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|Title:||How animals move along? Exactly solvable model of superdiffusive spread resulting from animal's decision making|
|Authors:||Petrovskiy, Sergei V.|
Tilles, Paulo F. C.
|Citation:||Journal of Mathematical Biology, 2016|
|Abstract:||Patterns of individual animal movement have been a focus of considerable attention recently. Of particular interest is a question how different macroscopic properties of animal dispersal result from the stochastic processes occurring on the microscale of the individual behavior. In this paper, we perform a comprehensive analytical study of a model where the animal changes the movement velocity as a result of its behavioral response to environmental stochasticity. The stochasticity is assumed to manifest itself through certain signals, and the animal modifies its velocity as a response to the signals. We consider two different cases, i.e. where the change in the velocity is or is not correlated to its current value. We show that in both cases the early, transient stage of the animal movement is super-diffusive, i.e. ballistic. The large-time asymptotic behavior appears to be diffusive in the uncorrelated case but super-ballistic in the correlated case. We also calculate analytically the dispersal kernel of the movement and show that, whilst it converge to a normal distribution in the large-time limit, it possesses a fatter tail during the transient stage, i.e. at early and intermediate time. Since the transients are known to be highly relevant in ecology, our findings may indicate that the fat tails and superdiffusive spread that are sometimes observed in the movement data may be a feature of the transitional dynamics rather than an inherent property of the animal movement.|
|Rights:||Copyright © the authors, 2015. After embargo this version will be an open-access article distributed under the terms of the Creative Commons Attribution-Non Commercial-No Derivatives License (http://creativecommons.org/licenses/by-nc-nd/4.0/ ), which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.|
|Appears in Collections:||Published Articles, Dept. of Mathematics|
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