Evolutionary branching/speciation: Contrasting results from systems with explicit or emergent carrying capacities

In this paper, we use the theory of adaptive dynamics to highlight the differences in evolutionary behaviour when contrasting formulations of the carrying capacity are used. We use two predator - prey systems, one with a fixed carrying capacity and one in which the carrying capacity is an emergent property compounded of an intrinsic growth rate and a susceptibility to crowding. We consider prey evolution in both systems and link the evolving parameters by a trade-off which requires that prey with higher per capita growth experience a greater risk of predation. We find that the two approaches for representing the carrying capacity can lead to markedly different evolutionary behaviour. In particular, the possibility of exhibiting evolutionary branching requires an emergent carrying capacity. This is significant, since evolutionary branching is regarded as a possible mechanism by which sympatric speciation may occur.