An animal movement model incorporating home range and habitat selection

Wildlife biologists are often interested in how an animal uses space and the habitat resources within that space. We propose a single model that estimates an animal’s home range and habitat selection parameters within that range while accounting for the inherent autocorrelation in frequently sampled telemetry data. The model is applied to brown bear telemetry data in southeast Alaska. This article is based on a portion of this author’s Ph.D. dissertation completed in 2003 at the University of Iowa.     

Generalized functional responses for species distributions

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

Habitat selection predicts genetic relatedness in an alpine ungulate

Landscape heterogeneity plays an integral role in shaping ecological and evolutionary processes. Despite links between the two disciplines, ecologists and population geneticists have taken different approaches to evaluating habitat selection, animal movement, and gene flow across the landscape. Ecologists commonly use statistical models such as resource selection functions (RSFs) to identify habitat features disproportionately selected by animals, whereas population genetic approaches model genetic differentiation according to the distribution of habitat variables. We combined ecological and genetic approaches by using RSFs to predict genetic relatedness across a heterogeneous landscape. We constructed sex- and season-specific resistance surfaces based on RSFs estimated using data from 102 GPS (global positioning system) radio-collared mountain goats (Oreamnos americanus) in southeast Alaska, USA. Based on mountain goat ecology, we hypothesized that summer and male surfaces would be the best predictors of relatedness. All individuals were genotyped at 22 microsatellite loci, which we used to estimate genetic relatedness. Summer resistance surfaces derived from RSFs were the best predictors of genetic relatedness, and winter models the poorest. Mountain goats generally selected for areas close to escape terrain and with a high heat load (a metric related to vegetative productivity and snow depth), while avoiding valleys. Male- and female-specific surfaces were similar, except for winter, for which male habitat selection better predicted genetic relatedness. The null models of isolation-by-distance and barrier only outperformed the winter models. This study merges high-resolution individual locations through GPS telemetry and genetic data, that can be used to validate and parameterize landscape genetics models, and further elucidates the relationship between landscape heterogeneity and genetic differentiation.     

Persistence models for mark-recapture

The stable of models available for analyzing mark-recapture data (Otis et al. Wild Momogr 66:135, 1978) includes those having behavioral characteristics, time variation, heterogeneity, along with combinations of those characteristics. This paper proposes use of a series of models based on the persistence model of Ramsey and Usner (Biometrics 59:331–339, 2003). We show that persistence can be modeled in combination with behavior and with time variation. We apply the persistence model to situations in which capture occasions are not equally-spaced in time. Two case studies illustrate the use of these extended persistence models.     

Nest selection by snow petrels Pagodroma nivea in East Antarctica: Validating predictive habitat selection models at the continental scale

Little is known on the factors controlling distribution and abundance of snow petrels in Antarctica. Studying habitat selection through modeling may provide useful information on the relationships between this species and its environment, especially relevant in a climate change context, where habitat availability may change. Validating the predictive capability of habitat selection models with independent data is a vital step in assessing the performance of such models and their potential for predicting species’ distribution in poorly documented areas.From the results of ground surveys conducted in the Casey region (2002–2003, Wilkes Land, East Antarctica), habitat selection models based on a dataset of 4000 nests were created to predict the nesting distribution of snow petrels as a function of topography and substrate. In this study, the Casey models were tested at Mawson, 3800 km away from Casey. The location and characteristics of approximately 7700 snow petrel nests were collected during ground surveys (Summer 2004–2005). Using GIS, predictive maps of nest distribution were produced for the Mawson region with the models derived from the Casey datasets and predictions were compared to the observed data. Models performance was assessed using classification matrixes and Receiver operating characteristic (ROC) curves. Overall correct classification rates for the Casey models varied from 57% to 90%. However, two geomorphologically different sub-regions (coastal islands and inland mountains) were clearly distinguished in terms of habitat selection by Casey model predictions but also by the specific variations in coefficients of terms in new models, derived from the Mawson data sets. Observed variations in the snow petrel aggregations were found to be related to local habitat availability.We discuss the applicability of various types of models (GLM, CT) and investigate the effect of scale on the prediction of snow petrel habitats. While the Casey models created with data collected at the nest scale did not perform well at Mawson due to regional variations in nest micro-characteristics, the predictive performance of models created with data compiled at a coarser scale (habitat units) was satisfactory. Substrate type was the most robust predictor of nest presence between Casey and Mawson. This study demonstrate that it is possible to predict at the large scale the presence of snow petrel nests based on simple predictors such as topography and substrate, which can be obtained from aerial photography. Such methodologies have valuable applications in the management and conservation of this top predator and associated resources and may be applied to other Antarctic, Sub-Antarctic and lower latitudes species and in a variety of habitats.     

Spatial selection and inheritance: applying evolutionary concepts to population dynamics in heterogeneous space

Organisms in highly suitable sites generally produce more offspring, and offspring can inherit this suitability by not dispersing far. This combination of spatial selection and spatial inheritance acts to bias the distribution of organisms toward suitable sites and thereby increase mean fitness (i.e., per capita population increase). Thus, population growth rates in heterogeneous space change over time by a process conceptually analogous to evolution by natural selection, opening avenues for theoretical cross-pollination between evolutionary biology and ecology. We operationally define spatial inheritance and spatial selective differential and then combine these two factors in a modification of the breeder's equation, derived from simple models of population growth in heterogeneous space. The modified breeder's equation yields a conservative criterion for persistence in hostile environments estimable from field measurements. We apply this framework for understanding gypsy moth population persistence amidst abundant predators and find that the predictions of the modified breeder's equation match initial changes in population growth rate in independent simulation output. The analogy between spatial dynamics and natural selection conceptually links ecology and evolution, provides a spatially implicit framework for modeling spatial population dynamics, and represents an important null model for studying habitat selection.     

Assessing hypotheses about nesting site occupancy dynamics

Hypotheses about habitat selection developed in the evolutionary ecology framework assume that individuals, under some conditions, select breeding habitat based on expected fitness in different habitat. The relationship between habitat quality and fitness may be reflected by breeding success of individuals, which may in turn be used to assess habitat quality. Habitat quality may also be assessed via local density: if high-quality sites are preferentially used, high density may reflect high-quality habitat. Here we assessed whether site occupancy dynamics vary with site surrogates for habitat quality. We modeled nest site use probability in a seabird subcolony (the Black-legged Kittiwake, Rissa tridactyla) over a 20-year period. We estimated site persistence (an occupied site remains occupied from time t to t+1) and colonization through two subprocesses: first colonization (site creation at the timescale of the study) and recolonization (a site is colonized again after being deserted). Our model explicitly incorporated site-specific and neighboring breeding success and conspecific density in the neighborhood. Our results provided evidence that reproductively "successful" sites have a higher persistence probability than "unsuccessful" ones. Analyses of site fidelity in marked birds and of survival probability showed that high site persistence predominantly reflects site fidelity, not immediate colonization by new owners after emigration or death of previous owners. There is a negative quadratic relationship between local density and persistence probability. First colonization probability decreases with density, whereas recolonization probability is constant. This highlights the importance of distinguishing initial colonization and recolonization to understand site occupancy. All dynamics varied positively with neighboring breeding success. We found evidence of a positive interaction between site-specific and neighboring breeding success. We addressed local population dynamics using a site occupancy approach integrating hypotheses developed in behavioral ecology to account for individual decisions. This allows development of models of population and metapopulation dynamics that explicitly incorporate ecological and evolutionary processes.     

Quantifying the impact of vegetation-based metrics on species persistence when choosing offsets for habitat destruction

Developers are often required by law to offset environmental impacts through targeted conservation actions. Most offset policies specify metrics for calculating offset requirements, usually by assessing vegetation condition. Despite widespread use, there is little evidence to support the effectiveness of vegetation-based metrics for ensuring biodiversity persistence. We compared long-term impacts of biodiversity offsetting based on area only; vegetation condition only; area × habitat suitability; and condition × habitat suitability in development and restoration simulations for the Hunter Region of New South Wales, Australia. We simulated development and subsequent offsetting through restoration within a virtual landscape, linking simulations to population viability models for 3 species. Habitat gains did not ensure species persistence. No net loss was achieved when performance of offsetting was assessed in terms of amount of habitat restored, but not when outcomes were assessed in terms of persistence. Maintenance of persistence occurred more often when impacts were avoided, giving further support to better enforce the avoidance stage of the mitigation hierarchy. When development affected areas of high habitat quality for species, persistence could not be guaranteed. Therefore, species must be more explicitly accounted for in offsets, rather than just vegetation or habitat alone. Declines due to a failure to account directly for species population dynamics and connectivity overshadowed the benefits delivered by producing large areas of high-quality habitat. Our modeling framework showed that the benefits delivered by offsets are species specific and that simple vegetation-based metrics can give misguided impressions on how well biodiversity offsets achieve no net loss.     

A multispecies test of source–sink indicators to prioritize habitat for declining populations

For species at risk of decline or extinction in source–sink systems, sources are an obvious target for habitat protection actions. However, the way in which source habitats are identified and prioritized can reduce the effectiveness of conservation actions. Although sources and sinks are conceptually defined using both demographic and movement criteria, simplifications are often required in systems with limited data. To assess the conservation outcomes of alternative source metrics and resulting prioritizations, we simulated population dynamics and extinction risk for 3 endangered species. Using empirically based habitat population models, we linked habitat maps with measured site‐ or habitat‐specific demographic conditions, movement abilities, and behaviors. We calculated source–sink metrics over a range of periods of data collection and prioritized consistently high‐output sources for conservation. We then tested whether prioritized patches identified the habitats that most affected persistence by removing them and measuring the population response. Conservation decisions based on different source–sink metrics and durations of data collection affected species persistence. Shorter time series obscured the ability of metrics to identify influential habitats, particularly in temporally variable and slowly declining populations. Data‐rich source–sink metrics that included both demography and movement information did not always identify the habitats with the greatest influence on extinction risk. In some declining populations, patch abundance better predicted influential habitats for short‐term regional persistence. Because source–sink metrics (i.e., births minus deaths; births and immigrations minus deaths and emigration) describe net population conditions and cancel out gross population counts, they may not adequately identify influential habitats in declining populations. For many nonequilibrium populations, new metrics that maintain the counts of individual births, deaths, and movement may provide additional insight into habitats that most influence persistence.     

Populations in small, ephemeral habitat patches may drive dynamics in a Daphnia magna metapopulation

Migration is the key process to understand the dynamics and persistence of a metapopulation. Many metapopulation models assume a positive correlation between habitat patch size or stability and the number of emigrants. However, few empirical data exist, and habitat patch size and habitat stability may affect dispersal differently than they affect local persistence. Here, we studied the production of the migration stage (i.e., resting eggs called ephippia) of the cladoceran Daphnia magna in a metapopulation consisting of 530 rock pool habitat patches over 25 years. Earlier, the functioning of this metapopulation was explained with a Levins-type metapopulation model or with a mainland-island metapopulation model, based on local extinction and colonization data or time series data, respectively. We used pool volume, hydroperiod length, and number of desiccation events to calculate per-pool production of ephippia (i.e., migration stages). We estimated that populations in small and ephemeral habitat patches produced more than half of the 250 000 to 1 million ephippia that were produced in the metapopulation as a whole per year between 1982 and 2006. Furthermore, these small populations contributed approximately 90% of the ephippia exposed during desiccation events, while the contribution of the long-lived populations in large pools was minimal. We term this an "inverse mainland-island" type metapopulation and propose that populations in small, ephemeral habitat patches may also be the driving force for metapopulation dynamics in other systems.     

Planning for robust reserve networks using uncertainty analysis

Planning land-use for biodiversity conservation frequently involves computer-assisted reserve selection algorithms. Typically such algorithms operate on matrices of species presence–absence in sites, or on species-specific distributions of model predicted probabilities of occurrence in grid cells. There are practically always errors in input data—erroneous species presence–absence data, structural and parametric uncertainty in predictive habitat models, and lack of correspondence between temporal presence and long-run persistence. Despite these uncertainties, typical reserve selection methods proceed as if there is no uncertainty in the data or models. Having two conservation options of apparently equal biological value, one would prefer the option whose value is relatively insensitive to errors in planning inputs. In this work we show how uncertainty analysis for reserve planning can be implemented within a framework of information-gap decision theory, generating reserve designs that are robust to uncertainty. Consideration of uncertainty involves modifications to the typical objective functions used in reserve selection. Search for robust-optimal reserve structures can still be implemented via typical reserve selection optimization techniques, including stepwise heuristics, integer-programming and stochastic global search.     

Dynamic reserve design with the union-find algorithm

When reserve networks are established over time, there is a risk that sites will be developed in areas planned for future reservation, reducing the effectiveness of reserves. We developed a dynamic reserve design model that maximizes the expected number of species conserved, taking account of the risk of future habitat loss and fragmentation. The model makes use of the union-find algorithm, which is an efficient method for maintaining a list of connected regions in a graph as nodes and edges are inserted. A simple extension of the algorithm allows us to efficiently determine, for each species, when a sequence of site selections results in a reserve in which the species can persist. The extension also allows us to determine when a sequence of deforestation events results in the species becoming non-viable. The dynamic reserve design model is much more effective than commonly used heuristics, particularly when multiple connected sites are required for species persistence. The model also is able to solve much larger problems with greater effectiveness than the only previous dynamic reserve design model that considered site connectivity relationships. The union-find algorithm has much scope for addressing ecological management problems in which dynamic connectivity needs to be considered.     

Testing the robustness of management decisions to uncertainty: Everglades restoration scenarios.

To effectively manage large natural reserves, resource managers must prepare for future contingencies while balancing the often conflicting priorities of different stakeholders. To deal with these issues, managers routinely employ models to project the response of ecosystems to different scenarios that represent alternative management plans or environmental forecasts. Scenario analysis is often used to rank such alternatives to aid the decision making process. However, model projections are subject to uncertainty in assumptions about model structure, parameter values, environmental inputs, and subcomponent interactions. We introduce an approach for testing the robustness of model-based management decisions to the uncertainty inherent in complex ecological models and their inputs. We use relative assessment to quantify the relative impacts of uncertainty on scenario ranking. To illustrate our approach we consider uncertainty in parameter values and uncertainty in input data, with specific examples drawn from the Florida Everglades restoration project. Our examples focus on two alternative 30-year hydrologic management plans that were ranked according to their overall impacts on wildlife habitat potential. We tested the assumption that varying the parameter settings and inputs of habitat index models does not change the rank order of the hydrologic plans. We compared the average projected index of habitat potential for four endemic species and two wading-bird guilds to rank the plans, accounting for variations in parameter settings and water level inputs associated with hypothetical future climates. Indices of habitat potential were based on projections from spatially explicit models that are closely tied to hydrology. For the American alligator, the rank order of the hydrologic plans was unaffected by substantial variation in model parameters. By contrast, simulated major shifts in water levels led to reversals in the ranks of the hydrologic plans in 24.1-30.6% of the projections for the wading bird guilds and several individual species. By exposing the differential effects of uncertainty, relative assessment can help resource managers assess the robustness of scenario choice in model-based policy decisions.     

Spatial uncertainty analysis of population models

This paper describes an approach for conducting spatial uncertainty analysis of spatial population models, and illustrates the ecological consequences of spatial uncertainty for landscapes with different properties. Spatial population models typically simulate birth, death, and migration on an input map that describes habitat. Typically, only a single “reference” map is available, but we can imagine that a collection of other, slightly different, maps could be drawn to represent a particular species’ habitat. As a first approximation, our approach assumes that spatial uncertainty (i.e., the variation among values assigned to a location by such a collection of maps) is constrained by characteristics of the reference map, regardless of how the map was produced. Our approach produces lower levels of uncertainty than alternative methods used in landscape ecology because we condition our alternative landscapes on local properties of the reference map. Simulated spatial uncertainty was higher near the borders of patches. Consequently, average uncertainty was highest for reference maps with equal proportions of suitable and unsuitable habitat, and no spatial autocorrelation. We used two population viability models to evaluate the ecological consequences of spatial uncertainty for landscapes with different properties. Spatial uncertainty produced larger variation among predictions of a spatially explicit model than those of a spatially implicit model. Spatially explicit model predictions of final female population size varied most among landscapes with enough clustered habitat to allow persistence. In contrast, predictions of population growth rate varied most among landscapes with only enough clustered habitat to support a small population, i.e., near a spatially mediated extinction threshold. We conclude that spatial uncertainty has the greatest effect on persistence when the amount and arrangement of suitable habitat are such that habitat capacity is near the minimum required for persistence.     

Continuous-time correlated random walk model for animal telemetry data

We propose a continuous-time version of the correlated random walk model for animal telemetry data. The continuous-time formulation allows data that have been nonuniformly collected over time to be modeled without subsampling, interpolation, or aggregation to obtain a set of locations uniformly spaced in time. The model is derived from a continuous-time Ornstein-Uhlenbeck velocity process that is integrated to form a location process. The continuous-time model was placed into a state-space framework to allow parameter estimation and location predictions from observed animal locations. Two previously unpublished marine mammal telemetry data sets were analyzed to illustrate use of the model, by-products available from the analysis, and different modifications which are possible. A harbor seal data set was analyzed with a model that incorporates the proportion of each hour spent on land. Also, a northern fur seal pup data set was analyzed with a random drift component to account for directed travel and ocean currents.     

Importance of movement constraints in habitat selection studies

The aim of this study is to empirically illustrate the importance of taking movement constraints into account when testing for habitat selection with telemetry data. Global Positioning System relocations of two Scandinavian brown bears were used to compare the results of two different tests of habitat selection by the bears within their home range. Both relied on the comparison of observed dataset with datasets simulated under the hypothesis of random habitat use. The first analysis did not take movement constraints into account (simulations were carried out by randomly distributing a set of points in the home range) whereas the second analysis accounted for these constraints (simulations were carried out by building random trajectories in the home range). The results for the two analyses showed contrasted results. Therefore, not accounting for movement constraints in analyses may result in a misleading biological interpretation. Autocorrelation between relocations is not undesirable: it contains information about ecological processes that should be integrated in habitat selection analyses.     

Landscape history, fragmentation, and patch occupancy: models for a forest bird with limited dispersal.

We developed and tested patch occupancy models for an endemic understory bird with limited dispersal ability, the Chucao Tapaculo (Scelorchilus rubecula), in two South American temperate rain forest landscapes that differed in levels and duration of forest loss. We assessed cover changes since 1961 in each landscape and surveyed patches for Chucao Tapaculo occupancy. We then developed incidence-based predictive models independently for each landscape and tested each model reciprocally in the alternative study area. We thereby assessed the domain of model applicability and identified those predictor variables with general effects and those that varied between the two landscapes. The two models were consistent regarding variable selection, and predictive accuracy of each model was high in the landscape where training data were collected. However, the models differed substantially in the magnitudes of effects related to patch size, with larger unoccupied patches observed in the landscape with the more advanced stage of fragmentation. Due to this discrepancy, each model performed poorly when applied to the alternative landscape, potentially reflecting the contrasting stages of habitat loss. Although it was impossible to dissociate effects of level and duration of forest loss, we viewed the landscapes as representing two extremes along a continuum of fragmentation, providing insights into potential trajectories for portions of the biome where deforestation is occurring. Further, our data suggest that static equilibrium models developed from distribution patterns in recently fragmented landscapes may overestimate persistence when used as a forecasting tool, or when extrapolated to alternative landscapes where fragmentation is more advanced. Thus, we suggest that landscapes used as standards for model building should be selected with caution. We recommend that distribution patterns be obtained from landscapes where fragmentation is advanced, preferably with histories of fragmentation long enough that time-delayed extinctions already would have occurred.     

Continuous versus binary representations of landscape heterogeneity in spatially-explicit models of mobile populations

How a landscape is represented is an important structural assumption in spatially-explicit simulation models. Simple models tend to specify just habitat and non-habitat (binary), while more complex models may use multiple levels or a continuum of habitat quality (continuous). How these different representations influence model projections is unclear. To assess the influence of landscape representation on population models, I developed a general, individual-based model with local dispersal and examined population persistence across binary and continuous landscapes varying in the amount and fragmentation of habitat. In binary and continuous landscapes habitat and non-habitat were assigned a unique mean suitability. In continuous landscapes, suitability of each individual site was then drawn from a normal distribution with fixed variance. Populations went extinct less often and abundances were higher in continuous landscapes. Production in habitat and non-habitat was higher in continuous landscapes, because the range of habitat suitability sampled by randomly dispersing individuals was higher than the overall mean habitat suitability. Increasing mortality, dispersal distance, and spatial heterogeneity all increased the discrepancy between continuous and binary landscapes. The effect of spatial structure on the probability of extinction was greater in binary landscapes. These results show that, under certain circumstances, model projections are influenced by how variation in suitability within a landscape is represented. Care should be taken to assess how a given species actually perceives the landscape when conducting population viability analyses or empirical validation of theory.     

Measuring impacts on species with models and metrics of varying ecological and computational complexity

Approaches to assess the impacts of landscape disturbance scenarios on species range from metrics based on patterns of occurrence or habitat to comprehensive models that explicitly include ecological processes. The choice of metrics and models affects how impacts are interpreted and conservation decisions. We explored the impacts of 3 realistic disturbance scenarios on 4 species with different ecological and taxonomic traits. We used progressively more complex models and metrics to evaluate relative impact and rank of scenarios on the species. Models ranged from species distribution models that relied on implicit assumptions about environmental factors and species presence to highly parameterized spatially explicit population models that explicitly included ecological processes and stochasticity. Metrics performed consistently in ranking different scenarios in order of severity primarily when variation in impact was driven by habitat amount. However, they differed in rank for cases where dispersal dynamics were critical in influencing metapopulation persistence. Impacts of scenarios on species with low dispersal ability were better characterized using models that explicitly captured these processes. Metapopulation capacity provided rank orders that most consistently correlated with those from highly parameterized and data-rich models and incorporated information about dispersal with little additional computational and data cost. Our results highlight the importance of explicitly considering species’ ecology, spatial configuration of habitat, and disturbance when choosing indicators of species persistence. We suggest using hybrid approaches that are a mixture of simple and complex models to improve multispecies assessments.