Modeling genetic architecture: A multilinear theory of gene interaction

The map from genotype to phenotype is an exceedingly complex function of ce ntral importance in biology. In this work we derive and analyze a mathemati cally tractable model of the genotype-phenotype map that allows for any ord er of gene interaction. By assuming that the alterations of the effect of a gene substitution due to changes in the genetic background can be describe d as a linear transformation, we show that the genotype-phenotype map is a sum of linear and multilinear terms of operationally defined "reference" ef fects at each locus. The "multilinear" model is used to study the effect of epistasis on quantitative genetic variation, on the response to selection, and on genetic canalization. It is shown how the model can be used to esti mate the strength of "functional" epistasis from a variety of genetic exper iments. (C) 2001 Academic Press.