The equation for the response to selection and its use for prediction

The Breeder Genetic Algorithm BGA was designed according to the theories and methods used in the science of livestock breeding The prediction of a breeding experiment is based on the response to selection RS equation This equation relates the change in a popula tion s tness to the standard deviation of its tness as well as to the parameters selection intensity and realized heritability In this paper the exact RS equation is derived for propor tionate selection given an in nite population in linkage equilibrium In linkage equilibrium the genotype frequencies are the product of the univariate marginal frequencies The equation contains Fisher s fundamental theorem of natural selection as an approximation The theorem shows that the response is approximately equal to the quotient of a quantity called additive ge netic variance VA and the average tness We compare Mendelian two parent recombination with gene pool recombination which belongs to a special class of genetic algorithms which we call univariate marginal distribution algorithms UMD algorithms UMD algorithms keep the genotypes in linkage equilibrium For UMD algorithms an exact RS equation is proven which can be used for long term prediction Empirical and theoretical evidence is provided which in dicates that Mendelian two parent recombination is also mainly exploiting the additive genetic variance We compute an exact RS equation for binary tournament selection It shows that the two classical methods for estimating realized heritability the regression heritability and the heritability in the narrow sense may give poor estimates Furthermore realized heritability for binary tournament selection can be very di erent from that of proportionate selection The paper ends with a short survey about methods which extend standard genetic algorithms and UMD algorithms by detecting interacting variables in nonlinear tness functions and using this information to sample new points

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