Alternate Models of Replicator Dynamics - Wesson, Elizabeth N.; Rand, Richard H. (Journal of Applied Nonlinear Dynamics, 2026)
Models of evolutionary dynamics are often approached via the replicator equation, which in its standard form is given by ˙ xi = xi ( fi (x)−φ ) , i = 1, . . . ,n, where xi is the frequency of strategy i, fi is its fitness, and φ = Σn i=1 xi fi is the average fitness. A game-theoretic aspect is introduced to the model via the payoff matrix A by taking fi(x) = (A · x)i. This model is based on the exponential model of population growth, ˙ xi = xi fi, with φ introduced in order both to hold the total population constant and to model competition between strategies. We analyze the dynamics of analogous models for the replicator equation of the form ˙ xi = g(xi)( fi −φ ), for selected growth functions g.