Fig. 1.

The stochastic dynamics fluctuates around the deterministic predictions in large populations (black lines). Each panel refers to one of the three characteristic classes of interactions as determined by the ranking of payoffs. Evolutionary trajectories for X (blue) and Y (red) types are shown for initially small ($x_0=10$, $y_0=90$, pale colors) and large ($x_0=\mathrm{1,000}$, $y_0=\mathrm{1,000}$ saturated colors) populations. Regardless of the game both types tend to increase for low initial population sizes, whereas both types decrease in densities at large initial sizes. In all cases the deterministic predictions agrees well with the stochastic dynamics in that the stochastic trajectories fluctuate around the deterministic average [parameters $M=\mathrm{2,000}$, ${\lambda }_{x\to xx}={\lambda }_{y\to yy}=0.6$, and ${\lambda }_{x\to 0}={\lambda }_{y\to 0}=0.1$, which translates into $K^x=\mathrm{1,000}$ and $K^y=250$ (A) and $K^y=500$ (B and C)].