Evolutionary dynamics, evolutionary forces, and robustness: A nonequilibrium statistical mechanics perspective

Abstract

SignificanceEvolution through natural selection is an overwhelmingly complex process, and it is not surprising that theoretical approaches are strongly simplifying it. For instance, population genetics considers mainly dynamics of gene allele frequencies. Here, we develop a complementary approach to evolutionary dynamics based on three elements-organism reproduction, variations, and selection-that are essential for any evolutionary theory. By considering such general dynamics as a stochastic thermodynamic process, we clarify the nature and action of the evolutionary forces. We show that some of the forces cannot be described solely in terms of fitness landscapes. We also find that one force contribution can make organism reproduction insensitive (robust) to variations.

Keywords: Darwinian evolution; evolutionary dynamics; genetic robustness; phenotypic robustness.

Fig. 1.

Schematic representation ofthe evolutionary dynamics as modeled by the transition probabilities in Eq. 5. The symbols $°,\mathrm{\star },$ and $\square$ (circle, star, and square) represent different types of γ present at generation $\tau -1$, in a population of N = 7 organisms. As variants are generated—dashed lines—a new type appears, $△$. Continuous lines denote no variation. The variation probabilities ${\pi }_{\gamma \to \gamma \prime }$ as well as the probability that no variation occurs, $1-{\mu }_{\gamma }$, are also reported. Selection—finely dashed lines on the right—finally determines which types and in what amount make it to the next generation. The reproduction rate $f_{\gamma }$ determines the chances of being selected.

Fig. 2.

Pictorial illustration of sensitivity. Each square represents a type: fast-reproducing types are represented by large orange squares, whereas slow-reproducing ones are represented by small gray squares. Arrows identify possible variations, and their thickness reflects the probability of variations. Consider two types with high reproduction rate, central orange squares. (Left) A sensitive type is very likely to vary into a type with lower reproduction rate. (Right) A robust type varies with high probability into types with similarly high reproduction rate.