Eco-evolutionary dynamics of a two-stage social insect model with trait-dependent cannibalism and handling saturation

Egg cannibalism is a widespread trait in social insects with profound consequences for colony persistence and adaptation, yet its eco-evolutionary roles remain incompletely understood. Building on prior two-stage eco-evolutionary frameworks, we develop an extended model that incorporates a saturating functional response for cannibalism and allows each life history rate, such as reproduction, cannibalism intensity, mortality, maturation and the associated saturation effects to depend on the evolving trait through distinct functional relationships. We first derive general conditions under which the population is driven to extinction under arbitrary trait-dependence, and then focus on biologically relevant scenarios where only one demographic rate varies with the trait as well as cases in which the egg-cannibalism rate co-evolves with one additional key parameter. Our analysis reveals that nonlinear cannibalism with handling saturation can give rise to up to three coexistence equilibria when a single demographic parameter evolves with the trait. However, when the cannibalism rate evolves alongside another trait-dependent rate, at most two coexistence equilibria emerge when cannibalism co-evolves with survival saturation, and only one in other pairwise combinations. The existence and stability of these equilibria depend sensitively on how trait variation shapes different demographic processes. Evolutionary dynamics can either promote or restrict coexistence, depending on whether the trait-dependent parameters respond in compatible or opposing directions. These findings provide insight into how trait-driven regulation and nutritional recycling interact to shape the stability and adaptive trajectories of social insect colonies.