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Linkage disequilibrium in finite populations

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Summary

A theoretical investigation has been made of the influence of population size (N) and recombination fraction (c) on linkage disequilibrium (D) between a pair of loci. Two situations were studied: (i) where both loci had no effect on fitness and (ii) where they showed heterozygote superiority, but no epistacy.

If the populations are initially in linkage equilibrium, then the mean value ofD remains zero with inbreeding, but the mean ofD2 increases to a maximum value and decreases until fixation is reached at both loci. The tighter the linkage and the greater the selection, then the later is the maximum in the mean ofD2 reached, and the larger its value. The correlation of gene frequencies,r, in the population of gametes within segregating lines was also studied. It was found that, for a range of selection intensities and initial gene frequencies, the mean value ofr2 was determined almost entirely byN c and time, measured proportional toN.

The implication of these results on observations of linkage disequilibrium in natural populations is discussed.

Zusammenfassung

Es wurde eine theoretische Untersuchung über den Einfluß der Populationsgröße (N) und der Rekombinationsfraktion (c) auf das Koppelungs-Ungleichgewicht (D) zwischen einem Paar von Loci angestellt. Die nachfolgenden zwei Situationen wurden studiert:

  1. 1.

    Beide Loci haben keinen Effekt auf die Fitness.

  2. 2.

    Die Heterozygoten zeigen Überlegenheit, jedoch keine Epistasie.

Befinden sich die Populationen in einem ursprünglichen Koppelungsgleichgewicht, so bleibt der mittlere Wert vonD bei Inzucht gleich null, jedoch steigt das Mittel vonD2 bis zu einem Maximalwert und fällt, bis die Fixierung an beiden Loci erreicht worden ist. Je enger die Koppelung und je stärker die Selektion ist, desto später wird das Maximum im Mittel vonD2 erreicht und desto größer ist sein Wert. Ferner wurde die Korrelation von Genfrequenzen,r, in der Population von Gameten innerhalb spaltender Linien untersucht. Es wurde gefunden, daß der mittlere Wert vonr2 für einen Bereich von Selektionsintensitäten und ursprünglichen Genfrequenzen praktisch vollkommen bestimmt wurde durchNc und die Zeit, gemessen proportional zuN. Abschließend wird die Bedeutung dieser Ergebnisse für Beobachtungen von Koppelungs-Ungleichgewichten in natürlichen Populationen diskutiert.

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Authors and Affiliations

  1. Institute of Animal Genetics, Edinburgh 9

    W. G. Hill & Alan Robertson

Authors
  1. W. G. Hill

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  2. Alan Robertson

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Member of the A.R.C. Unit of Animal Genetics.

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