Upwind searching for an odor plume is sometimes optimal

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Abstract
A model is presented that suggests that the optimal strategy for an animal walking or crawling on a substrate while searching for the source of a chemical carried by a shifting wind or current may be to move upwind (or against the current). The requirements are that (1) the current direction fluctuates rapidly within a range that exceeds 30 ° on both sides of the mean direction, and (2) the searching animal can move accurately up- or downwind and, once within the influence of the chemical plume, can move efficiently to the source. Under these conditions, an upwind search is shorter (on the average) by 0.9–0.3 of the range of influence of the chemical stimulus. Thus, this strategy is relatively more important when the total search path is short, i.e., when sources are typically close by. The mean length of the downwind search path is given by 〈L d 〉=d +r[(1/E) + cos α]/2 and the upwind search path by 〈L u 〉=d +r[(2/E) − (α/sin α) − cos α]/2 whered is the starting distance up- or downwind of the source,r is the range of stimulus influence,E is the efficiency with which the searcher moves to the source within the influence of the plume,a is the angle of the maximum extent of wind direction from the mean, and the average, 〈 〉, is taken over all starting positions across the wind direction that lead to search paths that intercept the area swept by the plume.