Toby A. Patterson

Modelling group dynamic animal movement

Summary n nGroup dynamics are a fundamental aspect of many species movements. The need to adequately model individuals interactions with other group members has been recognized, particularly in order to differentiate the role of social forces in individual movement from environmental factors. However, to date, practical statistical methods, which can include group dynamics in animal movement models, have been lacking. nWe consider a flexible modelling framework that distinguishes a group-level model, describing the movement of the groups centre, and an individual-level model, such that each individual makes its movement decisions relative to the group centroid. The basic idea is framed within the flexible class of hidden Markov models, extending previous work on modelling animal movement by means of multistate random walks. nWhile in simulation experiments parameter estimators exhibit some bias in non-ideal scenarios, we show that generally the estimation of models of this type is both feasible and ecologically informative. nWe illustrate the approach using real movement data from 11 reindeer (Rangifer tarandus). Results indicate a directional bias towards a group centroid for reindeer in an encamped state. Though the attraction to the group centroid is relatively weak, our model successfully captures group-influenced movement dynamics. Specifically, as compared to a regular mixture of correlated random walks, the group dynamic model more accurately predicts the non-diffusive behaviour of a cohesive mobile group. nAs technology continues to develop, it will become easier and less expensive to tag multiple individuals within a group in order to follow their movements. Our work provides a first inferential framework for understanding the relative influences of individual versus group-level movement decisions. This framework can be extended to include covariates corresponding to environmental influences or body condition. As such, this framework allows for a broader understanding of the many internal and external factors that can influence an individuals movement.

Reproductive schedules in southern bluefin tuna: are current assumptions appropriate?

Southern bluefin tuna (SBT) appear to comprise a single stock that is assumed to be both mixed across its distribution and having reproductive adults that are obligate, annual spawners. The putative annual migration cycle of mature SBT consists of dispersed foraging at temperate latitudes with migration to a single spawning ground in the tropical eastern Indian Ocean. Spawning migrations have been assumed to target two peaks in spawning activity; one in September-October and a second in February-March. SBT of sizes comparable to that of individuals observed on the spawning ground were satellite tagged in the Tasman Sea region (2003–2008) and demonstrated both migrations to the spawning grounds and residency in the Tasman Sea region throughout the whole year. All individuals undertaking apparent spawning migrations timed their movements to coincide with the second recognised spawning peak or even later. These observations suggest that SBT may demonstrate substantial flexibility in the scheduling of reproductive events and may even not spawn annually as currently assumed. Further, the population on the spawning grounds may be temporally structured in association with foraging regions. These findings provide new perspectives on bluefin population and spatial dynamics and warrant further investigation and consideration of reproductive schedules in this species.

Determining trends and environmental drivers from long-term marine mammal and seabird data: examples from Southern Australia

Climate change is acknowledged as an emerging threat for top-order marine predators, yet obtaining evidence of impacts is often difficult. In south-eastern Australia, a marine global warming hotspot, evidence suggests that climate change will profoundly affect pinnipeds and seabirds. Long-term data series are available to assess some species’ responses to climate. Researchers have measured a variety of chronological and population variables, such as laying dates, chick or pup production, colony-specific abundance and breeding success. Here, we consider the challenges in accurately assessing trends in marine predator data, using long-term data series that were originally collected for other purposes, and how these may be driven by environmental change and variability. In the past, many studies of temporal changes and environmental drivers used linear analyses and we demonstrate the (theoretical) relationship between the magnitude of a trend, its variability, and the duration of a data series required to detect a linear trend. However, species may respond to environmental change in a nonlinear manner and, based on analysis of time-series from south-eastern Australia, it appears that the assumptions of a linear model are often violated, particularly for measures of population size. The commonly measured demographic variables exhibit different degrees of variation, which influences the ability to detect climate signals. Due to their generally lower year-to-year variability, we illustrate that monitoring of variables such as mass and breeding chronology should allow detection of temporal trends earlier in a monitoring programme than observations of breeding success and population size. Thus, establishing temporal changes with respect to climate change from a monitoring programme over a relatively short time period requires careful a priori choice of biological variables.

Developing Integrated Database Systems for the Management of Electronic Tagging Data

Recent advances in electronic tag technology have resulted in an explosion of data for marine biologists. Providing descriptions of data management systems and discussion of their strengths and weaknesses will be important in promoting a dialogue with the ultimate goal of building better systems to support research. The importance of this will only increase as large multinational, multi-institutional studies become more common. Modern memory components permit a single archival tag to collect many megabytes of data. Effective handling of the volume of data generated by multiple tag deployments is a major challenge, and an essential step before data analysis can be performed. Tags are deployed on multiple species and a single animal may carry several different tag types. Data handling systems must be flexible enough to accommodate the variety of ways tags are used, as well as the changes to tag specifications over time. This paper describes a relational database system that has been developed to meet these requirements. This database stores data from a variety of electronic tags from different manufacturers, including archival tags, satellite tags and acoustic tags. The data are downloaded, processed and stored automatically where possible. Centralising data storage allows flexibility in data access, quality control, exploration and analysis. Software programs allow access to the data from local servers or via the internet and include initial visualization of animal tracks via a mapping system. A suite of environmental data and products can also be matched to the selected track(s), which aids initial analyses and development and refinement of scientific hypotheses.

Multi year observations reveal variability in residence of a tropical Demersal Fish, Lethrinus nebulosus: implications for spatial management.

Off the Ningaloo coast of North West Western Australia, Spangled Emperor Lethrinus nebulosus are among the most highly targeted recreational fish species. The Ningaloo Reef Marine Park comprises an area of 4,566 km2 of which 34% is protected from fishing by 18 no-take sanctuary zones ranging in size from 0.08–44.8 km2. To better understand Spangled Emperor movements and the adequacy of sanctuary zones within the Ningaloo Reef Marine Park for this species, 84 Spangled Emperor of a broad spectrum of maturity and sex were tagged using internal acoustic tags in a range of lagoon and reef slope habitats both inside and adjacent to the Mangrove Bay Sanctuary zone. Kernel Utilisation Distribution (KUD) was calculated for 39 resident individuals that were detected for more than 30 days. There was no relationship with fish size and movement or site fidelity. Average home range (95% KUD) for residents was 8.5±0.5 km2 compared to average sanctuary zone size of 30 km2. Calculated home range was stable over time resulting in resident animals tagged inside the sanctuary zone spending ∼80% of time within the sanctuary boundaries. The number of fish remaining within the array of receivers declined steadily over time and after one year more than 60% of tagged fish had moved outside the sanctuary zone and also beyond the 28 km2 array of receivers. Long term monitoring identified the importance of shifting home range and was essential for understanding overall residency within protected areas and also for identifying spawning related movements. This study indicates that despite exhibiting stable and small home ranges over periods of one to two years, more than half the population of spangled emperor move at scales greater than average sanctuary size within the Ningaloo Reef Marine Park.

Statistical modelling of individual animal movement: an overview of key methods and a discussion of practical challenges

With the influx of complex and detailed tracking data gathered from electronic tracking devices, the analysis of animal movement data has recently emerged as a cottage industry among biostatisticians. New approaches of ever greater complexity are continue to be added to the literature. In this paper, we review what we believe to be some of the most popular and most useful classes of statistical models used to analyse individual animal movement data. Specifically, we consider discrete-time hidden Markov models, more general state-space models and diffusion processes. We argue that these models should be core components in the toolbox for quantitative researchers working on stochastic modelling of individual animal movement. The paper concludes by offering some general observations on the direction of statistical analysis of animal movement. There is a trend in movement ecology towards what are arguably overly complex modelling approaches which are inaccessible to ecologists, unwieldy with large data sets or not based on mainstream statistical practice. Additionally, some analysis methods developed within the ecological community ignore fundamental properties of movement data, potentially leading to misleading conclusions about animal movement. Corresponding approaches, e.g. based on Lévy walk-type models, continue to be popular despite having been largely discredited. We contend that there is a need for an appropriate balance between the extremes of either being overly complex or being overly simplistic, whereby the discipline relies on models of intermediate complexity that are usable by general ecologists, but grounded in well-developed statistical practice and efficient to fit to large data sets.

Dynamic optimal foraging theory explains vertical migrations of Bigeye tuna

Bigeye tuna are known for remarkable daytime vertical migrations between deep water, where food is abundant but the water is cold, and the surface, where water is warm but food is relatively scarce. Here we investigate if these dive patterns can be explained by dynamic optimal foraging theory, where the tuna maximizes its energy harvest rate. We assume that foraging efficiency increases with body temperature, so that the vertical migrations are thermoregulatory. The tunas state is characterized by its mean body temperature and depth, and we solve the optimization problem numerically using dynamic programming. With little calibration of model parameters, our results are consistent with observed data on vertical movement: we find that small tuna should display constant-depth strategies while large tuna should display vertical migrations. The analysis supports the hypothesis that the tuna behaves such as to maximize its energy gains. The model therefore provides insight into the processes underlying observed behavioral patterns and allows generating predictions of foraging behavior in unobserved environments.

Movement behaviour responses to environment: fast inference of individual variation with a mixed effects model

Telemetry data provide a rich source of information on animals use of space, habitat preferences and movement behaviour. Yet habitat models fit to these data are blind to the underlying behavioural context. Conversely, behavioural models accounting for individual variability are too slow for meaningful analysis of large telemetry datasets. Applying new fast-estimation tools, we show how a model incorporating mixed effects within a flexible random walk movement process rapidly infers among-individual variability in environment-movement behaviour relationships. We demonstrate our approach using southern elephant seal (Mirounga leonina) telemetry data. Seals consistently reduced speed and directionality (move persistence) with increasing sea ice coverage, had variable responses to chlorophyll concentration and consistently reduced move persistence in regions where circumpolar deep water shoaled. Our new modelling framework is extensible and substantively advances analysis of telemetry data by allowing fast and flexible mixed effects estimation of potential drivers of movement behaviour processes.

Oceanic diel vertical migrations arising from a predator-prey game

The deep scattering layer is an ubiquitous aggregation of zooplankton and forage fish in the ocean. It features the striking phenomenon of diel vertical migration, where animals remain in deep, dark water in daylight hours and migrate upwards at dusk. The common explanation for this is that prey avoid vulnerability to visual predators. Here, we develop a game-theoretic explanation for the deep scattering layer and its diel vertical migrations, focusing on one generic predator species and one generic prey species. The model is formulated in continuous time and space, and by neglecting the cost of locomotion, it allows fine-grained predictions of vertical distributions. The Nash equilibrium features a distinct deep scattering layer which undertakes diel vertical migrations, the range of which increases with predator abundance. Maximum feeding rates are predicted to occur at dawn and dusk. Predator interference emerges from the game dynamics in the form of a complicated functional dependency of gross encounter rates on predator abundance. In turn, the growth rate of the prey decreases monotonically with predator abundance. In addition to providing a mechanistic explanation for the striking phenomenon of diel vertical migrations, the model yields quantitative predictions of vertical distributions and diel patterns in feeding intake, which may be compared with acoustic data, observed individual behavior, or stomach data.

Scaling marine fish movement behavior from individuals to populations

Abstract 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 animals 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.