  In this paper we introduce a multilocus diffusion model of a population of
$N$ haploid, asexually reproducing individuals. The model includes
parent-dependent mutation and interlocus selection, the latter limited to
pairwise relationships but among a large number of simultaneous loci. The
diffusion is expressed as a system of stochastic differential equations (SDEs)
that are coupled in the drift functions through a Shahshahani gradient-like
structure for interlocus selection. The system of SDEs is derived from a
sequence of Markov chains by weak convergence. We find the explicit stationary
(invariant) density by solving the corresponding stationary Fokker-Planck
equation under parent-independent mutation, i.e., Kingman's house-of-cards
mutation. The density formula enables us to readily construct families of
Wright-Fisher models corresponding to networks of loci.
