Is the sky the limit? On the expansion threshold of a species’ range
Fig 6
Dispersal aids adaptation in small populations because the neighbourhood size 𝒩 increases with the square of generational dispersal, whereas the effective environmental gradient B increases only linearly.
This chart shows a set of simulated populations, with dispersal increasing from left to right and bottom to top. The hue of the dots indicates the rate of expansion (light to dark blue and purple) or collapse (orange to red). The rates of expansion and collapse are shown in dependency on B and 𝒩. Open circles indicate limited adaptation, in which a species’ range is fragmented and each subpopulation is only matching a single optimum, whilst its genetic variance is very small. As dispersal increases, population characteristics get above the expansion threshold (dashed line), and hence, uniform adaptation becomes stable throughout the species’ range. Local population density stays fairly constant, around N = 3.5, whilst total population size increases abruptly above the expansion threshold as the population maintains a wide range (not shown). Parameters for these simulations are given in the Individual-based simulations section of the Methods; the scaling of 𝒩 and B with dispersal σ is clear from the Methods, section Parameters. The rate of range change is not significantly different from zero for the first three simulations above the expansion threshold; black centre (bottom left) indicates extinction.