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Pleiotropy As a Factor Maintaining Genetic Variation in Quantitative Characters Under Stabilizing Selection

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Pleiotropy As a Factor Maintaining Genetic Variation in Quantitative Characters Under Stabilizing Selection Genet. Res. Camb. (1996), 68, pp. 65-73 With 1 text-figure Copyright © 1996 Cambridge University Press 65 Pleiotropy as a factor maintaining genetic variation in quantitative characters under stabilizing selection A. GIMELFARB Department of Ecology and Evolution, University of Chicago, Chicago, IL 60637, USA (Received 11 July 1995 and in revised form 16 January 1996) Summary A model of pleiotropy with TV diallelic loci contributing additively to N quantitative traits and stabilizing selection acting on each of the traits is considered. Every locus has a major contribution to one trait and a minor contribution to the rest of them, while every trait is controlled by one major locus and N—\ minor loci. It is demonstrated that a stable equilibrium with the allelic frequency equal to 0-5 in all A' loci can be maintained in such a model for a wide range of parameters. Such a ' totally polymorphic' equilibrium is maintained for practically any strength of selection and any recombination, if the relative contribution by a minor locus to a trait is less than 20 % of the contribution by a major locus. The dynamic behaviour of the model is shown to be quite complex with a possibility under sufficiently strong selection of multiple stable equilibria and positive linkage disequilibria between loci. It is also suggested that pleiotropy among loci controlling traits experiencing direct selection can be responsible for apparent selection on neutral traits also controlled by these loci. mutation-selection balance models, it remains un- 1. Introduction certain whether this mechanism can account for the The maintenance of genetic variation under natural amounts of genetic variation in quantitative characters selection in multilocus genetic systems controlling that are observed in natural populations (Barton & quantitative traits is an important and long-standing Turelli, 1989; Keightley & Hill, 1990). problem in population biology. Given that phenotypic In addition to models of natural selection acting variation is practically always reduced by stabilizing directly on the character of interest, models have been selection (Shnoll & Kondrashov, 1993), what bio- proposed in which genetic variation for a given trait is logical mechanisms can counterbalance the effect of a result of polymorphisms in the loci controlling the selection and be responsible for the maintenance of trait, but the forces maintaining the polymorphisms genetic variation in natural populations? For some are not related to the trait itself. The polymorphisms time the field of quantitative genetics was dominated can be maintained due to either overdominance for by polygenic models assuming that a quantitative fitness (Robertson, 1956; Gillespie, 1984; Barton, character is controlled by many loci contributing 1990), or selection against unconditionally deleterious additively and equally to the trait. It has been mutations (Barton, 1990; Keightley & Hill, 1990; demonstrated for such models that, if selection is Kondrashov & Turelli, 1992), or epistatic viability weak relative to recombination, no genetic variation selection (Gavrilets & De Jong, 1993). Thus, the (except for a possible polymorphism in just one locus) character itself is neutral, but differences in fitness can be maintained under stabilizing selection without between individuals with differing values of the trait an input of new variation (Wright, 1935; Robertson, give an appearance of stabilizing selection on the trait. 1956; Lewontin, 1964; Barton, 1986). It is important, however, that, while there is ex- Models have been proposed in which mutations perimental evidence of unconditionally deleterious provide new variation, and genetic variation in a mutations, overdominance for fitness or the particular population is maintained by the balance between forms of epistasis for viability are just postulated in stabilizing selection and mutations (Lande, 1975; the above models, but no known developmental or Turelli, 1984; Barton, 1986; Slatkin, 1987; Burger, hereditary mechanisms have been suggested which 1988; Bulmer, 1989). In spite of an intensive study of would produce these phenomena. On the other hand, Downloaded from https://www.cambridge.org/core. IP address: 170.106.202.226, on 01 Oct 2021 at 23:04:46, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0016672300033899 A. Gimelfarb 66 while the balance between deleterious mutations and multicharacter systems, and have concluded that, if selection can explain the maintenance of polymorp- selection is weak relative to recombination, the number hisms in mutating loci, it cannot explain the evolution of loci maintaining a stable polymorphism cannot be of phenotypes, and, hence, different biological mech- greater than the number of characters they control. A anisms are supposed to be responsible for the stable polymorphism can, however, be maintained in maintenance of genetic variation and for phenotypic more loci than the number of traits they control, if evolution, yet there is no evidence of this. Also, while selection is sufficiently strong (Gavrilets & Hastings, it is conceivable that some biological traits are neutral 1994a). Indeed, a model of several loci contributing with respect to natural selection, there must also be additively to two traits with half the loci contributing traits (e.g. obvious adaptations) experiencing direct, similarly to both traits and the other half contributing and possibly quite strong, natural selection. Models antagonistically was shown to maintain a stable are needed, therefore, that can explain the main- polymorphism in as many as six (Gimelfarb, 1992) tenance of genetic variation under selection acting and eight (Gavrilets & Hastings, 1994a) loci. directly on quantitative traits. Even if as many loci are maintained polymorphic as It has become quite evident by now that genetic the number of traits they control, pleiotropy can still variation can be maintained in a multilocus system be an important factor responsible for the maintenance controlling a quantitative trait, even if it is under of genetic variation in natural populations, since the direct stabilizing selection, if some of the assumptions number of pleiotropically related traits can be po- of the polygenic model are relaxed. This was shown tentially quite large. In this paper, we shall investigate for unequal effects of loci (Gale & Kearsey, 1968; the maintenance of polymorphisms in a model of Kearsey & Gale, 1968; Nagylaki, 1989; Gavrilets & pleiotropy with N loci controlling N quantitative Hastings, 1993, 1994a, b), for selection strong relative traits. The model is inspired by experimental evidence to recombination (Gavrilets & Hastings, 1993, 1994a, that not all loci controlling a trait contribute equally b; Gimelfarb, 1995), for dominance (Lewontin, 1964) to the trait (Edwards et al 1987; Paterson et al. 1990; and for epistasis (Gimelfarb, 1989). Mackay et al. 1992). The majority of quantitative In spite of the scarcity of direct experimental traits whose genetic basis has been investigated appear evidence of pleiotropy among quantitative traits, it is to be ' under control of a few major genes supported supposed to be ubiquitous based on the widespread by numerous genes with smaller effects' (Shrimpton & genetic correlations between different traits (Falconer, Robertson, 1988). 1989), on the complexity and interconnection of biochemical processes underlying the development of 2. The model quantitative traits (Wright, 1968; Barton, 1990) and on the general philosophical consequence of an It is assumed that N diallelic loci contribute additively organism being 'a unity of an infinite number of traits to N quantitative characters. Each locus has a major and finite number of genes' (Serebrovsky, 1973). effect on one of the characters and a minor effect on Recently, evidence of pleiotropy among quantitative the rest of them. On the other hand, each character is traits has been obtained experimentally based on controlled by one major locus and by TV—1 minor spontaneous and P-element induced mutations loci. The contribution to any trait by one of the alleles (Mackay et al. 1992; Santiago et al. 1992; Clark et al. in each locus is zero. The contribution by the other 1995). The effect of pleiotropy on genetic correlations allele depends on whether the locus is major or minor between quantitative traits has been studied quite for the trait. If Lt is a minor locus for a trait Xs{i =t= f), extensively, particularly in mutation-selection balance its contribution is assumed to be a fraction, bip of the models (Lande, 1980; Turelli, 1985; Wagner, 1989; contribution to the trait by the major locus, L}, i.e. Slatkin & Frank, 1990). Relatively little work has major and minor loci contribute to a trait in a been done, however, investigating pleiotropy among proportion \:bir It is also assumed without loss of loci controlling several quantitative traits as a potential generality that the minimum and the maximum of any factor directly responsible for the maintenance of trait are 0 and 1, respectively. Hence, the actual allelic genetic variation in multilocus systems under natural contributions to a trait X} are selection. Rose (1982) has shown that a stable a} = 0-5/B} (major locus), (1 a) polymorphism can be maintained in two loci having /? = 0-5b /B (minor locus), (1 b) antagonistic pleiotropic effects on components of 0 t] } fitness. Gimelfarb (1986) proposed a model of two loci where Bs = 1 +'Llc^jbkj.
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