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

Date:
[1975]
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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.

    121/440 page 101
    610 Mr НаМапе, A mathematical theory If mating be at random, the rates of production of the three female phenotypes at time t are F{t)M{^ . F{t)m(t) + f{t)M{t) M (¿) + m (í) ' ' M (í) + m it) ' ■ Ж (í) + m {t) ' The group aged œ at time t was hatched or born at time t — x. Therefore 2i'' {t~x)M {t - x) + F (t - a;) m(t - .г) + f(t- x) M {t - .v) j. 'Jo M (t - .X) +m (t - X) / F(t-x)m(l-x) +f(t-x) M{t-x)+if{t-x)m{t -x) . • ' (, jV (f - .т)^■m (('-.г) Í ^ f {t - x) m (t- x) k(x) dx Jo JIJ (t-x)+m(t-x} ^ / (t - Д) t (t - Д) +/ ж) ^ 'Jo M [t - x)+ m(t - x) m (í) = i I ' ~ ^ ~ (t - ж) + 2/ (t - д) m (t - a.-) ^ ^ lo ' л/(t - X)+m (t - x) Í / {{ - x) mit- .1.) I (.tJ d.r Jo M (t - x) + m {t-x) Since selection and population growth are slow, we may put F(t — x) = F(t) — xF'(t), etc., M(t) — XF(t), m(t) = \f{t), all to the first order of small quantities. Hence, to this degree of approximation, F (ti J KFin ■ («)+/(')] Л/(i) . iK'[F- (/)+/' (Í)].U (П !¿K' [F (О +/(í)] it) - M (t) m' (t) M(t)+vi(1) Similarly + ^ F it) + fit) 1 rp(f\ I +/(0] ^(0 T'p'(f\ .V{t)-U,F(t) + ÍF(t) m it) - , Lf (0 + - LJ (t) - , ail approximately. Therefore .ìi (í) ' [lí (O ^ 2,- l^g] LF(,) + 21/ (.) - 2Г/,Г (O - i/ (t) ^11 ^ LF (t) + 2Lf (t) - _ 2lf (f) 101
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