Sewall Wright and the factors of evolution

Last year around this time, I noted that I happened to be reading Sewall Wright during a TV episode that mentioned Sewall Wright. It's not so unusual for me to be reading Wright, but in this instance I was directed to something I hadn't paid much attention to before.

I'm reminded of the article today because I talked about its basic theme during a lecture, and also because I'm writing up some stuff about effective population size, a concept attributed to Wright.

John Gillespie's 2000 article, "Genetic drift in an infinite population," introduced the concept of pseudohitchhiking, or "genetic draft." An important thing about pseudohitchhiking is that it behaves as a stochastic force very much like genetic drift. The formal difference between the two is that the stochasticity of a pseudohitchhiking locus depends on recombination and selection, while genetic drift depends on neither. Gillespie's paper considered to what extent pseudohitchhiking led to similar predictions for the change in allele frequency. This is a connection he made more explicit in his 2001 article, "Is the population size of a species relevant to its evolution?" by drawing out the first and second moments of neutral evolution under both drift and pseudohitchhiking. For drift, these are (Gillespie 2001:2161, eqs. 1 and 2):

First and second moments of neutral evolution

The first equation means that the expected change in allele frequency under drift is zero. This is otherwise known as the deterministic component. Under selection, the expected change in allele frequency depends on the current frequency and the fitnesses of genotypes. Under drift all genotypes have equal fitnesses and the only possible changes are stochastic, therefore the expected change is zero irrespective of the current allele frequency.

The second equation describes the variance of the change in allele frequency. You might think this variance would be zero, since the expected amount of change is zero. But the variance represents the magnitude of possible changes from the expected value due to random sampling a finite number of individuals. This is the stochastic component of allele frequency evolution.

The magnitude of these stochastic changes is directly proportional to heterozygosity and inversely proportional to population size. Larger populations have smaller potential changes in allele frequency due to random sampling. Intermediate allele frequencies (near 50 percent) can change more due to random sampling than high or low frequencies. These relations are embodied by the second equation above -- and if you're keeping score, this second equation is used in defining the variance effective population size.

The two equations help to frame the discussion of effective population size. The size of a population is relevant to its evolution only under certain contexts. If the deterministic change in allele frequencies is the dominant pattern of evolution, then population size is irrelevant to the outcome. In contrast, if random sampling is the most important cause of allele frequency changes, then the outcome (fixation or loss) may be indeterminate, but the population size is very important to the rate of the process.

As Gillespie's article makes clear, genetic drift is not the only stochastic process affecting the evolution of allele frequencies. His mechanism of pseudohitchhiking is one. And there are many others -- all non-deterministic in that their outcomes cannot be predicted from the frequencies of alleles or their phenotypic effects. The rate of these processes depends on different things: some internal to the population and some external. Genetic drift depends on the size of the population and its allele frequencies; genetic draft depends on the rate of recombination, the rate of generation of new favorable mutations, and the relative fitnesses of these mutations. Environmental stochasticity depends on the demography of other species as well as physical factors such as water availability and the weather.

Sewall Wright tried to categorize these stochastic processes, as well as the deterministic ones, making a catalog of of the processes that can cause evolutionary changes. Those of us who teach intro classes are well accustomed to talking about the "forces of evolution" -- selection, drift, gene flow, and mutation. These are important because they constitute different patterns of change in allele frequencies. But Sewall Wright went beyond this four-fold categorization, linking different aspects of these patterns with their stochastic and deterministic effects.

First, he defines the problem in terms of allele frequencies:

As is now generally appreciated, the seemingly very diverse factors that must be taken into account in population genetics can best be brought under a common viewpoint by considering their effects on gene frequency (Wright 1955:17).

Then he provides a full breakdown of different patterns of evolutionary change, or "modes" of change of the gene frequencies in a population:

Modes of Change of Gene Frequency
I. Immediate
1. Directed processes (mean change in allele frequencies determinate in principle)
a. Recurrent mutation
b. Recurrent immigration and crossbreeding
c. Mass selection
2. Random processes (variance in change in allele frequencies determinate in principle)
a. Fluctuations in mutation
b. Fluctuations in immigration
c. Fluctuations in selection
d. Accidents of sampling
3. Unique events
a. Novel favorable mutation
b. Unique hybridization
c. Swamping by mass immigration
d. Unique selective incident
e. Unique reduction in numbers
II. Secular change in system of coefficients
1. From internal causes (control by new adaptive peak)
2. From changes in environment
a. In home territory
b. In colonized territory

This breakdown clearly separates the deterministic factors of evolution (here, category 1, "Directed processes") from the stochastic factors (everything else). I find a couple of things very interesting from this perspective:

1. Wright makes a distinction between recurrent mutation, whose effect is more or less deterministic on allele frequencies, and "novel favorable mutation", each of which is a random, unlikely event. Both are distinguished from "fluctuations in mutation," which might be described as an intermediate between the two -- although writing in 1955 it is plausible that Wright may actually have meant alterations in the propensity toward mutations due to variation in radiational or chemical processes. This is one indication of the difference between Wright and Fisher, who felt that novel mutations might become more or less predictable in large populations.

I also noticed how many of Wright's "unique events" have been marshalled by one or another researcher to explain human evolution.

Another point of interest, reflecting the several instances of interesting evolutionary trends under domestication that I've linked this week, is Wright's accommodation of artificial selection within this scheme:

It may be noted here that artificial selection also imposes a new system of peaks toward one of which mass selection may be expected to drive the population rapidly. Since the peak attained is not a natural one, progress is almost inevitably at the expense of fecundity and viability. On relaxation, the population may be expected to return toward the original peak, or to another, and usually lower one, if the artificial selection has driven it across what was naturally a valley (Wright 1955:17).

This should be amended, in that selection comes at the expense of fecundity and viability in the previous environment, not the new artificially selected one. But the prediction that artificial selection should decrease fitness in the species' natural environment comes straightforwardly considering the nature of selection as a deterministic force. If the species was initially well adapted to its natural environment, any changes resulting from artificial selection would likely make it worse, not better.

Wright's well-known idea was that the stochastic factors might play an important role allowing a population to explore the adaptive landscape. In his "shifting balance" formulation, the division of an abundant species into many small subpopulations tends to maximize the species' ability to evolve toward higher fitness peaks, because a small group might have a fortuitous combination of alleles allowing it to move to a higher fitness peak. This model has been controversial even up to the present day, because of our lack of knowledge about the characteristics of "fitness landscapes".

But it is worth pointing out Wright's definition of the stochastic factors here, each of which might operate in conjunction with genetic drift in the shifting balance model. It is clear from the list that the balance between these different factors might itself change over time -- for instance, in our acceleration idea, the incidence of novel mutations is greatly accelerated in a growing population, ultimately increasing the scope of the deterministic process.

References:

Gillespie JH. 2000. Genetic drift in an infinite population: the pseudohitchhiking model. Genetics 155:909-919.

Gillespie JH. 2001. Is the population size of a species relevant to its evolution? Evolution 55:2161-2169.

Wright S. 1955. Classification of the factors of evolution. Cold Spring Harbor Symp Quant Biol 20:16-24.