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* Corresponding author 1 LIPHY-BIOP LIPhy - Laboratoire Interdisciplinaire de Physique Saint Martin d’Hères

Abstract : The breeder-s equation is a cornerstone of quantitative genetics and is widely used in evolutionary modeling. The equation which reads R=h^{2}S relates response to selection R the mean phenotype of the progeny to the selection differential S mean phenotype of selected parents through a simple proportionality relation. The validity of this relation however relies strongly on the normal Gaussian distribution of parent-s genotype which is an unobservable quantity and cannot be ascertained. In contrast, we show here that if the fitness or selection function is Gaussian, an alternative, exact linear equation in the form of R-=j^{2}S- can be derived, regardless of the parental genotype distribution. Here R- and S- stand for the mean phenotypic lag behind the mean of the fitness function in the offspring and selected populations. To demonstrate this relation, we derive the exact functional relation between the mean phenotype in the selected and the offspring population and deduce all cases that lead to a linear relation between these quantities. These computations, which are confirmed by individual based numerical simulations, generalize naturally to the multivariate Lande-s equation \Delta\mathbf{\bar{z}}=GP^{-1}\mathbf{S} .

Keywords : quantitative genetics breeder-s equation lande equation phenotypic evolution reponse to selection

Autor: Bahram Houchmandzadeh -



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