A social-insect model for flexible collective defense
Living systems, from cells to superorganismic insect colonies, have an organizational boundary between inside and outside and must allocate resources to defend it. Whereas the micro-scale dynamics of cell walls can be difficult to study, the adaptive allocation of workers to defense in social-insect colonies is more conspicuous. This is particularly the case for Tetragonisca angustula stingless bees, which employ a combination of defensive strategies found across other social insects and colonial animals: 1) morphological specialization (distinct soldiers (majors) are produced over weeks); 2) age-based polyethism (young majors transition to guarding tasks over days); and 3) task switching (small workers (minors) replace soldiers within minutes under crisis). To better understand how these timescales of reproduction, development, and behavior integrate to balance defensive demands with other colony needs, we developed a demographic model using a Filippov ODE system to study the effect of these processes on task allocation and colony size. Our analytical results provide conditions for colony survival and show that, if guard maturation is slow, increasing the production of defense specialized majors can reduce the long-term fraction of guarding workers. This model elucidates the demographic factors constraining collective defense regulation in social insects while also suggesting new explanations for variation in defensive allocation at smaller scales where the microscale mechanisms underlying defensive processes are not yet easily observable. Moreover, our work helps to establish social insects as models for understanding other systems where the transaction costs for component turnover are nontrivial, as in manufacturing systems and just-in-time supply chains.