Fig 4. A metapopulation can form when the population is below the expansion threshold throughout its range.

The population fragments rapidly (within tens of generations) to small patches of tens to a few hundred individuals whilst losing local adaptive variation. In two-dimensional habitats, such a metapopulation with limited adaptation can persist for a long time. Nevertheless, the population very slowly contracts, eventually forming a narrow band adapted to a single optimum. (a) The distribution of phenotypes across space is fragmented. (b) The subpopulations are transient, although they are stabilised by dispersal across space, especially along the neutral direction with no change in the optimum (Y). Locally, the population density may be higher than under uniform adaptation; blue contours depict the deterministic prediction for population density under uniform adaptation, N = 3. The realised density is about $\overline{N}=3.05\pm 1.7$ (standard deviation); darker shading represents higher density. (c) The adaptive genetic variance is low on average ($\overline{V_G}=0.02\pm 0.06$)—about an order of magnitude lower than would be maintained by gene flow under uniform adaptation (shown in green contours, V_G = 0.23). Typically, only a few clines in allele frequencies contribute to the genetic variance within a subpopulation. The parameterisation and predictions are detailed in the Individual-based simulations section of the Methods; predicted neighbourhood size is $\widehat{\mathcal{N}}=2.7$, effective environmental gradient is B = 0.48. Shown here after 5000 generations—the population collapses to a narrow band (at X = 45) after a further 20,000 generations and then appears persistent.