A resource selection function (RSF) is any model that yields values proportional to the probability of use of a resource unit. RSF models often are fitted using generalized linear models (GLMs) although a variety of statistical models might be used. Information criteria such as the Akaike Information Criteria (AIC) or Bayesian Information Criteria (BIC) are tools that can be useful for selecting a model from a set of biologically plausible candidates. Statistical inference procedures, such as the likelihood-ratio test, can be used to assess whether models deviate from random null models. But for most applications of RSF models, usefulness is evaluated by how well the model predicts the location of organisms on a landscape. Predictions from RSF models constructed using presence/absence (used/ unused) data can be evaluated using procedures developed for logistic regression, such as confusion matrices, Kappa statistics, and Receiver Operating Characteristic (ROC) curves. However, RSF models estimated from presence/ available data create unique problems for evaluating model predictions. For presence/available models we propose a form of k -fold cross validation for evaluating prediction success. This involves calculating the correlation between RSF ranks and area-adjusted frequencies for a withheld sub-sample of data. A similar approach can be applied to evaluate predictive success for out-of-sample data. Not all RSF models are robust for application in different times or different places due to ecological and behavioral variation of the target organisms. #

A trophic cascade recently has been reported among wolves, elk, and aspen on the northern winter range of Yellowstone National Park, Wyoming, USA, but the mechanisms of indirect interactions within this food chain have yet to be established. We investigated whether the observed trophic cascade might have a behavioral basis by exploring environmental factors influencing the movements of 13 female elk equipped with GPS radio collars. We developed a simple statistical approach that can unveil the concurrent influence of several environmental features on animal movements. Paths of elk traveling on their winter range were broken down into steps, which correspond to the straight-line segment between successive locations at 5-hour intervals. Each observed step was paired with 200 random steps having the same starting point, but differing in length and/or direction. Comparisons between the characteristics of observed and random steps using conditional logistic regression were used to model environmental features influencing movement patterns. We found that elk movements were influenced by multiple factors, such as the distance from roads, the presence of a steep slope along the step, and the cover type in which they ended. The influence of cover type on elk movements depended on the spatial distribution of wolves across the northern winter range of the park. In low wolf-use areas, the relative preference for end point locations of steps followed: aspen stands Ͼ open areas Ͼ conifer forests. As the risks of wolf encounter increased, the preference of elk for aspen stands gradually decreased, and selection became strongest for steps ending in conifer forests in high wolf-use areas. Our study clarifies the behavioral mechanisms involved in the trophic cascade of Yellowstone's wolf-elk-aspen system: elk respond to wolves on their winter range by a shift in habitat selection, which leads to local reductions in the use of aspen by elk.

913 may also lead to dependence between species (phylogenetic structure) or populations of species (genetic structure) with more recent divergence will tend to be more similar than those which diverged longer ago (Harvey and Pagel 1991). While such underlying structures in the data are not fundamentally problematic for statistical analyses, they tend to create two undesirable outcomes. First, model error, as well as neglected processes and variables connected to these structures, often leads to dependence structures in the model residuals, which violates the critical assumption of independence present in many models and methods (Legendre and Fortin 1989, Miller et al. 2007). Second, because predictor variables are often correlated with underlying dependence structures (e.g. climate with space), models may use predic-tors to overfit the residual dependence structure and thereby remove it, partially or completely.

Summary 1.A resource selection function is a model of the likelihood that an available spatial unit will be used by an animal, given its resource value. But how do we appropriately define availability?Step selection analysis deals with this problem at the scale of the observed positional data, by matching each 'used step' (connecting two consecutive observed positions of the animal) with a set of 'available steps' randomly sampled from a distribution of observed steps or their characteristics. 2. Here we present a simple extension to this approach, termed integrated step selection analysis (iSSA), which relaxes the implicit assumption that observed movement attributes (i.e. velocities and their temporal autocorrelations) are independent of resource selection. Instead, iSSA relies on simultaneously estimating movement and resource selection parameters, thus allowing simple likelihood-based inference of resource selection within a mechanistic movement model. 3. We provide theoretical underpinning of iSSA, as well as practical guidelines to its implementation. Using computer simulations, we evaluate the inferential and predictive capacity of iSSA compared to currently used methods. 4. Our work demonstrates the utility of iSSA as a general, flexible and user-friendly approach for both evaluating a variety of ecological hypotheses, and predicting future ecological patterns.

Applications of logistic regression in a used‐unused design in wildlife habitat studies often suffer from asymmetry of errors: used resource units (landscape locations) are known with certainty, whereas unused resource units might be observed to be used with greater sampling intensity. More appropriate might be to use logistic regression to estimate a resource selection function (RSF) tied to a use‐availability design based on independent samples drawn from used and available resource units. We review the theoretical motivation for RSFs and show that sample “contamination” and the exponential form commonly assumed for the RSF are not concerns, contrary to recent statements by Keating and Cherry (2004; Use and interpretation of logistic regression in habitat‐selection studies. Journal of Wildlife Management 68:774–789). To do this, we re‐derive the use‐availability likelihood and show that it can be maximized by logistic regression software. We then consider 2 case studies that illustrate our findings. For our first case study, we fit both RSFs and resource selection probability functions (RSPF) to point count data for 4 bird species with varying levels of occurrence among sample blocks. Drawing on our new derivation of the likelihood, we sample available resource units with replacement and assume overlapping distributions of used and available resource units. Irrespective of overlap, we observed approximate proportionality between predictions of a RSF and RSPF. For our second case study, we evaluate the classic use‐availability design suggested by Manly et al. (2002), where availability is sampled without replacement, and we systematically introduce contamination to a sample of available units applied to RSFs for woodland caribou (Rangifer tarandus caribou). Although contamination appeared to reduce the magnitude of one RSF beta coefficient, change in magnitude exceeded sampling variation only when >20% of the available units were confirmed caribou use locations (i.e., contaminated). These empirically based simulations suggest that previously recommended sampling designs are robust to contamination. We conclude with a new validation method for evaluating predictive performance of a RSF and for assessing if the model deviates from being proportional to the probability of use of a resource unit.

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Recent progress in positioning technology facilitates the collection of massive amounts of sequential spatial data on animals. This has led to new opportunities and challenges when investigating animal movement behaviour and habitat selection. Tools like Step Selection Functions (SSFs) are relatively new powerful models for studying resource selection by animals moving through the landscape. SSFs compare environmental attributes of observed steps (the linear segment between two consecutive observations of position) with alternative random steps taken from the same starting point. SSFs have been used to study habitat selection, human-wildlife interactions, movement corridors, and dispersal behaviours in animals. SSFs also have the potential to depict resource selection at multiple spatial and temporal scales. There are several aspects of SSFs where consensus has not yet been reached such as how to analyse the data, when to consider habitat covariates along linear paths between observations rather than at their endpoints, how many random steps should be considered to measure availability, and how to account for individual variation. In this review we aim to address all these issues, as well as to highlight weak features of this modelling approach that should be developed by further research. Finally, we suggest that SSFs could be integrated with state-space models to classify behavioural states when estimating SSFs.

Abstract. Both means and year-to-year variances of climate variables such as temperature and precipitation are predicted to change. However, the potential impact of changing climatic variability on the fate of populations has been largely unexamined. We analyzed multiyear demographic data for 36 plant and animal species with a broad range of life histories and types of environment to ask how sensitive their long-term stochastic population growth rates are likely to be to changes in the means and standard deviations of vital rates (survival, reproduction, growth) in response to changing climate. We quantified responsiveness using elasticities of the long-term population growth rate predicted by stochastic projection matrix models. Short-lived species (insects and annual plants and algae) are predicted to be more strongly (and negatively) affected by increasing vital rate variability relative to longer-lived species (perennial plants, birds, ungulates). Taxonomic affiliation has little power to explain sensitivity to increasing variability once longevity has been taken into account. Our results highlight the potential vulnerability of short-lived species to an increasingly variable climate, but also suggest that problems associated with short-lived undesirable species (agricultural pests, disease vectors, invasive weedy plants) may be exacerbated in regions where climate variability decreases.