How competition between overlapping generations can influence optimal egg-laying strategies in annual social insects

Annual social insects are an integral functional group of organisms, particularly in temperate environments. An emblematic part of their annual cycle is the social phase, during which the colony-founding queen rears workers that later assist her in rearing sexual progeny (gynes and drones). In many annual social insects, such as species of bees, wasps, and other groups, developing larvae are provisioned gradually as they develop (progressive provisioning) leading to multiple larval generations being reared simultaneously. We present a model for how the queen in such cases should optimize her egg-laying rate throughout the social phase depending on number-size trade-offs, colony age-structure, and energy balance. Complementing previous theory on optimal allocation between workers vs. sexuals in annual social insects and on temporal egg-laying patterns in solitary insects, we elucidate how resource competition among overlapping larval generations can influence optimal egg-laying strategies. With model parameters informed by knowledge of a common bumblebee species, the optimal egg-laying schedule consists of two temporally separated early broods followed by a more continuous rearing phase, matching empirical observations. However, eggs should initially be laid continuously at a gradually increasing rate when resources are scarce or mortality risks high and in cases where larvae are fully supplied with resources at the egg-laying stage (mass-provisioning). These factors, alongside sexual:worker body size ratios, further determine the overall trend in egg-laying rates over the colony cycle. Our analysis provides an inroad to study and mechanistically understand variation in colony development strategies within and across species of annual social insects.