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bioRxiv · 10.1101/440420

The impact of short- and long-range perception on population movements

Johnston, S.·Painter, K.
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Abstract

Navigation of cells and organisms is typically achieved by detecting and processing orienteering cues. Occasionally, a cue may be assessed over a much larger range than the individuals body size, as in visual scanning for landmarks. In this paper we formulate models that account for orientation in response to short- or long-range cue evaluation. Starting from an underlying random walk movement model, where a generic cue is evaluated locally or nonlocally to determine a preferred direction, we state corresponding macroscopic partial differential equations to describe population movements. Under certain approximations, these models reduce to well-known local and nonlocal biological transport equations, including those of Keller-Segel type. We consider a case-study application: \"hilltopping\" in Lepidoptera and other insects, a phenomenon in which populations accumulate at summits to improve encounter/mating rates. Nonlocal responses are shown to efficiently filter out the natural noisiness (or roughness) of typical landscapes and allow the population to preferentially accumulate at a subset of hilltopping locations, in line with field studies. Moreover, according to the timescale of movement, optimal responses may occur for different perceptual ranges.

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Johnston, S., Painter, K.. 2018-10-10. The impact of short- and long-range perception on population movements. https://doi.org/10.1101/440420

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