Fig. 5

Mean extinction time, T, for mixed dispersal syndromes as a function of the dispersal fraction α (top) and of linear system size L (bottom). Parameters of the single phenotype syndromes are set to \(p_{\text {int}}=\bar p_{\text {ext}}=0.25\), n=5, δ=0.05 and σ=0.25, corresponding to the absorbing phase (see Fig. 3). Each point was computed averaging over 10³ realizations of the simulations. Most error bars are smaller than point size. Dashed lines have been included to facilitate comparisons across panels. (Upper panel) Extinction time is always maximum when 0.25<α<0.5 and converges to α ^∗≈0.4 for large sizes of the system). (Lower panel) Populations exhibiting any of the single-phenotype strategies (α=0 and α=1) are in the absorbing phase, as indicated by the downward curves on the log-log scale, i.e., their extinction is unavoidable (deterministic extinction). Conversely, intermediate values of α lead to extinction times that grow exponentially with system size, and thus maintain populations in the active phase