Mate choice when males are in patches: optimal strategies and good rules of thumb

In standard mate-choice models, females encounter males sequentially and decide whether to inspect the quality of another male or to accept a male already inspected. What changes when males are clumped in patches and there is a significant cost to travel between patches? We use stochastic dynamic programming to derive optimum strategies under various assumptions. With zero costs to returning to a male in the current patch, the optimal strategy accepts males above a quality threshold which is constant whenever one or more males in the patch remain uninspected; this threshold drops when inspecting the last male in the patch, so returns may occur only then and are never to a male in a previously inspected patch. With non-zero within-patch return costs, such a two-threshold rule still performs extremely well, but a more gradual decline in acceptance threshold is optimal. Inability to return at all need not decrease performance by much. The acceptance threshold should also decline if it gets harder to discover the last males in a patch. Optimal strategies become more complex when mean male quality varies systematically between patches or years, and females estimate this in a Bayesian manner through inspecting male qualities. It can then be optimal to switch patch before inspecting all males on a patch, or, exceptionally, to return to an earlier patch. We compare performance of various rules of thumb in these environments and in ones without a patch structure. A two-threshold rule performs excellently, as do various simplifications of it. The best-of-N rule outperforms threshold rules only in non-patchy environments with between-year quality variation. The cutoff rule performs poorly.