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On total hereditary variance, in the case of certain mating systems

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5. Summary

A model is specified based on the assumption of an oversimplified situation: a measurable character fully determined by a single diallelic locus. The generality of the model is shown to be complete.

Elementary mathematical analysis is used to derive the formal dependence of σ 2H onF, whereF is defined in a manner which attributes to it a wider range than its conventional definition (the conventional range is entirely contained in this extended one). A formula is obtained for the value ofF at which σ 2H takes its greatest value for given allele-frequency and degree of dominance. Considering the bounds imposed on the values of this extendedF, this greatest value of σ 2H is shown to be antained in a manner determined by the relationship between the measure of allele-frequency and of degree of dominance. The character of this determination is illustrated by geometrical collation of the analytical results.

A scheme, which provides a biological background for the model, is described. This scheme contains no contradictions to the features of processes verified to exist in artificial or natural selection.

The Tables, in which the geometrically collated results are set out, are explained in the concepts and terminology of biometrical population genetics.

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Authors and Affiliations

  1. Division of Animal Genetics, C.S.I.R.O., Poultry Research Centre, Werribee, Victoria

    F. E. Binet & J. A. Morris

Authors
  1. F. E. Binet
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  2. J. A. Morris
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Binet, F.E., Morris, J.A. On total hereditary variance, in the case of certain mating systems. J Genet 58, 108–121 (1962). https://doi.org/10.1007/BF02986122

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  • DOI: https://doi.org/10.1007/BF02986122

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