The Rank Ordering of Genotypic Fitness Values Predicts Genetic Constraint on Natural Selection on Landscapes Lacking Sign Epistasis

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ABSTRACT

Sewall Wright's genotypic fitness landscape makes explicit one mechanism by which epistasis for fitness can constrain evolution by natural selection. Wright distinguished between landscapes possessing multiple fitness peaks and those with only a single peak and emphasized that the former class imposes substantially greater constraint on natural selection. Here I present novel formalism that more finely partitions the universe of possible fitness landscapes on the basis of the rank ordering of their genotypic fitness values. In this report I focus on fitness landscapes lacking sign epistasis (i.e., landscapes that lack mutations the sign of whose fitness effect varies epistatically), which constitute a subset of Wright's single peaked landscapes. More than one fitness rank ordering lacking sign epistasis exists for L > 2 (where L is the number of interacting loci), and I find that a highly statistically significant effect exists between landscape membership in fitness rank-ordering partition and two different proxies for genetic constraint, even within this subset of landscapes. This statistical association is robust to population size, permitting general inferences about some of the characteristics of fitness rank orderings responsible for genetic constraint on natural selection.

NEARLY 75 years ago Sewall WRIGHT (1930, 1932) pointed out that fitness interactions between alleles at different loci, also called epistasis for fitness, could constrain evolution by natural selection since alleles may not confer an equal fitness effect in all genetic backgrounds visited by an evolving population. Genotype fitness landscapes (WRIGHT 1932; WEINREICH et al. 2005) represent the mapping from sequence space (MAYNARD SMITH 1970) to fitness and permit the explicit representation of all possible fitness interaction. (Note that other conceptions of the fitness landscape, e.g., mapping from allele frequency or phenotype to fitness, are less suitable for the problem at hand.) In this context the most familiar example of epistatic consequences for natural selection is the problem of population escape from a local peak (WRIGHT 1932). Nevertheless the fields of population genetics and molecular evolution have largely ignored the implications of epistasis for fitness on Wright's fitness landscape, perhaps because the neutral paradigm has focused attention away from the process of selective fixations in natural populations. More fundamentally the widely held assumption of linkage equilibrium (e.g., FISHER 1918) renders epistasis largely irrelevant since cooccurring alleles will not be reliably cotransmitted to offspring. Moreover, to develop a general treatment of epistasis, models must accommodate distinct fitness values for each genotype instead of for each allele, and so analytic treatment is difficult because the size of the problem grows exponentially with the number of loci. In this article I argue first that because evidence for adaptive evolution is becoming quite common and per-nucleotide rates of recombination are low, general evolutionary questions arising as a consequence of fitness interaction deserve theoretical attention. second I present a novel apparatus that partitions the space of all possible fitness landscapes into a finite number of equally sized fractions, offering some hope in the face of this very large combinatoric problem. Finally I show that this partitioning provides predictive and explanatory insight into some of the variation in evolutionary constraint imposed by alternative fitness landscapes.

KIMURA (1983) argued that few molecular fixation events were the consequence of positive (Darwinian) selection on the basis of two observations: the apparent regularity of the molecular clock (ZUCKERKANDL and PAULING 1965; KIMURA 1969; DICKERSON 1971) and the high average rate of amino acid fixation (KiMURA 1968), which appeared to approach or exceed theoretical limits imposed by Haldane's cost-of-selection calculation (HALDANE 1957). …