multiple loci - senecio7の日記

Bürger R 2020 Multilocus population-genetic theory. Theor Popul Biol 133:40-48.

commentary
in linkage equilibrium (LE), allele frequencies at different loci do not change independently
the direction and intensity of selection on a particular locus generally depend on the allele-frequency distribution of its genetic background

I focus on deterministic multilocus models
the first two-locus model with selection and explicit recombination was designed by Kimura (1956), who analyzed the conjecture by Fisher (1930) that selection can lead to tighter linkage
the general two-locus two-allele (TLTA) model for the dynamics under selection and recombination was derived by Lewontin and Kojima (1960)
also the most important ingredients, such as LD, LE, and epistasis are defined for the TLTA case

in the absence of selection, global convergence to LE was proved much earlier by Geiringer (1944)

under the assumption of LE, i.e., D(t) ≡ 0, which yields the gradient-like selection dynamics for two independent loci, coupled only by mean fitness, one equilibrium configuration (in the sense of topological equivalence) may admit several topologically nonequivalent flows

an important dynamical property of single-locus systems is that mean fitness is nondecreasing along trajectories and constant only at equilibrium
this is a special case of the classical interpretation of Fisher's (1930) Fundamental Theorem of Natural Selection
for multilocus systems, mean fitness increases if loci contribute additively to fitness
with epistasis mean fitness may decrease
for weak selection or weak epistasis, LD decays rapidly to small values as time proceeds
once this so-called state of quasi-linkage equilibrium has been reached, mean fitness may increase for a long time
all linkage disequilibria decay rapidly to order s
their change per generation is only O(s²)
the per-generation change ΔW of mean fitness is, to leading order in s, W⁻¹V_g
V_g is the additive genetic variance in fitness
Fisher strongly opposed the interpretation of his Fundamental Theorem of Natural Selection (Fisher, 1930) that selection acts to maximize mean fitness
an interpretation that has been prevalent for a long time
Ewens and Lessard (2015) discuss interpretations of the Fundamental Theorem that indeed are very general (by admitting multiple loci, epistasis, strong selection, and also nonrandom mating), but that concern certain partial changes in mean fitness

Turelli (1984) refuted Lande's (1975) claim that multilocus mutation-selection balance may provide a universal explanation for a large fraction of the empirically observed levels of quantitative genetic variation
this initiated a controversy about the relevance of mutation-selection balance as an explanation for genetic variation in quantitative traits

my personal entry into population genetics was through Feldman and Karlin (1971)
the first population genetics paper I studied

among the most interesting phenomena, both for empiricists and for theoreticians, are clines in phenotype or genotype frequencies
two- or multilocus studies, initiated by Slatkin (1975) for spatially varying selection and by Barton (1983) for hybrid zones, are quite rare, presumably because of the severe technical difficulties that arise
the multilocus work on clines has been applied successfully to advance our understanding of natural hybrid zones and the underlying genomics

a proper treatment of these topics as well as of the adaptation of quantitative traits, including the detection of the resulting polygenic footprints, must ultimately be based on stochastic multilocus models
Höllinger et al. (2019) derived the stochastic patterns of allele-frequency change at individual loci in a finite population
this work initiates a synthesis between the population-genetic and the quantitative-genetic views of adaptation
multilocus models including the effects of drift, especially on neutral markers, are increasingly often combined with genomic data