Demographic genetics / edited by Kenneth M. Weiss and Paul A. Ballonoff.

Date:
[1975]
Catalogue details

Licence: Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)

Credit: Demographic genetics / edited by Kenneth M. Weiss and Paul A. Ballonoff. Source: Wellcome Collection.

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    •28 H. T. J. Norton [Nov. 11, By the definition of Mendelian allelomorphic factors, if u is a pure type, all the offspring of u-u matches, half those of u-v matches, and a quarter those of v-v matches are w's, and none of the offspring of other combinations. Adding the three numbers together, we get fA2 ГЛ2 _ (f ß) ]л N(t)N{e) + y-t)v{y-t)] X [Kiiy, у—в)и{у — в)-\-К2{у, y — e)v{y—6)]dtde, and this must be equal to u{y)dy. Similarly, if v is a hybrid type, half the offspring of v-v matches, v-v matches, and v-w matches, and all the offspring of u-w matches are hybrids. We thus get 2г>0у)=|^ 1 N(t)N%) + y-t)v{y-t)] X [K^iy, i/—e)v{y—e)-\-K3{y,y — e)w(y—e)']dtde. And similarly, «'(¿/) = è|^ ÍKaiy, y-t) w{y-t) + K2{y, y-t) г?(0] X iK^iy, y — B) v{y — 0)-\-K^{y, y — e)w{y — 9)]dtde. If we add half the second equation to the first equation and then to the third, w(í/) + '^(¿/) = è [K^{y,y — t)u{.y—f)-\-K2{y,y — t)v{y — t)]^^ dOdt, í'(í/)+«'(¿/) = i {К^{у, y — t)v{y — t)-\-K^y, y — t)w{y — t)]^^ ^^^^dOdt. The quantity | is what was called, in the preceding part, the iustautaueoiis biith-rate in the conununity, v(t, у—t). If now we introduce the assumption that the ages of parents vary independently, B) = TTyit) ТГу(в), and we have, in the first place, the equation v\ij) = u{y)w{y), (12.1 and, secondly, we can consider v(f, у—t) as independent of the age distribution in the couuuunity, and equal to v(f). If the ages of parents do not vary independently, v(f, y — i) is necessarily a function of the &gf distribution. Assiuuing, further, that the death-rates in the three 114
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