near neutrality

Gu X 2007 Evolutionary framework for protein sequence evolution and gene pleiotropy. Genetics 175:1813–1822.

• the evolutionary fate of a mutant is largely determined by the prespecified fitness value (the coefficient of selection) and the effective population size
• this classical treatment has successfully removed the complexity of genotype–phenotype association
• problems may appear when the association itself has been one of the research highlights

• the ith diagonal element σ²_w,i measures the strength of stabilizing selection on the ith molecular phenotype
• the ijth nondiagonal element σ²_w,ij measures the correlated stabilizing selection on y_i and y_j
• a pleiotropic mutational effect can be described by a multivariate normal distribution

• Equations 22–24 provide the theoretical foundation for estimating K when N_eα_i ≫ 1
• in this case, the parameter K is interpreted as the number of molecular phenotypes that have experienced strong stabilizing selection
• we refer to K_e as the effective number of molecular phenotypes, which is less than the true number of molecular phenotypes
• if the ratio g_K is known, K_e can be estimated according to Equation 24

• the estimated effective number of molecular phenotypes K_e ranges from 2.3 to 20.4, with an average of 8.77
• the median is 8.23
• most genes are highly pleiotropic
• ~73% of the among-gene variation in the d_N / d_S ratio can be explained by the variation in K_e among genes
• the level of gene pleiotropy associated with a gene may be the dominant factor for predicting sequence conservation, as predicted by Fisher (1930)
• the effective mean selection intensity (S_e) ranges from 5.39 to 23.63