Some Distinguishing Features of Models of Search Behavior and Mate Choice

We develop analytical predictions about how females should behave when either a (infinite time horizon) sequential search tactic or best-of-n rule is employed to search for mates. The likelihood that a male is rejected on first encounter with a female should decline with male quality if females use a sequential search tactic. If females employ a best-of-n rule, however, the probability that a first encountered male is rejected should not depend on male quality; the proportion of males of any quality rejected on first encounter with a female equals the proportion of females that perceive the optimal number of males to be sampled prior to mating to be more than one. The behavior of females using either rule, however, depends on the distribution of quality among potential mates. We show that a variance-preserving increase of mean male quality results in an increase of the critical value of the threshold of acceptance under a sequential search rule; that is, females become more choosy. However, such a shift is not expected to change female search behavior if a best-of-n tactic is employed. A mean-preserving increase of the variance of male quality results in an increase of n among females that employ a best-of-n rule, whereas the number of males sampled prior to mating may increase, decrease, or remain unchanged following such a shift if females use a sequential search rule. The threshold acceptance criterion under sequential search, however, increases (decreases) with a mean-preserving increase (reduction) of the variance of male quality. Patterns of resampling of males by females and the position of accepted males in a search sequence have often been used to distinguish between the best-of-n and sequential search tactics. Predictions of each pattern under a sequential search model depend on both whether the time horizon over which search takes place is assumed to be finite or infinite and whether or not recall (resampling) of previously encountered males is permitted and sometimes resemble predictions of a best-of-n model of search behavior. Because finite time horizon models of sequential search are currently poorly developed, such information is not likely to provide good evidence that females are using either rule The predictions that we derive, however, should be relatively robust to assumptions about recall and the time horizon over which sampling takes place. An experimental protocol in which mate quality is altered may consequently provide a valuable approach to the study of search behavior and mate choice.