Costly defense traits in structured populations

We propose a model for the dynamics of frequencies costly defense trait. More precisely, we consider Lotka-Volterra-type models involving prey (or host) population consisting two types and predator parasite) population, where one type individuals - modeling carriers trait is more effective in defending against predators but has weak reproductive disadvantage. Under certain assumptions prove that relative frequency these defenders total converges to spatially structured Wright-Fisher diffusions with frequency-dependent migration rates. For many-demes limit (mean-field approximation) hereof, show goes fixation/extinction if only selective disadvantage smaller/larger than an explicit function ecological parameters.