Figure 2.

A simple model of the accumulation of mutants in an asexual population. Here we consider a mutant subpopulation emerging within a much larger wild-type population (not shown). For simplicity, mutation and growth are treated deterministically: each generation the wild-type population doubles its size and produces twice as many new mutants, whereas preexistent mutants produce exactly r offspring (indicated with an arrow in the diagram). These assumptions will be relaxed later in the computer simulation models. Generation count starts at 0, when the wild-type population reaches a size of N₀ = 1/μ individuals, where μ is the per-generation mutation rate. This period is referred to in the literature as the Luria–Delbrück period. General formulas for the size of clones from generation t’ at time t (s_t(t’)), number of mutants (m_t), and number of clones (c_t) are shown. Note how the clonal distribution becomes increasingly uneven provided that clones undergo some growth (r > 1).