Integration of Immediate and Long Term Sperm Precedence Patterns and Mating Costs in an Optimization Model of Insect Copulation Duration

The optimal copulation duration (t) in insects is strongly influenced by the existence and importance of sperm precedence mechanisms. Using an optimization model, we predict the effects of sperm precedence patterns on the copulation duration for which "number of fertilized eggs"/"costs" is maximized. Effects of the costs of territoriality and clutch size were also analysed. Initially, we assumed that males can only respond to the population average of any particular parameter, and, hence, that each male has only one topt (only inter-individual differences). We extended these conclusions to situations in which the male can adjust his behaviour to exact values of particular parameters, resulting in a variable topt for each male (intra-individual differences). For inter-individual comparisons, the model predicts the following: (i) The existence of (long-term) sperm mixing within the female genital tract will increase topt; (ii) In addition to this effect, sperm mixing combined with either a higher probability of a take-over between or during the first oviposition bouts, or a prolonged expected time between copulation and oviposition, will result in an increase of topt . However, in the absence of long-term sperm mixing neither of these behavioural characteristics will influence topt ; (iii) topt also increases with the mate encounter time for the male. It is not influenced by the expected clutch size of the female; (iv) Both energetic and territorial costs will reduce topt when high. For cases in which intra-individual adjustment of topt is possible, we made the following predictions: (i) The presence of a higher than average probability of a take-over of the female before or during the following oviposition bouts, will reduce topt; (ii) A larger than average clutch size will increase topt.