Model of effectively neutral mutations in which selective constraint is incorporated

Abstract

Based on the idea that selective neutrality is the limit when the selective disadvantage becomes indefinitely small, a model of neutral (and nearly neutral) mutations is proposed that assumes that the selection coefficient (s') against the mutant at various sites within a cistron (gene) follows a r distribution; Ass') = aPe-as's.-l/P(,B), in which a = fi/i and s' is the mean selection coefficient against the mutants (?'> 0; 1 _ ft > 0). The shown that we have roughly kg = ve. The situation becomes quite different if slightly advantageous mutations occur at a constant rate independent of environmental conditions. In this case, the evolutionary rate can become enormously higher in a species with a very large population size than in a species with a small population size, contrary to the observed pattern of evolution at the molecular level.Among difficult questions that confront the neutral mutation theory purporting to treat quantitatively the evolution and variation at the molecular level, the following two are particularly acute. 3440The publication costs of this article were defrayed in part by page charge payment. This article must therefore be hereby marked "advertisement" in accordance with 18 U. S. C. §1734 solely to indicate this fact.

The Nearly Neutral and Selection Theories of Molecular Evolution Under the Fisher Geometrical Framework: Substitution Rate, Population Size, and Complexity

“…Theoretical studies of molecular evolution assume predefined distributions of selection coefficients of mutants (e.g., Ohta 1973Ohta , 1977Kimura 1979;Ohta and Tachida 1990;Gillespie 1993Gillespie , 1994. Thus the rate and proportion of different types of mutations are dependent only upon the population size and some parameters of the distribution of the selection coefficients (typically s and s s , the mean and the standard deviation of selection coefficients, respectively).…”

Using Computer Simulation to Understand Mutation Accumulation Dynamics and Genetic Load

“…However, across a wide range of parameter space the bins nearest to zero fill at essentially the same rate, regardless of whether or not selection is being applied. Experimentally, these "nearly-neutral" mutations are consistently found to be un-selectable -in accordance with mathematical theory [6] [7]. Mutations with intermediate levels of impact accumulate at intermediate rates.…”

A remark on rare variants

“…Equations (13)(14)(15), that is, the powers of their denominators, directly show the conclusion of Risch and Merikangas 5 that in linkage analysis the necessary sample size is much more sensitive to a decline of risk allele frequency p or effect size g (also see Figure 1). An allele's association with a trait (that is, preferential transmission in case of an affected child) may still be noticeable when the correlation of its transmissions to two or more affected relatives is already obscured by noise (that is, by incomplete penetrance, genocopies and phenocopies).…”

“…Kimura 14 argued that advantageous mutations are very rare whereas nearly neutral mutations predominate. Therefore, he modeled u(s) as a reflected gamma distribution that can accommodate enough probability mass in the region of nearly neutral mutations.…”