When do leading and rear edges of the range shift slower or faster than climate? Insights from a mathematical model

Many species have spread towards cooler climates and/or went extinct at the warm margin of their range as a result of climate warming. The large diversity in observed range shifts however remains poorly understood. We here explore how evolution of the climatic niche at range margins may alter range shifts patterns. We use previously developed mathematical results to predict the velocity at which rear and leading edge move in an asexual species adapting to an environment that changes in space and time. As in previous studies, we find a critical climate change velocity beyond which the species cannot persist. We further predict the critical climate velocities, below which, the leading edge shifts faster than climate, or the species persists at its rear edge. We derive predictions along one-dimensional and two-dimensional ranges. We also examine the effect of a local disturbance on the velocity of range limits. Our simple mathematical model shows that evolution of species climatic niches at range margins can already generate a large diversity of types of range shift in a warming climate. This diversity is also observed in simulations assuming sexual reproduction or finite population sizes. The expectation of a simple climate tracking may therefore be too simplistic, underestimating the resilience capacity at the warm margins and either overestimating or underestimating the capacity for spread at the cold margin, with important consequences for management of biodiversity in a changing climate.