compensatory evolution - senecio7の日記

Razeto-Barry P, Díaz J & Vásquez RA 2012 The nearly neutral and selection theories of molecular evolution under the Fisher geometrical framework: substitution rate, population size, and complexity. Genetics 191:523-534.

compensatory mutations cannot explain the high rate of fixations driven by positive selection currently found in DNA sequences, contrary to what has been previously suggested

Figure 1
(D) the balanced mutation theory also incorporates slightly deleterious mutations (N^-), but also postulates an important fraction of advantageous (compensatory) mutations fixed after the fixations of slightly deleterious mutations
50% of no neutral substitutions have s > 0 and 50% have s < 0

Gu (2007a,b) used the FGM to model the slightly deleterious mutation theory under the shift model framework
the gamma distribution case used by Kimura corresponds to n = 1 phenotypic dimensions
the exponential distribution of Ohta corresponds to n = 2
the assumptions of Gu's model in the FGM inherit the problems of the original shift models, which were strongly criticized because of their biologically unreasonable assumptions
shift models require that all mutations be deleterious
here we relaxed the assumptions of Gu's model in the FGM and developed a model that supports a balanced mutation theory of molecular evolution
the steady state in the FGM has been understood as a nearly neutral evolutionary process
it is in some aspects similar to the house-of-cards nearly neutral model

we simulated asexual populations under the assumption of weak mutation
Nu < 1, where u is the genomic mutation rate
the evolutionary process is depicted as a succession of fixations and neglects the effects of polymorphisms
the number of dimensions n is not interpreted as the number of orthogonal traits affected by mutations in a gene, but rather as the number of orthogonal traits affected by mutations in the entire organismal genome
in contrast to Gu (2007a,b) we utilized a top-down approach to isotropic random vector generation (Poon and Otto 2000)
we directly specified only the distribution of total mutation length and did not specify the marginal distributions along each axis
a change in the number of dimensions does not affect the total length of the mutation's effects, which allows us to distinguishing between the effect of dimensionality and the effect of mutation size on the molecular evolutionary rate
the distribution used for mutation magnitudes was uniform

the distribution of selection coefficients of substitutions (Figure 3, right) follows a leptokurtic but symmetric distribution independently of the mutation size
the expected proportion of advantageous substitutions is always 0.5

the SR showed similarities to the house-of-cards or "fixed" model of molecular evolution
evolution is an alternating process with half of the substitutions being advantageous and the other half deleterious
most of these advantageous mutations would be compensatory, i.e., intragenic or intergenic mutations that restore the fitness loss due to previous deleterious mutations

the SR model overcomes some problems of the house-of-cards model
the house-of-cards model is not a plausible model of molecular evolution because the substitution rate is a rapidly decreasing (typically concave) function of the strength of selection (2Nσs), which stops when 2Nσs > 4
in the SR the relationship between substitution rate and population size (and thus the strength of selection) is convex
evolution does not stop even for 2Nσs ≈ 260
the SR may be considered to be a plausible nearly neutral model of molecular evolution without the apparent deficiencies of previous models, giving new support to the balanced nearly neutral models
in contrast to the house-of-cards model, evolution does not stop because of low strength of selection in the SR, since in the FGM it is possible to overshoot the optimum phenotypic value
mutations directed to the phenotype with highest fitness in the FGM can decrease the fitness (because they can overshoot the optimum value)
thus more mutations can behave as effectively neutral
in the house-of-cards model all mutations directed toward higher fitness confer higher fitness if they are fixed, because advantageous mutations can take unlimited positive selection coefficients
molecular evolution in the house-of-cards models tends to stop because the pressure toward higher fitness decreases the number of possible further advantageous mutations

the current evidence for a high rate of advantageous mutations fixed by positive selection, ~50% or more (Fay et al. 2002; Bierne and Eyre-Walker 2004; Eyre-Walker 2006; Bachtrog 2008), could be explained as the effect of compensatory mutations (Kondrashov et al. 2002; DePristo et al. 2005; Pál et al. 2006; Camps et al. 2007)
this idea was proposed earlier by Hartl and Taubes (1996) using the FGM framework, stating that in the steady state there is "selection without adaptation," i.e., positive selection but upholding only the status quo in a balance between deleterious mutations and later advantageous compensatory mutations
we found that the proportion of advantageous (compensatory) mutations fixed by positive selection (i.e., strictly advantageous mutations) is very low in the steady state
the explanation for this result is that compensatory mutations are abundant and thus come after one or a very small number of deleterious mutations previously fixed by drift
both are mainly effectively neutral
given the small selection coefficients of advantageous mutations, it is difficult to explain the high rate of mutations fixed by positive selection
if compensatory mutations were very rare, on the average several deleterious substitutions could be fixed before an advantageous mutation compensated the previous effect of the deleterious ones.
a higher proportion of compensatory substitutions could be of greater size and strictly advantageous
our model assumes a high rate of compensatory mutations, which is in agreement with current studies
Poon et al.'s (2005) study in viruses, prokaryotes, and eukaryotes revealed that on average there are 11.8 compensatory mutations per deleterious mutation

the SR may also be understood as a nearly neutral model
it is important to distinguish the SR from the slightly deleterious mutation theory
the differences between the slightly deleterious mutation models and the SR are important in their predictions about both mutations and substitutions
there are two major differences:
(i) the mutation assumptions of the SR involve a higher fraction of advantageous (mainly compensatory) mutations than the slightly deleterious mutation models
(ii) the predictions of the SR imply a much greater fraction of advantageous substitutions than the slightly deleterious mutation models
thus the SR predicts 50% advantageous substitutions

when a population is close to the optimum, a Gaussian fitness function is a good local approximation for many arbitrary fitness functions
models relaxing the assumption of Nu < 1 should be developed in the future

contrary to the suggestion of Orr (1998) the uniform distribution we assumed for mutation sizes (see also Kimura 1983) is consistent with the majority of current empirical and theoretical evidence on distributions of the fitness effects of mutations
all these studies (empirical and theoretical) dealt with the size of the fitness effects of mutations (selection coefficients), not with the size of the phenotypic effects of mutations
taking a uniform distribution of mutational (phenotypic) effects (r), the distribution of fitness effects (selection coefficients, s) is leptokurtic
when the average mutational size (r) is large enough (Figure 3A), the distribution of s among deleterious mutations is L-shaped rather than exponential, which coincides with the literature
the distribution of s among beneficial mutations is exponential-like, which also coincides with the literature
the exponential distribution of s arises from different mutational distributions of r, including the uniform

a benefit of the FGM is that it makes some of the distributions used in molecular evolution biologically interpretable
the distribution determined by evolutionary dynamics will differ in important ways from distributions assumed a priori

the ratio between advantageous and deleterious mutations is locked
it cannot take arbitrarily independent values
it yields a maximum value of 1 when mutation size tends to zero (Figure 3C, according to Fisher 1930)
when mutation size is small, the limiting factor for the selection coefficient of deleterious and advantageous mutations is the size of mutations (Figure 3C), and a large proportion (50%) of nearly neutral mutations are advantageous
this fact was suggested verbally by Gillespie (1995) as a criticism to Ohta's (1977, 1992) assumptions, based on Fisher’s (1930) classical result

compensatory substitutions cannot take arbitrary values
necessarily a low proportion of compensatory substitutions are strictly advantageous
the proportion of advantageous substitutions has a minimum of 0.5 (for very low environmental variability)
the proportion of advantageous mutations has a maximum of 0.5 (for very small mutation size)
the absolute magnitude of the coefficient of variation of selection coefficients approaches one
these conclusions support the importance of obtaining values for these parameters by modeling the evolutionary process and not by a priori decisions