Modelling the evolution and expected lifetime of a deme’s principal gene sequence

The principal gene sequence (PGS), defined as the most common gene sequence in a deme, is replaced over time because new gene sequences are created and compete with the current PGS, and a small fraction become PGSs. We have developed a set of coupled difference equations to represent an ensemble of demes, in which new gene sequences are introduced via chromosomal inversions. The set of equations used to calculate the expected lifetime of an existing PGS include inversion size and rate, recombination rate and deme size. Inversion rate and deme size effects are highlighted in this work. Our results compare favourably with a cellular automaton-based representation of a deme.