Roland Langrock

Flexible and practical modeling of animal telemetry data: hidden Markov models and extensions

We discuss hidden Markov-type models for fitting a variety of multistate random walks to wildlife movement data. Discrete-time hidden Markov models (HMMs) achieve considerable computational gains by focusing on observations that are regularly spaced in time, and for which the measurement error is negligible. These conditions are often met, in particular for data related to terrestrial animals, so that a likelihood-based HMM approach is feasible. We describe a number of extensions of HMMs for animal movement modeling, including more flexible state transition models and individual random effects (fitted in a non-Bayesian framework). In particular we consider so-called hidden semi-Markov models, which may substantially improve the goodness of fit and provide important insights into the behavioral state switching dynamics. To showcase the expediency of these methods, we consider an application of a hierarchical hidden semi-Markov model to multiple bison movement paths.

moveHMM: an R package for the statistical modelling of animal movement data using hidden Markov models

Summary Due to the substantial progress in tracking technology, recent years have seen an explosion in the amount of movement data being collected. This has led to a huge demand for statistical tools that allow ecologists to draw meaningful inference from large tracking data sets. The class of hidden Markov models (HMMs) matches the intuitive understanding that animal movement is driven by underlying behavioural modes and has proven to be very useful for analysing movement data. For data that involve a regular sampling unit and negligible measurement error, these models usually are sufficiently flexible to capture the complex correlation structure found in movement data, yet are computationally inexpensive compared to alternative methods. The R package moveHMM allows ecologists to process GPS tracking data into series of step lengths and turning angles, and to fit an HMM to these data, allowing, in particular, for the incorporation of environmental covariates. The package includes assessment and visualization tools for the fitted model. We illustrate the use of moveHMM using (simulated) movement of the legendary wild haggis Haggis scoticus. Our findings illustrate the role our software, and movement modelling in general, can play in conservation and management by illuminating environmental constraints.

On the application of mixed hidden Markov models to multiple behavioural time series.

Analysing behavioural sequences and quantifying the likelihood of occurrences of different behaviours is a difficult task as motivational states are not observable. Furthermore, it is ecologically highly relevant and yet more complicated to scale an appropriate model for one individual up to the population level. In this manuscript (mixed) hidden Markov models (HMMs) are used to model the feeding behaviour of 54 subadult grey mouse lemurs (Microcebus murinus), small nocturnal primates endemic to Madagascar that forage solitarily. Our primary aim is to introduce ecologists and other users to various HMM methods, many of which have been developed only recently, and which in this form have not previously been synthesized in the ecological literature. Our specific application of mixed HMMs aims at gaining a better understanding of mouse lemur behaviour, in particular concerning sex-specific differences. The model we consider incorporates random effects for accommodating heterogeneity across animals, i.e. accounts for different personalities of the animals. Additional subject- and time-specific covariates in the model describe the influence of sex, body mass and time of night.

Using Hidden Markov Models to Deal with Availability Bias on Line Transect Surveys

We develop estimators for line transect surveys of animals that are stochastically unavailable for detection while within detection range. The detection process is formulated as a hidden Markov model with a binary state-dependent observation model that depends on both perpendicular and forward distances. This provides a parametric method of dealing with availability bias when estimates of availability process parameters are available even if series of availability events themselves are not. We apply the estimators to an aerial and a shipboard survey of whales, and investigate their properties by simulation. They are shown to be more general and more flexible than existing estimators based on parametric models of the availability process. We also find that methods using availability correction factors can be very biased when surveys are not close to being instantaneous, as can estimators that assume temporal independence in availability when there is temporal dependence.

Sex-specific and individual preferences for hunting strategies in white sharks

1. Fine-scale predator movements may be driven by many factors including sex, habitat anddistribution of resources. There may also be individual preferences for certain movementstrategies within a population which can be hard to quantify.2. Within top predators, movements are also going to be directly related to the mode of hunting,for example sit-and-wait or actively searching for prey. Although there is mounting evidencethat different hunting modes can cause opposing trophic cascades, there has been littlefocus on the modes used by top predators, especially those in the marine environment.3. Adult white sharks (Carcharhodon carcharias) are well known to forage on marine mammalprey, particularly pinnipeds. Sharks primarily ambush pinnipeds on the surface, but there hasbeen less focus on the strategies they use to encounter prey.4. We applied mixed hidden Markov models to acoustic tracking data of white sharks in acoastal aggregation area in order to quantify changing movement states (area-restricted searching(ARS) vs. patrolling) and the factors that influenced them. Individuals were re-tracked overmultiple days throughout a month to see whether state-switching dynamics varied or if individualspreferred certain movement strategies.5. Sharks were more likely to use ARS movements in the morning and during periods of chummingby ecotourism operators. Furthermore, the proportion of time individuals spent in the two differentstates and the state-switching frequency, differed between the sexes and between individuals.6. Predation attempts/success on pinnipeds were observed for sharks in both ARS and patrollingmovement states and within all random effects groupings. Therefore, white sharks can use both a ‘sitand-wait’ (ARS) and ‘active searching’ (patrolling) movements to ambush pinniped prey on the surface.7. White sharks demonstrate individual preferences for fine-scale movement patterns, whichmay be related to their use of different hunting modes. Marine top predators are generallyassumed to use only one type of hunting mode, but we show that there may be a mix withinpopulations. As such, individual variability should be considered when modelling behaviouraleffects of predators on prey species.

Nonparametric inference in hidden Markov models using P-splines

Hidden Markov models (HMMs) are flexible time series models in which the distribution of the observations depends on unobserved serially correlated states. The state-dependent distributions in HMMs are usually taken from some class of parametrically specified distributions. The choice of this class can be difficult, and an unfortunate choice can have serious consequences for example on state estimates, and more generally on the resulting model complexity and interpretation. We demonstrate these practical issues in a real data application concerned with vertical speeds of a diving beaked whale, where we demonstrate that parametric approaches can easily lead to overly complex state processes, impeding meaningful biological inference. In contrast, for the dive data, HMMs with nonparametrically estimated state-dependent distributions are much more parsimonious in terms of the number of states and easier to interpret, while fitting the data equally well. Our nonparametric estimation approach is based on the idea of representing the densities of the state-dependent distributions as linear combinations of a large number of standardized B-spline basis functions, imposing a penalty term on non-smoothness in order to maintain a good balance between goodness-of-fit and smoothness.

Analysis of animal accelerometer data using hidden Markov models

1.Use of accelerometers is now widespread within animal biotelemetry as they provide a means of measuring an animals activity in a meaningful and quantitative way where direct observation is not possible. In sequential acceleration data there is a natural dependence between observations of behaviour, a fact that has been largely ignored in most analyses. 2.Analyses of acceleration data where serial dependence has been explicitly modelled have largely relied on hidden Markov models (HMMs). Depending on the aim of an analysis, an HMM can be used for state prediction or to make inferences about drivers of behaviour. For state prediction, a supervised learning approach can be applied. That is, an HMM is trained to classify unlabelled acceleration data into a finite set of pre-specified categories. An unsupervised learning approach can be used to infer new aspects of animal behaviour when biologically meaningful response variables are used, with the caveat that the states may not map to specific behaviours. 3.We will provide the details necessary to implement and assess an HMM in both the supervised and unsupervised learning context and discuss the data requirements of each case. We outline two applications to marine and aerial systems (shark and eagle) taking the unsupervised learning approach, which is more readily applicable to animal activity measured in the field. HMMs were used to infer the effects of temporal, atmospheric and tidal inputs on animal behaviour. 4.Animal accelerometer data allow ecologists to identify important correlates and drivers of animal activity (and hence behaviour). The HMM framework is well suited to deal with the main features commonly observed in accelerometer data, and can easily be extended to suit a wide range of types of animal activity data. The ability to combine direct observations of animal activity with statistical models, which account for the features of accelerometer data, offers a new way to quantify animal behaviour, energetic expenditure and deepen our insights into individual behaviour as a constituent of populations and ecosystems. This article is protected by copyright. All rights reserved.

Maximum likelihood estimation of mark–recapture–recovery models in the presence of continuous covariates

We consider mark-recapture-recovery (MRR) data of animals where the model parameters are a function of individual time-varying continuous covariates. For such covariates, the covariate value is unobserved if the corresponding individual is unobserved, in which case the survival probability cannot be evaluated. For continuous-valued covariates, the corresponding likelihood can only be expressed in the form of an integral that is analytically intractable, and, to date, no maximum likelihood approach that uses all the information in the data has been developed. Assuming a first-order Markov process for the covariate values, we accomplish this task by formulating the MRR setting in a state-space framework and considering an approximate likelihood approach which essentially discretizes the range of covariate values, reducing the integral to a summation. The likelihood can then be eciently calculated and maximized using standard techniques for hidden Markov models. We initially assess the approach using simulated data before applying to real data relating to Soay sheep, specifying the survival probability as a function of body mass. Models that have previously been suggested for the corresponding covariate process are typically of the form of diusive random walks. We consider an alternative non-diusive

Some applications of nonlinear and non-Gaussian state–space modelling by means of hidden Markov models

Nonlinear and non-Gaussian state–space models (SSMs) are fitted to different types of time series. The applications include homogeneous and seasonal time series, in particular earthquake counts, polio counts, rainfall occurrence data, glacial varve data and daily returns on a share. The considered SSMs comprise Poisson, Bernoulli, gamma and Student-t distributions at the observation level. Parameter estimations for the SSMs are carried out using a likelihood approximation that is obtained after discretization of the state space. The approximation can be made arbitrarily accurate, and the approximated likelihood is precisely that of a finite-state hidden Markov model (HMM). The proposed method enables us to apply standard HMM techniques. It is easy to implement and can be extended to all kinds of SSMs in a straightforward manner.

A multivariate mixed hidden Markov model for blue whale behaviour and responses to sound exposure

A MULTIVARIATE MIXED HIDDEN MARKOV MODEL FOR BLUE WHALE BEHAVIOUR AND RESPONSES TO SOUND EXPOSURE1 BY STACY L. DERUITER∗,†, ROLAND LANGROCK‡,†, TOMAS SKIRBUTAS†, JEREMY A. GOLDBOGEN§, JOHN CALAMBOKIDIS¶, ARI S. FRIEDLAENDER‖,∗∗ AND BRANDON L. SOUTHALL∗∗ Calvin College∗, University of St Andrews†, Bielefeld University‡, Stanford University§, Cascadia Research Collective¶, Oregon State University‖ and SEA, Inc.∗∗