Colony and evolutionary dynamics of a two‐stage model with brood cannibalism and division of labor in social insects

Division of labor (DOL) is a major factor for the great success of social insects because it increases the efficiency of a social group where different individuals perform different tasks repeatedly and presumably with increased performance. Cannibalism plays an important role in regulating colony growth and development by regulating the number of individuals in a colony and increasing survival by providing access to essential nutrients and minimizing competition among colony mates. To understand the synergy effects of DOL and cannibalistic behavior on colony dynamic outcomes, we propose and study a compartmental two‐stage model using ecological and evolutionary game theory settings. Our analytical results of the ecological and evolutionary models suggest that: (1) A noncannibalistic colony can survive if the efficiency of energy investment reflecting the DOL is greater than the relative death rate of the older population. (2) A cannibalistic colony can die out if both the efficiency of energy investment and the relative cannibalism rate (where each is also reflecting the DOL) are too large; or if the relative cannibalism rate alone is too small. (3) From our numerical analysis, cannibalism can increase or reduce the colony's total population size, which greatly depends on the benefit of egg cannibalism increasing or decreasing of adult's lifespan. (4) A cannibalistic and noncannibalistic colony can experience bistability due to cooperative behavior. (5) In the evolutionary settings, DOL can prevent colony death and natural selection can preserve strong Allee effects by selecting the traits with the largest investment on brood care and the lowest cannibalism rate. (6) Evolutionary dynamics may increase the fitness of the colony, i.e., the successful production of workforce which results in the increase of total worker population size, colony survival, and reproduction. Our results suggest both cannibalism and DOLs are adaptive strategies that increase the size of the worker population, and therefore, persistence of the colony.