Evolutionary effects of different dispersal modes on the origin of polymorphic crypsis in predator-prey systems

Scenario: Using adaptive dynamic theory, expose a monomorphic prey population to two habitat types and a visual predator. Questions: What circumstances can lead to the evolution of polymorphic crypsis? How is the outcome affected by the dispersal pattern of the prey and predator, by the amount of predation, and by the trade-off strength between the habitats? Mathematical method: I modelled three different dispersal modes: passive dispersal for the prey and a stationary predator; passive dispersal for the prey and habitat choice for the predator; and habitat choice for the prey and no dispersal for the predator. Conclusions: The different dispersal models produce only minor differences in outcomes. Dispersal rate also seems to have relatively little influence on the evolutionary outcome, with low dispersal rate slightly favouring evolutionary divergence. Other factors (such as the amount of predation and strength of trade-off between the habitats) appear to be more crucial.