Figure 2.

Models of rescue from SGV and de novo mutations. (A) A branching process model of population growth, whose dynamics can be described by a diffusion approximation (Martin et al. 2013). The wild type (pink) has mean growth rate r₀ and reproductive variance σ₀. At a reproduction event, mutation (lightning bolt) to a resistant variant (red) can occur. This variant has reproduction parameters drawn from a specified distribution f_R. (B) A viral dynamics model (Alexander and Bonhoeffer 2012). Free virus (V) infects target cells; infected cells in turn produce free virus. Two strains, drug-sensitive (wild type) and drug-resistant, are characterized by their distinct rates of replication cycle events. Mutation (lightning bolt), for clarity shown only from the wild type, can occur upon either cell infection or free virus production. Under treatment, a drug can block the sensitive strain at either of these replication steps (inhibition arrows). (C) Schematic of population size over time, leading to an outcome of either extinction or rescue. The size of ovals represents population size (pink, wild type; red, resistant), while circles indicate individuals within the population. Resistant variants leading to rescue can arise from two sources. (i) Standing genetic variation (SGV): Resistant individuals are maintained at mutation-selection balance under permissive conditions. After the switch to stressful conditions, a resistant individual is at a selective advantage and succeeds in establishing a lineage with probability π_f(0). (ii) De novo production: Under stressful conditions, the wild-type population (size N(t)) declines, but residual replication leads to ongoing production of resistant mutants at per capita rate u_S(t). A resistant individual arising at time t has probability of establishment π_f(t).