Do amplifiers of selection maximise average fitness?

Abstract

Evolutionary dynamics on graphs has remarkable features: For example, it has been shown that amplifiers of selection exist that - compared to an unstructured population - increase the fixation probability of advantageous mutations, while they decrease the fixation probability of disadvantageous mutations. So far, the theoretical literature has focused on the case of a single mutant entering a graph structured population, asking how the graph affects the probability that a mutant takes over a population and the time until this typically happens. For continuously evolving systems, the more relevant case is when mutants constantly arise in an evolving population. Typically, such mutations occur with a small probability during reproduction events. We thus focus on the low mutation rate limit. The probability distribution for the fitness in this process converges to a steady-state at long times. Intuitively, amplifiers of selection are expected to increase the populations mean fitness in the steady-state. Similarly, suppressors of selection are expected to decrease the populations mean fitness in the steady-state. However, we show that another category of graphs, called suppressor of fixation, can attain the highest population mean fitness. The key reason behind this is their ability to efficiently reject deleterious mutants. This illustrates the importance of the deleterious mutant regime for the long-term evolutionary dynamics, something that seems to have been overlooked in the literature so far.