Optimal fissioning strategies of social insects with respect to colony dynamics and nest founding probability

Social insects demonstrate two fundamentally different modes of reproduction, independent colony foundation (ICF) by single fertilized queens or dependent colony foundation (DCF) by fissioning of existing colonies into two or several new colonies (swarms). In some species, both reproductive modes occur in parallel. The benefits and disadvantages of DCF vs. ICF have been widely discussed and been subject to empirical studies, but a formal theoretical treatment of the topic is still incomplete. Taking honey bees as example, we provide a resource allocation model of colony dynamics to analyze the ecological conditions under which DCF may be favored over ICF. Using mathematical and numerical methods, we show that it critically depends on the survivorship function linking swarm size to the probability of swarm establishment whether ICF or DCF results in a higher output of surviving new colonies. Because building larger swarms requires larger inter-swarm time intervals, DCF can only be a better strategy if this disadvantage is over-compensated for by a strong size-dependent swarm survivorship and survival of single queens is very low. Colony growth rate has no effect on this decision and the impact of maximum possible colony size is negligible. Further, there is a discontinuity in the optimal swarm size, so that either a swarm size of 1 (ICF) is the best strategy, or emitting swarms of considerable size (DCF). Consequently, a direct evolutionary transition from ICF to DCF appears unlikely and may have been triggered by selective pressures promoting movement of complete nests or distributing single colonies over several nests (polydomy).