When do adaptive plasticity and genetic evolution prevent extinction of a density-regulated population?

We study the dynamics of evolutionary recovery after an abrupt environmental shift in a density-regulated population with evolving plasticity. Maladaptation to the new environment initially causes the population to decline, until adaptive phenotypic plasticity and genetic evolution restore positive population growth rate. We assume that selection on a quantitative trait is density-independent and that the initial cost of plasticity is much lower than the benefit of the initial plastic response. The initial partially adaptive plasticity reduces the effective magnitude of the environmental shift, whereas evolution of plasticity increases the rate of adaptation. Both effects greatly facilitate population persistence. In contrast, density dependence of population growth always hinders persistence. With theta-logistic population regulation, a lower value of theta produces a faster initial population decline and a higher extinction risk.