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.     

Modeling continuous auxiliary covariate data in generalized linear mixed models using the kernel smoother

Auxiliary covariate data are often collected in biomedical studies when the primary exposure variable is only assessed on a subset of the study subjects. In this study, we investigate a semiparametric‐estimated likelihood estimation for the generalized linear mixed models (GLMM) in the presence of a continuous auxiliary variable. We use a kernel smoother to handle continuous auxiliary data. The method can be used to deal with missing or mismeasured covariate data problems in a variety of applications when an auxiliary variable is available and cluster sizes are not too small. Simulation study results show that the proposed method performs better than that which ignores the random effects in GLMM and that which only uses data in the validation data set. We illustrate the proposed method with a real data set from a recent environmental epidemiology study on the maternal serum 1,1‐dichloro‐2,2‐bis(p‐chlorophenyl) ethylene level in relationship to preterm births.     

Prediction of protein domain boundaries from inverse covariances

It has been known even since relatively few structures had been solved that longer protein chains often contain multiple domains, which may fold separately and play the role of reusable functional modules found in many contexts. In many structural biology tasks, in particular structure prediction, it is of great use to be able to identify domains within the structure and analyze these regions separately. However, when using sequence data alone this task has proven exceptionally difficult, with relatively little improvement over the naive method of choosing boundaries based on size distributions of observed domains. The recent significant improvement in contact prediction provides a new source of information for domain prediction. We test several methods for using this information including a kernel smoothing‐based approach and methods based on building alpha‐carbon models and compare performance with a length‐based predictor, a homology search method and four published sequence‐based predictors: DOMCUT, DomPRO, DLP‐SVM, and SCOOBY‐DOmain. We show that the kernel‐smoothing method is significantly better than the other ab initio predictors when both single‐domain and multidomain targets are considered and is not significantly different to the homology‐based method. Considering only multidomain targets the kernel‐smoothing method outperforms all of the published methods except DLP‐SVM. The kernel smoothing method therefore represents a potentially useful improvement to ab initio domain prediction. Proteins 2013. © 2012 Wiley Periodicals, Inc.     

Circulating miRNA‐375 as a potential novel biomarker for active Kaposi’s sarcoma in AIDS patients

The aim of this study was to identify circulating microRNAs (miRNAs) that could be used as biomarkers in patients at risk for or affected by AIDS‐Kaposi's sarcoma (KS). Screening of 377 miRNAs was performed using low‐density arrays in pooled plasma samples of 10 HIV/human herpesvirus 8 (HHV8)‐infected asymptomatic and 10 AIDS‐KS patients before and after successful combined antiretroviral therapy (cART). MiR‐375 was identified as a potential marker of active KS, being the most down‐regulated in AIDS‐KS patients after cART and the most up‐regulated in naïve AIDS‐KS patients compared to naïve asymptomatic subjects. Validation on individual plasma samples confirmed that miR‐375 levels were higher in AIDS‐KS compared to asymptomatic patients, decreased after cART‐induced remission in most AIDS‐KS patients and increased in patients with active KS. In asymptomatic patients miR‐375 was up‐regulated after cART in both screening and validation. Statistical analyses revealed an association between miR‐375 changes and CD4 cell counts, which could explain the discordant cases and the opposite trend between asymptomatic and AIDS‐KS patients. These data suggest that circulating miR‐375 might be a good indicator of active AIDS‐KS. Moreover, changes in miR‐375 levels may have a prognostic value in HIV/HHV8‐infected patients undergoing treatment. Further large‐scale validation is needed.     

Improved estimates of incident radiation and heat load using non‐ parametric regression against topographic variables

Question: Can non‐parametric multiplicative regression (NPMR) improve estimates of potential direct incident radiation (PDIR) and heat load based on topographic variables, as compared to least‐squares multiple regression against trigonometric transforms of the predictors? Methods: We used a multiplicative kernel smoothing technique to interpolate between tabulated values of PDIR, using a locally linear model and a Gaussian kernel, with slope, aspect, and latitude as predictors. Heat load was calculated as a 45 degree rotation of the PDIR response surface. Results: This method yielded a fit to a complex response surface with R² > 0.99 and eliminated the areas of poor fit given by a previously published method based on least squares multiple regression with trigonometric functions of the predictors. Conclusions: Improved estimates of PDIR and heat load based on topographic variables can be obtained by using non‐parametric multiplicative regression (NPMR). The main drawback to the method is that it requires reference to the data tables, since those data are part of the model.     

An adaptive bivariate kernel smoothing method for determining instars of Austrosimulium tillyardianum (Diptera: Simuliidae) larvae

1. In insects, instar determination is generally based on the frequency distribution of sclerotised body part measurements. Commonly used univariate methods, such as histograms and univariate kernel smoothing, are not sufficient to reflect the distribution of the measurements, because development of sclerotised body parts is multidimensional. 2. This study used an adaptive bivariate kernel smoothing method, based on 10 pairs of separating variables, to differentiate instars of Austrosimulium tillyardianum (Diptera: Simuliidae) larvae in two‐dimensional space. A variable bandwidth matrix was used and separation lines between instars were defined. Using the Crosby growth ratio, Brooks' rule and the new standard recently proposed, larvae were separated into nine instars. It was found that, using the bivariate kernel smoothing method, the clustering accuracy and determination of separation lines as instar class limits were higher than those associated with the univariate kernel smoothing method. With the exceptions of the paired separating variables, head capsule length and antennal segment 3 length (AS3L), the mean probabilities of correct classifications was > 85%. The pair of separating variables that yielded the greatest classification accuracy comprised mandible length (ML) and AS3L, which had mean probabilities of 0.8984. The clustering accuracy was higher for early‐ and late‐instar larvae, but lower for instars 6 and 7. The adaptive bivariate kernel smoothing method was better than univariate methods for instar determination, especially in the detection of divisions between instars and identification of a larval instar.     

Mapping Cancer Risk in Southwestern Ontario with Changing Census Boundaries

Summary Mapping disease risk often involves working with data that have been spatially aggregated to census regions or postal regions, either for administrative reasons or confidentiality. When studying rare diseases, data must be collected over a long time period in order to accumulate a meaningful number of cases. These long time periods can result in spatial boundaries of the census regions changing over time, as is the case with the motivating example of exploring the spatial structure of mesothelioma lung cancer risk in Lambton County and Middlesex County of southwestern Ontario, Canada. This article presents a local‐EM kernel smoothing algorithm that allows for the combining of data from different spatial maps, being capable of modeling risk for spatially aggregated data with time‐varying boundaries. Inference and uncertainty estimates are carried out with parametric bootstrap procedures, and cross‐validation is used for bandwidth selection. Results for the lung cancer study are shown and discussed.     

Denoising functional magnetic resonance imaging time-series using anisotropic spatial averaging

We propose a novel iterative scheme for adaptive smoothing of functional MR images. The method estimates a signal model at every voxel in the time-series, which is subsequently used in determining the weights of the smoothing kernel. The method does not require any information about the test hypothesis and is well-suited as a preprocessing step for both hypothesis-driven and data-driven analysis techniques. We demonstrate the performance of the proposed method by applying it to preprocess both simulated and real fMRI data. The method is found to effectively suppress the noise while preserving the shapes of the active brain regions.     

Information‐theoretic model selection affects home‐range estimation and habitat preference inference: a case study of male Reeves’s Pheasants Syrmaticus reevesii

Reeves’s Pheasant Syrmaticus reevesii is a vulnerable forest bird inhabiting broadleaved habitats dominated by oaks Quercus spp. in central China. Identifying home‐ranges and habitat associations is important for understanding the biology of this species and developing effective management and conservation plans. We used information‐theoretic criteria to evaluate the relative performance of four parametric (exponential power, one‐mode bivariate normal, two‐mode bivariate normal and two‐mode bivariate circle) and two non‐parametric models (adaptive and fixed kernel) for estimating home‐ranges and habitat associations of Reeves’s Pheasants. For parametric models, Akaike’s information criterion (AIC_c) and the likelihood cross‐validation criterion (CVC) were relatively consistent in ranking the bivariate exponential power model the least acceptable, whereas the two‐mode bivariate models performed better. The CVC suggested that kernel models, particularly the adaptive kernel, performed best among all six models evaluated. The average core area and 95% contour area based on the model with greatest support were 6.1 and 54.9 ha, respectively, and were larger than those estimated from other models. The discrepancy in estimates between models with highest and the lowest support decreased as the contour size increased; however, home‐range shapes differed between models. Minimum convex polygons that removed 5% of extreme data points (MCP95) were roughly half the size of home‐ranges based on kernel models. Estimates of home‐range and model evaluation were not affected by sample size (> 50 observations for each bird). Inference about habitat preference based on composition analysis and home‐range overlap varied between models. That with strongest support suggested that Reeves’s Pheasants selected mature fir and mixed forest, avoided farmland, and had mean among‐individual home‐range overlaps of 20%. We recommend non‐parametric methods, particularly the adaptive kernel method, for estimating home‐ranges and core areas for species with complex multi‐polar habitat preferences in heterogeneous environments with large habitat patches. However, we caution against the traditional convenience of using a single model to estimate home‐ranges and recommend exploration of multiple models for describing and understanding the ecological processes underlying space use and habitat associations.     

Markov models and network analysis reveal sex‐specific differences in the space‐use of a coastal apex predator

Understanding the links between external variables such as habitat and interactions with conspecifics and animal space‐use is fundamental to developing effective management measures. In the marine realm, automated acoustic tracking has become a widely used method for monitoring the movement of free‐ranging animals, yet researchers generally lack robust methods for analysing the resulting spatial‐usage data. In this study, acoustic tracking data from male and female broadnose sevengill sharks Notorynchus cepedianus, collected in a system of coastal embayments in southeast Tasmania were analyzed to examine sex‐specific differences in the sharks’ coastal space‐use and test novel methods for the analysis of acoustic telemetry data. Sex‐specific space‐use of the broadnose sevengill shark from acoustic telemetry data was analysed in two ways: The recently proposed spatial network analysis of between‐receiver movements was employed to identify sex‐specific space‐use patterns. To include the full breadth of temporal information held in the data, movements between receivers were furthermore considered as transitions between states of a Markov chain, with the resulting transition probability matrix allowing the ranking of the relative importance of different parts of the study area. Both spatial network and Markov chain analysis revealed sex‐specific preferences of different sites within the study area. The identification of priority areas differed for the methods, due to the fact that in contrast to network analysis, our Markov chain approach preserves the chronological sequence of detections and accounts for both residency periods and movements. In addition to adding to our knowledge of the ecology of a globally distributed apex predator, this study presents a promising new step towards condensing the vast amounts of information collected with acoustic tracking technology into straightforward results which are directly applicable to the management and conservation of any species that meet the assumptions of our model.     

Running on empty: recharge dynamics from animal movement data

Vital rates such as survival and recruitment have always been important in the study of population and community ecology. At the individual level, physiological processes such as energetics are critical in understanding biomechanics and movement ecology and also scale up to influence food webs and trophic cascades. Although vital rates and population‐level characteristics are tied with individual‐level animal movement, most statistical models for telemetry data are not equipped to provide inference about these relationships because they lack the explicit, mechanistic connection to physiological dynamics. We present a framework for modelling telemetry data that explicitly includes an aggregated physiological process associated with decision making and movement in heterogeneous environments. Our framework accommodates a wide range of movement and physiological process specifications. We illustrate a specific model formulation in continuous‐time to provide direct inference about gains and losses associated with physiological processes based on movement. Our approach can also be extended to accommodate auxiliary data when available. We demonstrate our model to infer mountain lion (Puma concolor; in Colorado, USA) and African buffalo (Syncerus caffer; in Kruger National Park, South Africa) recharge dynamics.     

Bayesian semiparametric intensity estimation for inhomogeneous spatial point processes

In this work we propose a fully Bayesian semiparametric method to estimate the intensity of an inhomogeneous spatial point process. The basic idea is to first convert intensity estimation into a Poisson regression setting via binning data points on a regular grid, and then model the log intensity semiparametrically using an adaptive version of Gaussian Markov random fields to smooth the corresponding counts. The inference is carried by an efficient Markov chain Monte Carlo simulation algorithm. Compared to existing methods for intensity estimation, for example, parametric modeling and kernel smoothing, the proposed estimator not only provides inference regarding the dependence of the intensity function on possible covariates, but also uses information from the data to adaptively determine the amount of smoothing at the local level. The effectiveness of using our method is demonstrated through simulation studies and an application to a rainforest dataset.     

Multivariate adaptation and classification method for characteristic sample properties

Characteristic properties of samples can be measured by spectrometers, cameras or other applicable equipment. To achieve meaningful classification results with a user‐friendly arrangement of the overall system, a new approach is pursued in which principally unaltered input data are reduced to their essential content using a Wavelet transform and are refined with a special smoothing method in such a manner that certain dimension‐reducing techniques can also be employed in a numerically stable way for discontinuous data sets as they occur, for example, in classification tasks. The introduced multivariate adaptive embedding (MAE) process acts as a universal approximator in the adaptation phase, to a very large extent without iterations and parameter adjustments, and deduces a redundancy‐free model with which untrained input data with outstanding generalization properties, in terms of an application, can be processed in the application phase. While taking advantage of the proximity relationships of the data points, the entire information is mapped into a low‐dimensional coordinate system using a supervised learning process and is scaled and adapted to the respective application using an unsupervised learning process. This approach allows classification of highly related and confused data as they may occur in identification/classification setups for bacteria and other substances using spectroscopic methods.     

Count-dependent filter for smoothing bivariate FCM histograms

A data-smoothing filter has been developed that permits the improvement in accuracy of individual elements of a bivariate flow cytometry (FCM) histogram by making use of data from adjacent elements, a knowledge of the two-dimensional measurement system point spread function (PSF), and the local count density. For FCM data, the PSF is assumed to be a set of two-dimensional Gaussian functions with a constant coefficient of variation for each axis. A set of space variant smoothing kernels are developed from the basic PSF by adjusting the orthogonal standard deviations of each Gaussian smoothing kernel according to the local count density. This adjustment in kernel size matches the degree of smoothing to the local reliability of the data. When the count density is high, a small kernel is sufficient. When the density is low, however, a broader kernel should be used. The local count density is taken from a region defined by the measurement PSF. The smoothing algorithm permits the reduction in statistical fluctuations present in bivariate FCM histograms due to the low count densities often encountered in some elements. This reduction in high-frequency spatial noise aids in the visual interpretation of the data. Additionally, by making more efficient use of smaller samples, systematic errors due to system drift may be minimized.     

Multiclass molecular cancer classification by kernel subspace methods with effective kernel parameter selection

Microarray techniques provide new insights into molecular classification of cancer types, which is critical for cancer treatments and diagnosis. Recently, an increasing number of supervised machine learning methods have been applied to cancer classification problems using gene expression data. Support vector machines (SVMs), in particular, have become one of the most effective and leading methods. However, there exist few studies on the application of other kernel methods in the literature. We apply a kernel subspace (KS) method to multiclass cancer classification problems, and assess its validity by comparing it with multiclass SVMs. Our comparative study using seven multiclass cancer datasets demonstrates that the KS method has high performance that is comparable to multiclass SVMs. Furthermore, we propose an effective criterion for kernel parameter selection, which is shown to be useful for the computation of the KS method.     

Inference Based on Kernel Estimates of the Relative Risk Function in Geographical Epidemiology

Kernel smoothing is a popular approach to estimating relative risk surfaces from data on the locations of cases and controls in geographical epidemiology. The interpretation of such surfaces is facilitated by plotting of tolerance contours which highlight areas where the risk is sufficiently high to reject the null hypothesis of unit relative risk. Previously it has been recommended that these tolerance intervals be calculated using Monte Carlo randomization tests. We examine a computationally cheap alternative whereby the tolerance intervals are derived from asymptotic theory. We also examine the performance of global tests of hetereogeneous risk employing statistics based on kernel risk surfaces, paying particular attention to the choice of smoothing parameters on test power (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Study on the foraging behaviour of the European nightjar Caprimulgus europaeus reveals the need for a change in conservation strategy in Belgium

Effective nature conservation requires coherent actions based on the best available evidence concerning protected species. Recent studies have suggested that European nightjars Caprimulgus europaeus forage outside their recognized breeding habitats, yet, for Flanders (northern Belgium) information on nightjar foraging behaviour and key foraging habitats is lacking. To assess whether the foraging ecology of nightjars in Flanders is similar to that observed in other parts of Europe, we studied the crepuscular behaviour of this species in Bosland (northeastern Flanders) during a five‐year radio telemetry study. Tracking of 48 individuals within a coniferous forest was standardized and home ranges were calculated using a kernel density estimator (fixed kernel). Habitat use was investigated by comparing kernel placement to available habitat. Average maximal foraging distance was 2603 ± 1094 m and home ranges extended up to 691 ha. We identified the key foraging habitats to be extensively‐cultivated grasslands and recreational areas, areas that were previously assumed unsuitable for Belgian nightjars. Our results indicate the importance of foraging sites outside the breeding territory, confirming the findings of previous studies performed elsewhere in Europe. Incorporating our findings into future conservation plans could, therefore, lead to improved efficiency of EU conservation measures, designed for the protection of this bird species in Flanders.     

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.     

Accounting for phenology in the analysis of animal movement

The analysis of animal tracking data provides important scientific understanding and discovery in ecology. Observations of animal trajectories using telemetry devices provide researchers with information about the way animals interact with their environment and each other. For many species, specific geographical features in the landscape can have a strong effect on behavior. Such features may correspond to a single point (eg, dens or kill sites), or to higher dimensional subspaces (eg, rivers or lakes). Features may be relatively static in time (eg, coastlines or home‐range centers), or may be dynamic (eg, sea ice extent or areas of high‐quality forage for herbivores). We introduce a novel model for animal movement that incorporates active selection for dynamic features in a landscape. Our approach is motivated by the study of polar bear (Ursus maritimus) movement. During the sea ice melt season, polar bears spend much of their time on sea ice above shallow, biologically productive water where they hunt seals. The changing distribution and characteristics of sea ice throughout the year mean that the location of valuable habitat is constantly shifting. We develop a model for the movement of polar bears that accounts for the effect of this important landscape feature. We introduce a two‐stage procedure for approximate Bayesian inference that allows us to analyze over 300 000 observed locations of 186 polar bears from 2012 to 2016. We use our model to estimate a spatial boundary of interest to wildlife managers that separates two subpopulations of polar bears from the Beaufort and Chukchi seas.