Estimated home ranges can misrepresent habitat relationships on patchy landscapes

Home ranges of animals are generally structured by the selective use of resource-bearing patches that comprise habitat. Based on this concept, home ranges of animals estimated from location data are commonly used to infer habitat relationships. Because home ranges estimated from animal locations are largely continuous in space, the resource-bearing patches selected by an animal from a fragmented distribution of patches would be difficult to discern; unselected patches included in the home range estimate would bias an understanding of important habitat relationships. To evaluate potential for this bias, we generated simulated home ranges based on optimal selection of resource-bearing patches across a series of simulated resource distributions that varied in the spatial continuity of resources. For simulated home ranges where selected patches were spatially disjunct, we included interstitial, unselected cells most likely to be traveled by an animal moving among selected patches. We compared characteristics of the simulated home ranges with and without interstitial patches to evaluate how insights derived from field estimates can differ from actual characteristics of home ranges, depending on patchiness of landscapes. Our results showed that contiguous home range estimates could lead to misleading insights on the quality, size, resource content, and efficiency of home ranges, proportional to the spatial discontinuity of resource-bearing patches. We conclude the potential bias of including unselected, largely irrelevant patches in the field estimates of home ranges of animals can be high, particularly for home range estimators that assume uniform use of space within home range boundaries. Thus, inferences about the habitat relationships that ultimately define an animal's home range can be misleading where animals occupy landscapes with patchily distributed resources.     

Using the bootstrap and fast Fourier transform to estimate confidence intervals of 2D kernel densities

Kernel density estimators are often used to estimate the utilization distributions (UDs) of animals. Kernel UD estimates have a strong theoretical basis and perform well, but are usually reported without estimates of error or uncertainty. It is intuitively and theoretically appealing to estimate the sampling error in kernel UD estimates using bootstrapping. However, standard equations for kernel density estimates are complicated and computationally expensive. Bootstrapping requires computing hundreds or thousands of probability densities and is impractical when the number of observations, or the area of interest is large. We used the fast Fourier transform (FFT) and discrete convolution theorem to create a bootstrapping algorithm fast enough to run on commonly available desktop or laptop computers. Application of the FFT method to a large (n>20,000) set of radio telemetry data would provide a 99.6% reduction in computation time (i.e., 1.6 as opposed to 444 hours) for 1000 bootstrap UD estimates. Bootstrap error contours were computed using data from a radio-collared polar bear (Ursus maritimus) in the Beaufort Sea north of Alaska.     

Eigenanalysis of selection ratios from animal radio-tracking data

The development of methods to analyze habitat selection when resources are defined by several categories (e.g., vegetation types) is a topical issue in radio-tracking studies. The White and Garrott statistic, an extension of the widely used test of Neu et al., can be used to determine whether habitat selection is significant. As well, Manly's selection ratio, a particularly useful measure of resource selectivity by resource users, allows detection of the most strongly selected habitat types. However, when both the number of animals and types of habitat are large, the biologist often has to deal with an excessively large number of measures. In this paper we present a new method, the eigenanalysis of selection ratios, that generalizes these two common methods within the framework of eigenanalyses. This method undertakes an additive linear partitioning of the White and Garrott statistic, so that the difference between habitat use and availability is maximized on the first factorial axes. The eigenanalysis of selection ratios is therefore optimal in habitat selection studies. Although we primarily consider the case where the habitat availability is the same for all animals (design II), we also extend this analysis to the case where the habitat availability varies from one animal to another (design III). An application of this method is provided using radio-tracking data collected on 17 squirrels in five habitat types. The results indicate variability in habitat selection, with two groups of animals displaying two patterns of preference. This difference between the two groups is explained by the patch structure of the study area. Because this method is mainly exploratory, and therefore does not rely on any distributional assumption, we recommend its use in studies of habitat selection.     

A general approach to the analysis of habitat selection

The investigation of animal habitat selection aims at the detection of selective usage of habitat types and the identification of covariates influencing their selection. The results not only allow for a better understanding of the habitat selection process but are also intended to help improve the conservation of animals. Usually, habitat selection by larger animals is assessed by radio-tracking or visual observation studies, where the chosen habitat is determined for some animals at a set of specific points in time. Hence the resulting data often have the following structure: a categorical variable indicating the habitat type selected by an animal at a specific point in time is repeatedly observed and will be explained by covariates. These may either describe properties of the habitat types currently available and/or properties of the animal. In this paper, we present a general approach to the analysis of such data in a categorical regression setup. The proposed model generalizes and improves upon several of the approaches previously discussed in the literature. In particular, it accounts for changing habitat availability due to the movement of animals within the observation area. It incorporates both habitat- and animal-specific covariates, and includes individual-specific random effects to account for correlations introduced by the repeated measurements on single animals. Furthermore, the assumption that the effects are linear can be dropped by including the effects in nonparametric manner based on a penalized spline approach. The methodology is implemented in a freely available software package. We demonstrate the general applicability and the potential of the proposed approach in two case studies: The analysis of a songbird community in South-America and a study on brown bears in Central Europe.     

What are the strengths and limitations of direct and indirect assessment of dispersal? Insights from a long-term field study in a group-living bird species

Molecular methods of assessing dispersal have become increasingly powerful and have superseded direct methods of studying dispersal. Although now less popular, direct methods of studying dispersal remain important tools for understanding the evolution of dispersal. Here, we use data from Siberian jays Perisoreus infaustus, a group-living bird species, to compare natal dispersal distances and rates using visual mark–recapture, radio-tracking and microsatellite data. Siberian jays have bimodal natal dispersal timing; socially dominant offspring remain with their parents for up to 5 years (delayed dispersers), while they force their subordinate brood mates to leave the parental territory at independence (early dispersers). Early dispersers moved about 9,000 m (visual mark–recapture, radio-tracking) before settling in a group as a non-breeder. In contrast, delayed dispersers moved about 1,250 m (visual mark–recapture only) and mainly moved to a breeding opening. Dispersal distances were greater in managed habitat compared to natural habitat for both early and delayed dispersers. Molecular estimates based on 23 microsatellite loci and geographical locations supported distance estimates from the direct methods. Our study shows that molecular methods are at least 22 times cheaper than direct methods and match estimates of dispersal distance from direct methods. However, molecular estimates do not give insight into the behavioural mechanisms behind dispersal decisions. Thus, to understand the evolution of dispersal, it is important to combine direct and indirect methods, which will give insights into the behavioural processes affecting dispersal decisions, allowing proximate dispersal decisions to be linked to the ultimate consequences thereof.     

K-select analysis: a new method to analyse habitat selection in radio-tracking studies

Two kinds of wildlife habitat studies can be distinguished in the literature: hindcasting and forecasting studies. Hindcasting studies aim to emphasize among a large set of habitat variables those that are of interest for the focus species, whereas forecasting studies are intended to predict habitat selection according to a small number of habitat variables for a given area. We provide here a new analytical tool which relies on the concept of ecological niche, the K-select analysis, for hindcasting studies of habitat selection by animals using radio-tracking data. Each habitat variable defines one dimension in the ecological space. For each animal, the difference between the vector of average available habitat conditions and the vector of average used conditions defines the marginality vector. Its size is proportional to the importance of habitat selection, and its direction indicates which variables are selected. By performing a non-centered principal component analysis of the table containing the coordinates of the marginality vectors of each animal (row) on the habitat variables (column), the K-select analysis returns a linear combination of habitat variables for which the average marginality is greatest. It is a synthesis of variables which contributes the most to the habitat selection. As with principal component analysis, the biological significance of the factorial axes is deduced from the loading of variables. An example is provided: habitat selection by wild boar is studied in a Mediterranean habitat using the K-select analysis. The numerous advantages of the analysis (a large number of variables that can be included, individual variability in habitat selection taken into account, a lack of too strict underlying hypotheses) make it a powerful approach in radio-tracking studies designed to identify habitat variables that are selected by animals.     

The role of time and species identities in spatial patterns of species richness and conservation

Many conservation actions are justified on the basis of managing biodiversity. Biodiversity, in terms of species richness, is largely the product of rare species. This is problematic because the intensity of sampling needed to characterize communities and patterns of rarity or to justify the use of surrogates has biased sampling in favor of space over time. However, environmental fluctuations interacting with community dynamics lead to temporal variations in where and when species occur, potentially affecting conservation planning by generating uncertainty about results of species distribution modeling (including range determinations), selection of surrogates for biodiversity, and the proportion of biodiversity composed of rare species. To have confidence in the evidence base for conservation actions, one must consider whether temporal replication is necessary to produce broad inferences. Using approximately 20 years of macrofaunal data from tidal flats in 2 harbors, we explored variation in the identity of rare, common, restricted range, and widespread species over time and space. Over time, rare taxa were more likely to increase in abundance or occurrence than to remain rare or disappear and to exhibit temporal patterns in their occurrence. Space–time congruency in ranges (i.e., spatially widespread taxa were also temporally widespread) was observed only where samples were collected across an environmental gradient. Fifteen percent of the taxa in both harbors changed over time from having spatially restricted ranges to having widespread ranges. Our findings suggest that rare species can provide stability against environmental change, because the majority of species were not random transients, but that selection of biodiversity surrogates requires temporal validation. Rarity needs to be considered both spatially and temporally, as species that occur randomly over time are likely to play a different role in ecosystem functioning than those exhibiting temporal structure (e.g., seasonality). Moreover, temporal structure offers the opportunity to place management and conservation activities within windows of maximum opportunity.     

Habitat Loss and Changes in the Species-Area Relationship

Abstract: The species-area relationship (SAR) has been used successfully to predict extinction from extent of habitat reduction. These extinction estimates assume that species have uniformly distributed range requirements and a minimum abundance level required for persistence; how many species are lost depends solely on how much habitat is removed, not on where it is removed. We consider another limiting case in which range requirements, rather than abundances, determine extinctions. We used a new method for constructing SARs based on assumptions about geographic ranges of species. Our results show that habitat destruction can change the SAR and consequently the number of species predicted to be lost due to habitat destruction. Our method generates SARs that vary in shape according to the specific distributions of geographic range and occupancy but that have the common feature of being described by a power law with an exponent of <1. When the geographic range of species was included in the SAR, the way habitat was lost became important. Although the SAR before habitat destruction is often used to predict species loss after habitat destruction, assumptions must be clearly stated. To predict the damage caused by habitat loss with our model, it is necessary to know the fraction of aggregated species, the distribution of geographic ranges, the form of habitat destruction, and the sampling protocol. The remaining theoretical challenge is to develop a full theory that links abundance and range.     

Modeling species-habitat relationships with spatially autocorrelated observation data.

Spatial autocorrelation in wildlife observation data arises when extrinsic environmental processes and patterns that influence the spatial distribution of wildlife are themselves spatially structured, or when species are subject to intrinsic population processes, causing contagion or dispersion effects. Territoriality, Allee effects, dispersal limitations, and social clustering are examples of intrinsic processes. Both forms of autocorrelation can violate the assumptions of generalized linear regression models, resulting in biased estimation of model coefficients and diminished predictive performance. Such consequences may be avoided for extrinsic autocorrelation when autocorrelated environmental variables are available for use as model covariates, whereas intrinsic spatial autocorrelation requires an alternative modeling approach. The autologistic model provides an approach suited to the binary observations often obtained in wildlife surveys, but its performance has not been tested across widely varying sampling intensities or strengths of intrinsic spatial structure. Here we use simulated data to test the autologistic model under a range of sampling conditions. The autologistic model obtains better fits and substantially better predictive performance than the standard logistic regression model over the full range of sampling designs and intensities tested. We provide a simple Bayesian implementation of the autologistic model, which until now has not been achieved with standard statistical software alone. A step-by-step procedure is given for characterizing and modeling spatial autocorrelation in binary observation data, along with computer code for fitting autologistic models in WinBUGS, a freeware Bayesian analysis package. This approach avoids normal approximations to the pseudo-likelihood, in contrast to previous Bayesian applications of the autologistic model. We provide a sample application of the autologistic model, fitted to survey data for a gliding marsupial in southeastern Australia.     

Old models explain new observations of butterfly movement at patch edges

Understanding movement in heterogeneous environments is central to predicting how landscape changes affect animal populations. Several recent studies point out an intriguing and distinctive looping behavior by butterflies at habitat patch edges and hypothesize that this behavior requires a new framework for analyzing animal movement. We show that this looping behavior could be caused by a longstanding movement model, biased correlated random walk, with bias toward habitat patches. The ability of this longstanding model to explain recent observations reinforces the point that butterflies respond to habitat heterogeneity and do not move randomly through heterogeneous environments. We discuss the implications of different movement models for predicting butterfly responses to landscape change, and our rationale for retaining longstanding movement models, rather than developing new modeling frameworks for looping behavior at patch edges.     

Efficacy of Land-Cover Models in Predicting Isolation of Marbled Salamander Populations in a Fragmented Landscape

Abstract:  Amphibians worldwide are facing rapid declines due to habitat loss and fragmentation, disease, and other causes. Where habitat alteration is implicated, there is a need for spatially explicit conservation plans. Models built with geographic information systems (GIS) are frequently used to inform such planning. We explored the potential for using GIS models of functional landscape connectivity as a reliable proxy for genetically derived measures of population isolation. We used genetic assignment tests to characterize isolation of marbled salamander populations and evaluated whether the relative amount of modified habitat around breeding ponds was a reliable indicator of population isolation. Using a resampling analysis, we determined whether certain land-cover variables consistently described population isolation. We randomly drew half the data for model building and tested the performance of the best models on the other half 100 times. Deciduous forest was consistently associated with lower levels of population isolation, whereas salamander populations in regions of agriculture and anthropogenic development were more isolated. Models that included these variables and pond size explained 65–70% of variation in genetically inferred isolation across sites. The resampling analysis confirmed that these habitat variables were consistently good predictors of isolation. Used judiciously, simple GIS models with key land-cover variables can be used to estimate population isolation if field sampling and genetic analysis are not possible.     

A method for quantifying bias in modeled concentrations and source impacts for secondary particulate matter

A method for quantifying source impacts for secondary PM_2.5 species is derived. The method provides estimates of bias in modeled concentrations. Adjusted concentrations match corresponding observations at monitored locations. Sources impacts on secondary species are estimated over the US for 20 sources. Community Multi-Scale Air Quality (CMAQ) estimates of sulfates, nitrates, ammonium, and organic carbon are highly influenced by uncertainties in modeled secondary formation processes, such as chemical mechanisms, volatilization, and condensation rates. These compounds constitute the majority of PM_2.5 mass, and reducing bias in estimated concentrations has benefits for policy measures and epidemiological studies. In this work, a method for adjusting source impacts on secondary species is developed that provides estimates of source contributions and reduces bias in modeled concentrations compared to observations. The bias correction adjusts concentrations and source impacts based on the difference between modeled concentrations and observations while taking into account uncertainties at the location of interest; and it is applied both spatially and temporally. We apply the method over the US for 2006. The mean bias for initial CMAQ concentrations compared to observations is −0.28 (OC), 0.11 (NO₃), 0.05 (NH₄), and −0.08 (SO₄). The normalized mean bias in modeled concentrations compared to observations was effectively zero for OC, NO₃, NH₄, and SO₄ after applying the secondary bias correction. 10-fold cross-validation was conducted to determine the performance of the spatial application of the bias correction. Cross-validation performance was favorable; correlation coefficients were greater than 0.69 for all species when comparing observations and concentrations based on kriged correction factors. The methods presented here address model uncertainties by improving simulated concentrations and source impacts of secondary particulate matter through data assimilation. Secondary-adjusted concentrations and source impacts from 20 emissions sources are generated for 2006 over continental US.     

Spatial scale of local breeding habitat quality and adjustment of breeding decisions

Experimental studies provide evidence that, in spatially and temporally heterogeneous environments, individuals track variation in breeding habitat quality to adjust breeding decisions to local conditions. However, most experiments consider environmental variation at one spatial scale only, while the ability to detect the influence of a factor depends on the scale of analysis. We show that different breeding decisions by adults are based on information about habitat quality at different spatial scales. We manipulated (increased or decreased) local breeding habitat quality through food availability and parasite prevalence at a small (territory) and a large (patch) scale simultaneously in a wild population of Great Tits (Parus major). Females laid earlier in high-quality large-scale patches, but laying date did not depend on small-scale territory quality. Conversely, offspring sex ratio was higher (i.e., biased toward males) in high-quality, small-scale territories but did not depend on large-scale patch quality. Clutch size and territory occupancy probability did not depend on our experimental manipulation of habitat quality, but territories located at the edge of patches were more likely to be occupied than central territories. These results suggest that integrating different decisions taken by breeders according to environmental variation at different spatial scales is required to understand patterns of breeding strategy adjustment.     

Effects of sampling error and temporal correlations in population growth on process variance estimators

Estimates of a population’s growth rate and process variance from time-series data are often used to calculate risk metrics such as the probability of quasi-extinction, but temporal correlations in the data from sampling error, intrinsic population factors, or environmental conditions can bias process variance estimators and detrimentally affect risk predictions. It has been claimed (McNamara and Harding, Ecol Lett 7:16–20, 2004) that estimates of the long-term variance that incorporate observed temporal correlations in population growth are unaffected by sampling error; however, no estimation procedures were proposed for time-series data. We develop a suite of such long-term variance estimators, and use simulated data with temporally autocorrelated population growth and sampling error to evaluate their performance. In some cases, we get nearly unbiased long-term variance estimates despite ignoring sampling error, but the utility of these estimators is questionable because of large estimation uncertainty and difficulties in estimating correlation structure in practice. Process variance estimators that ignored temporal correlations generally gave more precise estimates of the variability in population growth and of the probability of quasi-extinction. We also found that the estimation of probability of quasi-extinction was greatly improved when quasi-extinction thresholds were set relatively close to population levels. Because of precision concerns, we recommend using simple models for risk estimates despite potential biases, and limiting inference to quantifying relative risk; e.g., changes in risk over time for a single population or comparative risk among populations.     

The value, limitations, and challenges of employing local experts in conservation research

Abstract: Evidence suggests that the involvement of local people in conservation work increases a project's chances of success. Involving citizen scientists in research, however, raises questions about data quality. As a tool to better assess potential participants for conservation projects, we developed a knowledge gradient, K, along which community members occupy different positions on the basis of their experience with and knowledge of a research subject. This gradient can be used to refine the citizen–science concept and allow researchers to differentiate between community members with expert knowledge and those with little knowledge. We propose that work would benefit from the inclusion of select local experts because it would allow researchers to harness the benefits of local involvement while maintaining or improving data quality. We used a case study from the DeHoop Nature Preserve, South Africa, in which we conducted multiple interviews, identified and employed a local expert animal tracker, evaluated the expert's knowledge, and analyzed the data collected by the expert. The expert animal tracker J.J. created his own sampling design and gathered data on mammals. He patrolled 4653 km in 214 days and recorded 4684 mammals. He worked from a central location, and his patrols formed overlapping loops; however, his data proved neither spatially nor temporally autocorrelated. The distinctive data collected by J.J. are consistent with the notion that involving local experts can produce reliable data. We developed a conceptual model to help identify the appropriate participants for a given project on the basis of research budget, knowledge or skills needed, technical literacy requirements, and scope of the project.     

Kernel density estimators of home range: smoothing and the autocorrelation red herring

Two oft-cited drawbacks of kernel density estimators (KDEs) of home range are their sensitivity to the choice of smoothing parameter(s) and their need for independent data. Several simulation studies have been conducted to compare the performance of objective, data-based methods of choosing optimal smoothing parameters in the context of home range and utilization distribution (UD) estimation. Lost in this discussion of choice of smoothing parameters is the general role of smoothing in data analysis, namely, that smoothing serves to increase precision at the cost of increased bias. A primary goal of this paper is to illustrate this bias-variance trade-off by applying KDEs to sampled locations from simulated movement paths. These simulations will also be used to explore the role of autocorrelation in estimating UDs. Autocorrelation can be reduced (1) by increasing study duration (for a fixed sample size) or (2) by decreasing the sampling rate. While the first option will often be reasonable, for a fixed study duration higher sampling rates should always result in improved estimates of space use. Further, KDEs with typical data-based methods of choosing smoothing parameters should provide competitive estimates of space use for fixed study periods unless autocorrelation substantially alters the optimal level of smoothing.     

Determining Optimal Population Monitoring for Rare Butterflies

Abstract: Determining population viability of rare insects depends on precise, unbiased estimates of population size and other demographic parameters. We used data on the endangered St. Francis' satyr butterfly (Neonympha mitchellii francisci) to evaluate 2 approaches (mark–recapture and transect counts) for population analysis of rare butterflies. Mark–recapture analysis provided by far the greatest amount of demographic information, including estimates (and standard errors) of population size, detection, survival, and recruitment probabilities. Mark–recapture analysis can also be used to estimate dispersal and temporal variation in rates, although we did not do this here. Models of seasonal flight phenologies derived from transect counts (Insect Count Analyzer) provided an index of population size and estimates of survival and statistical uncertainty. Pollard–Yates population indices derived from transect counts did not provide estimates of demographic parameters. This index may be highly biased if detection and survival probabilities vary spatially and temporally. In terms of statistical performance, mark–recapture and Pollard–Yates indices were least variable. Mark–recapture estimates were less likely to fail than Insect Count Analyzer, but mark–recapture estimates became less precise as sampling intensity decreased. In general, count‐based approaches are less costly and less likely to cause harm to rare insects than mark–recapture. The optimal monitoring approach must reconcile these trade‐offs. Thus, mark–recapture should be favored when demographic estimates are needed, when financial resources enable frequent sampling, and when marking does not harm the insect populations. The optimal sampling strategy may use 2 sampling methods together in 1 overall sampling plan: limited mark–recapture sampling to estimate survival and detection probabilities and frequent but less expensive transect counts.     

Reliability of Absolute and Relative Predictions of Population Persistence Based on Time Series

Abstract:  Conventional population viability analysis (PVA) is often impractical because data are scarce for many threatened species. For this reason, simple count-based models are being advocated. The simplest of these models requires nothing more than a time series of abundance estimates, from which variance and autocorrelation in growth rate are estimated and predictions of population persistence are generated. What remains unclear, however, is how many years of data are needed to generate reliable estimates of these parameters and hence reliable predictions of persistence. By analyzing published and simulated time series, we show that several decades of data are needed. Predictions based on short time series were very unreliable mainly because limited data yielded biased, unreliable estimates of variance in growth rate, especially when growth rate was strongly autocorrelated. More optimistically, our results suggest that count-based PVA is sometimes useful for relative risk assessment (i.e., for ranking populations by extinction risk), even when time series are only a decade long. However, some conditions consistently lead to backward rankings. We explored the limited conditions under which simple count-based PVA may be useful for relative risk assessment.     

A Voronoi diagram based population model for social species of wildlife

A population model is presented that accounts for spatial structure within habitat patches. It is designed for social species of wildlife that form social group home ranges that are much smaller than patch size. The model represents social group home ranges by Voronoi regions that tessellate a patch to form a Voronoi diagram. Neighbouring social groups are linked with habitat-confined shortest paths and form a dispersal network. The model simulates population dynamics and makes use of Voronoi diagrams and dispersal networks as a spatial component. It then produces density maps as outputs. These are maps that show predicted animal densities across the patches of a landscape. A construction procedure for the particular Voronoi diagram type used by the model is described. As a test case, the model is run for the squirrel glider (Petaurus norfolcensis), a small arboreal marsupial native to Australia. A time series of density maps are produced that show squirrel glider density changing across a landscape through time.