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.

Are Fast Responses More Random? Testing the Effect of Response Time on Scale in an Online Choice Experiment

Scepticism over stated preference surveys conducted online revolves around the concerns over “professional respondents” who might rush through the questionnaire without sufficiently considering the information provided. To gain insight on the validity of this phenomenon and test the effect of response time on choice randomness, this study makes use of a recently conducted choice experiment survey on ecological and amenity effects of an offshore windfarm in the UK. The positive relationship between self-rated and inferred attribute attendance and response time is taken as evidence for a link between response time and cognitive effort. Subsequently, the generalised multinomial logit model is employed to test the effect of response time on scale, which indicates the weight of the deterministic relative to the error component in the random utility model. Results show that longer response time increases scale, i.e. decreases choice randomness. This positive scale effect of response time is further found to be non-linear and wear off at some point beyond which extreme response time decreases scale. While response time does not systematically affect welfare estimates, higher response time increases the precision of such estimates. These effects persist when self-reported choice certainty is controlled for. Implications of the results for online stated preference surveys and further research are discussed.

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.