙ 흈풊풎풑 0.032 0.036 0.031 0.031

ퟐ ퟐ ∙ 흈풐풃풔 0.094 0.095 0.095 0.074

풍풏 (푵 ) Model 1 Model 2 Model 3 Model 4 푷푪풕풓풖풆풋,풕 − 풍풏 (푵̂ 푷푪풋,풕) 흈ퟐ 0.238 0.217 0.282 0.262 풐풃풔 ퟐ ퟐ 흈풊풎풑 0.228 0.208 0.268 0.251

ퟐ Reference 0.245 0.202 0.267 0.256

ퟐ ퟐ ∙ 흈풊풎풑 0.247 0.203 0.269 0.269

ퟐ ퟐ ∙ 흈풐풃풔 0.191 0.151 0.151 0.212

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Figure 5-1 Map of the Canadian Arctic Archipelago and application of the Bayesian hierarchical framework to allow the transfer of information across the six island complexes.

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Chapter 6 Conclusions and Future Perspectives 6.1 Purpose of the Dissertation The overarching goal of my thesis was to establish a modelling framework that will address Peary caribou data gaps and will subsequently allow to delineate population trends over time across the Canadian Arctic Archipelago. My dissertation had five major objectives: (i) to develop a novel imputation model for infilling Peary caribou data; (ii) to determine the Peary caribou population temporal patterns across all the major island complexes in CAA; (iii) to characterize year-to-year variability of habitat conditions and recreate local population growth rates using climatic variables and landscape features; and (iv) to develop an ensemble modelling framework that allows to depict the relationship (and associated uncertainties) between environmental factors and Peary caribou populations. My work first offers a much-needed methodology to address the problem of missing data with Peary caribou populations. In this regard, one of the fundamental assumptions is the distinction between islands that act as the core areas from where Peary caribou migrate from, defined as "Primary", and islands where their populations migrate to, defined as "Secondary” and/or "Satellite”. In doing so, I postulated that the population trends in the Secondary and Satellite islands are closely associated with the trends in the Primary islands. Next, I developed multiple stochastic models to estimate population growth rates at a local scale and examined the ability of a suite of predictor variables to recreate Peary caribou occurrences for the summer seasons of each year between 2000 and 2013. This stochastic framework offered a regional characterization of Peary caribou activity in relation to climatic conditions and landscape characteristics, and can therefore form the basis for the development of a comprehensive habitat suitability tool in CAA. My final chapter presented a novel attempt to use multiple models with varying degrees of complexity to elucidate the causal linkages between weather conditions, vegetation abundance, and Peary caribou population trends in space and time. 6.1.1 Purpose and Key Findings of Chapter 3 The purpose of the third chapter was to address the problem of missing data with Peary caribou populations based on the hypothesis that Peary caribou numbers in any given secondary island are influenced by the population in the corresponding primary island. To accomplish this feat, I proposed an imputation method, which was founded on an empirical regression model. I used the population of the primary islands, the areal ratio of the pair of islands considered, and

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time, as the main predictors to characterize the Peary caribou population in secondary and/or satellite islands (Kaluskar et al., 2020). The explicit consideration of several important covariates to capture co-dependencies in time and space offered an excellent opportunity to understand the spatiotemporal patterns underlying the Peary caribou population data in CAA from 1970-2015. Next, I used the exponential growth model to project population rates of change before and after the imputation. Mean estimates of the island-specific population rates of change were not affected by the consideration or not of imputed data and were remarkably consistent. The same chapter also presented a Bayesian hierarchical configuration of the exponential model using both imputed and observed data along with the associated errors to predict the Peary caribou population growth rates within six distinct island complexes in the CAA from 1970-2015. My analysis provided evidence that the two islands (Banks and Northwest Victoria) of the Banks island complex were characterized by an average decline rate of 6% per year over the past four decades, which collectively reflects the dramatic population decrease from the early 1970s until the late 1990s, as well as the distinct recovery after the early 2000s. Similar “wax-and-wane” cycles characterize the Peary caribou population patterns on Melville and Bathurst island complexes. My analysis predicted positive rate of change of the Peary caribou population trends on Axel Heiberg and Ellesmere Islands, whereas a dramatic decline, nearing their extirpation, is registered on the Boothia island complex owing to overharvesting, higher predation, adverse climatic conditions, and limited forage availability. The novel features of my work, such as the ability to transfer information in both time and space, and the rigorous uncertainty assessment stemming from different sources, including the imputation error, may also influence the modelling practice in other scientific disciplines, when researchers are faced with severe data limitation problems. 6.1.2 Purpose and Key Findings of Chapter 4 The purpose of the fourth chapter was to elucidate the spatiotemporal patterns of Peary caribou activity in CAA, using climatic and landscape variables. An important feature of this study was the integration of scientific and empirical (Indigenous) knowledge to characterize the Peary caribou habitat conditions (Kaluskar et al., 2019a). Factor analysis was first conducted with a suite of climatic and landscape variables, to tease out any commonalities, and thus reduce the number of candidate predictors for each complex across the CAA. A two-pronged approach was developed to characterize the year-to-year variability of the Peary caribou habitat conditions across the CAA. First, a Bernoulli-logistic model based on a subset of predictor variables examined the likelihood of presence of Peary caribou within a particular habitat from 2000-2013. In the next step, the

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aforementioned estimates of the habitat suitability (or forage accessibility) were used to sample over the uncertainty associated with the Peary caribou population rates of change, as derived by the Bayesian hierarchical exponential model (Kaluskar et al., 2020), to identify locations where Peary caribou could experience more than 25% (or 50%) decrease relative to the population levels at the beginning of the study period. Consistent with the previous modelling results, this analysis also identified the Boothia island complex as a high-risk area, where the likelihood of a strong Allee effect could lead to extinction after episodic weather-related events or elevated incidental predation. My stochastic framework also suggests that the prevailing habitat conditions in Melville and Bathurst island complexes were generally favorable and could partly explain the recent Peary caribou population increase. My study concludes by identifying other unaccounted factors (e.g., higher predation, human disturbance, vegetation quantity and quality) that could further improve any future efforts to build an empirical modelling framework with quasi-mechanistic foundation and recreate the year-to-year forage accessibility in the Arctic environment. The effects of human- and climate-induced changes on the connectivity for both island-dwelling and mainland-migratory populations is another critical (unaccounted) factor in the dynamic landscape of the Canadian Arctic Archipelago. 6.1.3 Purpose and Key Findings of Chapter 5 The purpose of the fifth chapter was to identify population trends by evaluating the relationship between snow density, vegetation abundance, and Peary caribou abundance across CAA from 1985-2007. This chapter examined how a Bayesian ensemble approach can effectively support the decision making process by synthesizing the predictions of different models developed for the same system. I formulated four models with different strengths and weaknesses to understand the regional and seasonal variability of the associated causal linkages (i.e., vegetation, snow) with Peary caribou population dynamics in the CAA (Kaluskar et al., 2019b). The first model is the Bayesian hierarchical exponential growth model (Kaluskar et al., 2020), which was developed in the third chapter. The other three models explicitly accommodated the role of vegetation and snow based on different expressions of the relationship between the annual Peary caribou populations and their corresponding proxy variables NDVI and SWEI. These four models formed the basis of two ensemble strategies to obtain averaged predictions. In the first ensemble strategy, I weighted the projections of the four models by the corresponding model structural errors, whereas the projections with the second ensemble were weighted by the region-specific model performance values. According to my analysis, SWEI as a surrogate variable of the snow

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severity in the Canadian Arctic Archipelago on an annual basis was successful to tease out a strong negative signature on Melville, Axel Heiberg, and Banks, but less so on Boothia, Bathurst, and MacKenzie King island complexes. Similarly, the positive relationship NDVI (as a proxy for vegetation abundance) and Peary caribou was evident on Melville and Bathurst, but was weaker on the rest island complexes. From a technical standpoint, the presented modelling framework has three distinct features (hierarchical structure, consideration of the observation/imputation error, ensemble formulations) in order to account for different facets of the year-to-year variability of Peary caribou in the Canadian Arctic Archipelago. In particular, the explicit consideration of the observation/imputation errors pertaining to the Peary caribou dataset is a conceptually sound approach to recognize that the information used to guide the parameter estimation is based on imperfect empirical population estimates. However, my analysis showed that these error values must be assigned with caution, as the assumptions regarding the data credibility may impede the delineation of cause-effect relationships and could influence the degree of parameter identification.

6.2 Future work My dissertation presents one of the first attempts to use statistical modelling and integrate the disparate pieces of knowledge regarding the Peary caribou ecophysiology and distribution patterns. While the present work satisfactorily captures the Peary caribou spatiotemporal trends, the predictability of future population trends is more challenging. Future research involving Peary caribou modelling should reflect the possible impact of anthropogenic activities, predation, extreme climate events, and vegetation on their habitat selection in CAA. Several unaccounted human factors, such as shipping traffic and resource extraction (mining and oil and gas), past and present human infrastructure impact the Peary caribou habitat selection, and their population dynamics (Johnson et al., 2016). Additionally, NDVI data or other available land cover classifications for the Arctic may not be adequate to describe the habitat and vegetation differences observed in the field. Therefore, the role of forage abundance is inaccurately represented in the current Peary caribou habitat models. Peary caribou population declines are likely due to a combination of factors including several years of unusually severe winter and spring weather, hunting, and predation (Johnson et al. 2016). Unfortunately, information regarding several of these factors is still very limited. Thus, an essential augmentation of the present modelling framework should revolve around elucidating the net effects of human disturbance, hunting, predation and, climate and extreme weather-related events on the floral phenology and Peary caribou population

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dynamics. Quantifying these impacts would be meaningful in reducing some of the uncertainties underlying the habitat model predictions and improve model predictive capacity. In the current research, atmospheric variables were obtained from SNOWPACK and CanRCM4 models. These models are extremely useful, as they provide datasets that recreate past and present conditions in CAA with finer spatiotemporal granularity. Reanalysis products are continuously developed that could offer a more credible foundation for retrospective analysis (Saha et al., 2010; Bosilovich et al., 2013; Stickler et al., 2014). Nonetheless, several assumptions are made during the modelling of the climate system, and thus reanalysis data are also subjected to biases (Kennedy et al., 2011; Stickler et al., 2014). Hence, it is imperative to explicitly consider the errors associated with the reanalysis-derived variables and re-evaluate their explanatory power. A comparison with sounding-derived variables may be a worthwhile exercise to quantify the bias of the different climatic predictors or spurious trends (Kennedy et al., 2011). To better model population viability, data on vital rates are necessary. According to Tews et al., (2007 a,b), adult (2+ years) and first-year (0-1 year) survival rates are highly influential in predicting Peary caribou extinction risks in the Bathurst Island complex. Various population modelling approach suggest that the proportion of females producing calves may also have a large impact on population growth rates (Gunn and Dragon, 1998). Future research quantifying variation in these three parameters with changing environmental conditions may yield the best knowledge gains for assessing the type of habitat required for the protection of Peary caribou populations. In the field of biological conservation and sustainability, ecological modelling has been placed at the central stage of understanding population dynamics. The majority of interacting systems in the real world are far too complicated to model in their entirety, but mathematical models come close to mirroring their complexity by accounting for most of the ecological processes that can potentially become important in future conditions. As recognized in Chapter 5, the decision-making process usually prefers mechanistic models, when addressing complex problems like the recovery of natural animal populations and protection of species-at-risk. Their foundation upon the mathematical description of ecophysiological processes and behavioral patterns pertaining to their life cycles provides assurance that these models are better equipped to draw predictions and formulate theories about the interplay among human disturbances, climate variability, inter-specific competition, and higher predation. Several contemporary wildlife- population models, focusing on various metrics and parameters, have been introduced as conservation-management tools. For example, notable approaches in agent-based modelling

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(Semeniuk et al., 2012) and REMUS models (Weclaw and Hudson, 2004) integrate animal memory and forage competition into their frameworks, respectively. Other sophisticated simulation models, which include top-down (i.e., predation, harvesting and disturbance) and bottom-up controls (i.e., forage accessibility, disturbance years and climate), have also been presented in the literature, e.g., PCSimMod (Peary Caribou Simulation Model) by Tews et al. (2007 a,b). Steep data-requirements are consistent among all complex mechanistic models, and while data are generally available for a range of species that require conservation efforts (e.g., census information, recapture studies, and surveys), they can be incomplete; spatially/temporally misleading; and diverse, ranging from abundance, to vital rates, to expert opinions. Given the limited data availability and rudimentary understanding of Peary caribou ecology, my dissertation proposed statistical modelling techniques as a first step to gain insights into meaningful causal relationships and identify key parameters. As a natural next step of the present work, I believe that an agent-based model will be a meaningful augmentation to capture agent diversity and spatial heterogeneity (Akçakaya, 2000; Castella et al., 2005; Bazghandi, 2012). Agent-based models address these issues by explicitly modelling the behaviour of each individual considered. This granularity can yield insights not possible with other methodologies, such as migration, and more generalized spatial behaviors. In addition, variability is intrinsic to agent-based models, as each individual adheres to a unique parameterization and developmental trajectory, whereas other models the population is treated as homogenous. Further, modelling density-dependent population dynamics is complicated, more so when considering life-stage-dependent vital rates. Agent-based models require extensive data for adequate parameterization, but implementing a fixed-age-based structure can simplify the process (Akçakaya, 2000; Semeniuk et al., 2012). Notwithstanding the fact that individual growth rates within a cohort can vary with genetic and environmental factors, chance, or a combination of all three, I believe that such a parsimonious agent-based modelling tool will be a meaningful augmentation of the current Peary caribou modelling work. The lessons learned from the present study can be used to constraint several of the associated parameters and more effectively recreate the complex behavioral patterns influencing this endangered species in the Canadian Arctic Archipelago.

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Figure S6 Relationships among longitude (oW), air temperature (oC) or time (2001-2013), and habitat suitability for Peary caribou populations in grid cells of the Ellesmere island

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with latitude lower than 77o 0’N (top panels). Year-to-year variability of the Pear caribou population rates of change in the same grid cells, according to the random-walk models that postulate the location-specific population growth rates to be a function of their counterparts in 2000 (initial year of our study) and the preceding year, respectively. The corresponding probability thresholds c* are set equal to 33% (middle panels) or 50% (bottom panels).

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Figure S7 Time series of Normalized Difference Vegetation Index (NDVI) for Axel Heiberg, Banks,

Boothia, Melville, Bathurst and McKenzie King island complexes standardized relative to a mean of

0.119 and standard deviation of 0.096 over the entire Canadian Arctic Archipelago during the 1985-

2007 study period.

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Appendix A2

Years Banks Axel Boothia Melville Bathurst Mackenzie 1985 0.108 0.252 0.054 0.044 0.136 0.023 1986 0.121 0.038 0.055 0.123 0.105 0.074 1987 0.115 0.337 0.060 0.060 0.191 0.037 1988 0.178 0.083 0.083 0.108 0.141 0.082 1989 0.170 0.252 0.074 0.071 0.059 0.047 1990 0.182 0.259 0.091 0.083 0.053 0.061 1991 0.151 0.276 0.081 0.076 0.112 0.069 1992 0.146 0.114 0.074 0.079 0.076 0.052 1993 0.150 0.146 0.073 0.098 0.051 0.053 1994 0.165 0.050 0.080 0.074 0.057 0.043 1995 0.172 0.280 0.101 0.096 0.067 0.082 1996 0.185 0.111 0.103 0.085 0.048 0.101 1997 0.170 0.197 0.086 0.078 0.068 0.052 1998 0.189 0.059 0.118 0.115 0.078 0.079 1999 0.180 0.053 0.120 0.113 0.078 0.085 2000 0.158 0.338 0.086 0.074 0.157 0.051 2001 0.149 0.480 0.058 0.069 0.070 0.011 2002 0.140 0.350 0.051 0.060 0.052 0.177 2003 0.141 0.648 0.071 0.072 0.042 0.018 2004 0.101 0.000 0.003 0.016 0.071 0.000 2005 0.079 0.517 0.120 0.155 0.172 0.434 2006 0.123 0.131 0.062 0.085 0.125 0.119 2007 0.214 0.177 0.140 0.138 0.121 0.099

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Years Banks Axel Boothia Melville Bathurst Mackenzie 1985 14.77 24.06 12.07 15.98 20.09 14.66 1986 16.99 27.80 16.97 16.43 25.45 17.59 1987 15.43 26.27 16.03 24.16 25.77 18.53

1988 17.93 27.64 11.82 23.41 26.37 22.89 1989 16.64 28.37 15.48 23.81 29.24 18.67 1990 16.99 30.50 15.75 22.36 21.07 18.18

1991 19.03 19.41 14.83 20.13 22.23 13.45 1992 16.23 23.38 14.81 16.03 19.96 14.14

1993 16.95 28.37 16.64 18.88 20.09 14.77 1994 17.56 20.02 13.78 18.96 22.24 21.15 1995 22.06 32.52 14.06 23.02 24.94 19.10

1996 11.63 17.95 15.21 11.92 19.26 10.11 1997 19.43 26.79 16.40 27.62 27.12 16.63 1998 20.95 25.72 11.80 19.70 21.10 18.00

1999 15.47 27.94 17.01 16.96 18.51 13.62 2000 14.26 23.76 17.92 16.09 20.48 15.86 2001 17.52 37.35 15.22 19.00 24.53 16.21

2002 13.69 46.38 14.52 20.26 19.29 14.61 2003 16.89 32.44 12.05 18.42 19.78 18.33 2004 17.20 39.26 19.49 24.86 26.08 23.18

2005 17.01 20.73 16.90 21.83 26.99 19.60 2006 17.65 28.18 24.16 18.19 20.54 17.53

2007 17.27 26.35 13.96 18.88 16.43 15.97