Species' ranges and the steepening-gradient hypothesis

One hypothesis invoked to explain limits to species ranges is a mismatch in environmental conditions between the central and marginal areas of species ranges. Low population size at the margins causes genetic drift to outplay selection locally, and limits the accumulation of genetic variance, so that adaptation is hindered locally. Earlier theoretical work shows that, for a population expanding over a spatially heterogeneous environment without any geographical barriers, adaptation will fail abruptly and sharp range margins will establish only when the underlying environmental conditions change more and more severely across space, whereas an environment changing constantly will result either in infinite expansion or rapid global extinction. Here, we extend this "steepening-gradient hypothesis" to encompass situations when multiple (up to three) environmental factors impose selection on separate adaptive traits. We show that multiple selection gradients steepen each other and that it is sufficient that just one of the gradients steepen in space for sharp range margins to form. This is true even if this gradient is shallow throughout the realised range. Thus, despite its detrimental role in forming range margins, it could be overlooked in field studies. Finally, by decomposing an environmental gradient to selection on two (or three) adaptive traits, we show that a population can withstand harsher environmental conditions than when selection acts on one adaptive trait alone. This finding argues for the evolution of novel traits in harsh environments.