On evolution / John Maynard Smith.

  • John Maynard Smith
Date:
1972
Catalogue details

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

Credit: On evolution / John Maynard Smith. Source: Wellcome Collection.

    137/144 page 125
    Let the typical members of a population at any time produce «0 eggs and No sperm. On the average, each typical member will have one surviving offspring as a female, and one as a male. Now consider a mutant individual producing n' eggs and N' sperm. If each egg and sperm has the same chance of giving rise to a surviving offspring as those produced by a typical in¬ dividual, then a mutant individual will produce n'¡no offspring as a female, and N'¡No offspring as a male. ( This conclusion will not hold for a self-fertilizing hermaphrodite, or for herma¬ phrodites with internal fertilization, for which the fewer sperm are produced, the greater chance each sperm has of fertilizing an egg. ) Hence the total number of offspring produced by the mutant is r^n'Ino + N'INo, (2) and substituting from eq. ( 1 ), R-bN' N' R-bNo^ No ' Therefore • («) Hence if No<^RIb, dTjdN' is positive; that is, mutations increasing N increase fitness, and selection will therefore in¬ crease No. Conversely, if No>iR/ b, selection will decrease No. Thus there is a stable equilibrium when No — ^Rfb, or when bNo — ano — ^R. In other words, there is a stable equilibrium when the resource R is equally divided between eggs and sperm. The conclusion holds, however, only for hermaphro¬ dites with external fertilization. —
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