Equilibrium behavior of population genetic models with non-random mating. Part I: Preliminaries and special mating systems

1968 ◽  
Vol 5 (2) ◽  
pp. 231-313 ◽  
Author(s):  
Samuel Karlin
Keyword(s):  
Population Genetic ◽  
Mating Systems ◽  
Random Mating ◽  
Genetic Models ◽  
Equilibrium Behavior ◽  
Mating Part

Equilibrium behavior of population genetic models with non-random mating. Part II: Pedigrees, Homozygosity and Stochastic Models

1968 ◽  
Vol 5 (3) ◽  
pp. 487-566 ◽  
Author(s):  
Samuel Karlin
Keyword(s):  
Stochastic Models ◽  
Limit Theorems ◽  
Finite Population ◽  
Random Mating ◽  
Bayes Rule ◽  
Identity By Descent ◽  
Equilibrium Behavior ◽  
Path Coefficients ◽  
Complete Study ◽  
Mating Part

Wright (1921) computed various correlations of relatives by a rather cumbersome procedure called the “method of path coefficients”. Wright's method is basically a disguised form of the use of Bayes' rule and the law of total probabilities. Malecot (1948) reorganized Wright's calculations by introducing the fundamental concept of identity by descent and exploiting its properties. The method of identity by descent has been perfected and developed by Malécot and his students, especially Gillois, Jauquard and Bouffette. Kempthorne (1957) has applied the concept of identity by descent to the study of quantitative inheritance. Kimura (1963) elegantly employed the ideas of identity by descent in determining rates of approach to homozygosity in certain mating situations with finite population size. Later in this chapter we will extend and refine the results of Kimura (1963) to give a more complete study of rates of approach to homozygosity. Ellison (1966) established several important limit theorems corresponding to polyploid, multi-locus random mating infinite populations by judicious enlargement of the concepts of identity by descent. Kesten (unpublished)) has recently refined the technique of Ellison.

Equilibrium behavior of population genetic models with non-random mating. Part II: Pedigrees, Homozygosity and Stochastic Models

1968 ◽  
Vol 5 (03) ◽  
pp. 487-566 ◽  
Author(s):  
Samuel Karlin
Keyword(s):  
Stochastic Models ◽  
Limit Theorems ◽  
Finite Population ◽  
Random Mating ◽  
Bayes Rule ◽  
Identity By Descent ◽  
Equilibrium Behavior ◽  
Path Coefficients ◽  
Complete Study ◽  
Mating Part

Wright (1921) computed various correlations of relatives by a rather cumbersome procedure called the “method of path coefficients”. Wright's method is basically a disguised form of the use of Bayes' rule and the law of total probabilities. Malecot (1948) reorganized Wright's calculations by introducing the fundamental concept of identity by descent and exploiting its properties. The method of identity by descent has been perfected and developed by Malécot and his students, especially Gillois, Jauquard and Bouffette. Kempthorne (1957) has applied the concept of identity by descent to the study of quantitative inheritance. Kimura (1963) elegantly employed the ideas of identity by descent in determining rates of approach to homozygosity in certain mating situations with finite population size. Later in this chapter we will extend and refine the results of Kimura (1963) to give a more complete study of rates of approach to homozygosity. Ellison (1966) established several important limit theorems corresponding to polyploid, multi-locus random mating infinite populations by judicious enlargement of the concepts of identity by descent. Kesten (unpublished)) has recently refined the technique of Ellison.

scholarly journals DEVIATIONS OF GENOTYPIC STRUCTURES FROM HARDY-WEINBERG PROPORTIONS UNDER RANDOM MATING AND DIFFERENTIAL SELECTION BETWEEN THE SEXES

Genetics ◽  
1981 ◽  
Vol 98 (1) ◽  
pp. 215-230
Author(s):  
Martin Ziehe ◽  
Hans-Rolf Gregorius
Keyword(s):  
Population Genetic ◽  
Random Mating ◽  
Genetic Models ◽  
Selection Intensity ◽  
Differential Selection ◽  
Viability Selection ◽  
Strong Affinity ◽  
Genotype Frequencies ◽  
Two Generations ◽  
Differential Viability

ABSTRACT Population genetic models, such as differential viability selection between the sexes and differential multiplicative fecundity contributions of the sexes, are considered for a single multiallelic locus. These selection models usually produce deviations of the zygotic genotype frequencies from Hardy-Weinberg proportions. The deviations are investigated (with special emphasis put on equilibrium states) to quantify the effect of selective asymmetry in the two sexes. For many selection regimes, the present results demonstrate a strong affinity of zygotic genotype frequencies for Hardy-Weinberg proportions after two generations, at the latest. It is shown that the deviations of genotypic equilibria from the corresponding Hardy-Weinberg proportions can be expressed and estimated by means of selection components of only that sex with the lower selection intensity. This corresponds to the well-known fact that viability selection acting in only one sex yields Hardy-Weinberg equilibria.

scholarly journals Linkage Disequilibrium, Gene Trees and Selfing: An Ancestral Recombination Graph With Partial Self-Fertilization

Genetics ◽  
2000 ◽  
Vol 154 (2) ◽  
pp. 923-929 ◽  
Author(s):  
Magnus Nordborg
Keyword(s):  
Linkage Disequilibrium ◽  
Computational Methods ◽  
Population Genetic ◽  
Random Mating ◽  
Genetic Models ◽  
Gene Trees ◽  
Ancestral Recombination Graph ◽  
Self Fertilization ◽  
Simple Change ◽  
Selfing Species

Abstract It is shown that partial self-fertilization can be introduced into neutral population genetic models with recombination as a simple change in the scaling of the parameters. This means that statistical and computational methods that have been developed under the assumption of random mating can be used without modification, provided the appropriate parameter changes are made. An important prediction is that all forms of linkage disequilibrium will be more extensive in selfing species. The implications of this are discussed.

scholarly journals EVOLUTION OF INTERACTIONS IN FAMILY-STRUCTURED POPULATIONS: MIXED MATING MODELS

Genetics ◽  
1980 ◽  
Vol 96 (1) ◽  
pp. 275-296
Author(s):  
Richard E Michod
Keyword(s):  
Mating System ◽  
Mating Systems ◽  
Random Mating ◽  
Additive Model ◽  
Multiplicative Model ◽  
Structured Populations ◽  
Mixed Mating ◽  
Genotypic Distribution ◽  
Individual Fitness ◽  
Recessive Genes

ABSTRACT The effect of inbreeding on sociality is studied theoretically for the evolution of interactions between siblings in certain mixed mating systems that give rise to inbreeding: sib with random mating and selfing with random mating. Two approaches are taken. First, specific models of altruism are studied for the various mating systems. In the case of the additive model, inbreeding facilitates the evolution of altruistic genes. Likewise, for the multiplicative model this is usually the case, as long as the costs of altruism are not too great. Second, the case of total altruism, in which the gene has zero individual fitness but increases the fitness of associates, is studied for a general fitness formulation. In this case, inbreeding often retards the ability of such genes to increase when rare, and the equilibrium frequency of those recessive genes that can increase is totally independent of the mating system and, consequently, of the amount of inbreeding. It appears from the results presented that inbreeding facilitates most forms of altruism, but retards extreme altruism. These results stem from the fact that inbreeding increases the within-family relatedness by increasing the between-family variance in allele frequency. In most cases this facilitates altruism. However, in the case of total altruism, only heterozygotes can pass on the altruistic allele, and inbreeding tends to decrease this heterozygote class. In either case, the important effect of inbreeding lies in altering the genotypic distribution of the interactions.

scholarly journals Linking Dynamical and Population Genetic Models of Persistent Viral Infection

2003 ◽  
Vol 162 (1) ◽  
pp. 14-28 ◽  
Author(s):  
John K. Kelly ◽  
Scott Williamson ◽  
Maria E. Orive ◽  
Marilyn S. Smith ◽  
Robert D. Holt
Keyword(s):  
Viral Infection ◽  
Population Genetic ◽  
Genetic Models ◽  
Persistent Viral Infection

Population Genetic Models

2018 ◽  
pp. 87-117
Author(s):  
John S. Buckleton ◽  
Duncan Taylor ◽  
James M. Curran ◽  
Jo-Anne Bright
Keyword(s):  
Population Genetic ◽  
Genetic Models
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