Fig. 4

Stationary density for the mixed dispersal syndromes as a function of the dispersal propensity parameter α. Parameters of the single phenotype syndromes are set to \(p_{\text {int}}=\bar p_{\text {ext}}=0.25\) and n=5. Linear system size L=100 (total size N=10000). Stationary density for three different values of inbreeding depression (represented by red, green and blue curves, respectively) and environmental variability (darker shades indicate higher environmental unpredictability; labeled at α=1). Both δ and σ tend to reduce the population density in the pure strategies (α=0 or α=1, respectively) but, remarkably, relatively large densities can be attained by populations with mixed syndromes even in the presence of inbreeding depression and environmental unpredictability. Although the specific values of δ and σ are not intended to be biologically realistic, change in these parameters illustrates qualitatively the consequences of different genetic and environmental costs. Note that points at parameter values α=1 and σ=0.25 correspond to the absorbing region (see the calculation \(\bar p_{\text {ext}}^{c}\) in the Additional file 2: Appendix for \(\sigma =p_{\text {ext}}^{c}\)) however measurements of the (quasi)stationary density give small positive values, which decrease to zero for larger system sizes (not shown)