Nearly Neutral Theory of Molecular Evolution

The nearly neutral theory of molecular evolution is a foundational principle of evolutionary genetics formulated by Japanese geneticist Tomoko Ohta in 1973 (and expanded in 1992) as a major extension of Motoo Kimura's strict neutral theory of molecular evolution (1968). Whereas Kimura's original model partitioned newly arising mutations into two discrete classes—strictly neutral alleles (s = 0) whose fate is governed entirely by random genetic drift, and strongly deleterious or beneficial alleles (|*N*_e*s*| ≫ 1) whose fate is determined by deterministic natural selection—Ohta demonstrated that a vast continuum of mutations occupies the intermediate nearly neutral regime, where the magnitude of the selection coefficient s is comparable to the reciprocal of the effective population size (N_e), such that |*N*_e*s*| ≈ 1.

Within this boundary zone (typically defined as 0.1 ≤ |4*N*_e*s*| ≤ 10), random genetic drift and weak natural selection act simultaneously with comparable strength. Because the efficacy of purifying selection scales directly with N_e, the proportion of new mutations that behave as effectively neutral is not a fixed molecular constant; instead, it expands in species with small effective population sizes (such as large-bodied vertebrates) and contracts in species with large effective population sizes (such as pelagic marine invertebrates, Drosophila, and free-living prokaryotes).

By explicitly linking the probability of fixation of slightly deleterious mutations to N_e, Ohta's nearly neutral theory resolved a central empirical paradox of molecular evolution: why amino acid substitutions in proteins follow an approximate chronological-time molecular clock (constant per year) across lineages with wildly different generation times, whereas synonymous DNA substitutions track generation time (faster per year in short-lived rodents than in long-lived primates).

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Kimura's Diffusion Fixation Probability

In a diploid Wright–Fisher model population of census size N and effective population size N_e, consider a newly arisen mutation with additive (semidominant, h = 0.5) selective effect s per copy, such that the relative fitnesses of the wild-type homozygote (AA), heterozygote (Aa), and mutant homozygote (aa) are 1, 1 + s, and 1 + 2*s*, respectively. Using Kolmogorov backward diffusion equations, Kimura (1962) proved that the probability u(s) that a single new mutation starting at initial frequency p₀ = 1 / (2*N*) ultimately reaches fixation (p = 1) is:

u(s) = [ 1 − exp(−2*N*_es / N) ] / [ 1 − exp(−4*N*_es) ]

For weak selection (|*s*| ≪ 1) where the ratio N_e / N is incorporated into the effective scaling parameter S = 4*N*_es, this expression simplifies via series approximation (1 − exp[−*x*] ≈ x in the numerator) to:

u(s) ≈ [ 1 / (2*N*) ] × [ 4*N*_es / (1 − exp[−4*N*_es]) ]

Here, u(0) = 1 / (2*N*) is the baseline fixation probability of a strictly neutral allele. The relative rate of substitution k / μ (or the nonsynonymous-to-synonymous divergence ratio ω = d_N / d_S) for a class of mutations with selection coefficient s is therefore determined solely by the dimensionless population-scaled selection coefficient S = 4*N*_es:

ω(S) = u(s) / u(0) = S / [ 1 − exp(−*S*) ]

Evaluating this exponential function across regimes reveals three distinct evolutionary behaviors:

1. Effectively Neutral Regime (|4*N*_e*s*| ≪ 1, or |*N*_e*s*| < 0.25): A Taylor expansion of exp(−*S*) ≈ 1 − S + ½*S*² gives ω(S) ≈ 1 + ½*S* ≈ 1. Drift dominates over selection, and mutations fix at approximately the neutral rate k ≈ μ.
2. Nearly Neutral Regime (0.25 ≤ |*N*_e*s*| ≤ 2.5, or 1 ≤ |4*N*_e*s*| ≤ 10): For a slightly deleterious mutation with N_es = −0.5 (S = −2), ω(−2) = −2 / (1 − e²) = 2 / (7.389 − 1) ≈ 0.313. Thus, a deleterious mutation with |*N*_e*s*| = 0.5 still fixes at 31.3% of the neutral rate via random genetic drift. At N_es = −1 (S = −4), ω(−4) = 4 / (e⁴ − 1) ≈ 0.075 (7.5% of the neutral rate).
3. Strongly Selected Purifying Regime (N_es ≪ −2.5, or 4*N*_es < −10): For N_es = −5 (S = −20), ω(−20) = 20 / (e²⁰ − 1) ≈ 4.1 × 10⁻⁸ ≈ 0. Purifying selection eliminates the mutation with near-certainty before it can drift to fixation.

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The Gamma Distribution of Deleterious Mutations

Rather than sharing a single selection coefficient, newly arising nonsynonymous (amino-acid-altering) mutations draw their deleterious selection coefficients (s < 0) from a continuous probability density function known as the Distribution of Fitness Effects (DFE). Empirical analyses of site-frequency spectra across viral, bacterial, plant, insect, and mammalian genomes demonstrate that the deleterious DFE is well-approximated by a reflected gamma distribution with shape parameter β (typically 0.15 ≤ β ≤ 0.35, producing a highly leptokurtic L-shaped curve) and scale parameter s̄:

f(|*s*|) ∝ |*s*|^β−1 exp(−*β* |*s*| / s̄)

Integrating Kimura's fixation probability across a gamma-distributed DFE with shape parameter β yields a power-law relationship between the average nonsynonymous substitution ratio (ω = d_N / d_S) and the effective population size N_e (Ohta, 1977; Kimura, 1979; Welch et al., 2008):

d_N / d_S ∝ N_e^−*β*

Because β > 0, as effective population size N_e decreases, the selection–drift threshold |*s*| ≤ 1 / (4*N*_e) shifts outward to encompass a larger fraction of the gamma distribution, causing d_N / d_S to rise. Conversely, in huge populations (N_e > 10⁶), the threshold 1 / (4*N*_e) shrinks so close to zero that virtually all nonsynonymous mutations with functional consequences are purged by selection, driving d_N / d_S down.

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Protein Clocks vs. Synonymous DNA Clocks

One of the sharpest challenges to Kimura's 1968 strict neutral theory was the generation-time discrepancy:

• Because germline DNA replication errors occur primarily during cell divisions per generation, the neutral mutation rate per year is μ_year = μ_gen / g, where g is generation time in years.
• Consequently, short-lived organisms with short generation times (such as mice and rats, g ≈ 0.5 years) exhibit a 3- to 5-fold faster rate of synonymous nucleotide substitution (d_S per year) than long-lived organisms with long generation times (such as hominoid primates or elephants, g ≈ 20–25 years).
• Yet when Zuckerkandl, Pauling, and Kimura examined nonsynonymous amino acid replacements (d_N per year) in proteins, rodents and primates accumulated amino acid substitutions at nearly the same rate per chronological year!

Ohta (1972, 1992) explained this paradox through the ecological inverse correlation between body size/generation time (g) and effective population size (N_e). In terrestrial ecosystems, small-bodied, short-generation animals (such as murid rodents or Drosophila) maintain large effective population sizes (N_e ≈ 5 × 10⁵ to 2 × 10⁶), whereas large-bodied, long-generation animals (such as hominids, cetaceans, and proboscideans) maintain small effective population sizes (N_e ≈ 10⁴).

Let f₀ ∝ N_e^−*β* denote the fraction of newly arising amino acid mutations that fall within the effectively neutral window |*s*| < 1 / (4*N*_e). The amino acid substitution rate per year (k_year) is the product of the mutation rate per generation (μ_gen), the neutral fraction (f₀), and the number of generations per year (1 / g):

k_year = (μ_gen / g) × f₀(N_e)

• In Short-Generation Rodents: Small g increases the per-year mutation input (μ_gen / g), but large N_e shrinks the effectively neutral window f₀, purging most slightly deleterious amino acid variants.
• In Long-Generation Primates: Large g reduces the per-year mutation input (μ_gen / g), but small N_e widens the effectively neutral window f₀, allowing a larger fraction of slightly deleterious amino acid variants to drift to fixation.

The cancellation of g and N_e stabilizes protein evolution per chronological year while leaving strictly neutral synonymous sites (d_S, where f₀ ≈ 1 regardless of N_e) dependent on generation time.

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The McDonald–Kreitman Framework and Endosymbiont Genomes

The nearly neutral theory also explains why within-population polymorphism frequently exhibits a higher ratio of nonsynonymous-to-synonymous variants (P_N / P_S) than between-species fixed divergence (D_N / D_S) in the McDonald–Kreitman (1991) contingency table. Slightly deleterious mutations (−10 < 4*N*_es < −1) can drift to low or intermediate allele frequencies within a population—contributing substantially to standing polymorphism P_N—yet are eventually prevented from reaching complete fixation (p = 1), keeping D_N low.

Across the tree of life, comparative genomics confirms the inverse scaling of d_N / d_S, genome size, and intron/transposable-element accumulation (Lynch & Conery, 2003) with N_e:

In obligate intracellular bacterial endosymbionts of insects (such as Buchnera aphidicola in aphids and Wigglesworthia glossinidia in tsetse flies), vertical maternal transmission through small transovarial bottlenecks reduces N_e by orders of magnitude relative to free-living enteric bacteria. Consistent with Ohta's theory, Buchnera proteins accumulate slightly destabilizing amino acid substitutions at rates 2- to 5-fold higher than Escherichia coli, requiring the bacterium to devote up to 10% of its total cellular protein synthesis to the heat-shock chaperonin GroEL/GroES to prevent protein aggregation (Moran, 1996).

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How does the nearly neutral theory differ from Kimura's strict neutral theory?

Kimura's 1968 strict neutral theory assumed that almost all mutations are either completely neutral (s = 0) or so strongly deleterious (|*N*_e*s*| ≫ 1) that purifying selection eliminates them regardless of population size. Ohta's nearly neutral theory recognized a large class of slightly deleterious mutations with selection coefficients near the reciprocal of the effective population size (|*N*_e*s*| ≈ 1), whose fixation probability depends inversely on N_e.

Why do mammals have a higher d_N/d_S ratio than fruit flies or bacteria?

Mammals such as humans and whales have relatively small long-term effective population sizes (N_e ≈ 10⁴) compared to Drosophila (N_e ≈ 10⁶) or free-living bacteria (N_e > 10⁸). Because random genetic drift is stronger in small populations, mutations with weak deleterious effects (such as s = −10⁻⁵) behave as effectively neutral in humans (|4*N*_e*s*| = 0.4 < 1) and drift to fixation, whereas the same mutations are purged in Drosophila (|4*N*_e*s*| = 40 ≫ 1).

Can slightly beneficial mutations also be nearly neutral?

Yes. In Ohta's late-1990s formulation and modern diffusion models, the nearly neutral regime is symmetric around zero (−10 ≤ 4*N*_es ≤ +10). Slightly advantageous mutations—such as synonymous mutations Toward preferred codons or weakly compensatory amino acid changes—experience weak positive selection in large populations (N_es > 1) but behave as effectively neutral in small populations (N_es ≪ 1), explaining why adaptive codon usage bias is prominent in Drosophila and bacteria but weak in mammals.

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1. Ohta, T. (1973). "Slightly deleterious mutant substitutions in evolution." Nature, 246(5428), 96–98. https://doi.org/10.1038/246096a0
2. Ohta, T. (1992). "The nearly neutral theory of molecular evolution." Annual Review of Ecology and Systematics, 23(1), 263–286. https://doi.org/10.1146/annurev.es.23.110192.001403
3. Kimura, M. (1962). "On the probability of fixation of mutant genes in a population." Genetics, 47(6), 713–719. https://doi.org/10.1093/genetics/47.6.713
4. Moran, N. A. (1996). "Accelerated evolution and Muller's rachet in endosymbiotic bacteria." Proceedings of the National Academy of Sciences, 93(7), 2873–2878. https://doi.org/10.1073/pnas.93.7.2873