Modelling animal movement in heterogeneous environments: from statistical inferential models to individual-based models

Abstract

Modelling animal movement in heterogeneous environments is challenging because organisms experience a complex suite of internal and external stimuli that operate hierarchically over multiple temporal and spatial scales. A fundamental goal of movement ecology is to relate the behaviour of animals to their environments, especially with respect to how external information is perceived and processed in the decisions that guide their movements. With the continued development of tracking devices movement data are becoming available at increasingly higher spatio-temporal resolution, and sophisticated analytical methods developed with which to analyse them. However, with these advances in data-capture technologies, it is becoming increasingly difficult to match research questions to the analytical tools that are appropriate for interrogating complex, serially-dependent, multivariate movement data. The methods developed in my dissertation are designed to bridge the gaps between the underlying processes and observed patterns of movement behaviour, as well as the observational and process scales of movement models. First I extended the conceptual framework of movement ecology developed by Nathan et al. (2008) which depicts the interplay among four basic mechanistic components of movement (the internal state, motion, and navigation capacities of the individual and the external factors). I investigated the influences of environmental factors on movement by categorising them into two general classes: environmental stimuli perceived and responded to by animals, and environmental forces such as wind and water currents that physically displace animals. Using data describing grey-faced petrels (Pterodroma macroptera gouldi) movements, a Markov Chain Monte Carlo (MCMC) model, and a vector analysis, I illustrated that the behavioural states categorised by the MCMC model were actually a combination of movement behaviour and wind displacement. This analysis demonstrated how displacement by fluid external forces can change the interpretation of behavioural states inferred by statistical models of movement. I recommend that to realistically describe the movement behaviour of animals in fluid media, environmental factors, whenever possible, should be incorporated in statistical inferrentail movement models (IMMs). This can be achieved either by addition of environmental covariates directly into the model, or from a post hoc approach, such as by vector analysis. A strong criticism of using state-space approaches to infer behaviour from movement data is that such models assume that the behaviours underlying the observed movement can be adequately represented by combinations of correlated random walks. Gurarie et al. (2009) developed a likelihood-based technique (behaviour change point analysis, or BCPA) to identify behavioural bouts within movement trajectories that are not limited to specific movement mechanisms. I extended the BCPA approach into three sequentially applied statistical procedures: (1) BCPA to partition movement trajectories into discrete bouts of same-state behaviours, based on abrupt changes in the spatio-temporal autocorrelation structure of movement parameters; (2) hierarchical multivariate cluster analysis to determine the number of different behavioural states; and (3) k-means clustering to classify inferred bouts of same-state location observations into behavioural modes. I demonstrate application of the method by analysing synthetic trajectories of known ‘artificial behaviours’ comprised of different correlated random walks, as well as real foraging trajectories of little penguins (Eudyptula minor) obtained by GPS telemetry. The modelling procedure correctly classified 92.5% of all individual location observations in the synthetic trajectories, demonstrating reasonable ability to successfully discriminate behavioural modes. Most individual little penguins were found to exhibit three unique behavioural states (resting, commuting/active searching, area-restricted foraging), with variation in the timing and locations of observations apparently related to ambient light, bathymetry, and proximity to coastlines and river mouths. Addition of k-means clustering extends the utility of behavioural change point analysis, by providing a simple means through which the behaviours inferred for the location observations comprising individual movement trajectories can be objectively classified. Researchers are increasingly using individual-based models (IBMs) to explore ecological systems and, in particular, the emergent outcomes of individual-level processes. A major challenge in developing IBMs for study of movement ecology is that such models often seek to characterise complex phenomena, and thus must represent and parameterise multiple hierarchical levels of unobserved behaviours. Approaches based on Approximate Bayesian computation (ABC) methods have been used to support the parameterisation, calibration and evaluation of IBMs. However, the ABC approach requires selection and use of data to exclude parameter sets and unrealistic model structures that generate atypical or improbable patterns. I propose a modelling framework that integrates information derived from statistical inferential models to describe the behaviour of moving animals with ABC methodologies for parameterisation and analysis of IBMs. To demonstrate its application, I apply such a framework in an exemplar analysis to high-resolution movement trajectories of the foraging trips of black petrels (Procellaria parkinsoni), an endangered seabird endemic to New Zealand. Outcomes of this study show that use of inferential statistical models to summarise movement data can inform model selection and parameterisation procedures via ABC, and enable IBM to produce biologically relaistic movement patterns, and yield valuable insights regarding the movement ecology and behaviour of animals. Movement behaviour is shaped by the cognitive abilities and the experiences of individual animals. As a result, how animals perceive and process intrisnsic and extrinsic information is a central question in ecology. Determining what an animal knows about its environment, and how this information is translated into specific movement behaviours, is a significant conceptual challenge for movement ecology. I explored the functionality of cognition in relation to foraging movements, using a continuous-space IBM of animal movement that incorporated perception, memory and site fidelity. Using the IBM, I assessed the foraging efficiency of individuals with different combinations of cognitive parameters in 18 different landscape types with different combinations of resource amount and aggregation. Results show that in landscapes where resources were limited and aggregated in space, high memory accuracy and persistence were favoured for optimal foraing, and site-fidelity contributed most to foraging efficiency. As resources became more abundant, individuals with better perception were favoured. Compared to the null-model of a correlated random walk, cognition increased foraging efficiency and reduced space-use of indiviudals. These findings provide quantitative insights into the effects of spatial cognition and dynamic information on animal movement decisions. This study suggests that memory-driven foraging behaviours are likely to be important in landscapes with high-value, spatially aggregated resources, and information regarding both biological attributes and environmental structures need to be considered when modelling animal movement behaviour. Finally, I discuss the wider application of statistical and simulation models for analysing data describing animal movements. I advocate consideration of influences from both internal and external stimuli, as well as the costs of movement, cognition, and metabolism in scale-dependent movement models in future research.