Inference in MCMC step selection models

Habitat selection models are used in ecology to link the spatial distribution of animals to environmental covariates and identify preferred habitats. The most widely used models of this type, resource selection functions, aim to capture the steady-state distribution of space use of the animal, but they assume independence between the observed locations of an animal. This is unrealistic when location data display temporal autocorrelation. The alternative approach of step selection functions embed habitat selection in a model of animal movement, to account for the autocorrelation. However, inferences from step selection functions depend on the underlying movement model, and they do not readily predict steady-state space use. We suggest an analogy between parameter updates and target distributions in Markov chain Monte Carlo (MCMC) algorithms, and step selection and steady-state distributions in movement ecology, leading to a step selection model with an explicit steady-state distribution. In this framework, we explain how maximum likelihood estimation can be used for simultaneous inference about movement and habitat selection. We describe the local Gibbs sampler, a novel rejection-free MCMC scheme, use it as the basis of a flexible class of animal movement models, and derive its likelihood function for several important special cases. In a simulation study, we verify that maximum likelihood estimation can recover all model parameters. We illustrate the application of the method with data from a zebra.     

Fix Success and Accuracy of Global Positioning System Collars in Old-Growth Temperate Coniferous Forests

Abstract: Global Positioning System (GPS) telemetry is used extensively to study animal distribution and resource selection patterns but is susceptible to biases resulting from data omission and spatial inaccuracies. These data errors may cause misinterpretation of wildlife habitat selection or spatial use patterns. We used both stationary test collars and collared free-ranging American black bears (Ursus americanus) to quantify systemic data loss and location error of GPS telemetry in mountainous, old-growth temperate forests of Olympic National Park, Washington, USA. We developed predictive models of environmental factors that influence the probability of obtaining GPS locations and evaluated the ability of weighting factors derived from these models to mitigate data omission biases from collared bears. We also examined the effects of microhabitat on collar fix success rate and examined collar accuracy as related to elevation changes between successive fixes. The probability of collars successfully obtaining location fixes was positively associated with elevation and unobstructed satellite view and was negatively affected by the interaction of overstory canopy and satellite view. Test collars were 33% more successful at acquiring fixes than those on bears. Fix success rates of collared bears varied seasonally and diurnally. Application of weighting factors to individual collared bear fixes recouped only 6% of lost data and failed to reduce seasonal or diurnal variation in fix success, suggesting that variables not included in our model contributed to data loss. Test collars placed to mimic bear bedding sites received 16% fewer fixes than randomly placed collars, indicating that microhabitat selection may contribute to data loss for wildlife equipped with GPS collars. Horizontal collar errors of >800 m occurred when elevation changes between successive fixes were >400 m. We conclude that significant limitations remain in accounting for data loss and error inherent in using GPS telemetry in coniferous forest ecosystems and that, at present, resource selection patterns of large mammals derived from GPS telemetry should be interpreted cautiously.     

Correlation and studies of habitat selection: problem,red herring or opportunity?

With the advent of new technologies, animal locations are being collected at ever finer spatio-temporal scales. We review analytical methods for dealing with correlated data in the context of resource selection, including post hoc variance inflation techniques, ‘two-stage’ approaches based on models fit to each individual, generalized estimating equations and hierarchical mixed-effects models. These methods are applicable to a wide range of correlated data problems, but can be difficult to apply and remain especially challenging for use–availability sampling designs because the correlation structure for combinations of used and available points are not likely to follow common parametric forms. We also review emerging approaches to studying habitat selection that use fine-scale temporal data to arrive at biologically based definitions of available habitat, while naturally accounting for autocorrelation by modelling animal movement between telemetry locations. Sophisticated analyses that explicitly model correlation rather than consider it a nuisance, like mixed effects and state-space models, offer potentially novel insights into the process of resource selection, but additional work is needed to make them more generally applicable to large datasets based on the use–availability designs. Until then, variance inflation techniques and two-stage approaches should offer pragmatic and flexible approaches to modelling correlated data.     

Estimating space-use and habitat preference from wildlife telemetry data

Management and conservation of populations of animals requires information on where they are, why they are there, and where else they could be. These objectives are typically approached by collecting data on the animals' use of space, relating these positional data to prevailing environmental conditions and employing the resulting statistical models to predict usage at other geographical regions. Technical advances in wildlife telemetry have accomplished manifold increases in the amount and quality of available data, creating the need for a statistical framework that can use them to make population‐level inferences for habitat preference and space‐use. This has been slow‐in‐coming because wildlife telemetry data are spatio‐temporally autocorrelated, often unbalanced, presence‐only observations of behaviourally complex animals, responding to a multitude of cross‐correlated environmental variables. We review the evolution of regression models for the analysis of space‐use and habitat preference and outline the essential features of a framework that emerges naturally from these foundations. This allows us to derive a relationship between usage of points in geographical space and preference of habitats in environmental space. Within this framework, we discuss eight challenges, inherent in the spatial analysis of telemetry data and, for each, we propose solutions that can work in tandem. Specifically, we propose a logistic, mixed‐effects approach that uses generalized additive transformations of the environmental covariates and is fitted to a response data‐set comprising the telemetry and simulated observations, under a case‐control design. We apply this framework to a non‐trivial case‐study using satellite‐tagged grey seals Halichoerus grypus from the east coast of Scotland. We perform model selection by cross‐validation and confront our final model's predictions with telemetry data from the same, as well as different, geographical regions. We conclude that, despite the complex behaviour of the study species, flexible empirical models can capture the environmental relationships that shape population distributions.     

A log-linear modeling framework for selective mixing.

Nonrandom mixing can significantly alter the diffusion path of an infectious disease such as AIDS that requires intimate contact. Recent attempts to model this effect have sought a general framework capable of representing both simple and arbitrarily complicated mixing structures, and of solving the balancing problem in a nonequilibrium multigroup population. Log-linear models are proposed here as a general framework for solving the first problem. This approach offers several additional benefits: The parameters used to govern the mixing have a simple, intuitive interpretation, the framework provides a statistically sound basis for the estimation of these parameters from mixing-matrix data, and the resulting estimates are easily integrated into compartmental models for diffusion. A modified selection model is proposed to solve the second problem of generalizing the selection process to nonequilibrium populations. The distribution of contacts under this model is derived and is found to satisfy the assumptions of statistical inference for log-linear models. Together these techniques provide an integrated and flexible framework for modeling the role of selective mixing in the spread of disease.     

Animal movement tools (amt): R package for managing tracking data and conducting habitat selection analyses

Advances in tracking technology have led to an exponential increase in animal location data, greatly enhancing our ability to address interesting questions in movement ecology, but also presenting new challenges related to data management and analysis. Step‐selection functions (SSFs) are commonly used to link environmental covariates to animal location data collected at fine temporal resolution. SSFs are estimated by comparing observed steps connecting successive animal locations to random steps, using a likelihood equivalent of a Cox proportional hazards model. By using common statistical distributions to model step length and turn angle distributions, and including habitat‐ and movement‐related covariates (functions of distances between points, angular deviations), it is possible to make inference regarding habitat selection and movement processes or to control one process while investigating the other. The fitted model can also be used to estimate utilization distributions and mechanistic home ranges. Here, we present the R package amt (animal movement tools) that allows users to fit SSFs to data and to simulate space use of animals from fitted models. The amt package also provides tools for managing telemetry data. Using fisher (Pekania pennanti) data as a case study, we illustrate a four‐step approach to the analysis of animal movement data, consisting of data management, exploratory data analysis, fitting of models, and simulating from fitted models.     

A temporally explicit species distribution model for a long distance avian migrant,the common cuckoo

Modelling the distribution of migratory species has rarely been extended beyond breeding and wintering ranges despite many species showing much more complex movement patterns with multiple stopovers. We aimed to create a temporally explicit species distribution model describing the full annual distribution cycle, and use it to model the complex seasonal shifts in distribution of the common cuckoo Cuculus canorus, a declining long‐distance migrant. To do this we used full‐year satellite telemetry occurrence data, with their associated temporal information, to inform a temporally explicit species distribution model using MaxEnt. The resulting full‐year distribution model was highly predictive (AUC = 0.894) and appeared to have generality at the species‐level despite being informed by data from a single breeding population. Comparison of our methodology with seasonal distribution models describing the breeding, winter and migration ranges separately showed that our full‐year method provided more general and extensive predictions and performed better when tested with an independent dataset. When species distribution models based on a single season exclude environmental conditions experienced by birds in other parts of the annual cycle they risk underestimating niche breadth and neglecting the importance of stopover habitat. Conversely, models which simply average conditions across a season may miss the significance of finer scale within‐season movements and overestimate niche breadth. In contrast, our framework for a full‐year migrant distribution model successfully captures the finer‐scale changes expected in seasonal environments and can be used to inform conservation management at every stage of migration. The full‐year model framework appears to produce temporal distribution models generalised to the species‐level from occurrence data limited to few individuals of a single population and may have particular utility when aiming to describe the distribution of species with complex migration patterns from telemetry data.     

Are all data types and connectivity models created equal? Validating common connectivity approaches with dispersal data

Aim

There is enormous interest in applying connectivity modelling to resistance surfaces for identifying corridors for conservation action. However, the multiple analytical approaches used to estimate resistance surfaces and predict connectivity across resistance surfaces have not been rigorously compared, and it is unclear what methods provide the best inferences about population connectivity. Using a large empirical data set on puma (Puma concolor), we are the first to compare several of the most common approaches for estimating resistance and modelling connectivity and validate them with dispersal data.

Location

Southern California, USA.

Methods

We estimate resistance using presence‐only data, GPS telemetry data from puma home ranges and genetic data using a variety of analytical methods. We model connectivity with cost distance and circuit theory algorithms. We then measure the ability of each data type and connectivity algorithm to capture GPS telemetry points of dispersing pumas.

Results

We found that resource selection functions based on GPS telemetry points and paths outperformed species distribution models when applied using cost distance connectivity algorithms. Point and path selection functions were not statistically different in their performance, but point selection functions were more sensitive to the transformation used to convert relative probability of use to resistance. Point and path selection functions and landscape genetics outperformed other methods when applied with cost distance; no methods outperformed one another with circuit theory.

Main conclusions

We conclude that path or point selection functions, or landscape genetic models, should be used to estimate landscape resistance for wildlife. In cases where resource limitations prohibit the collection of GPS collar or genetic data, our results suggest that species distribution models, while weaker, may still be sufficient for resistance estimation. We recommend the use of cost distance‐based approaches, such as least‐cost corridors and resistant kernels, for estimating connectivity and identifying functional corridors for terrestrial wildlife.

     

Considering ecological dynamics in resource selection functions

1.  Describing distribution and abundance is requisite to exploring interactions between organisms and their environment. Recently, the resource selection function (RSF) has emerged to replace many of the statistical procedures used to quantify resource selection by animals.
2.  A RSF is defined by characteristics measured on resource units such that its value for a unit is proportional to the probability of that unit being used by an organism. It is solved using a variety of techniques, particularly the binomial generalized linear model.
3.  Observing dynamics in a RSF – obtaining substantially different functions at different times or places for the same species – alerts us to the varying ecological processes that underlie resource selection.
4.  We believe that there is a need for us to reacquaint ourselves with ecological theory when interpreting RSF models. We outline a suite of factors likely to govern ecologically based variation in a RSF. In particular, we draw attention to competition and density-dependent habitat selection, the role of predation, longitudinal changes in resource availability and functional responses in resource use.
5.  How best to incorporate governing factors in a RSF is currently in a state of development; however, we see promise in the inclusion of random as well as fixed effects in resource selection models, and matched case–control logistic regression.
6.  Investigating the basis of ecological dynamics in a RSF will allow us to develop more robust models when applied to forecasting the spatial distribution of animals. It may also further our understanding of the relative importance of ecological interactions on the distribution and abundance of species.     

A machine‐learning approach for extending classical wildlife resource selection analyses

Resource selection functions (RSFs) are tremendously valuable for ecologists and resource managers because they quantify spatial patterns in resource utilization by wildlife, thereby facilitating identification of critical habitat areas and characterizing specific habitat features that are selected or avoided. RSFs discriminate between known‐use resource units (e.g., telemetry locations) and available (or randomly selected) resource units based on an array of environmental features, and in their standard form are performed using logistic regression. As generalized linear models, standard RSFs have some notable limitations, such as difficulties in accommodating nonlinear (e.g., humped or threshold) relationships and complex interactions. Increasingly, ecologists are using flexible machine‐learning methods (e.g., random forests, neural networks) to overcome these limitations. Herein, we investigate the seasonal resource selection patterns of mule deer (Odocoileus hemionus) by comparing a logistic regression framework with random forest (RF), a popular machine‐learning algorithm. Random forest (RF) models detected nonlinear relationships (e.g., optimal ranges for slope and elevation) and complex interactions which would have been very challenging to discover and characterize using standard model‐based approaches. Compared with standard RSF models, RF models exhibited improved predictive skill, provided novel insights about resource selection patterns of mule deer, and, when projected across a relevant geographic space, manifested notable differences in predicted habitat suitability. We recommend that wildlife researchers harness the strengths of machine‐learning tools like RF in addition to “classical” tools (e.g., mixed‐effects logistic regression) for evaluating resource selection, especially in cases where extensive telemetry data sets are available.     

The effects of nucleotide substitution model assumptions on estimates of nonparametric bootstrap support

The use of parameter-rich substitution models in molecular phylogenetics has been criticized on the basis that these models can cause a reduction both in accuracy and in the ability to discriminate among competing topologies. We have explored the relationship between nucleotide substitution model complexity and nonparametric bootstrap support under maximum likelihood (ML) for six data sets for which the true relationships are known with a high degree of certainty. We also performed equally weighted maximum parsimony analyses in order to assess the effects of ignoring branch length information during tree selection. We observed that maximum parsimony gave the lowest mean estimate of bootstrap support for the correct set of nodes relative to the ML models for every data set except one. For several data sets, we established that the exact distribution used to model among-site rate variation was critical for a successful phylogenetic analysis. Site-specific rate models were shown to perform very poorly relative to gamma and invariable sites models for several of the data sets most likely because of the gross underestimation of branch lengths. The invariable sites model also performed poorly for several data sets where this model had a poor fit to the data, suggesting that addition of the gamma distribution can be critical. Estimates of bootstrap support for the correct nodes often increased under gamma and invariable sites models relative to equal rates models. Our observations are contrary to the prediction that such models cause reduced confidence in phylogenetic hypotheses. Our results raise several issues regarding the process of model selection, and we briefly discuss model selection uncertainty and the role of sensitivity analyses in molecular phylogenetics.     

Evaluation of Scat Deposition Transects versus Radio Telemetry for Developing a Species Distribution Model for a Rare Desert Carnivore,the Kit Fox

Development and evaluation of noninvasive methods for monitoring species distribution and abundance is a growing area of ecological research. While noninvasive methods have the advantage of reduced risk of negative factors associated with capture, comparisons to methods using more traditional invasive sampling is lacking. Historically kit foxes (Vulpes macrotis) occupied the desert and semi-arid regions of southwestern North America. Once the most abundant carnivore in the Great Basin Desert of Utah, the species is now considered rare. In recent decades, attempts have been made to model the environmental variables influencing kit fox distribution. Using noninvasive scat deposition surveys for determination of kit fox presence, we modeled resource selection functions to predict kit fox distribution using three popular techniques (Maxent, fixed-effects, and mixed-effects generalized linear models) and compared these with similar models developed from invasive sampling (telemetry locations from radio-collared foxes). Resource selection functions were developed using a combination of landscape variables including elevation, slope, aspect, vegetation height, and soil type. All models were tested against subsequent scat collections as a method of model validation. We demonstrate the importance of comparing multiple model types for development of resource selection functions used to predict a species distribution, and evaluating the importance of environmental variables on species distribution. All models we examined showed a large effect of elevation on kit fox presence, followed by slope and vegetation height. However, the invasive sampling method (i.e., radio-telemetry) appeared to be better at determining resource selection, and therefore may be more robust in predicting kit fox distribution. In contrast, the distribution maps created from the noninvasive sampling (i.e., scat transects) were significantly different than the invasive method, thus scat transects may be appropriate when used in an occupancy framework to predict species distribution. We concluded that while scat deposition transects may be useful for monitoring kit fox abundance and possibly occupancy, they do not appear to be appropriate for determining resource selection. On our study area, scat transects were biased to roadways, while data collected using radio-telemetry was dictated by movements of the kit foxes themselves. We recommend that future studies applying noninvasive scat sampling should consider a more robust random sampling design across the landscape (e.g., random transects or more complete road coverage) that would then provide a more accurate and unbiased depiction of resource selection useful to predict kit fox distribution.     

Evaluation of a black-footed ferret resource utilization function model

Resource utilization function (RUF) models permit evaluation of potential habitat for endangered species; ideally such models should be evaluated before use in management decision-making. We evaluated the predictive capabilities of a previously developed black-footed ferret (Mustela nigripes) RUF. Using the population-level RUF, generated from ferret observations at an adjacent yet distinct colony, we predicted the distribution of ferrets within a black-tailed prairie dog (Cynomys ludovicianus) colony in the Conata Basin, South Dakota, USA. We evaluated model performance, using data collected during post-breeding spotlight surveys (2007–2008) by assessing model agreement via weighted compositional analysis and count-metrics. Compositional analysis of home range use and colony-level availability, and core area use and home range availability, demonstrated ferret selection of the predicted Very high and High occurrence categories in 2007 and 2008. Simple count-metrics corroborated these findings and suggested selection of the Very high category in 2007 and the Very high and High categories in 2008. Collectively, these results suggested that the RUF was useful in predicting occurrence and intensity of space use of ferrets at our study site, the 2 objectives of the RUF. Application of this validated RUF would increase the resolution of habitat evaluations, permitting prediction of the distribution of ferrets within distinct colonies. Additional model evaluation at other sites, on other black-tailed prairie dog colonies of varying resource configuration and size, would increase understanding of influences upon model performance and the general utility of the RUF. © 2011 The Wildlife Society.     

Combining multiple biomarker models in logistic regression

Summary .   In medical research, there is great interest in developing methods for combining biomarkers. We argue that selection of markers should also be considered in the process. Traditional model/variable selection procedures ignore the underlying uncertainty after model selection. In this work, we propose a novel model-combining algorithm for classification in biomarker studies. It works by considering weighted combinations of various logistic regression models; five different weighting schemes are considered in the article. The weights and algorithm are justified using decision theory and risk-bound results. Simulation studies are performed to assess the finite-sample properties of the proposed model-combining method. It is illustrated with an application to data from an immunohistochemical study in prostate cancer.     

Identifying and correcting spatial bias in opportunistic citizen science data for wild ungulates in Norway

Many publications make use of opportunistic data, such as citizen science observation data, to infer large‐scale properties of species’ distributions. However, the few publications that use opportunistic citizen science data to study animal ecology at a habitat level do so without accounting for spatial biases in opportunistic records or using methods that are difficult to generalize. In this study, we explore the biases that exist in opportunistic observations and suggest an approach to correct for them. We first examined the extent of the biases in opportunistic citizen science observations of three wild ungulate species in Norway by comparing them to data from GPS telemetry. We then quantified the extent of the biases by specifying a model of the biases. From the bias model, we sampled available locations within the species’ home range. Along with opportunistic observations, we used the corrected availability locations to estimate a resource selection function (RSF). We tested this method with simulations and empirical datasets for the three species. We compared the results of our correction method to RSFs obtained using opportunistic observations without correction and to RSFs using GPS‐telemetry data. Finally, we compared habitat suitability maps obtained using each of these models. Opportunistic observations are more affected by human access and visibility than locations derived from GPS telemetry. This has consequences for drawing inferences about species’ ecology. Models naïvely using opportunistic observations in habitat‐use studies can result in spurious inferences. However, sampling availability locations based on the spatial biases in opportunistic data improves the estimation of the species’ RSFs and predicted habitat suitability maps in some cases. This study highlights the challenges and opportunities of using opportunistic observations in habitat‐use studies. While our method is not foolproof it is a first step toward unlocking the potential of opportunistic citizen science data for habitat‐use studies.     

"Smooth" semiparametric regression analysis for arbitrarily censored time-to-event data

Summary .   A general framework for regression analysis of time-to-event data subject to arbitrary patterns of censoring is proposed. The approach is relevant when the analyst is willing to assume that distributions governing model components that are ordinarily left unspecified in popular semiparametric regression models, such as the baseline hazard function in the proportional hazards model, have densities satisfying mild "smoothness" conditions. Densities are approximated by a truncated series expansion that, for fixed degree of truncation, results in a "parametric" representation, which makes likelihood-based inference coupled with adaptive choice of the degree of truncation, and hence flexibility of the model, computationally and conceptually straightforward with data subject to any pattern of censoring. The formulation allows popular models, such as the proportional hazards, proportional odds, and accelerated failure time models, to be placed in a common framework; provides a principled basis for choosing among them; and renders useful extensions of the models straightforward. The utility and performance of the methods are demonstrated via simulations and by application to data from time-to-event studies.     

The ideal free distribution: a review and synthesis of the game-theoretic perspective

The Ideal Free Distribution (IFD), introduced by Fretwell and Lucas in [Fretwell, D.S., Lucas, H.L., 1970. On territorial behavior and other factors influencing habitat distribution in birds. Acta Biotheoretica 19, 16-32] to predict how a single species will distribute itself among several patches, is often cited as an example of an evolutionarily stable strategy (ESS). By defining the strategies and payoffs for habitat selection, this article puts the IFD concept in a more general game-theoretic setting of the “habitat selection game”. Within this game-theoretic framework, the article focuses on recent progress in the following directions: (1) studying evolutionarily stable dispersal rates and corresponding dispersal dynamics; (2) extending the concept when population numbers are not fixed but undergo population dynamics; (3) generalizing the IFD to multiple species.For a single species, the article briefly reviews existing results. It also develops a new perspective for Parker’s matching principle, showing that this can be viewed as the IFD of the habitat selection game that models consumer behavior in several resource patches and analyzing complications involved when the model includes resource dynamics as well. For two species, the article first demonstrates that the connection between IFD and ESS is now more delicate by pointing out pitfalls that arise when applying several existing game-theoretic approaches to these habitat selection games. However, by providing a new detailed analysis of dispersal dynamics for predator-prey or competitive interactions in two habitats, it also pinpoints one approach that shows much promise in this general setting, the so-called “two-species ESS”. The consequences of this concept are shown to be related to recent studies of population dynamics combined with individual dispersal and are explored for more species or more patches.     

Are latrine sites an accurate predictor of seasonal habitat selection by river otters (<Emphasis Type="Italic">Lontra canadensis</Emphasis>) in freshwater systems?

Temporal variation in the availability of food resources is a likely driving factor influencing the distribution and habitat use of river otters (Lontra canadensis). Although latrine sites are commonly used to determine habitat selection, it is unclear if latrine sites are an accurate predictor or even a useful indicator of the seasonal habitat use and distribution of river otters. We apply resource selection functions (RSF) to both latrine and telemetry locations to investigate whether latrine sites identified along lake shorelines during the ice-free season are appropriate predictors of otter habitat selection along shorelines during the ice-free and ice-cover seasons in central British Columbia, Canada. We found that the top models describing otter latrine sites and telemetry locations during the ice-free season were similar. The top RSF models and associated coefficients for the ice-cover season differed, however, with otter presence being positively influenced by shallower water depths. For the spatial extrapolation of averaged RSF coefficients, we found that 21.4 and 69.3 % of predicted latrine habitat along lake shorelines overlapped with ice-cover and ice-free habitat generated from telemetry locations, respectively. The location and activity at latrine sites appear to be a useful method for monitoring otter distribution and habitat use during the ice-free, but not during the ice-cover season. The results of our RSF analyses as well as home range measurements of otters in our study area suggest that cold temperatures and ice cover may be a limiting factor for the distribution of otter populations at northern latitudes.     

Assessment of appropriate species-specific time intervals to integrate GPS telemetry data in ecological niche models

Ecological niche models use presence-only data, which is often affected by lack of true absences leading to sampling bias. Over the last decade, there has been an uptick in the integration of occurrence data from global positioning systems telemetry data in ecological niche models and/or species distribution models. These data types can be affected by serial autocorrelation at high relocation frequencies yet have been used in ecological niche models using geographic filters and subsampling techniques. Yet, no study to date has attempted to discern a method to identify the appropriate time interval for a particular species if integrating GPS telemetry occurrence data in a MaxEnt framework. We demonstrate a rigorous spatial technique using a robust contemporary dataset from ocelots (Leopardus pardalis) to assess the appropriate time intervals to use in a species-specific ecological niche model. We assessed a range of daily time intervals (every 0.5, 1–4, 6, 8, and 12 h) commonly used in teresstrial mammalian carnivore studies. We observed the predictive performance of shorter time intervals every 2 h was comparable to much longer intervals every 12 h. These shorter intervals under/overestimated the least amount of data compared to 12 h. This study demonstrates that by accounting for serial autocorrelation and conducting rigorous spatial analyses, scientists can identify the appropriate time interval to integrate GPS telemetry data use in ecological niche models in MaxEnt. These results can also be transferable across highly mobile terrestrial taxa at different spatial scales, which can help inform species management or conservation strategies.     

Model-supervised kernel smoothing for the estimation of spatial usage

The analysis of telemetry data obtained from tagged animals often requires that a smooth surface of spatial usage is fitted to the observations. Well‐established statistical techniques for doing this, such as kernel smoothing (KS), are based on asymptotic arguments that guarantee the convergence of their estimates to the truth with increasing sample size. Often, in addition to telemetry data, ecologists have access to a wealth of information relating to the animals’ distribution and movement. This additional information is potentially useful for the estimation of spatial usage but currently remains unused by existing methods. In this paper, I outline and begin the validation of model‐supervised kernel smoothing (MSKS), a modification of KS that uses such information to supervise surface‐fitting to telemetry data. MSKS initially requires an ad‐hoc synthesis of all the available information, excluding telemetry, into an auxiliary usage surface (the model). This is then combined with the kernel‐smoothed telemetry data into a hybrid surface that is the weighted average of the two. Automatic selection of the smoothing coefficient and the weight associated with the model is done by means of likelihood cross‐validation. I examine the performance of MSKS first, by extensive, numerical exploration on simulated data in one‐dimensional space and second, on two‐dimensional data obtained from an individual‐based simulation of a central‐place forager. The results for different models and sample sizes indicate that MSKS has three important properties. Firstly, it generally outperforms KS by an extent that depends on the quality of the auxiliary model. Secondly, when the auxiliary model is not informative, MSKS automatically reverts to a similar output as KS. Finally, in practical terms, MSKS is easy to implement and adds little to the computational requirements already made by KS methods. I illustrate the application of MSKS and further validate its performance on satellite telemetry data collected from a grey seal on the east coast of Scotland.