Priority versus brute force: when should males begin guarding resources?

When should males begin guarding a resource when both resources and guarders vary in quality? This general problem applies, for example, to migrant birds occupying territories in the spring and to precopula in crustaceans where males grab females before they molt and become receptive. Previous work has produced conflicting predictions. Theory on migrant birds predicts that the strongest competitors should often arrive first, whereas some models of mate guarding have predicted that the strongest competitors wait and then simply usurp a female from a weaker competitor. We build a general model of resource guarding that allows varying the ease with which takeovers occur. The model is phrased in terms of mate-guarding crustaceans, but the same logic can be applied to other forms of resource acquisition where priority plays a role but takeovers might be possible too. The race to secure breeding positions can lead to strong competitors (large males) taking females earliest, even though this means accepting a lower-quality female. Paradoxically, this means that small males, which have fewer breeding opportunities, are more choosy than larger ones. Such solutions are found when takeovers are impossible. The easier the takeovers and the higher the rate of finding guarded resources, the more likely are solutions where guarding durations are short, where strong competitors begin guarding only just before breeding, and where they do this by usurping the resource. The relationship between an individual's competitive ability and its timing of resource acquisition can also be nonlinear if takeovers are moderately common; if this is the case, then males of intermediate size guard the longest.