Mathematics of genetic diversity by J. F. C. Kingman

By J. F. C. Kingman

Attracts jointly a few mathematical principles which are important in inhabitants genetics, targeting a number of elements that are either biologically suitable and mathematically fascinating.

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Thus, all three chromosome pairs contain genes controlling such behavior. However, these taxis are not independent of environment. Environment may alter phototaxis. The beetle Blastophagus pinniperda L. is positively phototatic in spring, at temperatures between 10° and 35°C, but negatively phototactic below and above this temperature (Perttunen, 1958, 1959). In the fall, the temperature range is reduced to 20°-30°C. Thus, a tempera­ ture of 15° induces positive phototaxis in spring, and negative phototaxis in autumn, when the animal starts looking for winter shelter.

DeFries In his thoughtful discussion of my paper, Professor Fuller raises two issues which deserve further comment. The first concerns the assumption of the absence of a significant genotype-environment correlation in my derivations. Such simplifying assumptions were made for purposes of clarity of presentation, not because quantitative genetic theory is incapable of handling more general cases. As indicated in my paper, it may be shown that the between-group heritability (Af2) is equivalent to the regression of the mean additive genetic val- 22 JOHN L.

Thus, when rA^ is nonzero, prediction is still possible; however, more infor­ mation is required. If rAE is positive, prediction using only ht2 would yield an underestimate of the extent to which the observed group difference is heritable (ht2 is less than 6Afpfwhen rAE is positive). If rAE is negative, Af2 will overestimate the heritable nature of the group difference. If rAE were negative and large, the expected mean additive genetic value of the group with the lower mean phenotypic value might actually exceed that of the group with the higher mean phenotypic value.

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