The variability of male quality and female mate choice decisions: second-order stochastic dominance and the behavior of searchers under a sequential search strategy.

The strategy employed by a female to sample prospective mates determines the likelihood that a high-quality male is encountered in the search process. In general, the choosiness of females is expected to depend on the variability of quality amongst the males that are sampled. The sequential search strategy is a prominent model of search behavior that involves the use of a threshold criterion to evaluate encountered individuals. In this paper, we show that the stochastic dominance of one distribution of male quality over another at the second order is necessary and sufficient for the optimal threshold criterion to differ under two distributions of male quality when the cost to sample males is held constant and the mean quality of males under each of the distributions is identical. A difference of the variance of male quality between two distributions does not imply that one distribution stochastically dominates the other at the second order and, hence, should not, in general, be used to assess the relative variability of quality amongst prospective mates. The adjustment of the threshold criterion in response to experimental manipulations of the distribution of male quality has been inferred from induced differences of the duration of search or the number of males sampled in the search process. Here we show that such inferences are unjustified. In particular, the difference of the threshold criterion imposed by second-order stochastic dominance does not determine the distribution under which females are expected to sample a larger number of males in the search process.