near neutrality - senecio7の日記

Ohta T & Gillespie JH 1996 Development of neutral and nearly neutral theories. Theor Popul Biol 49:128-142.

emphasis is placed on the nearly neutral theory
as this version of the neutral theory has explained the widest range of phenomena

hemoglobins are evolving at a steady rate of 1.4 × 10^{− 7} amino acid substitutions per year
Kimura (1968a) realized the general significance of this finding
one nucleotide pair has been substituted in the population roughly every 2 yr
if these substitutions were caused by natural selection, the rate of substitution was too large to be compatible with Haldane's (1957) upper limit based on the cost of natural selection
therefore, he proposed that many of the substituted alleles must be neutral

Kimura's original argument for the neutral theory depended on the concept of the cost of natural selection or the substitutional load
subsequent discussions of the neutral theory became almost independent of genetic load considerations
the apparent constancy of the amino acid substitution rate, the molecular clock, was thought to support the neutral theory
King and Jukes published "Non-Darwinian Evolution"
this was the first paper to note the inverse relationship between the importance of a protein or site within a protein and its rate of evolution

another notable achievement in the 1960s was the infinite-allele model as formulated by Kimura and Crow (1964)
4Nu / (1 + 4Nu) ... (1)
Kimura and Crow, along with most population geneticists of that time, were unaware that Malécot (1948) had already derived Eq. (1)
more than two-thirds of the Kimura-Crow paper was devoted to the symmetric overdominance model, even though this paper has mostly been cited for its neutral allele results

the Ewens sampling distribution (Ewens 1972), has been used to develop tests of agreement between the neutral theory and observed polymorphisms
a mutation whose selection coefficient, s, is much less than the reciprocal of the population size, s ≪ 1 / N, behaves as if it were strictly neutral, s = 0
such mutations were called nearly neutral during the 1960s
later, nearly neutral mutations were defined as ones whose selection coefficients are close to the reciprocal of the population size, s ≈ 1 / N

do deleterious mutations with s ≈ 1 / N play an important role in molecular evolution or will they be eliminated like those of larger effect?
Ohta and Kimura (1971) and Ohta (1972, 1973, 1974) considered this problem and proposed that slightly deleterious borderline mutations might be quite common among amino acid substitutions
there will be a negative correlation between the evolutionary rate and the species population size

the theoretical modelling of near neutrality has come to a turning point in the 1990s
previous studies were based on the shift model, under which selection coefficients are chosen at random from some probability distribution
this is done, in part, to meet the assumption that all mutations are deleterious
the shift model was replaced with the fixed model, in which the distribution of selection coefficients is assumed to be fixed, independent of the fitness of the parent allele and the mean fitness of the population
the population fitness fluctuates as a result of mutant fixations rather than shifting as with the previous models (Ohta and Tachida, 1990)
the fixed model was originally called the house-of-cards model
the substitution rate fluctuates in the fixed model because the effects of each substitution remain to affect subsequent substitutions by changing the mean fitness of the population
in other words, substitutions are interrelated
the variance in the rate becomes larger than the simple Poisson model predicts

of the substitutions that actually fix under the fixed model, one-half are deleterious and one-half are advantageous
thus, the nearly neutral model is no longer a model with only deleterious mutant substitutions
but rather one with a mixture of substitutions of positive and negative effects
the principle of molecular evolution, that is more important regions evolve more slowly, remains one that is readily explained by the nearly neutral model
even though "nearly neutral" no longer implies deleterious
as it did in the past

several theories of molecular evolution where natural selection rather than genetic drift is the main force, causing fixation, have been pursued during the 1990s
one of these is called the mutational landscape model (Gillespie, 1984b, 1991)
which was proposed to explain the episodic nature of amino acid substitutions
an environmental shift is needed to move the population off of the local peak and into a burst of substitutions until it stagnates once again at another local maximum
as environmental changes set the pace of evolution rather than the mutation rate, this model does not exhibit a generation-time effect
Kauffman (1993) called his generalization of the mutational landscape model the NK model
this is a model of epistatic interaction among K + 1 amino acids
when N = K and both are large, we have the mutational landscape model
if the height of the peaks is much greater than the reciprocal of the population size, then environmental fluctuations are required for continuing evolution
if they are similar to 1 / N, then there will be nearly neutral evolution
this picture may be a modern view of the shifting balance theory (Wright, 1931)

the SAS-CFF model is similar to the TIM model
the SAS-CFF model has been developed to explain patterns of protein evolution mainly when selection is strong and mutation is weak (Gillespie, 1991)
one conclusion from a simulation study of many different population genetics models is that high values of R(t) are difficult to explain without environmental fluctuations that occur on very long time scales (Gillespie, 1994a)
while models based on fluctuating environments can explain the absence of a generation-time effect and large R(t) in protein evolution, they are conspicuously poor at providing explanations for other aspects of protein evolution
they cannot explain why the rate of amino acid substitution per site is so similar to the mutation rate for many proteins
they cannot explain why most proteins evolve slower than pseudogenes
they cannot explain why there is not even more variation in rates of substitution

while the 1990s will most likely be a decade dominated by the gathering of data, we would like to call attention to a looming crisis as theoretical investigations lag behind the phenomenology