# out of africa

Alan R. Rogers rogers at ANTHRO.UTAH.EDU
Mon Nov 25 17:45:21 EST 1991

```>HXH5>Is it not as likely that the greater diversity in Africa just reflects
>HXH5>higher effective size of the human population in Africa during the
>HXH5>later pleistocene?    It may have nothing to do with time.  And if
>HXH5>there is more diversity in Africa, then tree generating algorithms
>HXH5>will make trees that look like there are unique African lineages but
>HXH5>a lot of others that have both African and non-African representatives.
>
>Jones> At last, a serious and thought-provoking post.
>
>Well, it provoked my thought, but so far I'm drawing a blank as to how
>higher "effective size" [What does that mean?] of the human population in
>Africa really explains anything.  Doesn't the mtDNA clock run at the same
>rate regardless of population?  If so, the difference between the mtDNA of
>two individuals should provide a measure of the age of their youngest common
>ancestor in maternal lineages.  Even if lower fertility or higher death
>rates causes the real complete maternal tree of a particular population to
>less branched or more pruned, I don't see how this effects attempts to
>reconstruct a tree from a sampling of mtDNA from contemporary individuals --
>a tree which, necessarily, is severely pruned compared to the real tree
>since it includes only those lineages that lead to the sampled individuals.
>
>Don Bashford

The easiest way I know to gain an appreciation of the twin roles of time and
population size is to consider the evolution of the mean number of
nucleotide differences between pairs of individuals within a population.
Suppose that this statistic is equal to m(0) at time 0.  What value will it
have t generations later?  If the population size remains constant and if the
"infinite sites" model is a reasonable approximation (see note 1 below),
then the answer is a result due to Wen-Hsiung Li (see note 2):

m(t) = theta + (m(0) - theta) exp(-t/N)               (1)

where

theta = 2 N u
N = effective population size (defined in note 3 below)
u = mutation rate per cistron, the sum of per nucleotide mutation
rates

At equilibrium, the mean pairwise difference is

lim  m(t) = theta = 2 u N
t -> infinity

and is thus proportional to N, the population size.  There is thus a clear
rationale for considering m to measure population size.  However, people
often refer to m as a measure of the "age" of a population.  This appeals
(often implicitly) to the assumption that at some time in the past m was
very small.  This would happen, for example, if the population passed
through a very narrow bottleneck.  If m(0) is negligible compared with
theta, and if t << N, then equation 1 is approximately

m(t)   approx=   theta t/N = 2 u t

Thus, if the population has passed through a bottleneck fairly recently then
m is proportional to the time since that bottleneck rather than to
population size.  This is the rationale for referring to m as a measure of
the "age" of the population.

What then are we to make of the fact that m is significantly greater within
the African population than within other continental populations?  The
"replacement hypothesis" of modern human origins is often associated with
the assumption that these populations passed through a bottleneck at the
time Homo sapiens sapiens originated.  If so, then m is a measure of age and
we conclude that the African population is older than the others.  Thus, we
are led to suspect that modern humans originated there.  On the other hand,
proponents of the "multiregional hypothesis", which holds that modern humans
evolved in a widespread population that populated much of Africa, Asia, and
Europe, do not usually argue for any recent bottleneck.  In that case m is a
measure of population size, not of age, and the greater value within Africa
simply means that the African population has been larger.  Since the excess
African value of m can be accomodated by either hypothesis, it cannot *by
itself* be used in support of either one.

However, there is other evidence in favor of the bottleneck hypothesis.
First, the common mitochondrial ancestor of all modern humans seems to have
lived within the past 250,000 years (note 4).  The expected time (in
generations) to this event is 4 N, which would be roughly 100 N years.
Thus, if the human population has been large for a long time, then our
common mitochondrial mother lived much more recently than she should have.
Second, human mitochondrial variation also exhibits evidence of a pronounced
population expansion (or bottleneck) that seems to have occurred between
50,000 bp and 120,000 bp (note 5).

Unfortunately, the statistical properties of the estimates just discussed
are poorly understood, and we therefore cannot properly claim to have tested
either hypothesis.  The genetic evidence seems to favor the replacement
hypothesis, but in my view the case is not yet compelling.

NOTES:

(1) The infinite sites model assumes that at most one substitution has
occurred at each nucleotide site.  It is a good approximation provided that
the time, t, is small compared with the reciprocal of the subsitution rate
per nucleotide.

(2) Li, W.-H. 1977. Distribution of nucleotide differences between two
randomly chosen cistrons in a finite population. Genetics, 85:331-337.  See
Li's equation 6.

(3) In this context the effective population size is defined as the
reciprocal of the probability that two randomly chosen individuals had the
same mother.

(4) There are several pertinent references, but I will mention only one:
Hasegawa, M. and Horai, S. 1991. Time of the deepest root for polymorphism
in human mitochondrial DNA. Journal of Molecular Evolution 32:37-42.

(5) Rogers, A. R. and H. C. Harpending. 1992. Population growth makes waves
in the distribution of pairwise genetic differences. Molecular Biology and
Evolution, In Press.

Alan R. Rogers
INTERNET  : rogers at anthro.utah.edu
USMAIL    : Dept. of Anthropology, Univ. of Utah, S.L.C., UT 84112
WORK PHONE: (801) 581-5529
FAX       : (801) 581-6252

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