A game theoretic model of kleptoparasitism with strategic arrivals and departures of beetles at dung pats.

Dung beetles Onthophagus taurus lay their eggs in brood balls within dung pats. The dung that is used must be sufficiently fresh, and so beetles must keep moving from pat to pat to find fresh dung. If another beetle finds a brood ball it will usually eat the egg inside and lay its own egg in the brood ball instead of constructing its own ball. Thus, beetles will often stay near their eggs to guard them. We model a population of beetles where the times of arrival and departure from pats are strategic choices, and investigate optimal strategies depending upon environmental conditions, which can be reduced to two key parameters, the cost of brood ball construction and the ease of finding balls to parasitise. We predict that beetles should follow one of three distinct behaviors; stay in patches for only short periods, arrive late and be purely parasitic, remain in pats for longer periods in order to guard their brood balls. Under different conditions populations can consist of the first of these types only, a combination of the first and second types, or a combination of all three types.