Abstract
Population genetic models of evolution along linear environmental gradients cannot explain why adaptation stops at ecological margins. This is because, unless models impose reductions in carrying capacity at species' edges, the dominant effect of gene flow is to increase genetic variance and adaptive potential rather than swamping local adaptation. This allows the population to match even very steep changes in trait optima. We extend our previous simulations to explore two nonlinear models of ecological gradients: (a) a sigmoid (steepening) gradient and (b) a linear gradient with a flat centre of variable width. We compare the parameter conditions that allow local adaptation and range expansion from the centre, with those that permit the persistence of a perfectly adapted population distributed across the entire range. Along nonlinear gradients, colonization is easier, and extinction rarer, than along a linear gradient. This is because the shallow environmental gradient near the range centre does not cause gene flow to increase genetic variation, and so does not result in reduced population density. However, as gradient steepness increases, gene flow inflates genetic variance and reduces local population density sufficiently that genetic drift overcomes local selection, creating a finite range margin. When a flat centre is superimposed on a linear gradient, gene flow increases genetic variation dramatically at its edges, leading to an abrupt reduction in density that prevents niche expansion. Remarkably local interruptions in a linear ecological gradient (of a width much less than the mean dispersal distance) can prevent local adaptation beyond this flat centre. In contrast to other situations, this effect is stronger and more consistent where carrying capacity is high. Practically speaking, this means that habitat improvement at patch margins will make evolutionary rescue more likely. By contrast, even small improvements in habitat at patch centres may confine populations to limited areas of ecological space.