Graph-structured populations elucidate the role of deleterious mutations in long-term evolution

Birth-death models have long been employed to understand the interplay of genetic drift and natural selection. While well-mixed populations remain unaffected by the choice of replacement rules, the evolutionary outcomes in spatially structured populations are strongly impacted by this choice. Moving parent individuals to vacant sites gives rise to new update rules, leading to new fixation categories for spatial graphs. We discover a new category of graphs, amplifiers of fixation, where a structure has a higher probability of fixation for mutants than the well-mixed population, regardless of their fitness value. Under death-Birth updating with parents moving to vacant sites, the star graph is an amplifier of fixation. For very large population sizes, the probability to fix deleterious mutants on the star graph converges to a non-zero value, in contrast to the result from well-mixed populations where the probability goes to zero. Additionally, most random graphs are amplifiers of fixation for death-Birth updating, with parent individuals replacing dead individuals. Conversely, most random graphs are suppressors of fixation- graphs with lower fixation probability for mutants regardless of their fitnesses- for Birth-death updating with offspring replacing dead individuals. When subjected to long-term evolution, amplifiers of fixation, despite being more efficient at fixing beneficial mutants, attain lower fitness than the well-mixed population, whereas suppressors attain higher fitness despite their inferior ability to fix beneficial mutants. These surprising findings can be explained by their deleterious mutant regime. Therefore, the deleterious mutant regime can be as crucial as the beneficial mutant regime for adaptive evolution.