momentuHMM: R package for generalized hidden Markov models of animal movement

1. Discrete‐time hidden Markov models (HMMs) have become an immensely popular tool for inferring latent animal behaviours from telemetry data. While movement HMMs typically rely solely on location data (e.g. step length and turning angle), auxiliary biotelemetry and environmental data are powerful and readily‐available resources for incorporating much more ecological and behavioural realism. However, complex movement or observation process models often necessitate custom and computationally demanding HMM model‐fitting techniques that are impractical for most practitioners, and there is a paucity of generalized user‐friendly software available for implementing multivariate HMMs of animal movement. 2. Here, we introduce an open‐source R package, momentuHMM, that addresses many of the deficiencies in existing HMM software. Features include: (1) data pre‐processing and visualization; (2) user‐specified probability distributions for an unlimited number of data streams and latent behaviour states; (3) biased and correlated random walk movement models, including dynamic “activity centres” associated with attractive or repulsive forces; (4) user‐specified design matrices and constraints for covariate modelling of parameters using formulas familiar to most R users; (5) multiple imputation methods that account for measurement error and temporally irregular or missing data; (6) seamless integration of spatio‐temporal covariate raster data; (7) cosinor and spline models for cyclical and other complicated patterns; (8) model checking and selection; and (9) simulation. 3. After providing an overview of the main features of the package, we demonstrate some of the capabilities of momentuHMM using real‐world examples. These include models for cyclical movement patterns of African elephants, foraging trips of northern fur seals, loggerhead turtle movements relative to ocean surface currents, and grey seal movements among three activity centres. 4. momentuHMM considerably extends the capabilities of existing HMM software while accounting for common challenges associated with telemetry data. It therefore facilitates more realistic hypothesis‐driven animal movement analyses that have hitherto been largely inaccessible to non‐statisticians. While motivated by telemetry data, the package can be used for analysing any type of data that is amenable to HMMs. Practitioners interested in additional features are encouraged to contact the authors

The Langevin diffusion as a continuous-time model of animal movement and habitat selection

TM was supported by the Centre for Advanced Biological Modelling at the University of Sheffield, funded by the Leverhulme Trust, award number DS-2014-081.1. The utilisation 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 utilisation 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). 2. 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 utilisation distribution, and thus provides an intuitive framework to integrate movement and space use. We model the stationary (utilisation) distribution with a resource selection function to link the movement to spatial covariates, and allow inference about habitat preferences of animals. 3. 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). 4. Due to its continuous-time formulation, this method can be applied to irregular telemetry data. The movement model is specified using a habitat-dependent utilisation distribution, and it provides a rigorous framework to estimate long-term habitat selection from correlated movement data. The Langevin movement model can be approximated by linear model, which allows for very fast inference. Standard tools such as residuals can be used for model checking.PostprintPeer reviewe

Flexible hidden Markov models for behaviour-dependent habitat selection

Background There is strong incentive to model behaviour-dependent habitat selection, as this can help delineate critical habitats for important life processes and reduce bias in model parameters. For this purpose, a two-stage modelling approach is often taken: (i) classify behaviours with a hidden Markov model (HMM), and (ii) fit a step selection function (SSF) to each subset of data. However, this approach does not properly account for the uncertainty in behavioural classification, nor does it allow states to depend on habitat selection. An alternative approach is to estimate both state switching and habitat selection in a single, integrated model called an HMM-SSF. Methods We build on this recent methodological work to make the HMM-SSF approach more efficient and general. We focus on writing the model as an HMM where the observation process is defined by an SSF, such that well-known inferential methods for HMMs can be used directly for parameter estimation and state classification. We extend the model to include covariates on the HMM transition probabilities, allowing for inferences into the temporal and individual-specific drivers of state switching. We demonstrate the method through an illustrative example of plains zebra (Equus quagga), including state estimation, and simulations to estimate a utilisation distribution. Results In the zebra analysis, we identified two behavioural states, with clearly distinct patterns of movement and habitat selection (“encamped” and “exploratory”). In particular, although the zebra tended to prefer areas higher in grassland across both behavioural states, this selection was much stronger in the fast, directed exploratory state. We also found a clear diel cycle in behaviour, which indicated that zebras were more likely to be exploring in the morning and encamped in the evening. Conclusions This method can be used to analyse behaviour-specific habitat selection in a wide range of species and systems. A large suite of statistical extensions and tools developed for HMMs and SSFs can be applied directly to this integrated model, making it a very versatile framework to jointly learn about animal behaviour, habitat selection, and space use.Publisher PDFPeer reviewe

Identifying cues for self-organized nest wall-building behaviour in the rock ant, Temnothorax rugatulus, using hidden Markov models

Funding: E.I.’s Ph.D. was funded by the John Templeton Foundation as part of the research collaboration grant ‘Putting the extended evolutionary synthesis to the test’ (grant no. 60501). The postdoctoral research project that followed this initial work was funded by an ASAB research grant to M.W. and E.I.European Temnothorax albipennis and its American counterpart Temnothorax rugatulus build circular walls to limit their nest area within a rock crevice. To determine wall position, workers are thought to rely on a distance template (from the cluster of brood and nurses at the nest centre) and on indirect social (i.e. stigmergic) information found in the aggregations of already-deposited building material. Analytical and simulation models of this behaviour predict that the combination of these two mechanisms can produce the observed wall structure, but there is so far no empirical evidence of either mechanism. Here, we find statistical evidence in support of the stigmergic relationship between stone density and deposition behaviour. We apply hidden Markov models (HMMs) to analyse wall-building data from four colonies of T. rugatulus. We show that material deposition activity changes following a parabolic relationship with the density of building material at building sites, different from the linear relationship hypothesized previously. This parabolic curve is similar to behavioural response curves identified in the nest enlargement process of several ant species. In addition, HMM analysis indicates the existence of two distinct states in T. rugatulus building activity. These states are associated with different mean building rates (that is, the two states can be described as a high and a low activity state) and might be caused by changes in task priorities during the colony process of settling into a new nest. This study updates one of the earliest models of self-organized animal behaviour.Peer reviewe

Continuous time resource selection analysis for moving animals

1.Resource selection analysis (RSA) seeks to understand how spatial abundance covaries with environmental features. By combining RSA with movement, step selection analysis (SSA) has helped uncover the mechanisms behind animal relocations, thereby giving insight into the movement decisions underlying spatial patterns. However, SSA typically assumes that at each observed location, an animal makes a 'selection' of the next observed location. This conflates observation with behavioural mechanism and does not account for decisions occurring at any other time along the animal's path. 2.To address this, we introduce a continuous time framework for resource selection. It is based on a switching Ornstein‐Uhlenbeck (OU) model, parameterised by Bayesian Monte Carlo techniques. Such OU models have been used successfully to identify switches in movement behaviour, but hitherto not combined with resource selection. We test our inference procedure on simulated paths, representing both migratory movement (where landscape quality varies according to season) and foraging with depletion and renewal of resources (where the variation is due to past locations of the animals). We apply our framework to location data of migrating mule deer (Odocoileus hemionus) to shed light on the drivers of migratory decisions. 3.In a wide variety of simulated situations, our inference procedure returns reliable estimations of the parameter values, including the extent to which animals trade‐off resource quality and travel distance (within 95% posterior intervals for the vast majority of cases). When applied to the mule deer data, our model reveals some individual variation in parameter values. Nevertheless, the migratory decisions of most individuals are well‐described by a model that accounts for the cost of moving and the difference between instantaneous change of vegetation quality at source and target patches. 4.We have introduced a technique for inferring the resource‐driven decisions behind animal movement that accounts for the fact that these decisions may take place at any point along a path, not just when the animal's location is known. This removes an oft‐acknowledged but hitherto little‐addressed shortcoming of stepwise movement models. Our work is of key importance in understanding how environmental features drive movement decisions and, as a consequence, space use patterns

Understanding decision making in a food-caching predator using hidden Markov models

Financial support was provided by the People’s Trust for Endangered Species (PTES), Zoologische Gesellschaft für Arten- und Populationsschutz (ZGAP), Quagga Conservation Fund and IdeaWild.Background Tackling behavioural questions often requires identifying points in space and time where animals make decisions and linking these to environmental variables. State-space modeling is useful for analysing movement trajectories, particularly with hidden Markov models (HMM). Yet importantly, the ontogeny of underlying (unobservable) behavioural states revealed by the HMMs has rarely been verified in the field. Methods Using hidden Markov models of individual movement from animal location, biotelemetry, and environmental data, we explored multistate behaviour and the effect of associated intrinsic and extrinsic drivers across life stages. We also decomposed the activity budgets of different movement states at two general and caching phases. The latter - defined as the period following a kill which likely involves the caching of uneaten prey - was subsequently confirmed by field inspections. We applied this method to GPS relocation data of a caching predator, Persian leopard Panthera pardus saxicolor in northeastern Iran. Results Multistate modeling provided strong evidence for an effect of life stage on the behavioural states and their associated time budget. Although environmental covariates (ambient temperature and diel period) and ecological outcomes (predation) affected behavioural states in non-resident leopards, the response in resident leopards was not clear, except that temporal patterns were consistent with a crepuscular and nocturnal movement pattern. Resident leopards adopt an energetically more costly mobile behaviour for most of their time while non-residents shift their behavioural states from high energetic expenditure states to energetically less costly encamped behaviour for most of their time, which is likely to be a risk avoidance strategy against conspecifics or humans. Conclusions This study demonstrates that plasticity in predator behaviour depending on life stage may tackle a trade-off between successful predation and avoiding the risks associated with conspecifics, human presence and maintaining home range. Range residency in territorial predators is energetically demanding and can outweigh the predator’s response to intrinsic and extrinsic variables such as thermoregulation or foraging needs. Our approach provides an insight into spatial behavior and decision making of leopards, and other large felids in rugged landscapes through the application of the HMMs in movement ecology.Publisher PDFPeer reviewe

Understanding step selection analysis through numerical integration

1. Step selection functions (SSFs) are flexible statistical models used to jointly describe animals' movement and habitat preferences. The popularity of SSFs has grown rapidly, and various extensions have been developed to increase their utility, including the ability to use multiple statistical distributions to describe movement constraints, interactions to allow movements to depend on local environmental features, and random effects and latent states to account for within- and among-individual variability. Although the SSF is a relatively simple statistical model, its presentation has not been consistent in the literature, leading to confusion about model flexibility and interpretation. 2. We believe that part of the confusion has arisen from the conflation of the SSF model with the methods used for statistical inference, and in particular, parameter estimation. Notably, conditional logistic regression (CLR) can be used to fit SSFs in exponential form, and this model fitting approach is often presented interchangeably with the actual model (the SSF itself). However, reliance on CLR reduces model flexibility, and suggests a misleading interpretation of step selection analysis as being equivalent to a case–control study. 3. In this review, we explicitly distinguish between model formulation and inference technique, presenting a coherent framework to fit SSFs based on numerical integration and maximum likelihood estimation. We provide an overview of common numerical integration techniques (including Monte Carlo integration, importance sampling and quadrature), and explain how they relate to popular methods used in step selection analyses. 4. This general framework unifies different model fitting techniques for SSFs, and opens the way for improved inferential methods. In this approach, it is straightforward to model movement with distributions outside the exponential family, and to apply different SSF model formulations to the same data set and compare them with AIC. By separating the model formulation from the inference technique, we hope to clarify many important concepts in step selection analysis

Inference in MCMC step selection models

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

Rheological Characterization of the Bundling Transition in F-Actin Solutions Induced by Methylcellulose

In many in vitro experiments Brownian motion hampers quantitative data analysis. Therefore, additives are widely used to increase the solvent viscosity. For this purpose, methylcellulose (MC) has been proven highly effective as already small concentrations can significantly slow down diffusive processes. Beside this advantage, it has already been reported that high MC concentrations can alter the microstructure of polymer solutions such as filamentous actin. However, it remains to be shown to what extent the mechanical properties of a composite actin/MC gel depend on the MC concentration. In particular, significant alterations might occur even if the microstructure seems unaffected. Indeed, we find that the viscoelastic response of entangled F-actin solutions depends sensitively on the amount of MC added. At concentrations higher than 0.2% (w/v) MC, actin filaments are reorganized into bundles which drastically changes the viscoelastic response. At small MC concentrations the impact of MC is more subtle: the two constituents, actin and MC, contribute in an additive way to the mechanical response of the composite material. As a consequence, the effect of methylcellulose on actin solutions has to be considered very carefully when MC is used in biochemical experiments

Model of For3p-Mediated Actin Cable Assembly in Fission Yeast

Formin For3p nucleates actin cables at the tips of fission yeast cells for polarized cell growth. The results of prior experiments have suggested a possible mechanism for actin cable assembly that involves association of For3p near cell tips, For3p-mediated actin polymerization, retrograde flow of actin cables toward the cell center, For3p dissociation from cell tips, and cable disassembly. We used analytical and computational modeling to test the validity and implications of the proposed coupled For3p/actin mechanism. We compared the model to prior experiments quantitatively and generated predictions for the expected behavior of the actin cable system upon changes of parameter values. We found that the model generates stable steady states with realistic values of rate constants and actin and For3p concentrations. Comparison of our results to previous experiments monitoring the FRAP of For3p-3GFP and the response of actin cables to treatments with actin depolymerizing drugs provided further support for the model. We identified the set of parameter values that produces results in agreement with experimental observations. We discuss future experiments that will help test the model's predictions and eliminate other possible mechanisms. The results of the model suggest that flow of actin cables may establish actin and For3p concentration gradients in the cytoplasm that could be important in global cell patterning