Fig. 3.

Stochastic dynamics and large demographic fluctuations in a coexistence game. (A–C) ($M=\mathrm{2,000}$): According to the deterministic dynamics (solid black lines) the two types X (blue) and Y (red) coexist at their respective equilibrium, $K_{\text{cox}}^x$ and $K_{\text{cox}}^y$. The three stochastic realizations, however, reveal a different picture: In the first case (A), both types go extinct early on. In the second case (B), type X goes extinct first, which benefits type Y and results in a higher carrying capacity than the density of type Y individuals in the coexistence equilibrium, $K^y>K_{\text{cox}}^y$. In the third case (C), type Y goes extinct first and the new carrying capacity $K^x$ even exceeds the whole population size in the coexistence equilibrium $K^x>K_{\text{cox}}$. Pale lines represent the simulated SD (averaged over 500 independent simulations with $\ge {10}^6$ data points each). (D) The SD scaled by M in the coexistence equilibrium decreases with M, but differently for the two types (parameters ${\lambda }_{x\to xx}={\lambda }_{y\to yy}=0.6$, ${\lambda }_{x\to 0}={\lambda }_{y\to 0}=0.5$, $x_0=10$, and $y_0=10$, the same payoff matrix for all panels).