Estimating Population Abundance Using Sightability Models: R SightabilityModel Package

Sightability models are binary logistic-regression models used to estimate and adjust for visibility bias in wildlife-population surveys (Steinhorst and Samuel 1989). Estimation proceeds in 2 stages: (1) Sightability trials are conducted with marked individuals, and logistic regression is used to estimate the probability of detection as a function of available covariates (e.g., visual obstruction, group size). (2) The fitted model is used to adjust counts (from future surveys) for animals that were not observed. A modified Horvitz-Thompson estimator is used to estimate abundance: counts of observed animal groups are divided by their inclusion probabilites (determined by plot-level sampling probabilities and the detection probabilities estimated from stage 1). We provide a brief historical account of the approach, clarifying and documenting suggested modifications to the variance estimators originally proposed by Steinhorst and Samuel (1989). We then introduce a new R package, SightabilityModel, for estimating abundance using this technique. Lastly, we illustrate the software with a series of examples using data collected from moose (Alces alces) in northeastern Minnesota and mountain goats (Oreamnos americanus) in Washington State

Generalized Functional Responses for Species Distributions

Researchers employing resource selection functions (RSFs) and other related methods aim to detect correlates of space-use and mitigate against detrimental environmental change. However, an empirical model fit to data from one place or time is unlikely to capture species responses under different conditions because organisms respond nonlinearly to changes in habitat availability. This phenomenon, known as a functional response in resource selection, has been debated extensively in the RSF literature but continues to be ignored by practitioners for lack of a practical treatment. We therefore extend the RSF approach to enable it to estimate generalized functional responses (GFRs) from spatial data. GFRs employ data from several sampling instances characterized by diverse profiles of habitat availability. By modeling the regression coefficients of the underlying RSF as functions of availability, GFRs can account for environmental change and thus predict population distributions in new environments. We formulate the approach as a mixed-effects model so that it is estimable by readily available statistical software. We illustrate its application using (1) simulation and (2) wolf home-range telemetry. Our results indicate that GFRs can offer considerable improvements in estimation speed and predictive ability over existing mixed-effects approaches

A ‘How to’ Guide for Interpreting Parameters in Habitat-Selection Analyses

Habitat-selection analyses allow researchers to link animals to their environment via habitat-selection or step-selection functions, and are commonly used to address questions related to wildlife management and conservation efforts. Habitat-selection analyses that incorporate movement characteristics, referred to as integrated step-selection analyses, are particularly appealing because they allow modelling of both movement and habitat-selection processes. Despite their popularity, many users struggle with interpreting parameters in habitat-selection and step-selection functions. Integrated step-selection analyses also require several additional steps to translate model parameters into a full-fledged movement model, and the mathematics supporting this approach can be challenging for many to understand. Using simple examples, we demonstrate how weighted distribution theory and the inhomogeneous Poisson point process can facilitate parameter interpretation in habitat-selection analyses. Furthermore, we provide a ‘how to’ guide illustrating the steps required to implement integrated step-selection analyses using the AMT package By providing clear examples with open-source code, we hope to make habitat-selection analyses more understandable and accessible to end users

Used-habitat calibration plots: a new procedure for validating species distribution, resource selection, and step-selection models

“Species distribution modeling” was recently ranked as one of the top five “research fronts” in ecology and the environmental sciences by ISI's Essential Science Indicators (Renner and Warton 2013), reflecting the importance of predicting how species distributions will respond to anthropogenic change. Unfortunately, species distribution models (SDMs) often perform poorly when applied to novel environments. Compounding on this problem is the shortage of methods for evaluating SDMs (hence, we may be getting our predictions wrong and not even know it). Traditional methods for validating SDMs quantify a model's ability to classify locations as used or unused. Instead, we propose to focus on how well SDMs can predict the characteristics of used locations. This subtle shift in viewpoint leads to a more natural and informative evaluation and validation of models across the entire spectrum of SDMs. Through a series of examples, we show how simple graphical methods can help with three fundamental challenges of habitat modeling: identifying missing covariates, non-linearity, and multicollinearity. Identifying habitat characteristics that are not well-predicted by the model can provide insights into variables affecting the distribution of species, suggest appropriate model modifications, and ultimately improve the reliability and generality of conservation and management recommendations

An Historical Overview and Update of Wolf-Moose Interactions in Northeastern Minnesota

Wolf (Canis lupus) and moose (Alces americanus) populations in northeastern Minnesota, USA, have fluctuated for decades and, based on helicopter counts, moose numbers declined to a new low from 2006 to about 2012. Other steep declines were found in 1991 and 1998 during periods when moose counts were done with fixed-wing aircraft; these declines also appeared to be real. Winter wolf numbers, monitored in part of the moose range, had been increasing since about 2002 to the highest population in decades in 2009. However, from 2009 to 2016, wolves decreased precipitously, and the moose- population decline leveled off from 2012 to 2017. Calf:population ratios from 1985 to 1997 and from 2005 to 2016 were inversely related to wolf numbers in the wolf-study area the previous winter both as wolves increased and decreased in abundance. Similarly, log annual growth rates of moose numbers were negatively correlated with counts of wolves in the prior year. Other factors such as nutrition and parasites, and possibly climate change, likely have been involved in the recent moose decline. However, wolves, as in other areas, appear to have contributed to the decline in the northeastern Minnesota moose population at least in part through predation on calves, supporting earlier reports

COMPARING STRATIFICATION SCHEMES FOR AERIAL MOOSE SURVEYS

Stratification is generally used to improve the precision of aerial surveys. In Minnesota, moose (Alces alces) survey strata have been constructed using expert opinion informed by moose density from previous surveys (if available), recent disturbance, and cover-type information. Stratum-specific distributions of observed moose from plots surveyed during 2005-2010 overlapped, suggesting some improvement in precision might be accomplished by using a different stratification scheme. Therefore, we explored the feasibility of using remote-sensing data to define strata. Stratum boundaries were formed using a 2-step process: 1) we fit parametric and non-parametric regression models using land-cover data as predictors of observed moose numbers; 2) we formed strata by applying classical rules for determining stratum boundaries to the model-based predictions. Although land-cover data and moose numbers were correlated, we were unable to improve upon the current stratification scheme based on expert opinion

Establishing the link between habitat selection and animal population dynamics

Although classical ecological theory (e.g., on ideal free consumers) recognizes the potential effect of population density on the spatial distribution of animals, empirical species distribution models assume that species–habitat relationships remain unchanged across a range of population sizes. Conversely, even though ecological models and experiments have demonstrated the importance of spatial heterogeneity for the rate of population change, we still have no practical method for making the connection between the makeup of real environments, the expected distribution and fitness of their occupants, and the long-term implications of fitness for population growth. Here, we synthesize several conceptual advances into a mathematical framework using a measure of fitness to link habitat availability/selection to (density-dependent) population growth in mobile animal species. A key feature of this approach is that it distinguishes between apparent habitat suitability and the true, underlying contribution of a habitat to fitness, allowing the statistical coefficients of both to be estimated from multiple observation instances of the species in different environments and stages of numerical growth. Hence, it leverages data from both historical population time series and snapshots of species distribution to predict population performance under environmental change. We propose this framework as a foundation for building more realistic connections between a population's use of space and its subsequent dynamics (and hence a contribution to the ongoing efforts to estimate a species' critical habitat and fundamental niche). We therefore detail its associated definitions and simplifying assumptions, because they point to the framework's future extensions. We show how the model can be fit to data on species distributions and population dynamics, using standard statistical methods, and we illustrate its application with an individual-based simulation. When contrasted with nonspatial population models, our approach is better at fitting and predicting population growth rates and carrying capacities. Our approach can be generalized to include a diverse range of biological considerations. We discuss these possible extensions and applications to real data

Conceptual and methodological advances in habitat-selection modeling: guidelines for ecology and evolution

Habitat selection is a fundamental animal behavior that shapes a wide range of ecological processes, including animal movement, nutrient transfer, trophic dynamics and population distribution. Although habitat selection has been a focus of ecological studies for decades, technological, conceptual and methodological advances over the last 20 yr have led to a surge in studies addressing this process. Despite the substantial literature focused on quantifying the habitat-selection patterns of animals, there is a marked lack of guidance on best analytical practices. The conceptual foundations of the most commonly applied modeling frameworks can be confusing even to those well versed in their application. Furthermore, there has yet to be a synthesis of the advances made over the last 20 yr. Therefore, there is a need for both synthesis of the current state of knowledge on habitat selection, and guidance for those seeking to study this process. Here, we provide an approachable overview and synthesis of the literature on habitat-selection analyses (HSAs) conducted using selection functions, which are by far the most applied modeling framework for understanding the habitat-selection process. This review is purposefully non-technical and focused on understanding without heavy mathematical and statistical notation, which can confuse many practitioners. We offer an overview and history of HSAs, describing the tortuous conceptual path to our current understanding. Through this overview, we also aim to address the areas of greatest confusion in the literature. We synthesize the literature outlining the most exciting conceptual advances in the field of habitat-selection modeling, discussing the substantial ecological and evolutionary inference that can be made using contemporary techniques. We aim for this paper to provide clarity for those navigating the complex literature on HSAs while acting as a reference and best practices guide for practitioners

Within reach? Habitat availability as a function of individual mobility and spatial structuring

Organisms need access to particular habitats for their survival and reproduction. However, even if all necessary habitats are available within the broader environment, they may not all be easily reachable from the position of a single individual. Many species distribution models consider populations in environmental (or niche) space, hence overlooking this fundamental aspect of geographical accessibility. Here, we develop a formal way of thinking about habitat availability in environmental spaces by describing how limitations in accessibility can cause animals to experience a more limited or simply different mixture of habitats than those more broadly available. We develop an analytical framework for characterizing constrained habitat availability based on the statistical properties of movement and environmental autocorrelation. Using simulation experiments, we show that our general statistical representation of constrained availability is a good approximation of habitat availability for particular realizations of landscape-organism interactions. We present two applications of our approach, one to the statistical analysis of habitat preference (using step-selection functions to analyze harbor seal telemetry data) and a second that derives theoretical insights about population viability from knowledge of the underlying environment. Analytical expressions for habitat availability, such as those we develop here, can yield gains in analytical speed, biological realism, and conceptual generality by allowing us to formulate models that are habitat sensitive without needing to be spatially explicit