Adaptive dynamics on an environmental gradient that changes over a geological time-scale

The standard adaptive dynamics framework assumes two timescales, i.e. fast population dynamics and slow evolutionary dynamics. We further assume a third timescale, which is even slower than the evolutionary timescale. We call this the geological timescale and we assume that slow climatic change occurs within this timescale. We study the evolution of our model population over this very slow geological timescale with bifurcation plots of the standard adaptive dynamics framework. The bifurcation parameter being varied describes the abiotic environment that changes over the geological timescale. We construct evolutionary trees over the geological timescale and observe both gradual phenotypic evolution and punctuated branching events. We concur with the established notion that branching of a monomorphic population on an environmental gradient only happens when the gradient is not too shallow and not too steep. However, we show that evolution within the habitat can produce polymorphic populations that inhabit steep gradients. What is necessary is that the environmental gradient at some point in time is such that the initial branching of the monomorphic population can occur. We also find that phenotypes adapted to environments in the middle of the existing environmental range are more likely to branch than phenotypes adapted to extreme environments.