“The Theory was Beautiful Indeed”: Rise, Fall and Circulation of Maximizing Methods in Population Genetics (1930–1980)

Abstract

Describing the theoretical population geneticists of the 1960s, Joseph Felsenstein reminisced: "our central obsession was finding out what function evolution would try to maximize. Population geneticists used to think, following Sewall Wright, that mean relative fitness, W, would be maximized by natural selection" (Felsenstein 2000). The present paper describes the genesis, diffusion and fall of this "obsession", by giving a biography of the mean fitness function in population genetics. This modeling method devised by Sewall Wright in the 1930s found its heyday in the late 1950s and early 1960s, in the wake of Motoo Kimura's and Richard Lewontin's works. It seemed a reliable guide in the mathematical study of deterministic effects (the study of natural selection in populations of infinite size, with no drift), leading to powerful generalizations presenting law-like properties. Progress in population genetics theory, it then seemed, would come from the application of this method to the study of systems with several genes. This ambition came to a halt in the context of the influential objections made by the Australian mathematician Patrick Moran in 1963. These objections triggered a controversy between mathematically- and biologically-inclined geneticists, with affected both the formal standards and the aims of population genetics as a science. Over the course of the 1960s, the mean fitness method withered with the ambition of developing the deterministic theory. The mathematical theory became increasingly complex. Kimura re-focused his modeling work on the theory of random processes; as a result of his computer simulations, Lewontin became the staunchest critic of maximizing principles in evolutionary biology. The mean fitness method then migrated to other research areas, being refashioned and used in evolutionary quantitative genetics and behavioral ecology.

How frequency‐dependent selection affects population fitness, maladaptation and evolutionary rescue

“…In this sense, FD selection is one of several forms of adaptive evolution that can, in principle, reduce population fitness (Grodwohl, 2017;Leigh, 1977;Moran, 1963;Rankin, Bargum, & Kokko, 2007).…”

“…Rather, FD selection can, in some cases, drive evolutionary reductions in population fitness (Wright, 1942). This insight of Wright's is sometimes overlooked, given his tendency to emphasize fitness maximization in other contexts of natural selection (reviewed in Li, 1955;Grodwohl, 2017).…”

“…The relationship between population mean fitness, natural selection and the genetic composition of populations is difficult to predict when selection is frequency‐dependent, which has historically been a source of controversy underlying debates about the utility of the adaptive landscape metaphor and the question if selection maximizes population fitness (Fear & Price, ; Grodwohl, ; Kaplan, ; Okasha, ; Pigliucci, ; Rice, ; Svensson, ; Svensson & Calsbeek, ). Here, we develop a quantitative genetic model that is inspired by adaptive landscape theory and the existence of adaptive peaks, which has empirically turned out to be a useful and successful approach (Arnold, Pfrender, & Jones, ; Chenoweth, Hunt, & Rundle, ; Svensson & Calsbeek, ), although we are aware of the criticisms from some philosophers and theoretical population geneticists who have questioned the idea of fitness maximization behind adaptive landscapes (Grodwohl, ; Kaplan, ; Moran, ; Okasha, ; Pigliucci, ). We ask the question: To what extent does frequency‐dependent selection mediate increased or decreased population mean fitness, particularly under changing conditions?…”

Fisher’s Fundamental Theorem of Natural Selection Isn’t Fundamental After All

“…Further, apart from even adding mutations, Patrick Moran and Richard Lewontin demonstrated that fitness is not guaranteed to maximize if epistasis and gene linkage are modeled. Grodwohl characterized these shocking mathematical developments as "The Rise and Fall of Fitness Maximization" (Grodwohl, 2016).…”

The stagnation paradox: the ever-improving but (more or less) stationary population fitness

“…Perhaps it is too optimistic to assume that an overlap of the chosen trait would have been sufficient to spark crossfertilization of these fields: quantitative genetics, with its interest in predicting ongoing microevolution, and optimization approaches to life-history theory, which has the goal of trying to predict the precise location of the ultimate fitness peak, are to this day not cross-referencing each other very frequently. Attempts to point out equivalences and relationships between them exist [25][26][27][28][29][30][31][32][33] but for some reason do not appear to build much information flow between the mainstream currents of each field. As is, the insights in [20] have had a major impact on life-history theory, less so on the continued discussion that has Fisher [5] and Cooke et al [15] at its origin.…”