Marginal Value Theorem with Exploitation Time Costs: Diet, Sperm Reserves, and Optimal Copula Duration in Dung Flies

Abstract

The classical version of marginal value theorem (MVT) assumes constant costs of time spent in different activities (searching; resource uptake). This article investigates the logic of MVT when these have different costs. Models are developed specifically to offer a plausible adaptive explanation for results obtained by P. I. Ward and L. W. Simmons on the copula duration of the yellow dung fly: (1) copula duration does not alter during successive matings in a sequence, (2) copula duration declines with dietary restriction, and (3) the number of copulations in a sequence declines with dietary restriction. In dung flies, mate searching is energetically expensive, and copulation expends sperm. Both energy losses and sperm losses must be paid for by food foraging (for nectar and prey items, respectively). Two models are examined. In model 1, sperm reserves increase linearly during food foraging, and the organization of time between mate searching and foraging is unstated. It predicts that low prey densities du...