These models typically consider a single, abrupt environmental change.
These models typically work in continuous time and nearly always consider an abrupt environmental change (absence to presence of drugs).
Unlike models of evolutionary rescue by single mutations, the majority of quantitative-genetic models consider gradual rather than abrupt environmental change.
In the treatment of abrupt environmental change, populations adapt towards a novel but fixed optimum (Gomulkiewicz and Holt 1995; Boulding and Hay 2001).
For example, survival and reproductive output increase through time as fish populations adapt following an abrupt environmental change (Kinnison et al. 2008; Gordon et al. 2009).
We assume that predator mortality m consists of a basal mortality m0 under reference environmental conditions, combined with an additional mortality me due to abrupt environmental change that is detrimental to the predator (thus, m = m0 + me).
As abrupt environmental change increases predator mortality and eventually causes its extinction, an important value for evaluating evolutionary rescue is the maximum value of predator mortality m at which predator can persist (that is, its abundance is nonzero).
For this, models have 'coupled population dynamics and evolution by natural selection to identify conditions for which evolution succeed – or fails – to rescue a closed population from extinction following abrupt environmental change' (Gomulkiewicz and Holt 1995).
For abrupt environmental change, the situation might be more complex as, in addition to the evolutionary processes, demographic processes increase in importance (Gomulkiewicz and Holt 1995; Bell and Gonzalez 2009, 2011).
These studies are amenable to comparison because they share a number of similar structural features: both deal with stochastic population dynamics in a scenario of abrupt environmental change and discrete adaptive steps.
Response of humans to abrupt environmental transitions.
