Lévy patterns in seabirds are multifaceted describing both spatial and temporal patterning

Drivers of fine-scale diurnal space use by a coral-reef mesopredatory fish

The habitat preferences of many reef fishes are well established, but the use of space within these habitats by non-site-attached species is poorly studied. The authors examined the space use of a functionally important mesopredator, graysby (Cephalopholis cruentata), on six patch reefs in the Florida Keys. A 1 m² -scale grid was constructed on each reef and 16 individual C. cruentata were tracked diurnally in situ to identify space use. At the patch reef scale, larger C. cruentata were more active and had larger observed home ranges, although home ranges were also affected by fish density and the abundances of prey and predators. The total time in each 1 m² grid cell was regressed against a range of fine-scale biotic variables, including multiple variables derived from structure-from-motion three-dimensional digital reconstructions of each reef. Nonetheless, time in grid cells (preferred microhabitats) was only significantly positively correlated with the height of carbonate structures, likely because the cavities they enclose are particularly suitable for predator avoidance, resting and ambushing prey. The ongoing flattening of reefs in the region caused by negative carbonate budgets is thus likely to have significant effects on the abundance and space use of C. cruentata. In addition to examining spatial patterns, we analysed C. cruentata waiting times in each grid cell before moving. These times were best approximated by a truncated power-law (heavy-tailed) distribution, indicating a "bursty" pattern of relatively long periods of inactivity interspersed with multiple periods of activity. Such a pattern has previously been identified in a range of temperate ambush predators, and the authors extend this move-wait behaviour, which may optimize foraging success, to a reef fish for the first time. Understanding how C. cruentata uses space and time is critical to fully identify their functional role and better predict the implications of fishing and loss of reef structure.

Current status and future directions of Lévy walk research

Lévy walks are a mathematical construction useful for describing random patterns of movement with bizarre fractal properties that seem to have no place in biology. Nonetheless, movement patterns resembling Lévy walks have been observed at scales ranging from the microscopic to the ecological. They have been seen in the molecular machinery operating within cells during intracellular trafficking, in the movement patterns of T cells within the brain, in DNA, in some molluscs, insects, fish, birds and mammals, in the airborne flights of spores and seeds, and in the collective movements of some animal groups. Lévy walks are also evident in trace fossils (ichnofossils) – the preserved form of tracks made by organisms that occupied ancient sea beds about 252-66 million years ago. And they are utilised by algae that originated around two billion years ago, and still exist today. In September of 2017, leading researchers from across the life sciences, along with mathematicians and physicists, got together at a Company of Biologists' Workshop to discuss the origins and biological significance of these movement patterns. In this Review the essence of the technical and sometimes heated discussions is distilled and made accessible for all. In just a few pages, the reader is taken from a gentle introduction to the frontiers of a very active field of scientific enquiry. What emerges is a fascinating story of a truly inter-disciplinary scientific endeavour that is seeking to better understand movement patterns occurring across all biological scales.

Summary: Movement patterns resembling Lévy walks are found in a wide variety of organisms, from cells to humans. In this Review the latest research into their origins and biological significance is discussed.

Changing measurements or changing movements? Sampling scale and movement model identifiability across generations of biologging technology

Animal movement patterns contribute to our understanding of variation in breeding success and survival of individuals, and the implications for population dynamics. Over time, sensor technology for measuring movement patterns has improved. Although older technologies may be rendered obsolete, the existing data are still valuable, especially if new and old data can be compared to test whether a behavior has changed over time. We used simulated data to assess the ability to quantify and correctly identify patterns of seabird flight lengths under observational regimes used in successive generations of wet/dry logging technology. Care must be taken when comparing data collected at differing timescales, even when using inference procedures that incorporate the observational process, as model selection and parameter estimation may be biased. In practice, comparisons may only be valid when degrading all data to match the lowest resolution in a set. Changes in tracking technology, such as the wet/dry loggers explored here, that lead to aggregation of measurements at different temporal scales make comparisons challenging. We therefore urge ecologists to use synthetic data to assess whether accurate parameter estimation is possible for models comparing disparate data sets before planning experiments and conducting analyses such as responses to environmental changes or the assessment of management actions.

The evolutionary origins of Lévy walk foraging

We study through a reaction-diffusion algorithm the influence of landscape diversity on the efficiency of search dynamics. Remarkably, the identical optimal search strategy arises in a wide variety of environments, provided the target density is sparse and the searcher’s information is restricted to its close vicinity. Our results strongly impact the current debate on the emergentist vs. evolutionary origins of animal foraging. The inherent character of the optimal solution (i.e., independent on the landscape for the broad scenarios assumed here) suggests an interpretation favoring the evolutionary view, as originally implied by the Lévy flight foraging hypothesis. The latter states that, under conditions of scarcity of information and sparse resources, some organisms must have evolved to exploit optimal strategies characterized by heavy-tailed truncated power-law distributions of move lengths. These results strongly suggest that Lévy strategies—and hence the selection pressure for the relevant adaptations—are robust with respect to large changes in habitat. In contrast, the usual emergentist explanation seems not able to explain how very similar Lévy walks can emerge from all the distinct non-Lévy foraging strategies that are needed for the observed large variety of specific environments. We also report that deviations from Lévy can take place in plentiful ecosystems, where locomotion truncation is very frequent due to high encounter rates. So, in this case normal diffusion strategies—performing as effectively as the optimal one—can naturally emerge from Lévy. Our results constitute the strongest theoretical evidence to date supporting the evolutionary origins of experimentally observed Lévy walks.

How organisms improve the search for food, mates, etc., is a key factor to their survival. Mathematically, the best strategy to look for randomly distributed re-visitable resources—under scarce information and sparse conditions—results from Lévy distributions of move lengths (the probability of taking a step ℓ is proportional to 1/ℓ²). Today it is well established that many animal species in different habitats do perform Lévy foraging. This fact has raised a heated debate, viz., the emergent versus evolutionary hypotheses. For the former, a Lévy foraging is an emergent property, a consequence of searcher-environment interactions: certain landscapes induce Lévy patterns, but others not. In this view, the optimal strategy depends on the particular habitat. The evolutionary explanation, in contrast, is that Lévy foraging strategies are adaptations that evolved via natural selection. In this article, through simulations we exhaustively analyze the influence of distinct environments on the foraging efficiency. We find that the optimal procedure is the same in all situations, provided density is low and landscape information is scarce. So, the best search strategy is remarkably independent of details. These results constitute the strongest theoretical evidence to date supporting the evolutionary origins of experimentally observed Lévy walks.