From Individual Stochastic Processes to Macroscopic Models in Adaptive Evolution

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Polymorphic evolution sequence and evolutionary branching (2008, background): “We are thus led to study the individual-based process without mutation (u K = 0 for all K ≥ 1). So fix x1 ,..., xd ∈ X and assume that, for all i ∈{ 1 ,..., d}, � ν K 0 , 1{xi }� has bounded second-order moments and converges in distribution to ni (0) ∈ R+. Then, as proved in [ 6, Theorem 4.2 ], whe”