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Since its development, occupancy modeling has become a popular and useful tool for ecologists wishing to learn about the dynamics of species occurrence over time and space. Such models require presence–absence data to be collected at spatially indexed survey units. However, only recently have researchers recognized the need to correct for spatially induced overdisperison by explicitly accounting for spatial autocorrelation in occupancy probability. Previous efforts to incorporate such autocorrelation have largely focused on logit-normal formulations for occupancy, with spatial autocorrelation induced by a random effect within a hierarchical modeling framework. Although useful, computational time generally limits such an approach to relatively small data sets, and there are often problems with algorithm instability, yielding unsatisfactory results. Further, recent research has revealed a hidden form of multicollinearity in such applications, which may lead to parameter bias if not explicitly addressed. Combining several techniques, we present a unifying hierarchical spatial occupancy model specification that is particularly effective over large spatial extents. This approach employs a probit mixture framework for occupancy and can easily accommodate a reduced-dimensional spatial process to resolve issues with multicollinearity and spatial confounding while improving algorithm convergence. Using open-source software, we demonstrate this new model specification using a case study involving occupancy of caribou (Rangifer tarandus) over a set of 1080 survey units spanning a large contiguous region (108 000 km 2) in northern Ontario, Canada. Overall, the combination of a more efficient specification and open-source software allows for a facile and stable implementation of spatial occupancy models for large data sets.
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... Put simply, knowing that a species is present in one cell likely raises the probability of it being present in a neighbouring cell, even if the two locations have the same, or very similar, environmental covariates. The model presented here could be extended to also model spatial correlation, as was proposed for example in Johnson et al. (2013). ...
... Firstly, from a practical point of view, a spatial model would raise difficult computational challenges. Secondly, adding a spatial effect is also complicated by the problem of spatial confounding (Johnson et al., 2013;Hodges and Reich, 2010) which, summarised briefly, says that adding a spatial effect can cause bias in the estimates of the coefficients of a regression model. To address spatial confounding, the spatially-correlated errors are often modified to explain only variation not explained by the environmental covariates. ...
... In such a modified model, the estimated environmental coefficients have the same pos-terior means, but larger variances (see Figure 1 in Johnson et al. (2013), for example). ...
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Citizen science datasets can be very large and promise to improve species distribution modelling, but detection is imperfect, risking bias when fitting models. In particular, observers may not detect species that are actually present. Occupancy models can estimate and correct for this observation process, and multi-species occupancy models exploit similarities in the observation process, which can improve estimates for rare species. However, the computational methods currently used to fit these models do not scale to large datasets. We develop approximate Bayesian inference methods and use graphics processing units (GPUs) to scale multi-species occupancy models to very large citizen science data. We fit multi-species occupancy models to one month of data from the eBird project consisting of 186,811 checklist records comprising 430 bird species. We evaluate the predictions on a spatially separated test set of 59,338 records, comparing two different inference methods -- Markov chain Monte Carlo (MCMC) and variational inference (VI) -- to occupancy models fitted to each species separately using maximum likelihood. We fitted models to the entire dataset using VI, and up to 32,000 records with MCMC. VI fitted to the entire dataset performed best, outperforming single-species models on both AUC (90.4% compared to 88.7%) and on log likelihood (-0.080 compared to -0.085). We also evaluate how well range maps predicted by the model agree with expert maps. We find that modelling the detection process greatly improves agreement and that the resulting maps agree as closely with expert maps as ones estimated using high quality survey data. Our results demonstrate that multi-species occupancy models are a compelling approach to model large citizen science datasets, and that, once the observation process is taken into account, they can model species distributions accurately.
... The approach has been used in a wide variety of applications including species occupancy models in ecology (e.g. Hooten et al., 2003;Dorazio & Rodríguez, 2012;Johnson et al., 2013). ...
... We defined A as the adjacency matrix of sites in the unique Delaunay triangulation of the observation locations. The spatial random effect could be introduced at one of several locations in the hierarchical structure, but the most natural place is at the same level as the occupancy covariates (Johnson et al., 2013;Schmidt et al., 2015). Introducing the random effect in this way is convenient because ζ i has support given by the entire real line, and e ζ i may be interpreted as the extra multiplicative effect on the expected abundance at site i due to unobserved covariates. ...
... Buckland & Elston, 1993;MacKenzie et al., 2003;Royle & Kéry, 2007) and residual spatial dependence (e.g. Buckland & Elston, 1993;Hooten et al., 2003;Johnson et al., 2013). ...
Article
Binary regression models are ubiquitous in virtually every scientific field. Frequently, traditional generalised linear models fail to capture the variability in the probability surface that gives rise to the binary observations, and remedial methods are required. This has generated a substantial literature composed of binary regression models motivated by various applications. We describe an organisation of generalisations to traditional binary regression methods based on the familiar three‐part structure of generalised linear models (random component, systematic component and link function). This perspective facilitates both the comparison of existing approaches and the development of flexible models with interpretable parameters that capture application‐specific data‐generating mechanisms. We use our proposed organisational structure to discuss concerns with certain existing models for binary data based on quantile regression. We then use the framework to develop and compare several binary regression models tailored to occupancy data for European red squirrels (Sciurus vulgaris).
... As detection-nondetection data sources increase in both spatial extent and number of observed locations, accounting for spatial autocorrelation becomes increasingly more important (Guélat and Kéry, 2018). Accommodating sources of spatial dependency among observations is key to delivering valid inferences about species distributions and has led to the development of spatial occupancy models (Johnson et al., 2013;Hepler and Erhardt, 2021). Swanson et al. (2013), Jarzyna et al. (2014), Wright et al. (2021), and others have shown that including spatial dependence via spatially structured random effects can improve predictive performance in occurrence probabilities across a region of interest. ...
... In the context of SSOMs, MARK (White and Burnham, 1999), PRESENCE (Hines, 2006), and the R package unmarked (Fiske and Chandler, 2011) fit a variety of models for wildlife data under the frequentist paradigm, but lack functionality to account for spatial autocorrelation. The R packages stocc (Johnson et al., 2013), hSDM (Vieilledent, 2019), ...
... First, popular software packages used to fit occupancy models, such as MARK (White and Burnham, 1999), PRESENCE (Hines, 2006), and unmarked (Fiske and Chandler, 2011), lack functionality to account for spatial autocorrelation. Second, while there are a few available options to accommodate both spatial autocorrelation and imperfect detection (e.g., stocc ;Johnson et al. 2013), data sources are becoming increasingly large (e.g., eBird, BirdTrack, GBIF), potentially rendering current approaches as computationally infeasible. spOccupancy addresses these two concerns by providing user-friendly functions that fit a variety of spatial occupancy models, and by using NNGPs to ensure spatial occupancy models can be fit across locations that number in the 10s to 100s of thousands. ...
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Occupancy modeling is a common approach to assess spatial and temporal species distribution patterns, while explicitly accounting for measurement errors common in detection-nondetection data. Numerous extensions of the basic single species occupancy model exist to address dynamics, multiple species or states, interactions, false positive errors, autocorrelation, and to integrate multiple data sources. However, development of specialized and computationally efficient software to fit spatial models to large data sets is scarce or absent. We introduce the spOccupancy R package designed to fit single species, multispecies, and integrated spatially-explicit occupancy models. Using a Bayesian framework, we leverage P\'olya-Gamma data augmentation and Nearest Neighbor Gaussian Processes to ensure models are computationally efficient for potentially massive data sets. spOccupancy provides user-friendly functions for data simulation, model fitting, model validation (by posterior predictive checks), model comparison (using information criteria and k-fold cross-validation), and out-of-sample prediction. We illustrate the package's functionality via a vignette, simulated data analysis, and two bird case studies, in which we estimate occurrence of the Black-throated Green Warbler (Setophaga virens) across the eastern USA and species richness of a foliage-gleaning bird community in the Hubbard Brook Experimental Forest in New Hampshire, USA. The spOccupancy package provides a user-friendly approach to fit a variety of single and multispecies occupancy models, making it straightforward to address detection biases and spatial autocorrelation in species distribution models even for large data sets.
... 1-3, many extensions were developed to address model inadequacies. For example, to account for spatial dependence Johnson et al. (2013) added a correlated normally distributed site-level effect, η i (i.e., ðη 1 , η 2 , :::, η n Þ 0 ∼ N 0, Σ ð Þ; see ch. 26 in Hooten and Hefley 2019) to Eq. 3 that resulted in ...
... The approach by Johnson et al. (2013) has been effective in accounting for occupancy model inadequacies caused by traditional spatial dependence (e.g., Wright et al. 2019), which is assumed to have been generated from a correlated normally distributed random effect that imparts varying levels of smoothness on the spatial process. Discontinuities, abrupt transitions, and other "non-normal" spatial processes are common in ecological data, and the traditional spatial random effect may fail to capture such dynamics (e.g., Hefley et al. 2017). ...
... We applied our spatial occupancy modeling framework to the six synthetic data sets and compared the performance of four embedded machine learning approaches, which included regression trees, support vector regression, a low-rank Gaussian process, and a Gaussian Markov random field. The low-rank Gaussian process and Gaussian Markov random field are approaches that model traditional spatial dependence for data sets with a large number of sites and have been used in models for occupancy data (Johnson et al. 2013, Heaton et al. 2019. The regression tree and support vector regression are nontraditional approaches and may be capable of modeling nontraditional types of spatial dependence. ...
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Spatial models for occupancy data are used to estimate and map the true presence of a species, which may depend on biotic and abiotic factors as well as spatial autocorrelation. Traditionally researchers have accounted for spatial autocorrelation in occupancy data by using a correlated normally distributed site‐level random effect, which might be incapable of modeling nontraditional spatial dependence such as discontinuities and abrupt transitions. Machine learning approaches have the potential to model nontraditional spatial dependence, but these approaches do not account for observer errors such as false absences. By combining the flexibility of Bayesian hierarchal modeling and machine learning approaches, we present a general framework to model occupancy data that accounts for both traditional and nontraditional spatial dependence as well as false absences. We demonstrate our framework using six synthetic occupancy data sets and two real data sets. Our results demonstrate how to model both traditional and nontraditional spatial dependence in occupancy data which enables a broader class of spatial occupancy models that can be used to improve predictive accuracy and model adequacy.
... However, in this case, the spatial correlation is in the covariance of the nearby occupancy states, not their expected values, so occupancy covariates will not be useful. Explicit models for spatial correlation, including conditional auto-regressive models (Magoun et al. 2007), kriging (Pacifici et al. 2016), and restricted spatial regression (Johnson et al. 2013), should reduce the FPR, but they may not perform well with fewer detectors within a single year J o u r n a l P r e -p r o o f (i.e., sample size of detectors may be too small to accurately quantify spatial correlation). The most appropriate model to deal with this form of spatial dependence may be unmarked SCR , though this model often produces biased and/or very imprecise density estimates (Morin et al. this series) and are therefore unlikely to detect population declines with reasonable power. ...
... Both sources of dependence will be stronger at lower population densities where it is more likely that a single individual determines the occupancy states of multiple detectors across space and single detectors across time. Models to account for this spatio-temporal dependence exist, such as dynamic occupancy models (Banner et al. 2019) and/or occupancy models with spatial correlation in the occupancy process (Johnson et al. 2013). However, because we were interested in using realistic reserve sizes and realistically low population densities of Asian bears, we assumed the data sets for these populations will be too sparse to reliably fit the more complex models that can account for spatial correlation. ...
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Designing a population monitoring program for Asian bears presents challenges associated with their low densities and detectability, generally large home ranges, and logistical or resource constraints. The use of an occupancy-based method to monitor bear populations can be appropriate under certain conditions given the mechanistic relationship between occupancy and abundance. The form of the occupancy–abundance relationship is dependent on species-specific characteristics such as home range size and population density, as well as study area size. To assess the statistical power of tests to detect population change for Asian bears, we conducted a study using a range of scenarios by simulating spatially explicit individual-based capture-recapture data from a demographically open model. Simulations assessed the power to detect changes in population density via changes in site-level occupancy or abundance through time, estimated using a standard occupancy model or a Royle-Nichols model, both with point detectors (representing camera traps). We used IUCN Red List criteria as a guide in selection of two population decline scenarios (20% and 50%), but we chose a shorter time horizon (10 years = 1 bear generation), meaning that declines were steeper than used for IUCN criteria (3 generations). Our simulations detected population declines of 50% with high power (>0.80) and low false positive rates (FPR: incorrectly detecting a decline) (<0.10) when detectors were spaced at >0.67 times the home range diameter (home-range spacing ratio: HRSR, a measure of spatial correlation), such that bears would tend to overlap no more than two detectors. There was high (0.85) correlation between realized occupancy and N in these scenarios. The FPR increased as the HRSR decreased because of spatial correlation in the occupancy process induced when individual home ranges overlap multiple detectors. The mean statistical power to detect more gradual population declines (20% in 10 years) with HRSR >0.67 was low for occupancy models 0.22 (maximum power 0.67) and Royle-Nichols models (0.24; maximum power 0.67), suggesting that declines of this magnitude may not be described reliably with 10 years of monitoring. Our results demonstrated that under many realistic scenarios that we explored, false positive rates were unacceptably high. We highlight that when designing occupancy studies, the spacing between point detectors be at least 0.67 times the diameter of the home range size of the larger sex (e.g., males) when the assumptions of the spatial capture-recapture model used for simulation are met.
... Similarly, several advancements have been made for probit-link occupancy models accounting for spatial and spatio-temporal autocorrelation using efficient algorithms (Hepler & Erhardt, 2021;Johnson et al., 2013;Mohankumar & Hefley, 2022). Finally, implementing the PG scheme within a variational Bayes framework (Diana et al., 2021) leads to additional and substantial savings in computation time. ...
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1 There is increasing availability and use of unstructured and semi‐structured citizen science data in biodiversity research and conservation. This expansion of a rich source of ‘big data’ has sparked numerous research directions, driving the development of analytical approaches that account for the complex observation processes in these datasets. 2 We review outstanding challenges in the analysis of citizen science data for biodiversity monitoring. For many of these challenges, the potential impact on ecological inference is unknown. Further research can document these impacts and explore ways to address them. In addition to outlining research directions, describing these challenges may be useful in considering the design of future citizen science projects or additions to existing projects. 3 We outline challenges for biodiversity monitoring using citizen science data in four partially‐overlapping categories: challenges that arise as a result of 1) observer behaviour; 2) data structures; 3) statistical models; and 4) communication. Potential solutions for these challenges are combinations of: a) collecting additional data or metadata; b) analytically combining different datasets; c) developing or refining statistical models. 4 Whilst there has been important progress to develop models that tackle most of these challenges, there remain substantial gains in biodiversity monitoring and subsequent conservation actions that we believe will be possible by further research and development in these areas. The degree of challenge and opportunity that each of these presents varies substantially across different datasets, taxa, and ecological questions. In some cases, a route forward to address these challenges is clear, whilst in other cases there is more scope for exploration and creativity.
... Further interpretation of the spatial structure should clarify the relative importance of endogenous versus exogenous processes, but for now we emphasize that residual structure is still present and should be accounted for in a distribution map of the species. Neglecting spatial contagion easily leads to biased parameter estimates, potentially resulting in erroneous maps (Guélat & Kéry, 2018;Johnson et al., 2013). ...
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Aim Mapping species distributions is a crucial but challenging requirement of wildlife management. The frequent need to sample vast expanses of potential habitat increases the cost of planned surveys and rewards accumulation of opportunistic observations. In this paper, we integrate planned-survey data from roost counts with opportunistic samples from eBird, WikiAves and Xeno-canto citizen-science platforms to map the geographic range of the endangered Vinaceous-breasted Parrot. We demonstrate the estimation and mapping of species occurrence based on data integration while accounting for specifics of each dataset, including observation technique and uncertainty about the observations. Location Argentina, Brazil and Paraguay. Methods Our analysis illustrates (a) the incorporation of sampling effort, spatial autocorrelation and site covariates in a joint-likelihood, hierarchical, data integration model; (b) the evaluation of the contribution of each dataset, as well as the contribution of effort covariates, spatial autocorrelation and site covariates to the predictive ability of fitted models using a cross-validation approach; and (c) how spatial representation of the latent occupancy state (i.e. realized occupancy) helps identify areas with high uncertainty that should be prioritized in future fieldwork. Results We estimate a Vinaceous-breasted Parrot geographic range of 434,670 km², which is three times larger than the “Extant” area previously reported in the IUCN Red List. The exclusion of one dataset at a time from the analyses always resulted in worse predictions by the models of truncated data than by the Full Model, which included all datasets. Likewise, exclusion of spatial autocorrelation, site covariates or sampling effort resulted in worse predictions. Main conclusions The integration of different datasets into one joint-likelihood model produced a more reliable representation of the species range than any individual dataset taken on its own, improving the use of citizen-science data in combination with planned-survey results.
Article
Monitoring rare and elusive carnivores is inherently challenging because they often occur at low densities and require more resources to effectively assess status and trend. The fisher (Pekania pennanti) is an elusive mesocarnivore endemic to North America; in its western populations it is classified as a species of greatest conservation need. During winter of 2018–2019, we deployed remotely triggered cameras in randomly selected, spatially balanced 7.5‐km × 7.5‐km grid cells across a broad study area in western Montana, Idaho, and eastern Washington, USA. As part of this large‐scale, multi‐state monitoring effort, we conducted an occupancy assessment of the Northern Rocky Mountain fisher population at a range‐wide scale. We used non‐spatial occupancy models to determine the current extent of fisher occurrence in the Northern Rocky Mountains and to provide baseline occupancy estimates across a broad study area and a refined sampling frame for future monitoring. We used a spatial occupancy model to determine patterns in fisher occurrence across their Northern Rocky Mountain range while explicitly correcting for spatially induced overdispersion. Additionally, we assessed factors that influenced fisher occurrence through covariate occupancy modeling that considered predicted fisher habitat, site‐level environmental characteristics, and the influence of available harvest records (incidental and regulated). We detected fishers in 32 out of 318 (10%) of our surveyed cells, and estimated that overall, 160 (14%; 95% CI = 115–218) of 1,143 grid cells were occupied by fishers. Fisher occupancy was positively associated with our stratum that contained cells with a greater proportion of predicted fisher habitat and with proximity to nearest 2000–2015 harvest location. Fisher occupancy was weakly and positively associated with increased canopy cover. Our spatial model identified 2 areas with higher predicted occupancy: a large area across the Idaho Nez Perce‐Clearwater National Forest, and a smaller area in the Cabinet Mountain Range crossing the northern border of Idaho and Montana. We used spatial occupancy results from our original sampling frame to create a biologically derived refined sampling frame for future monitoring. Within the bounds of our refined sampling frame, we estimated that 155 (22%; 95% CI = 110–209) of 700 grid cells were occupied by fishers. By incorporating our increasing understanding of fisher habitat with contemporary analytical techniques, we defined current range‐wide occupancy of the Northern Rocky Mountain fisher population, identified core areas of fisher occurrence for future conservation efforts, and used our model results to create a refined sampling frame for future fisher monitoring in the Northern Rocky Mountains. We provide occupancy and detection probability data from the first multi‐state, range‐wide study of the Northern Rocky Mountain fisher population. We provide baseline data for comparison against future fisher surveys as well as a study design and protocol to conduct future surveys.
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Joint species distribution models have become ubiquitous for studying species-habitat relationships and dependence among species. Accounting for community structure often improves predictive power, but can also alter inference on species-habitat relationships. Modulated species-habitat relationships are indicative of community confounding: The situation in which interspecies dependence and habitat effects compete to explain species distributions. We discuss community confounding in a case study of mammalian responses to the Colorado bark beetle epidemic in the subalpine forest by comparing the inference from independent single species distribution models and a joint species distribution model. We present a method for measuring community confounding and develop a restricted version of our hierarchical model that orthogonalizes the habitat and species random effects. Our results indicate that variables associated with the severity and duration of the bark beetle epidemic suffer from community confounding. This implies that mammalian responses to the bark beetle epidemic are governed by interconnected habitat and community effects. Disentangling habitat and community effects can improve our understanding of the ecological system and possible management strategies. We evaluate restricted regression as a method for alleviating community confounding and distinguish it from other inferential methods for confounded models.
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Tourism is increasing in tundra ecosystems across the world, yet its influence on bird communities and its interaction with other drivers of change is poorly known. To help fill this gap, we paired an interview‐based survey of eleven people with local knowledge of Denali National Park and Preserve, with an occupancy study of 15 bird species in relation to road proximity, traffic volume, and hiking. Interviewees noted declines in American Golden Plover Pluvialis dominica, Arctic Tern Sterna paradisaea, Long‐tailed Jaeger Stercorarius longicaudus, and Northern Wheatear Oenanthe oenanthe over the past five decades. Our occupancy study confirmed these reports as we detected no Arctic Terns, few Northern Wheatears, and found both plovers and jaegers to be sensitive to hiking. Occupancy of tundra and shrub habitats by American Golden Plover, American Tree Sparrow Spizelloides arborea, Lapland Longspur Calcarius lapponicus, Long‐tailed Jaeger and Willow Ptarmigan Lagopus lagopus declined with increasing hiking intensity. We found that occupancy probability of tundra by Horned Lark Eremophia alpestris increased, while that of the shrub‐tolerant Wilson’s Warbler Cardellina pusilla decreased, with distance from the park road. Detection of species varied based on survey length, noise, start time presence of a trail, and date. The knowledge gained from this study reveals a loss in avian diversity over the past few decades that has the potential to cause a shifted baseline syndrome, and ongoing threats of hiking to sensitive tundra‐breeding birds. Park managers should seek to balance human recreation with the needs of sensitive tundra‐breeding birds to further protect species of conservation concern. This may be done by not building new trails in tundra, limiting access to tundra hiking areas during the early breeding season, reducing the spatial extent of hiking by improving maintained trails and designating a single, maintained path in areas with multiple unofficial hiking tracks, educating tourists about tundra‐nesting birds, and closing especially important nesting areas to the public.
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A vast literature in statistics, biometrics, and econometrics is concerned with the analysis of binary and polychotomous response data. The classical approach fits a categorical response regression model using maximum likelihood, and inferences about the model are based on the associated asymptotic theory. The accuracy of classical confidence statements is questionable for small sample sizes. In this article, exact Bayesian methods for modeling categorical response data are developed using the idea of data augmentation. The general approach can be summarized as follows. The probit regression model for binary outcomes is seen to have an underlying normal regression structure on latent continuous data. Values of the latent data can be simulated from suitable truncated normal distributions. If the latent data are known, then the posterior distribution of the parameters can be computed using standard results for normal linear models. Draws from this posterior are used to sample new latent data, and the process is iterated with Gibbs sampling. This data augmentation approach provides a general framework for analyzing binary regression models. It leads to the same simplification achieved earlier for censored regression models. Under the proposed framework, the class of probit regression models can be enlarged by using mixtures of normal distributions to model the latent data. In this normal mixture class, one can investigate the sensitivity of the parameter estimates to the choice of “link function,” which relates the linear regression estimate to the fitted probabilities. In addition, this approach allows one to easily fit Bayesian hierarchical models. One specific model considered here reflects the belief that the vector of regression coefficients lies on a smaller dimension linear subspace. The methods can also be generalized to multinomial response models with J > 2 categories. In the ordered multinomial model, the J categories are ordered and a model is written linking the cumulative response probabilities with the linear regression structure. In the unordered multinomial model, the latent variables have a multivariate normal distribution with unknown variance-covariance matrix. For both multinomial models, the data augmentation method combined with Gibbs sampling is outlined. This approach is especially attractive for the multivariate probit model, where calculating the likelihood can be difficult.
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A guide to data collection, modeling and inference strategies for biological survey data using Bayesian and classical statistical methods. This book describes a general and flexible framework for modeling and inference in ecological systems based on hierarchical models, with a strict focus on the use of probability models and parametric inference. Hierarchical models represent a paradigm shift in the application of statistics to ecological inference problems because they combine explicit models of ecological system structure or dynamics with models of how ecological systems are observed. The principles of hierarchical modeling are developed and applied to problems in population, metapopulation, community, and metacommunity systems. The book provides the first synthetic treatment of many recent methodological advances in ecological modeling and unifies disparate methods and procedures. The authors apply principles of hierarchical modeling to ecological problems, including * occurrence or occupancy models for estimating species distribution * abundance models based on many sampling protocols, including distance sampling * capture-recapture models with individual effects * spatial capture-recapture models based on camera trapping and related methods * population and metapopulation dynamic models * models of biodiversity, community structure and dynamics * Wide variety of examples involving many taxa (birds, amphibians, mammals, insects, plants) * Development of classical, likelihood-based procedures for inference, as well as Bayesian methods of analysis * Detailed explanations describing the implementation of hierarchical models using freely available software such as R and WinBUGS * Computing support in technical appendices in an online companion web site.
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1. A Bayesian analysis of site-occupancy data containing covariates of species occurrence and species detection probabilities is usually completed using Markov chain Monte Carlo methods in conjunction with software programs that can implement those methods for any statistical model, not just site-occupancy models. Although these software programs are quite flexible, considerable experience is often required to specify a model and to initialize the Markov chain so that summaries of the posterior distribution can be estimated efficiently and accurately. 2. As an alternative to these programs, we develop a Gibbs sampler for Bayesian analysis of site-occupancy data that include covariates of species occurrence and species detection probabilities. This Gibbs sampler is based on a class of site-occupancy models in which probabilities of species occurrence and detection are specified as probit-regression functions of site- and survey-specific covariate measurements. 3. To illustrate the Gibbs sampler, we analyse site-occupancy data of the blue hawker, Aeshna cyanea (Odonata, Aeshnidae), a common dragonfly species in Switzerland. Our analysis includes a comparison of results based on Bayesian and classical (non-Bayesian) methods of inference. We also provide code (based on the R software program) for conducting Bayesian and classical analyses of site-occupancy data.
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The demography, movement, and behaviour patterns of eight caribou populations (Kaminuriak, Nelchina, Central Arctic, Fortymile, Porcupine, British Columbia, Newfoundland, and Sndhetta) exposed to industrial activities or transportation corridors are reviewed. Eehaviour pat- terns of caribou encountering transportation corridors are explainable in terms of adaptive responses to natural environmental features. There is no evidence that disturbance activities or habitat alteration have affected productivity. Transportation corridors have adversely affected caribou numbers by facilitating access by hunters. There are no examples where physical features of corridors or associated disturbances have affected numbers or productivity. Caribou apparently have a high degree of resilience to human disturbance, and seasonal movement patterns and extent of range oc- cupancy appear to be a function of population size rather than of extrinsic disturbance. The carrying capacity of the habitat is based on the space caribou need to interact successfully with their natural predators. Caribou must not be prevented from crossing transportation corridors by the con- struction of physical barriers, by firing lines created by hunting activity along a corridor, or by intense harassment - a loss in usable space will ultimately result in reduced abundance.