Suppressors of fixation can increase average fitness beyond amplifiers of selection

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 that 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 population’s mean fitness in the steady state. Similarly, suppressors of selection are expected to decrease the population’s mean fitness in the steady state. However, we show that another set of graphs, called suppressors 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.

Theoretical understanding of evolutionary dynamics on inhomogeneous networks

“…However, all these networks amplify the selection of mutations at the cost of significantly slowing down the fixation dynamics, i.e., the fixation times in these systems are always larger than the fixation times for similar-size homogeneous well-mixed populations [28]. Although the fixation processes for inhomogeneous populations have been intensively studied in recent years [3, 5, 6, 16, 21, 27, 29], there is still no clear understanding on the microscopic origin of selection amplifications, the connections to the underlying network topology, and the correlations between the fixation probabilities and the fixation times.…”

Fixation dynamics on hypergraphs

“…The fixation time for hypergraphs including the comparison with the case of conventional networks warrants future work. Other topics for further investigations include the effects of different initial conditions [7,32,58,59], mathematical analyses of other symmetric hypergraphs, weak selection expansion of fixation probability [22] in the case of hypergraphs, amplification and suppression of natural selection in the mutation-selection equilibrium under a small mutation rate [60], and fixation probability of cooperation in evolutionary game dynamics on hypergraphs [15,16]. Focusing on fixation of a mutant (or resident) type in general allows us to use Markov chain theory to reach various mathematical insights.…”

Categorizing update mechanisms for graph-structured metapopulations

“…In graphs of individuals, three main events influence the evolution of a population: birth, mutation and death. In the long run, a mutation-selection balance is reached [8,[18][19][20][21]. Typically, the focus is on the low mutation regime in which the system reaches fixation or extinction of the mutant before the next mutation occurs.…”