Diffusion in Fractcal Landscapes: Simulations and Experimental Studies of Tenebrionid Beetle Movements

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Abstract
Organismal movement is frequently treated as a diffusion process arising from a simple random walk in a spatially uniform environment. However, anomalous diffusion may arise due to: (1) intrinsic departures from random movements of individuals; or (2) the effects of barriers that impede, or corridors that facilitate, movement. We examine anomalous diffusion in field studies of Eleodes beetles (Coleoptera: Tenebrionidae) and in simulations of correlated random walk on maps of real and artificial landscapes. We show how diffusion alternates between ordinary and anomalous diffusion depending on movement rules, landscape pattern, and the spatial and temporal scales of observation. Recent theories of diffusion in spatially complex media predict power law relations for anomalous diffusion. Over time scales of 5—500 s, Eleodes exhibited power laws for: (1) mean squared displacement with time; and (2) the mean time to travel from the center to the perimeter of circles of various radii. In grasslands, diffusion exponents changed significantly at a radius of 42 cm, which characterized the size of grass and bare soil patches. A second change in diffusion at scales of 24—600 h characterized home range activity. Marked discrepancies between the dynamics of beetles in the field and in simulations suggest a need for more comprehensive models of individual movement that use different rules for various domains of space and time. Studies of anomalous diffusion identify the relative effects of environment vs. innate behavior and reveal a range of scales over which the effects pertain.

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