Females of many species face a difficult sampling problem while searching for a mate. How do they find the best male possible when the constraints of time, memory, and mobility prevent them from visiting all the males in the population?
Five possible solutions are examined: random mating a fixed-threshold criterion, a fixed-threshold with last-chance option, an optimal one-step decision strategy, and the best-of-n-males strategy. Random mating is the worst strategy whenever the female gets more than one chance to mate. The two fixed-threshold strategies approach equal effectiveness as n increases but are always below the optimal one-step decision strategy. However, the best-of-n-males strategy always yields the highest expectation of fitness in a mate. The difference is especially great when n≳5.
Plotting the average fitness of males chosen vs n, the number of males examined, yields a negatively accelerating curve. Since the cost of searching will be an increasing function of n, the two curves can be combined to yield an optimum n: the point where the difference between the curves is greatest.
The one field study (Brown 1978) that addresses these problems in detail reveals that female mottled sculpins choose males on a relative, rather than absolute, basis, as theory suggests they should.