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.

Divergent Paths of Development: The Modern World-System and Democratization in South Africa and Zambia

This article examines whether a Modern World- Systems (MWS) perspective can provide an improved understanding of the processes of democratization in Africa (and other developing regions of the world) by conducting a comparative case study of South Africa and Zambia in the 1990s, examining the transitions to democracy and divergent processes of democratic consolidation in each country. Semiperipheral South Africa has, due to its more advantageous position in the world-system, been better equipped than peripheral Zambia to safeguard democracy against erosion and reversal. Th e central irony of the MWS is that the weakest states in the MWS can be pushed around by core powers and are more easily forced to democratize while at the same time they are least likely to possess the resources necessary for democratic consolidation. Semiperipheral states can maintain their independence vis-à-vis the core to a higher degree, but if the decision is made to undertake a democratic transition they are more likely to possess the resources necessary for successful consolidation. Th e MWS perspective allows for an improved understanding of the causal pathway of how position in the MWS translates into the ability to consolidate democracy than does approaches that emphasize domestic factors.