The effect of initial placement of mutant in subdivided population on fixation time and probability

Evolutionary graph theory investigates how population structure changes evolutionary dynamics. In this paper, we examine how the structure of a subdivided population impacts mutant fixation probability and time under the Moran Birth-death process with constant fitness. Specifically, we model the population as two fully connected subpopulations (cliques) linked by a few links. Using an analytical Markov-chain approach supplemented by Monte Carlo simulations, we explore how the size of the starting clique where the initial mutant arises influences its eventual fixation outcomes. We demonstrate that initiating the process in a smaller clique boosts fixation probability and acts as an amplifier of selection compared to a well-mixed population while a bigger starting clique acts as a suppressor of selection. Also, we show that both unconditional and conditional fixation time are affected by the starting clique size and fitness value. For small cliques, increased fitness reduces unconditional fixation time, whereas, for larger cliques, greater fitness prolongs it. Additionally, conditional fixation time grows with increased starting clique size until a critical size and then decreases. This critical size is different depending on fitness value. In general, a combination of fitness level and starting clique size serves to maximize the conditional fixation time.