Go Multivariate: Recommendations on Bayesian Multilevel Hidden Markov Models with Categorical Data

The multilevel hidden Markov model (MHMM) is a promising method to investigate intense longitudinal data obtained within the social and behavioral sciences. The MHMM quantifies information on the latent dynamics of behavior over time. In addition, heterogeneity between individuals is accommodated with the inclusion of individual-specific random effects, facilitating the study of individual differences in dynamics. However, the performance of the MHMM has not been sufficiently explored. We performed an extensive simulation to assess the effect of the number of dependent variables (1-8), number of individuals (5-90), and number of observations per individual (100-1600) on the estimation performance of a Bayesian MHMM with categorical data including various levels of state distinctiveness and separation. We found that using multivariate data generally alleviates the sample size needed and improves the stability of the results. Moreover, including variables only consisting of random noise was generally not detrimental to model performance. Regarding the estimation of group-level parameters, the number of individuals and observations largely compensate for each other. However, only the former drives the estimation of between-individual variability. We conclude with guidelines on the sample size necessary based on the level of state distinctiveness and separation and study objectives of the researcher.

Crabs ride the tide: incoming tides promote foraging of Giant Mud Crab (Scylla serrata)

BACKGROUND

Effective fisheries management of mobile species relies on robust knowledge of animal behaviour and habitat-use. Indices of behaviour can be useful for interpreting catch-per-unit-effort data which acts as a proxy for relative abundance. Information about habitat-use can inform stocking release strategies or the design of marine protected areas. The Giant Mud Crab (Scylla serrata; Family: Portunidae) is a swimming estuarine crab that supports significant fisheries harvest throughout the Indo-West Pacific, but little is known about the fine-scale movement and behaviour of this species.

METHODS

We tagged 18 adult Giant Mud Crab with accelerometer-equipped acoustic tags to track their fine-scale movement using a hyperbolic positioning system, alongside high temporal resolution environmental data (e.g., water temperature), in a temperate south-east Australian estuary. A hidden Markov model was used to classify movement (i.e., step length, turning angle) and acceleration data into discrete behaviours, while also considering the possibility of individual variation in behavioural dynamics. We then investigated the influence of environmental covariates on these behaviours based on previously published observations.

RESULTS

We fitted a model with two well-distinguished behavioural states describing periods of inactivity and foraging, and found no evidence of individual variation in behavioural dynamics. Inactive periods were most common (79% of time), and foraging was most likely during low, incoming tides; while inactivity was more likely as the high tide receded. Model selection removed time (hour) of day and water temperature (°C) as covariates, suggesting that they do not influence Giant Mud Crab behavioural dynamics at the temporal scale investigated.

CONCLUSIONS

Our study is the first to quantitatively link fine-scale movement and behaviour of Giant Mud Crab to environmental variation. Our results suggest Giant Mud Crab are a predominantly sessile species, and support their status as an opportunistic scavenger. We demonstrate a relationship between the tidal cycle and foraging that is likely to minimize predation risk while maximizing energetic efficiency. These results may explain why tidal covariates influence catch rates in swimming crabs, and provide a foundation for standardisation and interpretation of catch-per-unit-effort data-a commonly used metric in fisheries science.

Altered Larval Yellow Perch Swimming Behavior Due to Methylmercury and PCB126 Detected Using Hidden Markov Chain Models

Fish swimming behavior is a commonly measured response in aquatic ecotoxicology because behavior is considered a whole organism-level effect that integrates many sensory systems. Recent advancements in animal behavior models, such as hidden Markov chain models (HMM), suggest an improved analytical approach for toxicology. Using both new and traditional approaches, we examined the sublethal effects of PCB126 and methylmercury on yellow perch (YP) larvae (Perca flavescens) using three doses. Both approaches indicate larvae increase activity after exposure to either chemical. The middle methylmercury-dosed larvae showed multiple altered behavior patterns. First, larvae had a general increase in activity, typically performing more behavior states, more time swimming, and more swimming bouts per second. Second, when larvae were in a slow or medium swimming state, these larvae tended to switch between these states more often. Third, larvae swam slower during the swimming bouts. The upper PCB126-dosed larvae exhibited a higher proportion and a fast swimming state, but the total time spent swimming fast decreased. The middle PCB126-dosed larvae transitioned from fast to slow swimming states less often than the control larvae. These results indicate that developmental exposure to very low doses of these neurotoxicants alters YP larvae overall swimming behaviors, suggesting neurodevelopment alteration.

Caution is warranted when using animal space-use and movement to infer behavioral states

BACKGROUND

Identifying the behavioral state for wild animals that can't be directly observed is of growing interest to the ecological community. Advances in telemetry technology and statistical methodologies allow researchers to use space-use and movement metrics to infer the underlying, latent, behavioral state of an animal without direct observations. For example, researchers studying ungulate ecology have started using these methods to quantify behaviors related to mating strategies. However, little work has been done to determine if assumed behaviors inferred from movement and space-use patterns correspond to actual behaviors of individuals.

METHODS

Using a dataset with male and female white-tailed deer location data, we evaluated the ability of these two methods to correctly identify male-female interaction events (MFIEs). We identified MFIEs using the proximity of their locations in space as indicators of when mating could have occurred. We then tested the ability of utilization distributions (UDs) and hidden Markov models (HMMs) rendered with single sex location data to identify these events.

RESULTS

For white-tailed deer, male and female space-use and movement behavior did not vary consistently when with a potential mate. There was no evidence that a probability contour threshold based on UD volume applied to an individual's UD could be used to identify MFIEs. Additionally, HMMs were unable to identify MFIEs, as single MFIEs were often split across multiple states and the primary state of each MFIE was not consistent across events.

CONCLUSIONS

Caution is warranted when interpreting behavioral insights rendered from statistical models applied to location data, particularly when there is no form of validation data. For these models to detect latent behaviors, the individual needs to exhibit a consistently different type of space-use and movement when engaged in the behavior. Unvalidated assumptions about that relationship may lead to incorrect inference about mating strategies or other behaviors.

Identifying resting locations of a small elusive forest carnivore using a two-stage model accounting for GPS measurement error and hidden behavioral states

BACKGROUND

Studies of animal movement using location data are often faced with two challenges. First, time series of animal locations are likely to arise from multiple behavioral states (e.g., directed movement, resting) that cannot be observed directly. Second, location data can be affected by measurement error, including failed location fixes. Simultaneously addressing both problems in a single statistical model is analytically and computationally challenging. To both separate behavioral states and account for measurement error, we used a two-stage modeling approach to identify resting locations of fishers (Pekania pennanti) based on GPS and accelerometer data.

METHODS

We developed a two-stage modelling approach to estimate when and where GPS-collared fishers were resting for 21 separate collar deployments on 9 individuals in southern Oregon. For each deployment, we first fit independent hidden Markov models (HMMs) to the time series of accelerometer-derived activity measurements and apparent step lengths to identify periods of movement and resting. Treating the state assignments as given, we next fit a set of linear Gaussian state space models (SSMs) to estimate the location of each resting event.

RESULTS

Parameter estimates were similar across collar deployments. The HMMs successfully identified periods of resting and movement with posterior state assignment probabilities greater than 0.95 for 97% of all observations. On average, fishers were in the resting state 63% of the time. Rest events averaged 5 h (4.3 SD) and occurred most often at night. The SSMs allowed us to estimate the 95% credible ellipses with a median area of 0.12 ha for 3772 unique rest events. We identified 1176 geographically distinct rest locations; 13% of locations were used on > 1 occasion and 5% were used by > 1 fisher. Females and males traveled an average of 6.7 (3.5 SD) and 7.7 (6.8 SD) km/day, respectively.

CONCLUSIONS

We demonstrated that if auxiliary data are available (e.g., accelerometer data), a two-stage approach can successfully resolve both problems of latent behavioral states and GPS measurement error. Our relatively simple two-stage method is repeatable, computationally efficient, and yields directly interpretable estimates of resting site locations that can be used to guide conservation decisions.

Prospects for the Analysis and Reduction of Damaging Behaviour in Group-Housed Livestock, With Application to Pig Breeding

Innovations in the breeding and management of pigs are needed to improve the performance and welfare of animals raised in social groups, and in particular to minimise biting and damage to group mates. Depending on the context, social interactions between pigs can be frequent or infrequent, aggressive, or non-aggressive. Injuries or emotional distress may follow. The behaviours leading to damage to conspecifics include progeny savaging, tail, ear or vulva biting, and excessive aggression. In combination with changes in husbandry practices designed to improve living conditions, refined methods of genetic selection may be a solution reducing these behaviours. Knowledge gaps relating to lack of data and limits in statistical analyses have been identified. The originality of this paper lies in its proposal of several statistical methods for common use in analysing and predicting unwanted behaviours, and for genetic use in the breeding context. We focus on models of interaction reflecting the identity and behaviour of group mates which can be applied directly to damaging traits, social network analysis to define new and more integrative traits, and capture-recapture analysis to replace missing data by estimating the probability of behaviours. We provide the rationale for each method and suggest they should be combined for a more accurate estimation of the variation underlying damaging behaviours.

Northern pigtailed macaques rely on old growth plantations to offset low fruit availability in a degraded forest fragment

Space-use and foraging strategies are important facets to consider in regard to the ecology and conservation of primates. For this study, we documented movement, ranging, and foraging patterns of northern pigtailed macaques (Macaca leonina) for 14 months in a degraded habitat with old growth Acacia and Eucalyptus plantations at the Sakaerat Biosphere Reserve in northeastern Thailand. We used hidden Markov models and characteristic hull polygons to analyze these patterns in regard to fruit availability. Macaques' home range (HR) was 599 ha and spanned through a natural dry-evergreen forest (DEF), and plantation forest. Our results showed that active foraging increased with higher fruit availability in DEF. Macaques changed to a less continuous behavioral state during periods of lower fruit availability in DEF, repeatedly moving from foraging to transiting behavior, while extending their HR further into plantation forest and surrounding edge areas. Concomitantly, macaques shifted their diet from fleshy to dry fruit such as the introduced Acacia species. Our results showed that the diet and movement ecology adaptations of northern pigtailed macaques were largely dependent on availability of native fruits, and reflected a "high-cost, high-yield" foraging strategy when fresh food was scarce and dry fruit was available in plantation forest. Conversely, wild-feeding northern pigtailed macaque populations inhabiting pristine habitat approached a "low-cost, low-yield" foraging strategy. Our results outline the effects of habitat degradation on foraging strategies and show how a flexible species can cope with its nutritional requirements.

Classifying grey seal behaviour in relation to environmental variability and commercial fishing activity - a multivariate hidden Markov model

Classifying movement behaviour of marine predators in relation to anthropogenic activity and environmental conditions is important to guide marine conservation. We studied the relationship between grey seal (Halichoerus grypus) behaviour and environmental variability in the southwestern Baltic Sea where seal-fishery conflicts are increasing. We used multiple environmental covariates and proximity to active fishing nets within a multivariate hidden Markov model (HMM) to quantify changes in movement behaviour of grey seals while at sea. Dive depth, dive duration, surface duration, horizontal displacement, and turning angle were used to identify travelling, resting and foraging states. The likelihood of seals foraging increased in deeper, colder, more saline waters, which are sites with increased primary productivity and possibly prey densities. Proximity to active fishing net also had a pronounced effect on state occupancy. The probability of seals foraging was highest <5 km from active fishing nets (51%) and decreased as distance to nets increased. However, seals used sites <5 km from active fishing nets only 3% of their time at sea highlighting an important temporal dimension in seal-fishery interactions. By coupling high-resolution oceanographic, fisheries, and grey seal movement data, our study provides a scientific basis for designing management strategies that satisfy ecological and socioeconomic demands on marine ecosystems.

Incorporating movement patterns to discern habitat selection: black bears as a case study

Context Animals’ use of space and habitat selection emerges from their movement patterns, which are, in turn, determined by their behavioural or physiological states and extrinsic factors. Aim The aims of the present study were to investigate animal movement and incorporate the movement patterns into habitat selection analyses using Global Positioning System (GPS) location data from 16 black bears (Ursus americanus) in a fragmented area of Florida, USA. Methods Hidden Markov models (HMMs) were used to discern the movement patterns of the bears. These results were then used in step-selection functions (SSFs) to evaluate habitat selection patterns and the factors influencing these patterns. Key results HMMs revealed that black bear movement patterns are best described by three behavioural states: (1) resting (very short step-lengths and large turning angles); (2) encamped (moderate step-lengths and large turning angles); and (3) exploratory (long step-lengths and small turning angles). Bears selected for forested wetlands and marsh wetlands more than any other land cover type, and generally avoided urban areas in all seasons and when in encamped and exploratory behavioural states. Bears also chose to move to locations farther away from major roads. Conclusions Because habitat selection is influenced by how animals move within landscapes, it is essential to consider animals’ movement patterns when making inferences about habitat selection. The present study achieves this goal by using HMMs to first discern black bear movement patterns and associated parameters, and by using these results in SSFs to investigate habitat selection patterns. Thus, the methodological framework developed in this study effectively incorporates state-specific movement patterns while making inferences regarding habitat selection. The unified methodological approach employed here will contribute to an improved understanding of animal ecology as well as informed management decisions. Implications Conservation plans focused on preserving forested wetlands would benefit bears by not only providing habitat for resting and foraging, but also by providing connectivity through fragmented landscapes. Additionally, the framework could be applied to species that follow annual cycles and may provide a tool for investigating how animals are using dispersal corridors.

Running on empty: recharge dynamics from animal movement data

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

Scaling marine fish movement behavior from individuals to populations

Understanding how, where, and when animals move is a central problem in marine ecology and conservation. Key to improving our knowledge about what drives animal movement is the rising deployment of telemetry devices on a range of free-roaming species. An increasingly popular way of gaining meaningful inference from an animal's recorded movements is the application of hidden Markov models (HMMs), which allow for the identification of latent behavioral states in the movement paths of individuals. However, the use of HMMs to explore the population-level consequences of movement is often limited by model complexity and insufficient sample sizes. Here, we introduce an alternative approach to current practices and provide evidence of how the inclusion of prior information in model structure can simplify the application of HMMs to multiple animal movement paths with two clear benefits: (a) consistent state allocation and (b) increases in effective sample size. To demonstrate the utility of our approach, we apply HMMs and adapted HMMs to over 100 multivariate movement paths consisting of conditionally dependent daily horizontal and vertical movements in two species of demersal fish: Atlantic cod (Gadus morhua; n = 46) and European plaice (Pleuronectes platessa; n = 61). We identify latent states corresponding to two main underlying behaviors: resident and migrating. As our analysis considers a relatively large sample size and states are allocated consistently, we use collective model output to investigate state-dependent spatiotemporal trends at the individual and population levels. In particular, we show how both species shift their movement behaviors on a seasonal basis and demonstrate population space use patterns that are consistent with previous individual-level studies. Tagging studies are increasingly being used to inform stock assessment models, spatial management strategies, and monitoring of marine fish populations. Our approach provides a promising way of adding value to tagging studies because inferences about movement behavior can be gained from a larger proportion of datasets, making tagging studies more relevant to management and more cost-effective.

Hidden Markov models reveal complexity in the diving behaviour of short-finned pilot whales

Diving behaviour of short-finned pilot whales is often described by two states; deep foraging and shallow, non-foraging dives. However, this simple classification system ignores much of the variation that occurs during subsurface periods. We used multi-state hidden Markov models (HMM) to characterize states of diving behaviour and the transitions between states in short-finned pilot whales. We used three parameters (number of buzzes, maximum dive depth and duration) measured in 259 dives by digital acoustic recording tags (DTAGs) deployed on 20 individual whales off Cape Hatteras, North Carolina, USA. The HMM identified a four-state model as the best descriptor of diving behaviour. The state-dependent distributions for the diving parameters showed variation between states, indicative of different diving behaviours. Transition probabilities were considerably higher for state persistence than state switching, indicating that dive types occurred in bouts. Our results indicate that subsurface behaviour in short-finned pilot whales is more complex than a simple dichotomy of deep and shallow diving states, and labelling all subsurface behaviour as deep dives or shallow dives discounts a significant amount of important variation. We discuss potential drivers of these patterns, including variation in foraging success, prey availability and selection, bathymetry, physiological constraints and socially mediated behaviour.

Incorporating periodic variability in hidden Markov models for animal movement

BACKGROUND

Clustering time-series data into discrete groups can improve prediction and provide insight into the nature of underlying, unobservable states of the system. However, temporal variation in probabilities of group occupancy, or the rates at which individuals move between groups, can obscure such signals. We use finite mixture and hidden Markov models (HMMs), two standard clustering techniques, to model long-term hourly movement data from Florida panthers (Puma concolor coryi). Allowing for temporal heterogeneity in transition probabilities, a straightforward but little-used extension of the standard HMM framework, resolves some shortcomings of current models and clarifies the movement patterns of panthers.

RESULTS

Simulations and analyses of panther data showed that model misspecification (omitting important sources of variation) can lead to overfitting/overestimating the underlying number of movement states. Models incorporating temporal heterogeneity identify fewer underlying states, and can make out-of-sample predictions that capture observed diurnal and autocorrelated movement patterns exhibited by Florida panthers.

CONCLUSION

Incorporating temporal heterogeneity improved goodness of fit and predictive capability as well as reducing the selected number of movement states closer to a biologically interpretable level, although there is further room for improvement here. Our results suggest that incorporating additional structure in statistical models of movement can allow more accurate assessment of appropriate model complexity.