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

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ABSTRACT The general theories of molecular evolution depend on relatively arbitrary assumptions about the relative distribution and rate of advantageous, deleterious, neutral, and nearly neutral mutations. The Fisher geometrical model (FGM) has been used to make distributions of mutations biologically interpretable. We explored an FGM-based molecular model to represent molecular evolutionary processes typically studied by nearly neutral and selection models, but in which distributions and relative rates of mutations with different selection coefficients are a consequence of biologically interpretable parameters, such as the average size of the phenotypic effect of mutations and the number of traits (complexity) of organisms. A variant of the FGM-based model that we called the static regime (SR) represents evolution as a nearly neutral process in which substitution rates are determined by a dynamic substitution process in which the population's phenotype remains around a suboptimum equilibrium fitness produced by a balance between slightly deleterious and slightly advantageous compensatory substitutions. As in previous nearly neutral models, the SR predicts a negative relationship between molecular evolutionary rate and population size; however, SR does not have the unrealistic properties of previous nearly neutral models such as the narrow window of selection strengths in which they work. In addition, the SR suggests that 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. We also developed a generalization of SR in which the optimum phenotype can change stochastically due to environmental or physiological shifts, which we called the variable regime (VR). VR models evolution as an interplay between adaptive processes and nearly neutral steady-state processes. When strong environmental fluctuations are incorporated, the process becomes a selection model in which evolutionary rate does not depend on population size, but is critically dependent on the complexity of organisms and mutation size. For SR as well as VR we found that key parameters of molecular evolution are linked by biological factors, and we showed that they cannot be fixed independently by arbitrary criteria, as has usually been assumed in previous molecular evolutionary models.

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THE nearly neutral theory of molecular evolution (Ohta and Kimura 1971; Ohta 1972, 1973, 1977, 1992, 1996), as is generally understood, affirms that the vast majority of amino acid substitutions are slightly deleterious; hence, it has been called the slightly deleterious mutation theory (Figure 1C) (Ohta and Kimura 1971; Ohta 1972, 1973, 1977, 1987, 1996; Kimura 1983; Gillespie 1995, 2004; Kreitman 1996). In the original exponential "shift" model of Ohta (1977) selection coefficients are chosen at random from an exponential probability distribution, and the population mean fitness shifts back when a mutation is fixed (see also Ohta and Gillespie 1996). This model was modified by Kimura (1979), who proposed the gamma shiftmodel, to overcome Ohta's previous assumptions that imply a rate of substitution that is too low when population size is increased above moderate values (see also Nielsen and Yang 2003). Later, Ohta and Tachida (1990) and Tachida (1991) developed another kind of nearly neutral model to relax some criticized assumptions (see below), but those models produced a very different prediction than that of slightly deleterious mutation models. In fact, Gillespie (1994, 1995) uncovered that in these later models, known as the house-of-cards or "fixed" models, only half of the substitutions are deleterious and the other half are advantageous (see also Tachida 1996, 2000). Thus, these kinds of nearly neutral models may be subsumed in a different category that we will call the balanced mutation theory (Figure 1D). …