Optimal fissioning strategies of social insects in dependence of colony dynamics and nest founding probability

Abstract 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 an 'old' colony and one or several new colonies (swarms); at least in some species both modes can 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 lacking. Here we provide a model of colony dynamics to analyze the ecological conditions under which DCF may be favored over ICF. Using 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 \textit{surviving} new colonies (swarming rate). Due to the fundamentally rate reducing effect of emitting larger swarms, DCF can only be a better strategy if the survivorship function of swarms is sufficiently steep. Colony growth rate should have no effect on this decision and the impact of maximum colony size should at best be moderate. Further, a discontinuity in the optimal swarm size occurs in the parameter space: either a swarm size of 1 (ICF) is the best strategy or emitting swarms of considerable size (DCF). A direct evolutionary transition from ICF to DCF appears thus unlikely and may have been triggered by other selective pressures promoting movement of complete nests or distributing single colonies over several nests (polydomy)