Recruitment dynamics of social insect colonies

Recruitment plays a vital role in the ecological and evolutionary successes of social insect colonies. In this paper, we formulate a four-compartment model and its simplified version to explore how we should model the recruitment dynamics of workers in social insect colonies properly. Our four-compartment model has the components of the unalarmed patrollers, the alarmed patrollers, the alarmed recruiters, and the available workers, while its simplified version has three components where we combine the unalarmed patrollers and the alarmed patrollers into the patrollers. We perform complete mathematical and bifurcation analyses on both the full system and its simplified system. We have many interesting findings, including that (i) the simplified three-compartment system has only simple equilibrium dynamics, i.e., no periodic and chaotic dynamics; (ii) the four-compartment system has very complex dynamics; for example, it can have up to three subcritical Hopf bifurcations, two supercritical Hopf bifurcations, two limit point bifurcations, and a fold bifurcation of the limit cycle. Those important results provide theoretical guidance for modeling and studying recruitment dynamics of social insect colonies: It is critical to have proper compartments for biological systems as the number of compartments could lead to totally different dynamics, and hence affect policy-making.