Figure 3 .

The relation between probability of survival, P, and reproductive value, v, at times t = 10 (top), t = 30 (middle), and t = 50 (bottom). For each time, there are 1000 dots, each representing a single ancestor. Each dot gives the probability that a single copy of a gene in the ancestor will survive to time t, plotted against the ancestor’s relative contribution to the pedigree up to time t. The straight lines show the linear relation vP_N,t where P_N,t is the probability of survival of a neutral allele in a branching process with growth rate λ = 1. The curves show the approximation is ${\text{P}}_{\text{t}}=1-e^{-\upsilon {\tilde{P}}_t}$, where ${\tilde{P}}_t$ is an effective value determined by $P_{N,t}=1-\mathbb{E}\left[e^{-\upsilon {\tilde{P}}_t}\right]$. This calculation is simplified by using the fact that $\mathbb{E}\left[e^{-\upsilon \tilde{P}}\right]$ is the generating function for v (Equation 5) evaluated at $e^{-\tilde{P}}.$