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A theoretical system of selection for homostyle primula

, : A theoretical system of selection for homostyle primula. Sankhya Indian Jour Statistics 9(4): 325-342

Starting with the remark that the excess of activity in reproduction of a gene over its allele could not in general be equal to the effect of such gene substitution, the author quotes the example of homostyle allele Sh in Primula veris. This situation constitutes a system of selection in favor of the homostyle gene and unless the homozygous homostyles are either non-viable or at some physiological disadvantage, the theoretical expectation is that the homostyle gene should tend to 100%. This is, however, not observed and it appears that some check of unknown origin comes into play when the proportion of homostyle is high and perhaps in some other circumstances. To investigate into the nature of such checks a study of the theoretical system has been made. It is found that the genetic situation produced by Sh is such that the transformation due to one generation's breeding is non-linear in the genotype frequencies. A method of treating such iterated non-linear transformations is developed, appropriate to this case, using terminal expansions which may be in one or more variables. Each terminal expansion defines a consistent method of enumeration of generation in a continuum, and the consistency of these modes in the present problem has been checked to about eight places of decimals. It is, however, to be anticipated that small periodic discrepancies between the forms really exist, though on an exceedingly minute scale.


DOI: 10.2307/25047987

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