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Gupta M, Prasad NG, Dey S, Joshi A, Vidya T NC. Niche construction in evolutionary theory: the construction of an academic niche? J Genet 2019; 96:491-504. [PMID: 28761012 DOI: 10.1007/s12041-017-0787-6] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Affiliation(s)
- Manan Gupta
- Evolutionary Biology Laboratory, Evolutionary and Organismal Biology Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bengaluru 560 064, India.
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2
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Mopper S, Mitton JB, Whitham TG, Cobb NS, Christensen KM. GENETIC DIFFERENTIATION AND HETEROZYGOSITY IN PINYON PINE ASSOCIATED WITH RESISTANCE TO HERBIVORY AND ENVIRONMENTAL STRESS. Evolution 2017; 45:989-999. [DOI: 10.1111/j.1558-5646.1991.tb04365.x] [Citation(s) in RCA: 54] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
Affiliation(s)
- Susan Mopper
- Department of Biological Sciences Northern Arizona University Flagstaff Arizona 86011 USA
| | - Jeffry B. Mitton
- Department of Biological Sciences Northern Arizona University Flagstaff Arizona 86011 USA
| | - Thomas G. Whitham
- Department of Biological Sciences Northern Arizona University Flagstaff Arizona 86011 USA
| | - Neil S. Cobb
- Department of Biological Sciences Northern Arizona University Flagstaff Arizona 86011 USA
| | - Kerry M. Christensen
- Department of Biological Sciences Northern Arizona University Flagstaff Arizona 86011 USA
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3
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Otto SP. ON EVOLUTION UNDER SEXUAL AND VIABILITY SELECTION: A TWO‐LOCUS DIPLOID MODEL. Evolution 2017; 45:1443-1457. [DOI: 10.1111/j.1558-5646.1991.tb02647.x] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/1990] [Accepted: 01/17/1991] [Indexed: 11/26/2022]
Affiliation(s)
- Sarah Perin Otto
- Department of Biological Sciences Stanford University Stanford CA 94305 USA
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Smouse PE. THE FITNESS CONSEQUENCES OF MULTIPLE‐LOCUS HETEROZYGOSITY UNDER THE MULTIPLICATIVE OVERDOMINANCE AND INBREEDING DEPRESSION MODELS. Evolution 2017; 40:946-957. [DOI: 10.1111/j.1558-5646.1986.tb00563.x] [Citation(s) in RCA: 41] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/1985] [Accepted: 06/03/1986] [Indexed: 11/29/2022]
Affiliation(s)
- Peter E. Smouse
- Department of Human Genetics University of Michigan Ann Arbor MI 48109
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5
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Karlin S, Liberman U. A natural class of multilocus recombination processes and related measures of crossover interference. ADV APPL PROBAB 2016. [DOI: 10.2307/1426950] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
Various classifications and representations of multilocus recombination structures are delimited. A class of recombination distributions called the count–location chiasma process is parametrized by a distribution of the number of crossover events and for such crossover events by a conditional distribution of crossover locations. A number of properties and examples of this recombination structure are developed connecting orderings among the recombination mapping functions and the nature of interference.
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Abstract
The breeder’s equation is a cornerstone of quantitative genetics, widely used in evolutionary modeling. Noting the mean phenotype in parental, selected parents, and the progeny by E(Z0), E(ZW), and E(Z1), this equation relates response to selection R = E(Z1) − E(Z0) to the selection differential S = E(ZW) − E(Z0) through a simple proportionality relation R = h2S, where the heritability coefficient h2 is a simple function of genotype and environment factors variance. The validity of this relation relies strongly on the normal (Gaussian) distribution of the parent genotype, which is an unobservable quantity and cannot be ascertained. In contrast, we show here that if the fitness (or selection) function is Gaussian with mean μ, an alternative, exact linear equation of the form R′ = j2S′ can be derived, regardless of the parental genotype distribution. Here R′ = E(Z1) − μ and S′ = E(ZW) − μ stand for the mean phenotypic lag with respect to the mean of the fitness function in the offspring and selected populations. The proportionality coefficient j2 is a simple function of selection function and environment factors variance, but does not contain the genotype variance. To demonstrate this, we derive the exact functional relation between the mean phenotype in the selected and the offspring population and deduce all cases that lead to a linear relation between them. These results generalize naturally to the concept of G matrix and the multivariate Lande’s equation Δz¯=GP−1S. The linearity coefficient of the alternative equation are not changed by Gaussian selection.
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7
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Feldman MW. Sam Karlin and multi-locus population genetics. Theor Popul Biol 2009; 75:233-5. [DOI: 10.1016/j.tpb.2009.01.002] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2008] [Accepted: 01/07/2009] [Indexed: 10/21/2022]
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8
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Analysis of central equilibrium configurations for certain multi-locus systems in subdivided populations. Genet Res (Camb) 2009. [DOI: 10.1017/s0016672300018644] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022] Open
Abstract
SUMMARYThe multi-locus systems expressing non-epistatic and generalized symmetric selection lend themselves to the study of the stability of certain central polymorphic equilibria. These equilibria persist when any form of migration connects demes which share a common equilibrium. The analysis of the stability of the equilibrium in the global system is tractable, thus supplementing known protection results for two alleles at one locus with stability conditions on an internal equilibrium involving an arbitrary number of loci, each with an arbitrary number of alleles. Two of the principal findings are that stability of central Hardy–Weinberg type equilibria increase with ‘more’ migration and ‘more’ recombination. As a corollary, local stability in each deme implies stability in a system with migration superimposed; but instability in each deme when isolated does not imply instability when migration is superimposed.
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Puniyani A, Liberman U, Feldman MW. On the meaning of non-epistatic selection. Theor Popul Biol 2005; 66:317-21. [PMID: 15560910 DOI: 10.1016/j.tpb.2004.05.001] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2003] [Indexed: 10/26/2022]
Abstract
In population genetics, the additive and multiplicative viability models are often used for the quantitative description of models in which the genetic contributions of several different loci are independent; that is, there is no epistasis. Non-epistasis may also be quantitatively defined in terms of measures of interaction used widely in statistics. Setting these measures of epistasis to zero yields alternative definitions of non-epistasis. We show here that these two definitions of non-epistasis are equivalent; that is, in the most general case of a multilocus, multiallele system, the additive and multiplicative viability models are unique solutions of the additive and multiplicative conditions, respectively, for non-epistasis.
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Affiliation(s)
- Amit Puniyani
- Department of Biological Sciences, Stanford University, Stanford, CA 94305-5020, USA.
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11
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Xiaofeng Qi, Palmieri F. Theoretical analysis of evolutionary algorithms with an infinite population size in continuous space. Part I: Basic properties of selection and mutation. ACTA ACUST UNITED AC 1994; 5:102-19. [DOI: 10.1109/72.265965] [Citation(s) in RCA: 96] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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12
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Feldman MW, Christiansen FB, Otto SP. Lewontin and Kojima meet Fisher: linkage in a symmetric model of sex determination. Genetics 1991; 129:297-312. [PMID: 1936963 PMCID: PMC1204578 DOI: 10.1093/genetics/129.1.297] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Abstract
The effect of linkage and epistasis on the evolution of the sex-ratio is studied in a symmetric two-locus model of autosomal sex determination closely related to the symmetric viability model of R. C. Lewontin and K. Kojima. R. A. Fisher's expectation of an even sex ratio for autosomal sex determination by a single gene governs the dynamics when the loci are tightly linked. However, recombination may preclude optimization of the sex ratio just as occurs in viability selection models. Many of the evolutionary phenomena known for the symmetric viability model also occur here. In addition, we exhibit a series of new phenomena related to the presence of surfaces of even sex ratio.
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Affiliation(s)
- M W Feldman
- Department of Biological Sciences, Stanford University, California 94305
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13
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Christiansen FB. The generalized multiplicative model for viability selection at multiple loci. J Math Biol 1990; 29:99-129. [PMID: 2292671 DOI: 10.1007/bf00168174] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
Selection due to differential viability is studied in an n-locus two-allele model using a set indexation that allows the simplicity of the one-locus two-allele model to be carried to multi-locus models. The existence condition is analyzed for polymorphic equilibria with linkage equilibrium: Robbins' equilibria. The local stability condition is given for the Robbins' equilibria on the boundaries in the generalized non-epistatic selection regimes of Karlin and Liberman (1979). These generalized non-epistatic regimes include the additive selection model, the multiplicative selection model and the multiplicative interaction model, and their symmetric versions cover all the symmetric viability models.
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Affiliation(s)
- F B Christiansen
- Department of Ecology and Genetics, University of Aarhus, Denmark
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Liberman U, Feldman MW, Eshel I, Otto SP. Two-locus autosomal sex determination: on the evolutionary genetic stability of the even sex ratio. Proc Natl Acad Sci U S A 1990; 87:2013-7. [PMID: 2308959 PMCID: PMC53615 DOI: 10.1073/pnas.87.5.2013] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Abstract
In two-locus models of sex determination, there are two kinds of interior (polymorphic) equilibria. One class has the even sex ratio, and the other has equal allele frequencies in the two sexes. Equilibria of the second class may exhibit linkage disequilibrium. The condition for external stability of these second-class equilibria to invasion by a new allele is that the appropriately averaged sex ratio near the equilibrium be moved closer to the even sex ratio than the average among the resident genotypes. However, invasion by a new chromosome depends on the recombination fraction in a way that appears to preclude general results about the evolutionary genetic stability of the even sex ratio in this situation.
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Affiliation(s)
- U Liberman
- Department of Biological Sciences, Stanford University, CA 94305-5020
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Karlin S. Levels of multiallelic overdominance fitness, heterozygote excess and heterozygote deficiency. Theor Popul Biol 1990; 37:129-49. [PMID: 2326762 DOI: 10.1016/0040-5809(90)90031-p] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
Concepts and results on selection balance in multiallelic systems are described. These include a multidimensional concept of heterozygote excess and heterozygote deficiency, a hierarchy of means of assessment of heterozygote advantage, comparisons and contrasts of allelic versus gametic polymorphic states, and conditions defining stable equilibria of complementary gametic sets. The concepts are illustrated in the context of viability selection and behavioral models of kin selection and for two major categories of multilocus selection regimes.
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Affiliation(s)
- S Karlin
- Department of Mathematics, Stanford University, California 94305
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Affiliation(s)
- F B Christiansen
- Department of Ecology and Genetics, University of Aarhus, Denmark
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18
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Abstract
The n-locus two-allele symmetric viability model is considered in terms of the parameters measuring the additive epistasis in fitness. The dynamics is analysed using a simple linear transformation of the gametic frequencies, and then the recurrence equations depend on the epistatic parameters and Geiringer's recombination distribution only. The model exhibits an equilibrium, the central equilibrium, where the 2n gametes are equally frequent. The transformation simplifies the stability analysis of the central point, and provides the stability conditions in terms of the existence conditions of other equilibria. For total negative epistasis (all epistatic parameters are negative) the central point is stable for all recombination distributions. For free recombination either a central point (segregating one, two, ... or n loci) or the n-locus fixation states are stable. For no recombination and some epistatic parameters positive the central point is unstable and several boundary equilibria may be locally stable. The sign structure of the additive epistasis is therefore an important determinant of the dynamics of the n-locus symmetric viability model. The non-symmetric multiple locus models previously analysed are dynamically related, and they all have an epistatic sign structure that resembles that of the multiplicative viability model. A non-symmetric model with total negative epistasis which share dynamical properties with the similar symmetric model is suggested.
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Affiliation(s)
- F B Christiansen
- Department of Ecology and Genetics, University of Aarhus, Denmark
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19
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Liberman U. External stability and ESS: criteria for initial increase of new mutant allele. J Math Biol 1988; 26:477-85. [PMID: 3199045 DOI: 10.1007/bf00276375] [Citation(s) in RCA: 40] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
Affiliation(s)
- U Liberman
- Department of Statistics, Tel Aviv University, Israel
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20
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The deviation from linkage equilibrium with multiple loci varying in a stepping-stone cline. J Genet 1987. [DOI: 10.1007/bf02934455] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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21
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Feldman MW, Liberman U. An evolutionary reduction principle for genetic modifiers. Proc Natl Acad Sci U S A 1986; 83:4824-7. [PMID: 3460074 PMCID: PMC323834 DOI: 10.1073/pnas.83.13.4824] [Citation(s) in RCA: 60] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Abstract
The joint evolution of major genes under viability selection and a modifier locus that controls recombination between the major genes, mutation at the major gene, or migration between two demes is studied. The modifying locus is selectively neutral and may have an arbitrary number of alleles. For each case a class of polymorphic equilibria exists in which the frequencies of the modifying alleles are those computed by assuming that the recombination, mutation, or migration rates were viabilities and in which the major and modifier loci are not statistically associated. These are called viability-analogous Hardy-Weinberg (VAHW) equilibria. A new allele introduced near these equilibria will enter the population if its marginal average rate of recombination, mutation, or migration (whichever applies) is less than the population average prior to its introduction. Stability properties of these VAHW equilibria are also reported.
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Karlin S, Liberman U. The reduction property for central polymorphisms in nonepistatic systems. Theor Popul Biol 1982; 22:69-95. [PMID: 7147208 DOI: 10.1016/0040-5809(82)90036-3] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023]
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Karlin S, Avni H. Analysis of central equilibria in multilocus systems: A generalized symmetric viability regime. Theor Popul Biol 1981. [DOI: 10.1016/0040-5809(81)90012-5] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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26
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Ritland K, Jain S. A model for the estimation of outcrossing rate and gene frequencies using n independent loci. Heredity (Edinb) 1981. [DOI: 10.1038/hdy.1981.57] [Citation(s) in RCA: 416] [Impact Index Per Article: 9.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022] Open
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27
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Raper J, Karlin S. Preferential mating in symmetric multilocus systems. Proc Natl Acad Sci U S A 1981; 78:3730-3. [PMID: 16593038 PMCID: PMC319645 DOI: 10.1073/pnas.78.6.3730] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
A class of multilocus models that incorporate both preferential mating and viability selection is studied. Symmetry in alleles is supposed, resulting in the phenotypes being dependent only on the location of heterozygous loci. Otherwise, an arbitrary number of loci, number of alleles per locus, and arbitrary recombination schemes, viability parameters, and preferential mating pattern are allowed. The conditions for stability of a central polymorphism, c(*), are indicated and interpreted. Mating and viability parameters enter as one combined quantity for each phenotypic class, which represents a generalized fitness. The effect on stability of c(*) of increasing the number of alleles per locus and the number of loci requires the formulation to be set in terms of frequency-dependent preference parameters.
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Affiliation(s)
- J Raper
- Department of Genetics, University of Cambridge, Cambridge, CB2 3EH, England
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28
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Karlin S. The range of stability of a polymorphic linkage equilibrium state in a two-locus two-allele selection model. J Math Biol 1980. [DOI: 10.1007/bf00275841] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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29
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Ginzburg LR, Braumann CA. Multilocus population genetics: relative importance of selection and recombination. Theor Popul Biol 1980; 17:298-320. [PMID: 7434252 DOI: 10.1016/0040-5809(80)90029-5] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
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30
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Karlin S, Liberman U. Representation of Nonepistatic selection models and analysis of multilocus Hardy-Weinberg Equilibrium configurations. J Math Biol 1979; 7:353-74. [PMID: 469414 DOI: 10.1007/bf00275154] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
The paper develops conditions for the existence and the stability of central equilibria emanating from selection recombination interaction with generalized nonepistatic selection forms operating in multilocus multiallele systems. The selection structure admits a natural representation as simple sums of Kronecker products based on a common set of marginal selection components. A flexible parametrization of the recombination process is introduced leading to a canonical derivation of the transformation equations connecting gamete frequency states over successive generations. Conditions for the existence and stability of multilocus Hardy-Weinberg (H.W.) type equilibria are elaborated for the classical nonepistatic models (multiplicative and additive viability effects across loci) as well as for generalized nonepistatic selection expressions. It is established that the range of recombination distributions maintaining a stable H.W. polymorphic equilibrium is confined to loose linkage in the pure multiplicative case, but is not restricted in the additive model. In the bisexual case we ascertain for the generalized nonepistatic model the stability conditions of a common H.W polymorphism.
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