Pleiotropy can be effectively estimated without counting phenotypes through the rank of a genotype-phenotype map

Although pleiotropy, the capability of a gene to affect multiple phenotypes, has been well known as one of the common gene properties, a quantitative estimation remains a great challenge, simply because of the phenotype complexity. Not surprisingly, it is hard for general readers to understand how, without counting phenotypes, gene pleiotropy can be effectively estimated from the genetics data. In this article we extensively discuss the Gu-2007 method that estimated pleiotropy from the protein sequence analysis. We show that this method is actually to estimate the rank (K) of genotype-phenotype mapping that can be concisely written as K = min(r, Pmin), where Pmin is the minimum pleiotropy among all legitimate measures including the fitness components, and r is the rank of mutational effects of an amino acid site. Together, the effective gene pleiotropy (Ke) estimated by the Gu-2007 method has the following meanings: (i) Ke is an estimate of K = min(r, Pmin), the rank of a genotype-phenotype map; (ii) Ke is an estimate for the minimum pleiotropy Pmin only if Pmin < r; (iii) the Gu-2007 method attempted to estimate the pleiotropy of amino acid sites, a conserved proxy to the true gene pleiotropy; (iv) with a sufficiently large phylogeny such that the rank of mutational effects at an amino acid site is r → 19, one can estimate Pmin between 1 and 19; and (v) Ke is a conserved estimate of K because those slightly affected components in fitness have been effectively removed by the estimation procedure. In addition, we conclude that mutational pleiotropy (number of traits affected by a single mutation) cannot be estimated without knowing the phenotypes.