Distance metrics should not be equated with time

arlin at ac.dal.ca arlin at ac.dal.ca
Sat Jul 4 21:00:50 EST 1992

Traditionally, evolutionary distance is not restricted to units of time (as
Larry Moran suggests), nor is it directly observable (as others have
implied)-- "difference" is what is directly observable.  For instance, it is
clear that human and gorilla beta-hemoglobin differ at 1 site in their amino
acid sequences (Lys-104 in gorilla vs Arg-104 in humans, if I remember
correctly).  We may say that the proteins "have a single site DIFFERENCE;" or
"are DIFFERENT at 1/146 of sites (they have 146 amino acids, I think);" or
"are 0.68% DIFFERENT."

An evolutionist may inform us that this manifestly countable DIFFERENCE does
not tell the whole evolutionary story; that, actually, due to the small but
finite probability of parallel amino acid replacements in both
beta-hemoglobins (or forward and backward changes in one of them), a
difference of 0.68% corresponds to 0.71% expected amino acid replacements in
the divergence of the two sequences: this value, which is calculated from the
observed DIFFERENCE, is a DISTANCE.  As a distance measure, it would be based
on a model that purports to reflect at least some aspects of the actual series
of evolutionary events that took place, and accounts for the changes that are
hidden, as well as those that are apparent as present-day observable

The reason it is may be unwise to equate distance with time is simply that
entities evolve at different rates.  For instance, pea and cow Histone H2 have
a single amino acid difference, just like human and gorilla beta hemoglobin.
These two pairwise protein comparisons would therefore yield similar
difference and distance values.  However, the histone pair has been diverging
roughly 100 times as long as the beta-hemoglobin pair (compare 7 MY for
human/gorilla with perhaps 700 MY for pea/cow).

[Now that I've written this it occurs to me that pea and cow histone H2 may
actually have identical amino acid sequences, not a single difference, but
this would only strengthen the example.]

Arlin Stoltzfus
Department of Biochemistry
Dalhousie University
Halifax, Nova Scotia
arlin at ac.dal.ca

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