THE EFFECT OF INITIAL PLACEMENT OF MUTANT IN SUBDIVIDED POPULATION ON FIXATION PROBABILITY AND TIME

Evolutionary graph theory explores how population structure influences evolutionary dynamics. This paper examines the impact of a simple subdivided population structure on mutant fixation probability and time under the Moran Birth–death process with constant fitness. We model the population as two fully connected subpopulations (cliques) connected by a few links. Using an analytical Markov-chain approach complemented by Monte Carlo simulations, we investigate how the size of the initial clique, where the mutant first appears, affects its eventual fixation outcomes. Our results demonstrate that initiating the process in a bigger clique enhances fixation probability and acts as an amplifier of selection compared to a well-mixed population, while a smaller starting clique suppresses selection. Furthermore, we observe that for small cliques, increased fitness reduces unconditional fixation time, whereas for larger cliques, it prolongs it. Conditional fixation time increases with starting clique size until reaching a critical threshold, after which it decreases. This critical size varies depending on the fitness value. Overall, we find that the combination of fitness level and starting clique size plays a crucial role in maximizing conditional fixation time.