Nicolas E. Humphries

Scaling laws of marine predator search behaviour

Many free-ranging predators have to make foraging decisions with little, if any, knowledge of present resource distribution and availability. The optimal search strategy they should use to maximize encounter rates with prey in heterogeneous natural environments remains a largely unresolved issue in ecology. Lévy walks are specialized random walks giving rise to fractal movement trajectories that may represent an optimal solution for searching complex landscapes. However, the adaptive significance of this putative strategy in response to natural prey distributions remains untested. Here we analyse over a million movement displacements recorded from animal-attached electronic tags to show that diverse marine predators—sharks, bony fishes, sea turtles and penguins—exhibit Lévy-walk-like behaviour close to a theoretical optimum. Prey density distributions also display Lévy-like fractal patterns, suggesting response movements by predators to prey distributions. Simulations show that predators have higher encounter rates when adopting Lévy-type foraging in natural-like prey fields compared with purely random landscapes. This is consistent with the hypothesis that observed search patterns are adapted to observed statistical patterns of the landscape. This may explain why Lévy-like behaviour seems to be widespread among diverse organisms, from microbes to humans, as a ‘rule’ that evolved in response to patchy resource distributions.

Environmental context explains Lévy and Brownian movement patterns of marine predators.

An optimal search theory, the so-called Lévy-flight foraging hypothesis, predicts that predators should adopt search strategies known as Lévy flights where prey is sparse and distributed unpredictably, but that Brownian movement is sufficiently efficient for locating abundant prey. Empirical studies have generated controversy because the accuracy of statistical methods that have been used to identify Lévy behaviour has recently been questioned. Consequently, whether foragers exhibit Lévy flights in the wild remains unclear. Crucially, moreover, it has not been tested whether observed movement patterns across natural landscapes having different expected resource distributions conform to the theory’s central predictions. Here we use maximum-likelihood methods to test for Lévy patterns in relation to environmental gradients in the largest animal movement data set assembled for this purpose. Strong support was found for Lévy search patterns across 14 species of open-ocean predatory fish (sharks, tuna, billfish and ocean sunfish), with some individuals switching between Lévy and Brownian movement as they traversed different habitat types. We tested the spatial occurrence of these two principal patterns and found Lévy behaviour to be associated with less productive waters (sparser prey) and Brownian movements to be associated with productive shelf or convergence-front habitats (abundant prey). These results are consistent with the Lévy-flight foraging hypothesis, supporting the contention that organism search strategies naturally evolved in such a way that they exploit optimal Lévy patterns.

Foraging success of biological Lévy flights recorded in situ

It is an open question how animals find food in dynamic natural environments where they possess little or no knowledge of where resources are located. Foraging theory predicts that in environments with sparsely distributed target resources, where forager knowledge about resources’ locations is incomplete, Lévy flight movements optimize the success of random searches. However, the putative success of Lévy foraging has been demonstrated only in model simulations. Here, we use high-temporal-resolution Global Positioning System (GPS) tracking of wandering (Diomedea exulans) and black-browed albatrosses (Thalassarche melanophrys) with simultaneous recording of prey captures, to show that both species exhibit Lévy and Brownian movement patterns. We find that total prey masses captured by wandering albatrosses during Lévy movements exceed daily energy requirements by nearly fourfold, and approached yields by Brownian movements in other habitats. These results, together with our reanalysis of previously published albatross data, overturn the notion that albatrosses do not exhibit Lévy patterns during foraging, and demonstrate that Lévy flights of predators in dynamic natural environments present a beneficial alternative strategy to simple, spatially intensive behaviors. Our findings add support to the possibility that biological Lévy flight may have naturally evolved as a search strategy in response to sparse resources and scant information.

Lévy flight and Brownian search patterns of a free-ranging predator reflect different prey field characteristics.

1. Search processes play an important role in physical, chemical and biological systems. In animal foraging, the search strategy predators should use to search optimally for prey is an enduring question. Some models demonstrate that when prey is sparsely distributed, an optimal search pattern is a specialised random walk known as a Lévy flight, whereas when prey is abundant, simple Brownian motion is sufficiently efficient. These predictions form part of what has been termed the Lévy flight foraging hypothesis (LFF) which states that as Lévy flights optimise random searches, movements approximated by optimal Lévy flights may have naturally evolved in organisms to enhance encounters with targets (e.g. prey) when knowledge of their locations is incomplete. 2. Whether free-ranging predators exhibit the movement patterns predicted in the LFF hypothesis in response to known prey types and distributions, however, has not been determined. We tested this using vertical and horizontal movement data from electronic tagging of an apex predator, the great white shark Carcharodon carcharias, across widely differing habitats reflecting different prey types. 3. Individual white sharks exhibited movement patterns that predicted well the prey types expected under the LFF hypothesis. Shark movements were best approximated by Brownian motion when hunting near abundant, predictable sources of prey (e.g. seal colonies, fish aggregations), whereas movements approximating truncated Lévy flights were present when searching for sparsely distributed or potentially difficult-to-detect prey in oceanic or shelf environments, respectively. 4. That movement patterns approximated by truncated Lévy flights and Brownian behaviour were present in the predicted prey fields indicates search strategies adopted by white sharks appear to be the most efficient ones for encountering prey in the habitats where such patterns are observed. This suggests that C. carcharias appears capable of exhibiting search patterns that are approximated as optimal in response to encountered changes in prey type and abundance, and across diverse marine habitats, from the surf zone to the deep ocean. 5. Our results provide some support for the LFF hypothesis. However, it is possible that the observed Lévy patterns of white sharks may not arise from an adaptive behaviour but could be an emergent property arising from simple, straight-line movements between complex (e.g. fractal) distributions of prey. Experimental studies are needed in vertebrates to test for the presence of Lévy behaviour patterns in the absence of complex prey distributions.

High activity and Levy searches: jellyfish can search the water column like fish

Over-fishing may lead to a decrease in fish abundance and a proliferation of jellyfish. Active movements and prey search might be thought to provide a competitive advantage for fish, but here we use data-loggers to show that the frequently occurring coastal jellyfish (Rhizostoma octopus) does not simply passively drift to encounter prey. Jellyfish (327 days of data from 25 jellyfish with depth collected every 1 min) showed very dynamic vertical movements, with their integrated vertical movement averaging 619.2 m d−1, more than 60 times the water depth where they were tagged. The majority of movement patterns were best approximated by exponential models describing normal random walks. However, jellyfish also showed switching behaviour from exponential patterns to patterns best fitted by a truncated Lévy distribution with exponents (mean μ = 1.96, range 1.2–2.9) close to the theoretical optimum for searching for sparse prey (μopt ≈ 2.0). Complex movements in these ‘simple’ animals may help jellyfish to compete effectively with fish for plankton prey, which may enhance their ability to increase in dominance in perturbed ocean systems.

Long-Term GPS Tracking of Ocean Sunfish Mola mola Offers a New Direction in Fish Monitoring

Satellite tracking of large pelagic fish provides insights on free-ranging behaviour, distributions and population structuring. Up to now, such fish have been tracked remotely using two principal methods: direct positioning of transmitters by Argos polar-orbiting satellites, and satellite relay of tag-derived light-level data for post hoc track reconstruction. Error fields associated with positions determined by these methods range from hundreds of metres to hundreds of kilometres. However, low spatial accuracy of tracks masks important details, such as foraging patterns. Here we use a fast-acquisition global positioning system (Fastloc GPS) tag with remote data retrieval to track long-term movements, in near real time and position accuracy of <70 m, of the worlds largest bony fish, the ocean sunfish Mola mola. Search-like movements occurred over at least three distinct spatial scales. At fine scales, sunfish spent longer in highly localised areas with faster, straighter excursions between them. These ‘stopovers’ during long-distance movement appear consistent with finding and exploiting food patches. This demonstrates the feasibility of GPS tagging to provide tracks of unparalleled accuracy for monitoring movements of large pelagic fish, and with nearly four times as many locations obtained by the GPS tag than by a conventional Argos transmitter. The results signal the potential of GPS-tagged pelagic fish that surface regularly to be detectors of resource ‘hotspots’ in the blue ocean and provides a new capability for understanding large pelagic fish behaviour and habitat use that is relevant to ocean management and species conservation.

Ocean-wide tracking of pelagic sharks reveals extent of overlap with longline fishing hotspots

Significance Shark populations are declining worldwide because of overexploitation by fisheries with unknown consequences for ecosystems. Although the harvest of oceanic sharks remains largely unregulated, knowing precisely where they interact with fishing vessels will better aid their conservation. We satellite track six species of shark and two entire longline fishing vessel fleets across the North Atlantic over multiple years. Sharks actively select and aggregate in space-use “hotspots” characterized by thermal fronts and high productivity. However, longline fishing vessels also target these habitats and efficiently track shark movements seasonally, leading to an 80% spatial overlap. Areas of highest overlap between sharks and fishing vessels show persistence between years, suggesting current hotspots are at risk, and arguing for introduction of international catch limits. Overfishing is arguably the greatest ecological threat facing the oceans, yet catches of many highly migratory fishes including oceanic sharks remain largely unregulated with poor monitoring and data reporting. Oceanic shark conservation is hampered by basic knowledge gaps about where sharks aggregate across population ranges and precisely where they overlap with fishers. Using satellite tracking data from six shark species across the North Atlantic, we show that pelagic sharks occupy predictable habitat hotspots of high space use. Movement modeling showed sharks preferred habitats characterized by strong sea surface-temperature gradients (fronts) over other available habitats. However, simultaneous Global Positioning System (GPS) tracking of the entire Spanish and Portuguese longline-vessel fishing fleets show an 80% overlap of fished areas with hotspots, potentially increasing shark susceptibility to fishing exploitation. Regions of high overlap between oceanic tagged sharks and longliners included the North Atlantic Current/Labrador Current convergence zone and the Mid-Atlantic Ridge southwest of the Azores. In these main regions, and subareas within them, shark/vessel co-occurrence was spatially and temporally persistent between years, highlighting how broadly the fishing exploitation efficiently “tracks” oceanic sharks within their space-use hotspots year-round. Given this intense focus of longliners on shark hotspots, our study argues the need for international catch limits for pelagic sharks and identifies a future role of combining fine-scale fish and vessel telemetry to inform the ocean-scale management of fisheries.

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

Significance How best to search for food in heterogeneous landscapes is a universal problem facing mobile organisms. Diverse modern animals use a random search strategy called a Lévy walk, composed of many small move steps interspersed by rare long steps, which theoretically is optimal for locating sparse resources. Here, we find the first evidence, to our knowledge, that extinct animals, in this case 50 My-old sea urchins, used a Lévy-like search strategy. Our results are important because they indicate Lévy walks likely have an ancient origin and may arise from simple behaviors observed in much older fossil trails. This foraging strategy may have adapted in response to decreased food availability after productivity collapse associated with past climate change and mass extinctions. Efficient searching is crucial for timely location of food and other resources. Recent studies show that diverse living animals use 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 behavior and the search strategies of extinct organisms. Here, using simulations of self-avoiding trace fossil trails, we show 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 that optimal Lévy searches may emerge from simple behaviors observed in fossil trails. We then analyzed fossilized trails of benthic marine organisms by using a novel path analysis technique and find the first evidence, to our knowledge, of Lévy-like search strategies in extinct animals. Our results show that simple search behaviors 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 characterizing mass extinctions evident in the fossil record may have triggered adaptation of optimal Lévy-like searches. The findings suggest that Lévy-like behavior has been used by foragers since at least the Eocene but may have a more ancient origin, which might explain recent widespread observations of such patterns among modern taxa.

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

Summary 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 L evy flights. However, the identification of turning points, and therefore step-lengths, in a tortuous path is dependent onad-hoc parameter choices. Consequently, studies testing for movement patterns in these data, such as L evy 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 L evy 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 L evy-flight movements. We test the veracity of this symmetry by simulating several measurement errors common in empirical datasets and find L evy 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 L evy walk. For this high-resolution GPS data, we show that there is strong evidence for albatross foraging patterns approximated by truncated L evy flights spanning over 3 5o rders 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.

Spatial dynamics and expanded vertical niche of blue sharks in oceanographic fronts reveal habitat targets for conservation

Dramatic population declines among species of pelagic shark as a result of overfishing have been reported, with some species now at a fraction of their historical biomass. Advanced telemetry techniques enable tracking of spatial dynamics and behaviour, providing fundamental information on habitat preferences of threatened species to aid conservation. We tracked movements of the highest pelagic fisheries by-catch species, the blue shark Prionace glauca, in the North-east Atlantic using pop-off satellite-linked archival tags to determine the degree of space use linked to habitat and to examine vertical niche. Overall, blue sharks moved south-west of tagging sites (English Channel; southern Portugal), exhibiting pronounced site fidelity correlated with localized productive frontal areas, with estimated space-use patterns being significantly different from that of random walks. Tracked female sharks displayed behavioural variability in diel depth preferences, both within and between individuals. Diel depth use ranged from normal DVM (nDVM; dawn descent, dusk ascent), to reverse DVM (rDVM; dawn ascent, dusk descent), to behavioural patterns where no diel differences were apparent. Results showed that blue sharks occupy some of the most productive marine zones for extended periods and structure diel activity patterns across multiple spatio-temporal scales in response to particular habitat types. In so doing, sharks occupied an extraordinarily broad vertical depth range for their size (1.0–2.0 m fork length), from the surface into the bathypelagic realm (max. dive depth, 1160 m). The space-use patterns of blue sharks indicated they spend much of the time in areas where pelagic longlining activities are often highest, and in depth zones where these fisheries particularly target other species, which could account for the rapid declines recently reported for blue sharks in many parts of the worlds oceans. Our results provide habitat targets for blue shark conservation that may also be relevant to other pelagic species.