near neutrality & compensatory evolution

Gillespie JH 1995 On Ohta's hypothesis: most amino acid substitutions are deleterious. J Mol Evol 40:64-69.

Ohta's hypothesis that most amino acid substitutions are deleterious grew out of a class of population-genetics models called shift models
shift models have been shown to be biologically unreasonable and have been replaced by a more plausible house-of-cards model
the simplest form of the house-of-cards models is shown to be incompatible with most of the major features of protein evolution
this model is shown to not be a model of exclusively deleterious-allele evolution
rather to be a model with an equal mix of deleterious and advantageous substitutions

by 1971, five generalities about molecular evolution and polymorphism had emerged
providing the motivation and support for both Kimura's neutral theory of molecular evolution (Kimura 1968; Kimura and Ohta 1971)
and for Ohta's nearly neutral theory (Ohta and Kimura 1971; Ohta 1972)

the protein clock runs in real time rather than generational time
the DNA clock runs in generational time rather than real time

the neutral theory, circa 1971, could account for protein evolution or DNA evolution, but not both
at the same time, Ohta and Kimura (1971) introduced the nearly neutral theory, which could account for all five generalities
the nearly neutral theory was, in many ways, more revolutionary than the neutral theory
as it hypothesized that the vast majority of all amino acid substitutions were deleterious
but it, too, had an untenable assumption
the assumption concerned the assignment of fitnesses to mutations
the problem escaped notice for 19 years
during which time the nearly neutral theory became the dominant paradigm of molecular evolution

Ohta and Tachida have written a series of papers introducing a new version of the nearly neutral model
one with a more realistic assumption about the assignment of fitnesses (Ohta and Tachida 1990; Tachida 1991; Ohta 1992)
the papers do not spend time examining the new model in the context of the generalities that motivated the nearly neutral model in the first place
they contain little discussion on one vital point: are the fixations that occur under fixed models deleterious?

the new model does not appear to be a robust candidate for molecular evolution
only half of the substitutions are deleterious
the other half are advantageous
the reason for the slowdown in protein evolution (when compared to DNA evolution) under the new model is not the difficulty of fixing deleterious nearly neutral alleles
rather it is because evolution has taken proteins to such exalted states that mutation rates to alleles that are candidates for substitution drop to near zero
the model is fragile
a small change in its assumptions usually leads to a qualitative change in its dynamics

some background on Kimura and Ohta's neutral model as described in 1971
which addressed only protein evolution and polymorphism
the neutral mutation rate, measured in real time, is constant across species for a given locus
mutations come in two flavors: neutral and "very" deleterious
at the time, clock-time mutation rates were not generally accepted
thus, the neutral theory did not, as is commonly claimed, "predict" the molecular clock

one might quibble that the number of assumptions equals the number of generalities
but we will leave that for philosophers of science
the theory cannot, however, account for the generational clock of DNA evolution or any of the other three generalities
Ohta's theory did that

her generalization of the neutral allele theory to the "nearly neutral" theory
the mutation rate across species is constant per generation rather than per year
this is a significant departure from the assumption of the Kimura and Ohta paper
the great majority of all amino acid mutations, even those that are nearly neutral, are deleterious
the generation time is inversely proportional to the population size
mean selection coefficients of deleterious amino acid mutations are locus specific
clearly uncomfortable with the clock-time dependency of mutation rate assumed in their other paper of the same year

unlike the neutral model, the rate of substitution under the nearly neutral model depends on the population size
we have the clock-time protein clock without the awkward assumption that mutation rates are clock-time dependent
the "great leap forward" of the nearly neutral model

much of the development of the nearly neutral theory in the seventies concerned its implications for polymorphism rather than substitutions

there can be little doubt that Ohta's nearly neutral theory is the dominant paradigm for molecular evolution
Kimura himself finally turned to the theory in 1979 (Kimura 1979)
and used it for his book on molecular evolution (Kimura 1983)

I will argue that the great majority of nearly neutral mutations are not deleterious
most importantly, I will show that of those that are fixed, precisely one-half are deleterious and one-half are advantageous

the original nearly neutral models did not address the distribution of selection coefficients
the first use of a distribution appears to be in Ohta (1977)
there she cited Alan Robertson (Robertson 1967) as justifying the use of an exponential distribution
Robertson is discussing the distribution of effects across loci while Ohta is discussing the effects within a locus

Ohta felt that the fraction of mutations that are deleterious is so high that we will not be in serious error in assuming that all mutations are deleterious
she is not denying the existence of progressive evolution

Kimura (1979) suggested that a gamma distribution with shape parameter 1 / 2 is preferable to an exponential distribution
the gamma shift model, as it came to be known, was the model of protein evolution used in his book (Kimura 1983)

it is generally accepted that a great majority of new mutations are deleterious
it is natural to assume that a great majority of borderline mutations are deleterious as well
(Ohta 1977, page 149)

the error of logic should have been challenged at the time
but wasn't
the conflict with Fisher's (1958) view, based on an abstract model of phenotypic evolution, that the fraction of deleterious mutants should approach one-half as the strength of selection acting on mutations approaches zero, went unnoticed

shift models require that all mutations be deleterious
when a deleterious mutation fixes, all subsequent mutations must be less fit than it
not simply less fit than the allele it replaced
the frame of reference of mutant effects is constantly shifting
hence the name

in the 1990s, Ohta changed from shift models to fixed models for her nearly neutral theory
fixed models are more frequently called house-of-cards models in the population-genetics literature (Kingman 1978)
it is important to remember that the model only applies to mutations of relatively small effect
the full distribution of mutations, including lethals and other mutations of large effects, is irrelevant to molecular evolution and our discussion
the significance of the house-of-cards model is that it mimics very closely a view of progressive evolution held by many evolutionists
are "a great majority of borderline mutations deleterious as well?"

I have used computer simulations to explore the main feature of the model as well as those of a number of other models of deleterious alleles (Gillespie 1994)

the observation that a great majority of all mutations of large effect are deleterious does not logically lead to the assumption that the great majority of all those of small effect will be deleterious as well
of those that fix, precisely half are advantageous and half are deleterious
the house-of-cards is not a model of exclusively deleterious-allele evolution
the reason for the slowdown in evolution is not the difficulty of fixing deleterious alleles
they are as likely to fix as are advantageous ones
it is because the mutation rate to candidate alleles has dropped to near zero

Fig. 1 suggests that real populations will find themselves in one of two domains
in the left domain (α < 1), the house-of-cards model gives way to the neutral model
in the right domain (α > 4), there are not substitutions
house-of-cards model does not appear to be compatible with the clock-time dependency of the protein molecular clock

the move from the shift model to the house-of-cards model, a move toward greater biological plausibility in assumptions, makes Ohta's original hypothesis appear untenable

two additional assumptions could be added to the house-of-cards model to enrich its dynamics and possibly increase its fit to the data
fluctuations in population size or in fitness

when population size is small enough (α < 1), alleles will fix that would be too deleterious to fix in large populations
when the population size increases, a small burst of substitutions of advantageous alleles will replace the allele fixed in the small population
this scenario does not involve the fixation of any deleterious alleles
and is precisely the scenario that I have called the "mutational landscape" (Gillespie 1984, 1991)
Ohta has often called the substitutions that occur in the burst "compensatory" substitutions as they fix up the problems caused by the substitution of the neutral allele that later became deleterious