Environmental context explains Lévy and Brownian movement patterns of marine predators

An optimal search theory, the so-called Levy-flight foraging hypothesis(1), predicts that predators should adopt search strategies known as Levy flights where prey is sparse and distributed unpredictably, but that Brownian movement is sufficiently efficient for locating abundant prey(2-4). Empirical studies have generated controversy because the accuracy of statistical methods that have been used to identify Levy behaviour has recently been questioned(5,6). Consequently, whether foragers exhibit Levy 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 Levy patterns in relation to environmental gradients in the largest animal movement data set assembled for this purpose. Strong support was found for Levy search patterns across 14 species of open-ocean predatory fish (sharks, tuna, billfish and ocean sunfish), with some individuals switching between Levy and Brownian movement as they traversed different habitat types. We tested the spatial occurrence of these two principal patterns and found Levy 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 Levy-flight foraging hypothesis(1,7), supporting the contention(8,9) that organism search strategies naturally evolved in such a way that they exploit optimal Levy patterns.

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.

Intercepting beats in predesignated target zones

Moving to a rhythm necessitates precise timing between the movement of the chosen limb and the timing imposed by the beats. However, the temporal information specifying the moment when a beat will sound (the moment onto which one must synchronise one's movement) is not continuously provided by the acoustic array. Because of this informational void, the actors need some form of prospective information that will allow them to act sufficiently ahead of time in order to get their hand in the right place at the right time. In this acoustic interception study, where participants were asked to move between two targets in such a way that they arrived and stopped in the target zone at the same time as a beat sounded, we tested a model derived from tau-coupling theory (Lee DN (1998) Ecol Psychol 10:221-250). This model attempts to explain the form of a potential timing guide that specifies the duration of the inter-beat intervals and also describes how this informational guide can be used in the timing and guidance of movements. The results of our first experiment show that, for inter-beat intervals of less than 3 s, a large proportion of the movement (over 70%) can be explained by the proposed model. However, a second experiment, which augments the time between beats so that it surpasses 3 s, shows a marked decline in the percentage of information/movement coupling. A close analysis of the movement kinematics indicates a lack of control and anticipation in the participants' movements. The implications of these findings, in light of other research studies, are discussed.

A reliable externally fixated murine femoral fracture model that accounts for variation in movement between animals.

Fifty-two CFLP mice had an open femoral diaphyseal osteotomy held in compression by a four-pin external fixator. The movement of 34 of the mice in their cages was quantified before and after operation, until sacrifice at 4, 8, 16 or 24 days. Thirty-three specimens underwent histomorphometric analysis and 19 specimens underwent torsional stiffness measurement. The expected combination of intramembranous and endochondral bone formation was observed, and the model was shown to be reliable in that variation in the histological parameters of healing was small between animals at the same time point, compared to the variation between time-points. There was surprisingly large individual variation in the amount of animal movement about the cage, which correlated with both histomorphometric and mechanical measures of healing. Animals that moved more had larger external calluses containing more cartilage and demonstrated lower torsional stiffness at the same time point. Assuming that movement of the whole animal predicts, at least to some extent, movement at the fracture site, this correlation is what would be expected in a model that involves similar processes to those in human fracture healing. Models such as this, employed to determine the effect of experimental interventions, will yield more information if the natural variation in animal motion is measured and included in the analysis.