### Abstract

Identity disequilibrium, ID, is the difference between joint identity by descent and the product of the separate probabilities of identity by descent for two loci. The effects of ID on the additive by additive (a a) epistatic variance and joint dominance component between populations and in the additive, dominance and a a variance within populations, including the effects on covariances of relatives within populations, were studied for finite monoecious populations. The effects are formulated in terms of three additive partitions, ηb, ηa and ηd of the total ID, each of which increases from zero to a maximum at some generation dependent upon linkage and population size and decreases thereafter. ηd is about four times the magnitude of the other two but none is of any consequence except for tight linkage and very small populations. For single-generation bottleneck populations only d is not zero. With random mating of expanded populations ηb remains constant and ηa and ηd go to zero at a rate dependent upon linkage, very fast with free recombination. The contributions of joint dominance to the genetic components of variance within and between populations are entirely a function of the η's while those of a a variance to the components are functions mainly of the coancestry coefficient and only modified by the η's. The contributions of both to the covariances of half-sibs, full-sibs and parent-offspring follow the pattern expected from their contributions to the genetic components of variance within populations except for minor terms which most likely are of little importance.

Original language | English |
---|---|

Pages (from-to) | 63-70 |

Number of pages | 8 |

Journal | Genetical Research |

Volume | 53 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1989 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Genetics

### Cite this

*Genetical Research*,

*53*(1), 63-70. https://doi.org/10.1017/S0016672300027877

**Effects of identity disequilibrium and linkage on quantitative variation in finite populations.** / Tachida, Hidenori; Cockerham, C. Clark.

Research output: Contribution to journal › Article

*Genetical Research*, vol. 53, no. 1, pp. 63-70. https://doi.org/10.1017/S0016672300027877

}

TY - JOUR

T1 - Effects of identity disequilibrium and linkage on quantitative variation in finite populations

AU - Tachida, Hidenori

AU - Cockerham, C. Clark

PY - 1989

Y1 - 1989

N2 - Identity disequilibrium, ID, is the difference between joint identity by descent and the product of the separate probabilities of identity by descent for two loci. The effects of ID on the additive by additive (a a) epistatic variance and joint dominance component between populations and in the additive, dominance and a a variance within populations, including the effects on covariances of relatives within populations, were studied for finite monoecious populations. The effects are formulated in terms of three additive partitions, ηb, ηa and ηd of the total ID, each of which increases from zero to a maximum at some generation dependent upon linkage and population size and decreases thereafter. ηd is about four times the magnitude of the other two but none is of any consequence except for tight linkage and very small populations. For single-generation bottleneck populations only d is not zero. With random mating of expanded populations ηb remains constant and ηa and ηd go to zero at a rate dependent upon linkage, very fast with free recombination. The contributions of joint dominance to the genetic components of variance within and between populations are entirely a function of the η's while those of a a variance to the components are functions mainly of the coancestry coefficient and only modified by the η's. The contributions of both to the covariances of half-sibs, full-sibs and parent-offspring follow the pattern expected from their contributions to the genetic components of variance within populations except for minor terms which most likely are of little importance.

AB - Identity disequilibrium, ID, is the difference between joint identity by descent and the product of the separate probabilities of identity by descent for two loci. The effects of ID on the additive by additive (a a) epistatic variance and joint dominance component between populations and in the additive, dominance and a a variance within populations, including the effects on covariances of relatives within populations, were studied for finite monoecious populations. The effects are formulated in terms of three additive partitions, ηb, ηa and ηd of the total ID, each of which increases from zero to a maximum at some generation dependent upon linkage and population size and decreases thereafter. ηd is about four times the magnitude of the other two but none is of any consequence except for tight linkage and very small populations. For single-generation bottleneck populations only d is not zero. With random mating of expanded populations ηb remains constant and ηa and ηd go to zero at a rate dependent upon linkage, very fast with free recombination. The contributions of joint dominance to the genetic components of variance within and between populations are entirely a function of the η's while those of a a variance to the components are functions mainly of the coancestry coefficient and only modified by the η's. The contributions of both to the covariances of half-sibs, full-sibs and parent-offspring follow the pattern expected from their contributions to the genetic components of variance within populations except for minor terms which most likely are of little importance.

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UR - http://www.scopus.com/inward/citedby.url?scp=0024582994&partnerID=8YFLogxK

U2 - 10.1017/S0016672300027877

DO - 10.1017/S0016672300027877

M3 - Article

VL - 53

SP - 63

EP - 70

JO - Genetical Research

JF - Genetical Research

SN - 0016-6723

IS - 1

ER -