Scale-free animal movement patterns: Lévy walks outperform fractional Brownian motions and fractional Lévy motions in random search scenarios

2009 ◽  
Vol 42 (43) ◽  
pp. 434006 ◽  
Author(s):  
A M Reynolds
2010 ◽  
Vol 7 (53) ◽  
pp. 1753-1758 ◽  
Author(s):  
Andy M. Reynolds

For many years, the dominant conceptual framework for describing non-oriented animal movement patterns has been the correlated random walk (CRW) model in which an individual's trajectory through space is represented by a sequence of distinct, independent randomly oriented ‘moves’. It has long been recognized that the transformation of an animal's continuous movement path into a broken line is necessarily arbitrary and that probability distributions of move lengths and turning angles are model artefacts. Continuous-time analogues of CRWs that overcome this inherent shortcoming have appeared in the literature and are gaining prominence. In these models, velocities evolve as a Markovian process and have exponential autocorrelation. Integration of the velocity process gives the position process. Here, through a simple scaling argument and through an exact analytical analysis, it is shown that autocorrelation inevitably leads to Lévy walk (LW) movement patterns on timescales less than the autocorrelation timescale. This is significant because over recent years there has been an accumulation of evidence from a variety of experimental and theoretical studies that many organisms have movement patterns that can be approximated by LWs, and there is now intense debate about the relative merits of CRWs and LWs as representations of non-orientated animal movement patterns.


Oryx ◽  
2021 ◽  
pp. 1-9
Author(s):  
Helen M. K. O'Neill ◽  
Sarah M. Durant ◽  
Stefanie Strebel ◽  
Rosie Woodroffe

Abstract Wildlife fences are often considered an important tool in conservation. Fences are used in attempts to prevent human–wildlife conflict and reduce poaching, despite known negative impacts on landscape connectivity and animal movement patterns. Such impacts are likely to be particularly important for wide-ranging species, such as the African wild dog Lycaon pictus, which requires large areas of continuous habitat to fulfil its resource requirements. Laikipia County in northern Kenya is an important area for wild dogs but new wildlife fences are increasingly being built in this ecosystem. Using a long-term dataset from the area's free-ranging wild dog population, we evaluated the effect of wildlife fence structure on the ability of wild dogs to cross them. The extent to which fences impeded wild dog movement differed between fence designs, although individuals crossed fences of all types. Purpose-built fence gaps increased passage through relatively impermeable fences. Nevertheless, low fence permeability can lead to packs, or parts of packs, becoming trapped on the wrong side of a fence, with consequences for population dynamics. Careful evaluation should be given to the necessity of erecting fences; ecological impact assessments should incorporate evaluation of impacts on animal movement patterns and should be undertaken for all large-scale fencing interventions. Where fencing is unavoidable, projects should use the most permeable fencing structures possible, both in the design of the fence and including as many purpose-built gaps as possible, to minimize impacts on wide-ranging wildlife.


2015 ◽  
Vol 2 (5) ◽  
pp. 150085 ◽  
Author(s):  
Andrew M. Reynolds ◽  
Hayley B. C. Jones ◽  
Jane K. Hill ◽  
Aislinn J. Pearson ◽  
Kenneth Wilson ◽  
...  

Understanding the complex movement patterns of animals in natural environments is a key objective of ‘movement ecology’. Complexity results from behavioural responses to external stimuli but can also arise spontaneously in their absence. Drawing on theoretical arguments about decision-making circuitry, we predict that the spontaneous patterns will be scale-free and universal, being independent of taxon and mode of locomotion. To test this hypothesis, we examined the activity patterns of the European honeybee, and multiple species of noctuid moth, tethered to flight mills and exposed to minimal external cues. We also reanalysed pre-existing data for Drosophila flies walking in featureless environments. Across these species, we found evidence of common scale-invariant properties in their movement patterns; pause and movement durations were typically power law distributed over a range of scales and characterized by exponents close to 3/2. Our analyses are suggestive of the presence of a pervasive scale-invariant template for locomotion which, when acted on by environmental cues, produces the movements with characteristic scales observed in nature. Our results indicate that scale-finite complexity as embodied, for instance, in correlated random walk models, may be the result of environmental cues overriding innate behaviour, and that scale-free movements may be intrinsic and not limited to ‘blind’ foragers as previously thought.


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