Figure 1.

Illustration of the extend Moran model with exponential growth. Shown are the four different scenarios of population transition within a single discrete time step. (A) The population size remains constant and a single individual produces exactly two offspring (“Moran-type” reproductive event). (B) The population size remains constant and a single individual produces $\psi N_n$ offspring (“sweepstake” reproductive event). (C) The population size increases by ${\mathrm{\Delta }}_N^{\left(n\right)}$ individuals and a single individual produces exactly $\max \left[{\mathrm{\Delta }}_N^{\left(n\right)}+1,2\right]$ offspring. (D) The population size increases by ${\mathrm{\Delta }}_N^{\left(n\right)}$ individuals and a single individual produces exactly $\max \left[{\mathrm{\Delta }}_N^{\left(n\right)}+1,\psi N_n\right]$ offspring. Note that n denotes the number of steps in the past, such that $n=0$ denotes the present. An overview of the notation used in this model is given in Table 1.