# SEWALL WRIGHT, THE ADAPTIVE LANDSCAPE, AND WHAT WE DON'T KNOW (page 2)

*Evolution in Mendelian Populations*was published in

*Genetics*. This important paper was one of a few works in the early 1930’s that brought together Mendelian genetics and natural selection in a rigorous mathematical way.

*The Genetical Theory of Natural Selection*to review for the

*Journal of Heredity*. This book touched on many of the same topics as Wright’s paper, combining Mendelian genetics and evolutionary theory with rigorous mathematics.

*Genetics paper*, Wright begins to work out a two-loci case, but notes that "the frequency of A depends on the frequency and selection of B, becoming independent only if s

_{ab}= s

_{a}+ s

_{b}." Here s

_{a}is the selection coefficient for a change

*a*, s

_{b}is the selection coefficient for a change

*b*, and s

_{ab}is the selection coefficient for both changes together. Wright goes on to say "It does not seem profitable to pursue this subject further for the purpose of the present paper, since in the general case, each selection coefficient is a complicated function of the entire system of gene frequencies and can only be dealt with qualitatively." This is precisely the epistemological gap that Wright, Fisher, Haldane, and others stood at the edge of in 1932. Their mathematics could describe evolution in "a given population at a given moment," but they could not describe long-term dynamics in light of the "epistatic relationships" between genes, which is exactly captured by Wright's rejection of the assumption s

_{ab}= s

_{a}+ s

_{b}.

### (Frank’s Perspective On) Fisher’s Fundamental Theorem

*at any moment in time*" (Frank 2012, emphasis is mine). But while Fisher's mathematics theoretically considers all of the interactions present at one specific moment in a population, it makes no comment on genetic interactions that are one or several mutational steps away from individuals in the population. This means that without an explicit model for the structure of genetic interactions, the fundamental theorem can only comment on what is happening

*right now*, not what will happen once the first new genetic change takes place. Frank contends that Wright and many others have repeatedly failed to understand that the fundamental theorem "is clearly designed to express laws rather than to calculate long-term dynamics." More generally, Frank writes,

### Wright’s recognizes the gap, then leaps over it while people aren’t looking

*The Genetical Theory of Natural Selection*, Wright attempts to explain how the ubiquity of gene interactions leads to his theory. This is where the first reference to what would become known as the adaptive landscape emerges. He writes:

**long-term evolutionary dynamics within a system of interacting genetic factors**. The concept sits at the tense edge between quantitative analysis and qualitative interpretation, but at least in its first conception, it clearly falls on the qualitative side of the divide. As Serrelli writes,