The Fixed Sample Search Rule and Use of an Indicator Character to Evaluate Mate Quality

The phenotypic correlation observed between mated males and females is a direct result of the decision rules that individuals employ during search for a mate. We generalise the fixed sample search rule and examine how the functional relationship between a male indicator character and the fitness benefit of a mating decision influences female search behaviour. If the phenotypes of males and females combine additively to influence the benefit of a mating decision and fitness is a highly inclined function of phenotypic values the optimal value ofn, the number of males that females sample during search, is relatively large. The phenotype of the searcher has no impact on the optimal value ofnif fitness is a linear function; the optimalnincreases with the phenotype of females if the fitness function is convex; and a concave fitness function induces females with high trait values to sample relatively few males. Because females that sample many potential mates are expected to encounter a male with a high expression of the indicator trait linear, convex and concave fitness functions induce a random, assortive and disassortative combination of phenotypes between mated individuals, respectively. Thus, the fixed sample research tactic can produce the variety of phenotypic correlations observed between mated individuals in natural systems and our ability to derive rule-specific predictions of search behavior may generally require information on how characters used to evaluate potential mates are related to fitness.