Figure 3

Criterion for Altruists selection. ( a) fixation probabilities π _s (red squares) and π _A (blue circles) as a function of selection pressure $N_f\overline{s}$, for N _f  = 100 and $N_i=85,87,90,93,95,97$. Values are obtained by numerically solving eq.(8). Solid lines are theoretical values (eqs. 13,14). Increasing N _i are indicated by the arrow. (b) equilibrium selection pressure $N_f{\overline{s}}^{\ast }$ for which π _A = π _s for multiple combinations of $N_f\in \left[100,150\right]$ and $N_i\in \left[85,148\right]$, as a function of relative population increase, obtained numerically. The solid line is the theoretical value (eq.15).