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molecular clock question

Donald A. Lehn donnel at helix.nih.gov
Fri Sep 6 10:32:43 EST 1991

In article <9109052236.AA17124 at bambi.ccs.fau.edu> tomh at BAMBI.CCS.FAU.EDU (Tom Holroyd) writes:
/>Hi.  I'm doing a report on molecular clocks, and I thought I might find
/>some folks to talk to on the mol-evol list.  My background for this is
/>I've noticed that there is a lot of controversy over the "rate" of
/>evolution.  My mathematical training leads me to suppose that evolution
/>proceeds in a manner that may not even have a well defined "rate", let
/>alone a constant linear rate, as some have supposed.

The main problem is that there is not a good measure of evolution.  If
you cannot define EVOLUTION, then you cannot define d[EVOLUTION]/dt.

/>Recent theoretical work in self-organizing systems suggests that organisms
/>live at the boundary of order and chaos.  It may sound prosaic, but consider
/>that order is represented by fixed, periodic behavior, never changing -
/>any creature that never changes is not likely to survive long - and chaos
/>is a type of randomness - creatures that are too random, too disorganized,
/>are also unlikely.  A more precise formulation exists, but this will do for
/>now.  The point being that systems (and organisms) that live on the boundary
/>between order and chaos have just the right amount of flexibility to cope
/>with new situations, and yet also function in an organized, ordered fashion.
/>Mathematically, this region is characterized by "intermittency" - meaning
/>there may be "bursts" of change, followed by periods of relative stability.
/>This is a mathematical basis for the punctuated equilibrium theory of
/>evolutionary change.  PE has a good theoretical foundation.
/>Systems that behave this way show power law scaling of the bursts with
//>respect to time.  The cute way of saying this is "an order of magnitude
/>more bursts, an order of magnitude less often."  This means that the bursts
/>of change happen on all time scales, or, that there is no characteristic
/>time for change in such systems.  This would correspond to the "rate"
/>of evolution, if it existed, but these arguments suggest that the rate,
/>or characteristic time, is undefined: a power law scaling would be the
/>more appropriate description.
/>Another avenue of attack is that the genetic structure of an organism
/>is hierarchical.  If you start with the assumption that point mutations
/>are equally probably anywhere along the genome (a perhaps not too safe
/>assumption, but it would only help my argument if it was false), then you

It is probably safe to assume that the mutational rate of DNA is
fairly constant ( 5e-9 nucleotide substitutions per base per year).
However all mutations are not created equal.  The vast majority of
mutations in mammals are in regions of 'junk' DNA and are silent. 
Other mutations occur in the 'wobble' position of the triplet code
and are silent.  In these regions, the rate of mutation appears
to be constant and can be used to predict when two organisms
diverged.  Other mutations are lethal.  For instance, histones H3 and
H4 are virtually identical in all eukaryotes.  Therefore, if we
base the rate of evolution on their sequences, we would find that the
rate is extremely slow.  This doesn't imply that the H3/H4 DNA mutates
less frequently only that mutations there confer a strong selective
disadvantage.  As this illustrates,  the rate of evolution is multivarient.
It is not only a function of the rate of mutation of DNA with time 
(which is virtually constant) but also the rate at which these mutations 
can be propagated in future generations.  Thus, the determining factor
is more often the selective pressures in the environment.

/>can examine each point on the genome and ask the question "would a
/>mutation here produce a viable creature?"  If the answer is "no",
/>then you can ask "would an additional mutation somewhere else help?"
/>What I'm driving at is that some points are going to need mutations
/>at other points first, if the creature is to survive.  In fact, there
/>may be a large cascade of changes necessary before a single mutation
/>can be viable.  When this happens, the probabilities for change
/>become linked, and you multiply them, producing distributions of
/>viable mutations with long tails, i.e. power law scaling.
/>The point of all this is that mathematically, I don't expect mutations
/>to occur at a constant, linear rate.  I don't even expect there to

As pointed out previously, the mutations occur randomly and at a constant,
linear rate.  It is the phenotypic effects of these mutations that
will determine whether the particular mutation will lead to its
enhanced or limited propagation in future generations.

/>be a well defined rate, except that the variability of the mean might
/>settle down over a time scale of several hundred million years, making
/>molecular clocks useful on large time scales only.  Even then, though,
/>one cannot rule out the possibility that a "burst" may be waiting

'Bursts' happen all the time.  The trick is to recognize them.

/>to happen right around the corner, or just happened a few millenia
/>ago, leading to a large error in the time estimate.  Also, over such
/>large time scales, there is a good chance of some event occurring that
/>totally redefines all the probabilities (i.e. it's a non-stationary
/>The mathematics of percolation clusters and self-organized criticality
/>is also relevant here.  Life exists on the side of a sandpile, if you
/>know what that means.
/>A side note: how likely are totally neutral mutations?  Even if a codon
/>mutates to one coding for the same amino acid, the relative concentrations
/>of the appropriate tRNA, or interactions with DNA-binding regulatory
/>proteins could confer a selective advantage.
/>Any comments from the biologists (or the mathematicians)?
/>Tom Holroyd
/>Center for Complex Systems
/>Florida Atlantic University
/>tomh at bambi.ccs.fau.edu
/>P.S. I'd be happy to discuss any of the above mentioned models in detail.

Donald A. Lehn, Ph.D.                      Phone: (301) 496-2885
Bldg.37 Rm 3D20                            FAX:   (301) 496-8419
National Cancer Institute / NIH            Email: donnel at helix.nih.gov
Bethesda MD 20892

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