The mists of the adaptive fog

Richard Lawler pointed me to a new paper by Sean Rice, A stochastic version of the Price equation reveals the interplay of deterministic and stochastic processes in evolution. The Price Equation is the generalization of selective evolutionary dynamics by the amateur evolutionary biologist George Price which so impressed W. D. Hamilton. But as Rice notes it only captures a slice of the various parameters which influence evolutionary processes. Like some other papers I've pointed too Rice presents some relatively counter-intuitive results, or at least results which confound our general expectations, by scratching beyond the surface of the assumptions of conventional population genetic models:

I present a general equation for directional evolutionary change that incorporates both deterministic and stochastic processes and applies to any evolving system. This is essentially a stochastic version of the Price equation, but it is derived independently and contains terms with no analog in Price's formulation. This equation shows that the effects of selection are actually amplified by random variation in fitness. It also generalizes the known tendency of populations to be pulled towards phenotypes with minimum variance in fitness, and shows that this is matched by a tendency to be pulled towards phenotypes with maximum positive asymmetry in fitness. This equation also contains a term, having no analog in the Price equation, that captures cases in which the fitness of parents has a direct effect on the phenotype of their offspring.

Directional evolution is influenced by the entire distribution of individual fitness, not just the mean and variance. Though all moments of individuals' fitness distributions contribute to evolutionary change, the ways that they do so follow some general rules. These rules are invisible to the Price equation because it describes evolution retrospectively. An equally general prospective evolution equation compliments the Price equation and shows that the influence of stochastic processes on directional evolution is more diverse than has generally been recognized.

It is by going beyond the first two moments that the peculiar results emerge. This particular model has implications for our visual images of evolutionary landscapes:

The more appropriate visual image would be an adaptive fog, with variable density and thickness corresponding to different fitness distributions for different phenotypes. The dynamics of evolution through such a fog are described by Equations 1 and 2, and are determined not only by the slope of expected mean fitness...but also by variations in the thickness of the fog and by population size...Unfortunately, this image lacks the visual simplicity of the adaptive landscape, which remains a very useful concept but should be recognized as an approximation based on the assumption that fitness values are fixed.

The math isn't really that tricky, but tedious. I won't try to summarize it after one read through, though the paper is open access, so you're welcome to dive in yourself. I am more interested in the fact the author argues that traditional experiments might not give us true insight into how selection operates because of artificial constraints; e.g., keeping generational size constant across cohorts. We're a long way from R. A. Fisher's thermodynamics of evolutionary theory....