Composite correlated random walks have been posited as a strong alternative to Lévy walks as models of multi-scale forager movement patterns. Here it is shown that if plastic then intrinsic composite correlated random walks will, under selection pressures, evolve to resemble optimal Lévy walks when foraging is non-destructive. The fittest composite correlated random walkers are found to be those that come closest to being optimal Lévy walkers. This may explain why such a diverse range of foragers have movement patterns that can be approximated by optimal Lévy walks and shows that the 'Lévy-flight foraging' hypothesis has a broad hinterland. The new findings are consistent with recent observations of mussels Mytilus edulis and the Australian desert ant Melophorus bagoti which suggest that animals approximate a Lévy walk by adopting an intrinsic composite movement strategy with different modes.
Keywords: Composite correlated random walk; Lévy walks; Optimal foraging.
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