Results
Selection-mutation dynamics
Consider a fitness landscape \(\left(X,\ \Delta,\ \phi\right)\), consisting of a space of types \(X\), a mutation operator \(\Delta\) on \(X\) and a (Malthusian) fitness function \phi:X\rightarrow \mathbb{R}\(\phi:\ X\to\text{mathbb}\left\{R\right\}\) that assigns a reproductive rate to every possibly type. For genotypic landscapes, $X$ is a discrete graph, \textit{e.g.} a Hamming graph of $A$-ary sequences, and $\Delta$ is the corresponding graph Laplacian; for quantitative trait (phenotypic) landscapes, $X$ is a domain of $\mathbb{R}^d$ and $\Delta$ is a differential operator thereon, usually the Laplacian if mutational effects are sufficiently small and frequent.