Consistent multiscale modelling of movement and habitat selection

Estimating stepwise debromination pathways of polybrominated diphenyl ethers with an analogue Markov Chain Monte Carlo algorithm

Many ecological systems are organized hierarchically, and a full understanding of ecological systems is contingent on our understanding of linkages across levels in these hierarchies. Consider the hierarchy whereby individual organisms are organized into populations. The dynamics of animal populations are influenced by individual-level processes, such as establishment of home ranges and selection of habitat. These individual-level processes have important effects on demography, including reproduction, survival, emigration, and immigration, which collectively determine population dynamics. In turn, population dynamics influence how individual-level processes unfold; individual organisms are shaped by the populations they are a part of through forces such as resource competition and social interactions. Our ability to investigate both population- and individual-level processes has seen substantial growth in recent decades. Since the early 2000s, the study of animal population dynamics has been transformed due in part to the growing field of spatial capture–recapture modeling. Capture–recapture (also referred to as capture–mark–recapture, mark–recapture, and related terms) is a large set of statistical methods commonly used by ecologists to estimate abundance and related demographic parameters when it is difficult or impossible to observe (or "detect") all individuals in a population. Spatial capture–recapture is an important extension in which both demographic processes and our (imperfect) observation of these processes are modeled as spatially explicit. Spatial capture–recapture models have expanded our capacity for studying populations and have provided new insights into how populations function in space. Similarly, the study of individual movement has advanced in recent decades, owing largely to the rapid development of animal tracking technology and the simultaneous development of advanced statistical models of animal movement for tracking data. Increasingly realistic models of animal movement have provided exciting new insights about individual behavior, habitat selection, and space use. However, despite the potential for integration of these two frameworks to revolutionize our ability to understand linkages between population- and individual-level processes, there has been relatively little integration to date. In August 2019, we helped to organize a workshop at the University of Washington, with the express goal of advancing the integration of spatial capture–recapture and movement models. The papers in this Special Feature are an outgrowth of that workshop, are strongly influenced by it, or are based on independent work developed with similar goals. This collection of papers represents the state of the art in the integration of spatial capture–recapture and movement models. The papers demonstrate both the practical challenges of integrating these frameworks and the benefits of doing so, from improved demographic estimates for populations with complex movement dynamics to novel ecological insights into how environmental and social forces shape populations through space use. The papers in this Special Feature range from conceptual to applied, and each includes practical insights into how to fit these relatively complex integrated models. In their review and synthesis, McClintock et al. (2021) highlight the advantages of linking individual- and population-level process models to facilitate new and exciting inferences at the intersection of movement, population, and landscape ecology. They establish a common notation for the Special Feature and outline a general conceptual framework for the integration of spatial capture–recapture and animal movement models. They also identify potential challenges that lie ahead. Gardner et al. (2022) implement complex movement processes—such as simple random walks, correlated random walks, and habitat-driven Langevin diffusion—within spatial capture–recapture models using data augmentation in a Bayesian analysis framework. Using simulation, they demonstrate that these models can perform well with spatial capture–recapture data alone, but that as movement model complexity increases, there will be a need for more intensive location data. Thus, they also show how to integrate auxiliary data from animal-borne sensors to improve parameter estimation over models fit with only spatial capture–recapture data. Theng et al. (2022) explore the consequences of realistic animal movement for inferences arising from standard spatial capture–recapture models of closed population abundance and density. By simulating individual-level responses to internal (e.g., memory, territoriality) and external (e.g., resource dynamics) drivers as animals move through the landscape, the researchers demonstrate that spatial capture–recapture estimators of abundance can be robust to violations of assumptions induced by complex animal movement patterns as long as the resulting individual heterogeneity in detection is low. However, inferences about animal space use and home range size from standard spatial capture–recapture models can be problematic, and integrated spatial capture–recapture and animal movement models offer a potential solution. Much of the focus of the Special Feature is on animals that move independently of one another. However, in group-living species (e.g., many canids and ungulates), animal movement is statistically dependent, violating assumptions of traditional spatial capture–recapture models. To generate unbiased estimates of abundance and group size with properly estimated precision, Emmet et al. (2021) develop a group-living spatial capture–recapture model based on a clustered point process. They test their model using simulation and then apply it to camera trapping data on African wild dogs. Although their model currently requires a few restrictive assumptions (e.g., that group membership is known), we share their optimism that such requirements can be relaxed in future applications and we anticipate that their contribution will lay the groundwork for many future studies of group-living species. Focusing on landscape connectivity, Dupont et al. (2021) extend spatial capture–recapture models to accommodate a movement kernel based on so-called ecological distance instead of Euclidean distance. Unlike other integrated approaches in the Special Feature (i.e., Chandler et al., 2021; Gardner et al., 2022; Hostetter et al., 2022; McClintock et al., 2021), Dupont et al. (2021) use a step-selection model and discrete-space approximation for movement that can be fitted using maximum likelihood methods. Though it incorporates some restrictive assumptions, the model reduces computational burdens by avoiding the need to integrate over the latent movement paths during model fitting. This approach provides a straightforward modeling framework for including global positioning system (GPS) telemetry data to improve estimates of habitat-related cost functions. Hostetter et al. (2022) were motivated by the practical need to estimate the density of animals that move over large spatial areas. Polar bears (Ursus maritimus) can travel hundreds of kilometers over the course of mere days, exhibiting movement dynamics that clearly violate the standard spatial capture–recapture assumption of a bivariate normal home range and over areas that cannot be adequately sampled by available platforms. Using a combination of physical captures, resights, and telemetry data, they fit a series of integrated spatial capture–recapture movement models that specify more realistic movement processes, including simple and correlated random walks, and model the detection process over space and time conditional on movements. With this model, they provide robust estimates of movement and abundance for polar bears in the remote Chukchi Sea, as well as a framework for monitoring populations of highly mobile vertebrates in heterogeneous landscapes. Inspired by a white-tailed deer (Odocoileus virginianus) study where GPS telemetry and camera trapping were employed in the same study area, Chandler et al. (2021) develop a hierarchical model that integrates both data sets into a single analysis. By conditioning both data sets on a common movement model, the authors are able to estimate abundance and movement parameters simultaneously. Importantly, they are able to account for heterogeneous space use by different animals in a way that is typically not possible with spatial capture–recapture data alone. We suspect that their approach will be especially useful for those wishing to study the synergy between demography and animal behavior and to scale up inference about movement processes from individuals to populations. As the articles in this Special Feature illustrate, there is tremendous potential for modeling more realistic movement processes that integrate the social and environmental features of landscapes to which animals are responding while using the insights that emerge from these processes to understand demography. Our hope is that the Special Feature will inspire continued advances in integrated spatial capture–recapture movement models. The authors declare no conflict of interest.

Over the last decade, spatial capture–recapture (SCR) models have become widespread for estimating demographic parameters in ecological studies. However, the underlying assumptions about animal movement and space use are often not realistic. This is a missed opportunity because interesting ecological questions related to animal space use, habitat selection, and behavior cannot be addressed with most SCR models, despite the fact that the data collected in SCR studies — individual animals observed at specific locations and times — can provide a rich source of information about these processes and how they relate to demographic rates. We developed SCR models that integrated more complex movement processes that are typically inferred from telemetry data, including a simple random walk, correlated random walk (i.e., short‐term directional persistence), and habitat‐driven Langevin diffusion. We demonstrated how to formulate, simulate from, and fit these models with standard SCR data using data‐augmented Bayesian analysis methods. We evaluated their performance through a simulation study, in which we varied the detection, movement, and resource selection parameters. We also examined different numbers of sampling occasions and assessed performance gains when including auxiliary location data collected from telemetered individuals. Across all scenarios, the integrated SCR movement models performed well in terms of abundance, detection, and movement parameter estimation. We found little difference in bias for the simple random walk model when reducing the number of sampling occasions from T = 25 to T = 15. We found some bias in movement parameter estimates under several of the correlated random walk scenarios, but incorporating auxiliary location data improved parameter estimates and significantly improved mixing during model fitting. The Langevin movement model was able to recover resource selection parameters from standard SCR data, which is particularly appealing because it explicitly links the individual‐level movement process with habitat selection and population density. We focused on closed population models, but the movement models developed here can be extended to open SCR models. The movement process models could also be easily extended to accommodate additional “building blocks” of random walks, such as central tendency (e.g., territoriality) or multiple movement behavior states, thereby providing a flexible and coherent framework for linking animal movement behavior to population dynamics, density, and distribution.

BackgroundMovement links the distribution of habitats with the social environment of animals using those habitats. Despite the links between movement, habitat selection, and socioecology, their integration remains a challenge due to lack of shared vocabulary across fields, methodological gaps, and the implicit (rather than explicit) historical development of theory in the fields of social and spatial ecology. Given these challenges can be addressed, opportunity for further study will provide insight about the links between social, spatial, and movement ecology. Here, our objective was to disentangle the roles of habitat selection and social association as drivers of movement in caribou (Rangifer tarandus).MethodsTo accomplish our objective, we modelled the relationship between collective movement and selection of foraging habitats using socially informed integrated step selection function (iSSF). Using iSSF, we modelled the effect of social processes, i.e., nearest neighbour distance and social preference, and movement behaviour on patterns of habitat selection.ResultsBy unifying social network analysis with iSSF, we identified movement-dependent social association, where individuals took shorter steps in lichen habitat and foraged in close proximity to more familiar individuals.ConclusionsOur study demonstrates that social preference is context-dependent based on habitat selection and foraging behaviour. We therefore surmise that habitat selection and social association are drivers of collective movement, such that movement is the glue between habitat selection and social association. Here, we put these concepts into practice to demonstrate that movement is the glue connecting individual habitat selection to the social environment.

The utilization distribution of an animal describes the relative probability of space use. It is natural to think of it as the long‐term consequence of the animal's short‐term movement decisions: it is the accumulation of small displacements which, over time, gives rise to global patterns of space use. However, many estimation methods for the utilization distribution either assume the independence of observed locations and ignore the underlying movement (e.g. kernel density estimation), or are based on simple Brownian motion movement rules (e.g. Brownian bridges). We introduce a new continuous‐time model of animal movement, based on the Langevin diffusion. This stochastic process has an explicit stationary distribution, conceptually analogous to the idea of the utilization distribution, and thus provides an intuitive framework to integrate movement and space use. We model the stationary (utilization) distribution with a resource selection function to link the movement to spatial covariates, and allow inference about habitat preferences of animals. Standard approximation techniques can be used to derive the pseudo‐likelihood of the Langevin diffusion movement model, and to estimate habitat preference and movement parameters from tracking data. We investigate the performance of the method on simulated data, and discuss its sensitivity to the time scale of the sampling. We present an example of its application to tracking data of Steller sea lions Eumetopias jubatus. Due to its continuous‐time formulation, this method can be applied to irregular telemetry data. The movement model is specified using a habitat‐dependent utilization distribution, and it provides a rigorous framework to estimate long‐term habitat selection from correlated movement data. The Langevin movement model can be written as a linear model, which allows for very fast inference. Standard tools such as residuals can be used for model checking.

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

Understanding why, how, and when animals move is essential to many areas of ecology and related fields. Indeed, key aspects of animal behavior, population genetics, biological control, predator–prey dynamics, ecosystem engineering, and conservation biology all hinge upon knowing what critters are moving from where to where in a landscape, including information on how quickly, how regularly, and by what route they travel. The complexities involved in such processes have spawned tremendous efforts in both field research (where goals include measuring and characterizing such movements) and theoretical research (where goals include exploring the nature and potential consequences of movement). Ecologists today routinely receive some training in both empirical and theoretical research, and in the role of statistical analyses and model fitting as a way of linking the two perspectives. However, that has not always been the case. Spatial questions in ecology were long an area where the gulf between theory and reality was particularly wide. In part, this was due to the additional mathematical challenges of spatial models, but it also due to the perhaps greater technological challenges of measuring and contextualizing animal movements.

Markov Chain Monte Carlo (MCMC) algorithms are used to obtain samples from any target probability distribution and are widely used in stochastic processing techniques. Stochastic processing techniques such as machine learning and image processing need to compute large amounts of data in real-time, thus high throughput MCMC samplers are of utmost importance. Parallel (PT) MCMC has proven better mixing and convergence for high-dimensional and multi-modal distributions compared to other popular MCMC algorithms. In this paper, we employ a special case of Dth order Markov chains to modify the PT-MCMC algorithm, named Multiple Parallel Tempering (MPT). The modification converts one MCMC sampler into multiple independent samplers that generate and interleave their samples on one output line each clock cycle. A fully scalable and pipelined hardware accelerator for the PT and proposed MPT sampler is designed and implemented on Artix-7 Xilinx FPGA for chain numbers of 1, 2, and 8. The post-place and route FPGA implementation results indicate that the throughput of the proposed MPT sampler for chain numbers 1, 2, and 8 achieves 31x, 31x, and 28x respectively higher as compared to PT sampler with the same chain number configuration.

This paper proposes a consistent learning model based on Exchange Monte Carlo Method. The paper also gives discussion with respect to experiments on the synthesized case. Learning model is currently focusing on the model with the interface for input and output. On that model, preparing a dataset remains in human's work, and there is still not sufficient research how to prepare a valuable dataset efficiently. Exchange Monte Carlo is used widely for both purposes of optimization and estimation of a probability distribution, and it has the ability to combine any probability model in one and sample the model's state efficiency from the combined probability model. From this point of view, when we consider the three models, i.e., real space, learnt model, and model of parameter distribution, we can combine them and construct the consistent model that explains the phenomena of learning consistently. It is supposed that those samples give us valuable dataset and set of the learnt parameter, when the parameter space also modeled with Bayesian inference framework. With these ideas mentioned so far, this paper proposes a generalized consistent probability model of the real space, learning model, and parameters' distribution of the learning model. To challenge to the sampling problem on high-dimensionality of the consistent model, Exchange Monte Carlo and Hamiltonian dynamics are employed. Experiments show the proposed method works on the synthesized case, that is, the original distribution is approximated well and parameter is optimized too, only by sampling from the consistent model without preparing dataset.

We present a functional central limit theorem for a new class of interacting Markov chain Monte Carlo algorithms. These stochastic algorithms have been recently introduced to solve non-linear measure-valued equations. We provide an original theoretical analysis based on semigroup techniques on distribution spaces and fluctuation theorems for self-interacting random fields. Additionally we also present a series of sharp mean error bounds in terms of the semigroup associated with the first order expansion of the limiting measure-valued process. We illustrate our results in the context of Feynman-Kac semigroups

view Abstract Citations (155) References (27) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The velocity field of bright nearby galaxies. III - The distribution in space of galaxies within 80 megaparsecs - The north galactic density anomaly Yahil, A. ; Sandage, A. ; Tammann, G. A. Abstract The three-dimensional distribution of the nearby galaxies in the Revised Shapley-Ames Catalog is investigated to map the density contrasts in different directions for calculating the expected velocity perturbations due to the north galactic anomaly. It was shown that (1) the known concentration of galaxies in the north galactic atmosphere occurs for all galaxy types and is centered near the core of the Virgo cluster proper, (2) galaxies within the anomaly are concentrated toward the supergalactic plane described by de Vaucouleurs, but the concentration disappears for Virgocentric distances greater than 1000 km/s, and (3) if the total mass-energy density is at least proportional to the galactic density, the gravitational field generated by the north galactic anomaly should pull the Local Group toward Virgo. Publication: The Astrophysical Journal Pub Date: December 1980 DOI: 10.1086/158479 Bibcode: 1980ApJ...242..448Y Keywords: Density Distribution; Galaxies; Spatial Distribution; Velocity Distribution; Astronomical Catalogs; Astronomical Maps; Distribution Functions; Galactic Clusters; Gravitational Fields; Virgo Galactic Cluster; Astrophysics full text sources ADS |

Ecologists and conservation biologists increasingly rely on spatial capture-recapture (SCR) and movement modeling to study animal populations. Historically, SCR has focused on population-level processes (e.g., vital rates, abundance, density, and distribution), whereas animal movement modeling has focused on the behavior of individuals (e.g., activity budgets, resource selection, migration). Even though animal movement is clearly a driver of population-level patterns and dynamics, technical and conceptual developments to date have not forged a firm link between the two fields. Instead, movement modeling has typically focused on the individual level without providing a coherent scaling from individual- to population-level processes, whereas SCR has typically focused on the population level while greatly simplifying the movement processes that give rise to the observations underlying these models. In our view, the integration of SCR and animal movement modeling has tremendous potential for allowing ecologists to scale up from individuals to populations and advancing the types of inferences that can be made at the intersection of population, movement, and landscape ecology. Properly accounting for complex animal movement processes can also potentially reduce bias in estimators of population-level parameters, thereby improving inferences that are critical for species conservation and management. This introductory article to the Special Feature reviews recent advances in SCR and animal movement modeling, establishes a common notation, highlights potential advantages of linking individual-level (Lagrangian) movements to population-level (Eulerian) processes, and outlines a general conceptual framework for the integration of movement and SCR models. We then identify important avenues for future research, including key challenges and potential pitfalls in the developments and applications that lie ahead.

Theoretical and empirical results demonstrate that the G-matrix, which summarizes additive genetic variances and covariances of quantitative traits, changes over time. Such evolution and fluctuation of the G-matrix could potentially have wide-ranging effects on phenotypic evolution. Nevertheless, no studies have yet addressed G-matrix stability and evolution when movement of an intermediate optimum includes large, episodic jumps or stochasticity. Here, we investigate such scenarios by using simulation-based models of G-matrix evolution. These analyses yield four important insights regarding the evolution and stability of the G-matrix. (i) Regardless of the model of peak movement, a moving optimum causes the G-matrix to orient towards the direction of net peak movement, so that genetic variance is enhanced in that direction (the variance enhancement effect). (ii) Peak movement skews the distribution of breeding values in the direction of movement, which impedes the response to selection. (iii) The stability of the G-matrix is affected by the overall magnitude and direction of peak movement, but modes and rates of peak movement have surprisingly small effects (the invariance principle). (iv) Both episodic and stochastic peak movement increase the probability that a population will fall below its carrying capacity and go extinct. We also present novel equations for the response of the trait mean to multivariate selection, which take into account the higher moments of the distribution of breeding values.

Despite some populations of European wildcat Felis silvestris in central Europe are stable or increasing, the Iberian subpopulation is in decline and is listed as ‘vulnerable’. In Portugal, little is known about wildcat populations, making conservation policies extremely difficult to define. Furthermore, the secretive behaviour of these mammals, along with low population densities, make data collection complicated. Thus, it is crucial to develop efficient analytical tools to interpret existing data for this species. In this study, we determine the home‐range size and environmental factors related to wildcat spatial ecology in a Mediterranean ecosystem using a combined analysis of habitat selection and maximum entropy (Maxent) modelling. Simultaneously, we test the feasibility of using radio‐tracking locations to construct an ecologically meaningful distribution model. Six wildcats were captured and tracked. The average home‐range size (MCP95) was 2.28 km2 for females and 13.71 km2 for one male. The Maxent model built from radio‐tracking locations indicated that the abundance of the European rabbit Oryctolagus cuniculus and limited human disturbance were the most important correlates of wildcat presence. Habitat selection analysis revealed that wildcats tend to use scrubland areas significantly more than expected by chance. A mosaic of scrublands and agricultural areas, with a higher proportion of the former, benefits wildcat presence in the study area; however, species distribution is mainly constrained by availability of prey and resting sites. The Maxent model validation with camera‐trapping data indicated that highly adequate model performance. This technique may prove useful for recovering small radio‐tracking datasets as it provides a new alternative for handling data and maximizing the ecological information on a target population, which can then be used for conservation planning.

Movements of intertidal gastropods