A new approach for objective identification of turns and steps in organism movement data relevant to random walk modelling

1. A first step in the analysis of complex movement data often involves discretisation of the path into a series of step-lengths and turns, for example in the analysis of specialised random walks, such as Lévy flights. However, the identification of turning points, and therefore step-lengths, in a tortuous path is dependent on ad-hoc parameter choices. Consequently, studies testing for movement patterns in these data, such as Lévy flights, have generated debate. However, studies focusing on one-dimensional (1D) data, as in the vertical displacements of marine pelagic predators, where turning points can be identified unambiguously have provided strong support for Lévy flight movement patterns. 2. Here, we investigate how step-length distributions in 3D movement patterns would be interpreted by tags recording in 1D (i.e. depth) and demonstrate the dimensional symmetry previously shown mathematically for Lévy-flight movements. We test the veracity of this symmetry by simulating several measurement errors common in empirical datasets and find Lévy patterns and exponents to be robust to low-quality movement data. 3. We then consider exponential and composite Brownian random walks and show that these also project into 1D with sufficient symmetry to be clearly identifiable as such. 4. By extending the symmetry paradigm, we propose a new methodology for step-length identification in 2D or 3D movement data. The methodology is successfully demonstrated in a re-analysis of wandering albatross Global Positioning System (GPS) location data previously analysed using a complex methodology to determine bird-landing locations as turning points in a Lévy walk. For this high-resolution GPS data, we show that there is strong evidence for albatross foraging patterns approximated by truncated Lévy flights spanning over 3·5 orders of magnitude. 5. Our simple methodology and freely available software can be used with any 2D or 3D movement data at any scale or resolution and are robust to common empirical measurement errors. The method should find wide applicability in the field of movement ecology spanning the study of motile cells to humans.

Encounter success of free-ranging marine predator movements across a dynamic prey landscape

Movements of wide-ranging top predators can now be studied effectively using satellite and archival telemetry. However, the motivations underlying movements remain difficult to determine because trajectories are seldom related to key biological gradients, such as changing prey distributions. Here, we use a dynamic prey landscape of zooplankton biomass in the north-east Atlantic Ocean to examine active habitat selection in the plankton-feeding basking shark Cetorhinus maximus. The relative success of shark searches across this landscape was examined by comparing prey biomass encountered by sharks with encounters by random-walk simulations of ‘model’ sharks. Movements of transmitter-tagged sharks monitored for 964 days (16754km estimated minimum distance) were concentrated on the European continental shelf in areas characterized by high seasonal productivity and complex prey distributions. We show movements by adult and sub-adult sharks yielded consistently higher prey encounter rates than 90% of random-walk simulations. Behavioural patterns were consistent with basking sharks using search tactics structured across multiple scales to exploit the richest prey areas available in preferred habitats. Simple behavioural rules based on learned responses to previously encountered prey distributions may explain the high performances. This study highlights how dynamic prey landscapes enable active habitat selection in large predators to be investigated from a trophic perspective, an approach that may inform conservation by identifying critical habitat of vulnerable species.

Basking sharks and oceanographic fronts: quantifying associations in the north‐east Atlantic

Understanding the mechanisms linking oceanographic processes and marine vertebrate habitat use is critical to effective management of populations of conservation concern. The basking shark Cetorhinus maximus has been shown to associate with oceanographic fronts – physical interfaces at the transitions between water masses – to exploit foraging opportunities resulting from aggregation of zooplankton. However, the scale, significance and variability of these observed associations have not yet been established. Here, we quantify the influence of mesoscale (10s – 100s km) frontal activity on habitat use over timescales of weeks to months. We use animal-mounted archival tracking with composite front mapping via Earth Observation (EO) remote sensing to provide an oceanographic context to individual shark movements. We investigate levels of association with fronts occurring over two spatio-temporal scales, (i) broad-scale seasonally persistent frontal zones and (ii) contemporaneous mesoscale thermal and chl-a fronts. Using random walk simulations and logistic regression within an iterative generalised linear mixed modelling (GLMM) framework, we find that seasonal front frequency is a significant predictor of shark presence. Temporally-matched oceanographic metrics also indicate that sharks demonstrate a preference for productive regions, and associate with contemporaneous thermal and chl-a fronts more frequently than could be expected at random. Moreover, we highlight the importance of cross-frontal temperature change and persistence, which appear to interact to affect the degree of prey aggregation along thermal fronts. These insights have clear implications for understanding the preferred habitats of basking sharks in the context of anthropogenic threat management and marine spatial planning in the northeast Atlantic.

Basking sharks and oceanographic fronts: quantifying associations in the north-east Atlantic

Understanding the mechanisms linking oceanographic processes and marine vertebrate habitat use is critical to effective management of populations of conservation concern. The basking shark Cetorhinus maximus has been shown to associate with oceanographic fronts – physical interfaces at the transitions between water masses – to exploit foraging opportunities resulting from aggregation of zooplankton. However, the scale, significance and variability of these observed associations have not yet been established. Here, we quantify the influence of mesoscale (10s – 100s km) frontal activity on habitat use over timescales of weeks to months. We use animal-mounted archival tracking with composite front mapping via Earth Observation (EO) remote sensing to provide an oceanographic context to individual shark movements. We investigate levels of association with fronts occurring over two spatio-temporal scales, (i) broad-scale seasonally persistent frontal zones and (ii) contemporaneous mesoscale thermal and chl-a fronts. Using random walk simulations and logistic regression within an iterative generalised linear mixed modelling (GLMM) framework, we find that seasonal front frequency is a significant predictor of shark presence. Temporally-matched oceanographic metrics also indicate that sharks demonstrate a preference for productive regions, and associate with contemporaneous thermal and chl-a fronts more frequently than could be expected at random. Moreover, we highlight the importance of cross-frontal temperature change and persistence, which appear to interact to affect the degree of prey aggregation along thermal fronts. These insights have clear implications for understanding the preferred habitats of basking sharks in the context of anthropogenic threat management and marine spatial planning in the northeast Atlantic.

Can benthic community structure be used to predict the process of bioturbation in real ecosystems

Disentangling the roles of environmental change and natural environmental variability on biologically mediated ecosystem processes is paramount to predict future marine ecosystem functioning. Bioturbation, the biogenic mixing of sediments, has a regulating role in marine biogeochemical processes. However, our understanding of bioturbation as a community level process and of its environmental drivers is still limited by loose use of terminology, and a lack of consensus about what bioturbation is. To help resolve these challenges, this empirical study investigated the links between four different attributes of bioturbation (bioturbation depth, activity and distance, and biodiffusive transport); the ability of an index of bioturbation (BPc) to predict each of them; and their relation to seasonality, in a shallow coastal system – the Western Channel Observatory, UK. Bioturbation distance depended on changes in benthic community structure, while the other three attributes were more directly influenced by seasonality in food availability. In parallel, BPc successfully predicted bioturbation distance but not the other attributes of bioturbation. This study therefore highlights that community bioturbation results from this combination of processes responding to environmental variability at different time-scales. However, community level measurements of bioturbation across environmental variability are still scarce, and BPc is calculated using commonly available data on benthic community structure and the functional classification of invertebrates. Therefore, BPc could be used to support the growth of landscape scale bioturbation research, but future uses of the index need to consider which bioturbation attributes the index actually predicts. As BPc predicts bioturbation distance, estimated here using a random-walk model applicable to community settings, studies using either of the metrics should be directly comparable and contribute to a more integrated future for bioturbation research.

Basking sharks and oceanographic fronts: quantifying associations in the north-east Atlantic

Understanding the mechanisms linking oceanographic processes and marine vertebrate habitat use is critical to effective management of populations of conservation concern. The basking shark Cetorhinus maximus has been shown to associate with oceanographic fronts – physical interfaces at the transitions between water masses – to exploit foraging opportunities resulting from aggregation of zooplankton. However, the scale, significance and variability of these observed associations have not yet been established. Here, we quantify the influence of mesoscale (10s – 100s km) frontal activity on habitat use over timescales of weeks to months. We use animal-mounted archival tracking with composite front mapping via Earth Observation (EO) remote sensing to provide an oceanographic context to individual shark movements. We investigate levels of association with fronts occurring over two spatio-temporal scales, (i) broad-scale seasonally persistent frontal zones and (ii) contemporaneous mesoscale thermal and chl-a fronts. Using random walk simulations and logistic regression within an iterative generalised linear mixed modelling (GLMM) framework, we find that seasonal front frequency is a significant predictor of shark presence. Temporally-matched oceanographic metrics also indicate that sharks demonstrate a preference for productive regions, and associate with contemporaneous thermal and chl-a fronts more frequently than could be expected at random. Moreover, we highlight the importance of cross-frontal temperature change and persistence, which appear to interact to affect the degree of prey aggregation along thermal fronts. These insights have clear implications for understanding the preferred habitats of basking sharks in the context of anthropogenic threat management and marine spatial planning in the northeast Atlantic.

Individual-based modelling of the development and transport of a Karenia mikimotoi bloom on the North-West European continental shelf

In 2006, a large and prolonged bloom of the dinoflagellate Karenia mikimotoi occurred in Scottish coastal waters, causing extensive mortalities of benthic organisms including annelids and molluscs and some species of fish ( Davidson et al., 2009). A coupled hydrodynamic-algal transport model was developed to track the progression of the bloom around the Scottish coast during June–September 2006 and hence investigate the processes controlling the bloom dynamics. Within this individual-based model, cells were capable of growth, mortality and phototaxis and were transported by physical processes of advection and turbulent diffusion, using current velocities extracted from operational simulations of the MRCS ocean circulation model of the North-west European continental shelf. Vertical and horizontal turbulent diffusion of cells are treated using a random walk approach. Comparison of model output with remotely sensed chlorophyll concentrations and cell counts from coastal monitoring stations indicated that it was necessary to include multiple spatially distinct seed populations of K. mikimotoi at separate locations on the shelf edge to capture the qualitative pattern of bloom transport and development. We interpret this as indicating that the source population was being transported northwards by the Hebridean slope current from where colonies of K. mikimotoi were injected onto the continental shelf by eddies or other transient exchange processes. The model was used to investigate the effects on simulated K. mikimotoi transport and dispersal of: (1) the distribution of the initial seed population; (2) algal growth and mortality; (3) water temperature; (4) the vertical movement of particles by diurnal migration and eddy diffusion; (5) the relative role of the shelf edge and coastal currents; (6) the role of wind forcing. The numerical experiments emphasized the requirement for a physiologically based biological model and indicated that improved modelling of future blooms will potentially benefit from better parameterisation of temperature dependence of both growth and mortality and finer spatial and temporal hydrodynamic resolution.

Individual-based modelling of the development and transport of a Karenia mikimotoi bloom on the North-West European continental shelf

In 2006, a large and prolonged bloom of the dinoflagellate Karenia mikimotoi occurred in Scottish coastal waters, causing extensive mortalities of benthic organisms including annelids and molluscs and some species of fish ( Davidson et al., 2009). A coupled hydrodynamic-algal transport model was developed to track the progression of the bloom around the Scottish coast during June–September 2006 and hence investigate the processes controlling the bloom dynamics. Within this individual-based model, cells were capable of growth, mortality and phototaxis and were transported by physical processes of advection and turbulent diffusion, using current velocities extracted from operational simulations of the MRCS ocean circulation model of the North-west European continental shelf. Vertical and horizontal turbulent diffusion of cells are treated using a random walk approach. Comparison of model output with remotely sensed chlorophyll concentrations and cell counts from coastal monitoring stations indicated that it was necessary to include multiple spatially distinct seed populations of K. mikimotoi at separate locations on the shelf edge to capture the qualitative pattern of bloom transport and development. We interpret this as indicating that the source population was being transported northwards by the Hebridean slope current from where colonies of K. mikimotoi were injected onto the continental shelf by eddies or other transient exchange processes. The model was used to investigate the effects on simulated K. mikimotoi transport and dispersal of: (1) the distribution of the initial seed population; (2) algal growth and mortality; (3) water temperature; (4) the vertical movement of particles by diurnal migration and eddy diffusion; (5) the relative role of the shelf edge and coastal currents; (6) the role of wind forcing. The numerical experiments emphasized the requirement for a physiologically based biological model and indicated that improved modelling of future blooms will potentially benefit from better parameterisation of temperature dependence of both growth and mortality and finer spatial and temporal hydrodynamic resolution.

Optimal foraging strategies: Lévy walks balance searching and patch exploitation under a very broad range of conditions

While evidence for optimal random search patterns, known as Lévy walks, in empirical movement data is mounting for a growing list of taxa spanning motile cells to humans, there is still much debate concerning the theoretical generality of Lévy walk optimisation. Here, using a new and robust simulation environment, we investigate in the most detailed study to date (24×10(6) simulations) the foraging and search efficiencies of 2-D Lévy walks with a range of exponents, target resource distributions and several competing models. We find strong and comprehensive support for the predictions of the Lévy flight foraging hypothesis and in particular for the optimality of inverse square distributions of move step-lengths across a much broader range of resource densities and distributions than previously realised. Further support for the evolutionary advantage of Lévy walk movement patterns is provided by an investigation into the 'feast and famine' effect, with Lévy foragers in heterogeneous environments experiencing fewer long 'famines' than other types of searchers. Therefore overall, optimal Lévy foraging results in more predictable resources in unpredictable environments.

Hierarchical random walks in trace fossils and the origin of optimal search behavior

Efficient searching is crucial for timely location of food and other resources. Recent studies show diverse living animals employ a theoretically optimal scale-free random search for sparse resources known as a Lévy walk, but little is known of the origins and evolution of foraging behaviour and the search strategies of extinct organisms. Here we show using simulations of self-avoiding trace fossil trails that randomly introduced strophotaxis (U-turns) – initiated by obstructions such as ¬¬¬self-trail avoidance or innate cueing – leads to random looping patterns with clustering across increasing scales that is consistent with the presence of Lévy walks. This predicts optimal Lévy searches can emerge from simple behaviours observed in fossil trails. We then analysed fossilized trails of benthic marine organisms using a novel path analysis technique and find the first evidence of Lévy-like search strategies in extinct animals. Our results show that simple search behaviours of extinct animals in heterogeneous environments give rise to hierarchically nested Brownian walk clusters that converge to optimal Lévy patterns. Primary productivity collapse and large-scale food scarcity characterising mass extinctions evident in the fossil record may have triggered adaptation of optimal Lévy-like searches. The findings suggest Lévy-like behaviour has been employed by foragers since at least the Eocene but may have a more ancient origin, which could explain recent widespread observations of such patterns among modern taxa.