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).

社会性昆虫表现出两种根本不同的繁殖模式，即通过单个受精蚁后建立的独立群体基础（ICF）或通过将现有群体分裂成两个或几个新群体（群体）的依赖群体基础（DCF）。在某些物种中，两种繁殖模式同时发生。 DCF 与 ICF 的优缺点已被广泛讨论并进行了实证研究，但对该主题的正式理论处理仍然不完整。以蜜蜂为例，我们提供了群体动态的资源分配模型来分析DCF可能优于ICF的生态条件。使用数学和数值方法，我们表明，无论 ICF 还是 DCF 是否会导致新群体存活的更高产量，它关键取决于将群体大小与群体建立概率联系起来的生存函数。由于构建更大的群体需要更大的群体间时间间隔，因此如果这种劣势被强大的依赖于规模的群体生存能力过度补偿并且单个蚁后的生存率非常低，那么 DCF 只能是更好的策略。集落生长速率对此决定没有影响，最大可能集落大小的影响可以忽略不计。此外，最佳群体大小存在不连续性，因此群体大小为 1 (ICF) 是最佳策略，或者发射相当大小的群体 (DCF)。因此，从 ICF 到 DCF 的直接进化转变似乎不太可能，并且可能是由促进完整巢穴移动或将单个群体分布在多个巢穴上（一夫多妻制）的选择压力引发的。