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evidence for non-neutrality

Tom Holroyd tomh at BAMBI.CCS.FAU.EDU
Sun Sep 22 15:49:27 EST 1991

I picked up the following two references:

MacRae, A.F., and W.W. Anderson, Evidence for non-neutrality of mtDNA
haplotypes in Drosophila pseudoobscura.  Genetics 120: 485-494, 1988

Gillespie, J.H., The molecular clock may be an episodic clock.
PNAS 81: 8009-8013, 1984

MacRae and Anderson followed the mtDNA frequencies for up to 32 generations,
and found classical non-linear effects in 12 populations that were
polymorphic for mtDNA haplotypes.  In one population composed of two
strains (Bogota and Apple Hill 162), the frequency of the Bogota haplotype
increased 46% in 3 generations, reaching an apparently stable equilibrium
of 82% after 32 generations.  Perturbation of the equilibrium by adding
the less common strain caused a temporary decrease in the Bogota haplotype,
but a return to the same equilibrium.

The increase in frequency of the Bogota strain was non-linear (i.e.
non-constant), and the stable equilibrium that was reached seems to be
at odds with neutrality, which would assume that the frequency would
drift randomly until one or the other strains was fixed.

An obvious point (to me, at least) is that the haplotypes are not
neutral.  Is this true?  What exactly is a polymorphic mtDNA haplotype?
The paper says "Most evolutionary studies of mtDNA rely ... on the
neutral mutation theory, which assumes that mutations accrue at a constant
rate in mtDNA, to produce an estimated 2% sequence divergence per million
years."  Surely not *every possible* mutation is neutral?  Even among the
viable ones.

The Gillespie paper presents a mathematical model of protein evolution.
The abstract:
	"It is argued that the apparent constancy of the rate of molecular
evolution may be an artifact due to the very slow rate of evolution of
individual amino acids.  A statistical analysis of protein evolution using
a stationary point process as the null-hypothesis leads to the conclusion
that molecular evolution is episodic, with short bursts of rapid evolution
followed by long periods of slow evolution.  Such dynamics are incompatible
with the neutral allele theory and require a revision of the standard
interpretation of the molecular clock."

I don't understand all the statistics, but the basis of the argument seems
to be the dispersion, or the ratio of the variance to the mean of the number
of substitutions (X) among n lineages stemming from a common ancestor.  For
a purely neutral evolution, the X variables are distributed according to a
Poisson distribution and the dispersion (R) is equal to 1.  Gillespie does
simulations (using the stationary point process) with dispersion equal to
10, and shows that the observed dispersion with only 150 amino acids is
1.17, and that therefore Kimura's claim that R values close to 1 support
the neutrality hypothesis is "vacuous."  He suggests that the true R
value may be as high as 1000 for beta hemoglobin.  The R statistic is

This study seems pretty good, although I can't understand all of it.

As for cytochrome C, I came up with this (old) quote:

Richmond, R.C, Non-Darwinian Evolution: A critique.  Nature 225: 1025-1028,

"... according to Simpson (*) the hypothesis of a constant rate of amino
acid substitution is not supported when the available data are plotted
against the best estimates for the times of divergence of the species
in question."

(*) Simpson, G.G., Science 146: p1535, 1964.

I haven't read the reference, but I'm sure the error bars on paleontological
charts are big.  Also, I've seen some cytochrome C data, and it seems to go
way back (400-500 My) which, even if the rate were not constant, might be
enough time to generate a useful average (useful for dating things that are
500 My old, that is; not useful for dating things only 1 My old).

Tom Holroyd
Center for Complex Systems
Florida Atlantic University
tomh at bambi.ccs.fau.edu

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