Optimal search direction for an animal flying or swimming in a wind or current

Abstract

The problem of the optimal direction in which a flying or swimming animal should search for a chemical plume was addressed. Active spaces were approximated by sphere, prolate ellipsoids, or rectangular parallelepipeds of various length-to-width ratios. The optimum course direction for the sphere was in the direction of flow (downwind). For active spaces that were highly elongated along the direction of the wind or current, the optimal course heading (with respect to the moving medium) was nearly across the flow. For intermediate shapes, the optimal course was intermediate. Because of the effect of the moving medium, these course headings resulted in actual ground tracks that were more in the direction of the flow, depending on the relative speeds of flying (swimming) and the wind (current). When the two speeds were equal, the magnitude of the advantage of choosing the optimum direction over a random direction was close to 50% with a small dependence on the shape of the active space. If the active space was spherical or highly elongated or locomotor speed was much greater than the speed of the current, the advantage approached a factor of π/2 (≈ 1.57).