Moderate amounts of epistasis are not evolutionarily stable in small populations

Abstract

<jats:title>Abstract</jats:title><jats:p>High mutation rates select for the evolution of mutational robustness where populations inhabit flat fitness peaks with little epistasis, protecting them from lethal mutagenesis. Recent evidence suggests that a different effect protects small populations from extinction via the accumulation of deleterious mutations. In drift robustness, populations tend to occupy peaks with steep flanks and positive epistasis between mutations. However, it is not known what happens when mutation rates are high and population sizes are small at the same time. Using a simple fitness model with variable epistasis, we show that the equilibrium fitness has a minimum as a function of the parameter that tunes epistasis, implying that this critical point is an unstable fixed point for evolutionary trajectories. In agent-based simulations of evolution at finite mutation rate, we demonstrate that when mutations can change epistasis, trajectories with a subcritical value of epistasis evolve to decrease epistasis, while those with supercritical initial points evolve towards higher epistasis. These two fixed points can be identified with mutational and drift robustness, respectively.</jats:p>

Evolutionary models predict potential mechanisms of escape from mutational meltdown

“…At the same time, the altered selection coefficients of all mutations change the eco-evolutionary dynamics such that Muller’s ratchet becomes less severe and the population can cope with the increased mutation pressure. Sydykova et al (53) have recently explored a related model of tunable epistasis, in which they found that epistasis can evolve in different directions under high mutation rates. Whether weakening the effects of deleterious mutations can lead to survival has been modeled in the research area of quasi-species theory, where a so-called “error threshold” determines the condition in which mutation overwhelms selection (54, 55, e.g., for finite populations,).…”