A critical body size for use of pheromones in mate location

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Abstract
Pheromones have demonstrated importance in mate location in many insect species. Because chemoreception is the most universal sense, it has been assumed that pheromones also are important in aquatic organisms, including bacteria, but few have been found. The physical limits on effective strategies for organisms to come into contact for mating were modeled with assumptions appropriate for organisms less than a millimeter in size in an open aquatic environment. One sex was assumed to be motile, while the other sex was passive or devoted energy to locomotion or to diffusible pheromone production. Assuming spherical organisms, random locomotion by the second sex at the same velocity as the first sex increases the chances of contact by a factor of 4/3 over being passive; this ratio is independent of size. For detection by contact, the effectiveness of searching increases with the third power of the radius of the organisms; for detection by pheromones, search effectiveness increases with the seventh power of the radius above a critical size. Diverting energy from motility to pheromone production is not productive for organisms smaller than the critical size, which corresponds to a radius of 1.8 times the square root of the diffusion coefficient of the pheromone times the threshold concentration for detection divided by the rate of pheromone production per unit volume of organism. Thus, pheromone production is very favorable for organisms much above the critical size, which appears to be between 0.2 and 5 mm in water. On the other hand, bacteria are probably too small to use diffusable pheromones for mate location; most protozoans and rotifers may also be too small.