Next: Introduction
Genetic Measurement Theory of Epistatic Effects
Günter P. Wagner
Center for Computational Ecology and
Department of Ecology and Evolutionary Biology
Yale University
New Haven, CT 06520-8106
Manfred D. Laubichler
Program in History of Science
Princeton University
Princeton, NJ 08544
Homayoun Bagheri-Chaichian
Department of Ecology and Evolutionary Biology
Yale University
Keywords: epistasis, QTL, canalization, measurement theory
Abstract:
Epistasis is defined as the influence of the genotype at one locus
on the effect of a mutation at another locus. As such it plays a crucial role
in a variety of evolutionary phenomena such as speciation, population bottle
necks and the evolution of genetic architecture (i.e. the evolution of
dominance, canalization and genetic correlations). In mathematical population
genetics, however, epistasis is often represented as a mere noise term in an
additive model of gene effects. In this paper it is argued that epistasis
needs to be scaled in a way that is more directly related to the mechanisms
of evolutionary change. A review of general measurement theory shows that the
scaling of a quantitative concepts has to reflect the empirical relationships
among the objects. To apply these ideas to epistatic mutation effects it is
proposed to scale AxA epistatic effects as the change in the magnitude of the
additive effect of a mutation at one locus due to a mutation at a second
locus. It is shown that the absolute change in the additive effect at locus A
due to a substitution at B is always identical to the absolute change in B
due to the substitution at the A locus. The absolute AxA epistatic effects of
A on B and of B on A are identical, even if the relative effects can be
different. The proposed scaling of AxA epistasis leads to particularly simple
equations for the decomposition of genotypic variance. The Kacser Burns model
of metabolic flux is analyzed for the presence of epistatic effects on flux.
It is shown that the non-linearity of the Kacser Burns model is not sufficient
to cause AxA epistasis among the genes coding for the enzymes. It is concluded
that non-linearity of the genotype-phenotype map is not sufficient to cause
epistasis. Finally it is shown that there exist correlations among the
additive and epistatic effects among pairs of loci, caused by the inherent
symmetries of Mendelian genetic systems. For instance, it is shown that a
mutation which has a larger than average additive effect will tend to
decrease the additive effect of a second mutation, i.e. it will tend to have
a negative (canalizing) interaction with a subsequent gene substitution. This
is confirmed in a preliminary analysis of QTL-data for adult body weight
in mice.
Next: Introduction