A mathematical analysis of evolutionary rescue and niche construction

Laboratory experiments and field studies have shown that declining populations can avoid extinction by undergoing adaptation. This process, evolutionary rescue, entails a population approaching extinction until an adaptive mutation appears and subsequently establishes by escaping stochastic loss. While most models of evolutionary rescue emphasize mutations that allow organisms to persist in hostile environments, a less explored possibility---known as positive niche construction (hereafter niche construction)---involves mutants improving their fitness by modifying their environment. In Chapter 1 of this dissertation, I analyze a model of evolutionary rescue via a niche-constructing mutation. I show that the probability of rescue is highest under low-to-moderate rates of construction: some construction is needed to ensure that mutants proliferate quickly enough to avoid stochastic extinction; but because construction is costly, requiring time and energy to perform and develop, too much of it can lead to over-exploitation of the constructed habitats by the mutants' non-niche-constructing ancestors (hereafter residents). In Chapter 2, I then model a niche-constructing population that must undergo evolutionary rescue to withstand habitat exploitation by an invading species. I find that the same fecundity costs rendering constructors vulnerable to exploitation can help facilitate rescue from such exploitation by reducing the rate of construction and thus lowering the density of habitats available to invaders. The lower habitat density leads to slower invasion, which in turn buys constructors more time to mutate. Finally, in Chapter 3, I consider the possibility that invaders directly interact with the resident population instead of exploiting resident-constructed habitats. I show that a lower resident birth rate---whether it stems from a smaller resident density independent birth rate or stronger birth-limiting competition---can promote rescue by reducing variance in mutant fitness. Together, these findings suggest that lower reproductive success among members of a population can, under a range of conditions, improve the population's chances of evolutionary rescue.