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Primate population structure Evaluation of models.

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Primate Population Structure: Evaluation of Models
Department of Anthropology, Pennsylvania State University, University
Park, Pennsylvania 16802 (H.
H.);Department of Anthropology, University
of New Mexico, Albuquerque, New Mexico 87131 (S.C.)
Migration, Effective size, Gene frequencies, Breeding
Genetic markers among macaques on Cay0 Santiago island
were analyzed in an attempt to infer aspects of mating structure. Several
models that included high levels of gene flow among groups could not be
distinguished, but the data are clearly incompatible with group endogamy and
with high variance in male fitness. Drift effective size is approximately one
half census size in this population.
There are a large number of very detailed
studies of the local distribution of genetic
markers in human populations as well as in
populations of other species (for review, see
Jorde, 1980). Since relatively inexpensive
methods have become available for typing
genetic markers, the amount of such data
appearing in the literature seems to have
increased. The demographic and ethological
information accompanying these data vary
widely in quality, with the best information
being provided about human populations
where there are often high quality records of
births, matings, and migration.
Three sorts of rationale appear in the literature for doing this kind of work. The first
is from those who seek the signal of natural
selection among the noises of local genetic
drift. This effort has not produced much convincing evidence of natural selection, especially at the level of differences among local
populations, largely because gene frequencies and environmental variables are spatially autocorrelated and statistical inference
is very difficult and weak for such variables.
A second theme in the literature is to use the
distribution of markers to reconstruct population history (for review, see Felsenstein,
1982). While molecular taxonomy and dating
have been very valuable and useful for
studying taxa above the species level over
long (i.e., evolutionary) time periods, they
have not been very convincing for intraspecific work because time, effective population
size, and migration rates are inevitably confounded. Finally, there is the effort to use
local markers to measure aspects of population ethology. The hope here is that markers
will provide objective chemical evidence of
0 1986 ALAN R. LISS, INC.
social processes and that inference about
these processes can be made by examining
the distribution of chemical markers over
space and over social groups.
In this article we pursue the third tradition
of using chemical markers as social indicators. As Felsenstein (1982) remarks in his
review article, human geneticists have always had higher quality data than the zoologists have had, since people can talk, and
their methods have been somewhat more sophisticated. We propose here to apply some
current methods from human genetics to data
that have been collected about a free-ranging
primate population. Our interest is to see
whether contemporary population genetic
theory can inform us about aspects of the
population structure of these animals that
are not already well known.
We analyze the data on gene frequencies in
rhesus macaque troops on Cay0 Santiago island reported by McMillan and Duggleby
(1981) and by Duggleby (1978). These data
are excellent for our purposes since they are
a relatively complete sample of individuals
from a delimited population in which the
social structure is well known. If current
models in population genetics are to be really
useful for inference about feral mammals,
then they should at least be able to provide
meaningful information about this simple
A population of rhesus macaques was established on the Caribbean island of Cay0
Santiago in 1938, and it has been under more
Received April 9, 1984;revision accepted November 22,1985.
or less continuous scientific scrutiny since
that time. In the late 1970s there were approximately 300 animals on the island in
four troops, labeled F, I, J, and L in the literature. These troops remain after several others were removed in 1972. Gene frequency
data for these four troops are available in
Duggleby (1978; eight blood group loci) and
in Buettner-Janusch and Sockol(l974; transferrin variants). The differences among these
troops have been analyzed previously by
O'Rourke and Bach Enciso (1982), who apparently could detect a correspondence between differences among the groups and their
relative locations on the island.
Our purposes here are to use these very
excellent data about semifree-ranging primates t o evaluate three different models of
population breeding structure to see whether
population genetic data about feral mammals can give us useful insight into local
mating behavior. Our conclusions are essentially that these very high quality data are
entirely compatible with all three models and
that the genetic data cannot distinguish
among them. The three models all incorporate very high levels of gene flow among
troops. The genetic marker data are not compatible with either troop endogamy or with
the low effective size that would result from
a very few males fathering most of the offspring each generation.
All three models that we fit to the data are
special cases of the migration matrix model
of Smith (1969) and Bodmer and CavalliSfona (1968). In this model, genetic drift at
reproduction of each generation leads to dispersal of local gene frequencies from the array mean, while migration among groups
homogenizes local gene frequencies. These
two processes reach an equilibrium at which
drift is balanced by local gene flow. At such
an equilibrium, the dispersion in gene frequencies among newborns will be greater
than the dispersion of gene frequencies in
adults sampled after migration. We will call
the theoretical distribution of gene frequencies in newborns the child model and the
distribution in parents the adult modeL Since
in Duggleby's data animals are classified according to their troop of birth, the child model
rather than the adult model is appropriate.
We assume that the relative sizes of the
groups have been nearly constant for several
generations and that some fairly stable pattern of gene flow among the troops exists. (In
fact, we are considering models of high levels
of gene flow among troops, so these assump-
tions are not really necessary. As an extreme
case, recall that Hardy-Weinberg binomial
proportions follow from one generation of
random mating.)
In particular, gene flow among troops is
described by a migration matrix where the
entry in row i and column j is the frequency
among immigrants to thejth group each generation of those born in group i. "%is is a socalled backwards matrix, and each column
sums to unity. Given this, Rogers and Harpending (1985) show that the normalized
weighted gene frequency covariance matrix
among the adult members of the groups (that
is, after migration has occurred) is
Re) = VB(")V t
where B'"' (areferring to adults) is diagonal
In this expression, the matrix V is the matrix of left eigenvectors of the migration matrix, N is the total genetic effective size of
the array of subpopulations, and the
the second through the last eigenvalues of
the migration matrix. (The first eigenvalue
of the migration matrix is unity, and the
eigenvector corresponding t o the leading eigenvalue gives the relative group sizes,
which we assume to be constant.) The quantity Ro is a convenient overall measure of
genetic differentiation within the array of
subpopulations, equivalent to Wright's Fst.
Rogers and Harpending (1983)show that this
is given by the sum of the diagonal entries
B k of the matrix B'"). Notice that this formulation takes into account the variance generated by the random sampling of migrants
among groups, so it is an elaboration of and
a correction to the model given by Harpending and Ward (1982) and by Rogers and Harpending (1983), who neglected this source of
variance. Incorporating the randomness of
genes in migrants yields the curious result
that the adult model in this report is identical to the child model of Rogers and Harpending (1983): The stochasticity of gene frequencies in migrants has an effect equivalent
to the increment in drift from one generation
of reproduction.
The data from Cay0 Santiago, on the other
hand, require a slightly different model, since
individuals are classified according to the
troop in which they were born rather than
the troop with which they live. This is equivThis matrix has a leading eigenvalue of 1
alent to sampling newborn individuals in
troops rather than sampling adults. Rogers and three eigenvalues of zero. Substituting
= 0 in equation 2 yields
and Harpending (1985) show that the expected normalized covariance matrix for the
child model is
Ro=-. 3
N + 3
); = VB‘C’ vt
Random mating, then, yields the observed
where B“) (c referring to children) is a diago- value
= .0216 if the total effective size of
nal matrix with
the island population is 136. This is slightly
less than one half the census size and is an
entirely reasonable estimate of total effective
B!Ccc) = (1 - Ro) (2 - Af)
2N(1 - A)!
Under the random male migration model,
( 2 = 2,. . . . )
half of the genes are completely endogamous
(i.e., those in females) and their migration
matrix is just the identity matrix. The matrix for the other half of the gene pool is one
in which each row is composed of identical
entries, the relative size (“weight” wi)of the
Note that Ro measures overall differentia- group corresponding to that row. This is the
tion in this case in the same way as before, random mating model we just used. We take
except that the differentiation is now that the actual migration matrix of our model to
either among newborns or among individu- be the average of these two. Given troop sizes
als classified b place of birth. It is equal to of approximately 150:50:50:50,the model mithe trace of B“ ?
.The diagonal matrix B is not
gration matrix is the average of (representquite a matrix of eigenvalues of the R ma- ing the endogamous females)
trix, but of a related matrix that incorporates
relative population sizes (see Harpending and
Ward, 1982).
Given this general formulation, we now
derive parameters for three possible mating
situations: random mating, random male
mating, and random male exogamy.
By random mating we mean the random
allocation of parents-that is, if parents form and (representing random male movement)
groups and mate completely at random, then
gene frequency variation among the off.17
spring of these groups will be greater (by one
generation of drift)than the variation in their
parents. Thus, we cannot naively ‘test” for
random mating by using a chi-square statistic unless we are sampling adults after mi- which is
gration. But in these data individuals are
labeled by their birth troop, so the child
rather than the adult model is appropriate.
If adults are allocated at random, the cor.08
responding migration matrix is just a matrix
in which each row is the relative size of the
group corresponding to that row. For Cay0
Santiago, where the four troops are of apSince this is a totally connected probability
proximate sue 150:50:50:50, the random mi- transition matrix, it has a unique leading
gration matrix is
eigenvalue of 1 and three more eigenvalues
each equal to .5. Therefore, substituting into
equation 2 above, the predicted Bii for
i = 2 , 3 , 4 are
(1 - Ro) -*
The observed value of Ro is -0216, and this
would equal the prediction from this model if
the total effective size on the island were 159,
which is slightly more than one half of the
census size of 250. This may be about the
right ratio of effective to actual size for mammals like these, so the fit of the macaque
data to the random male migration model is
Finally, we may evaluate a model called
random male exogamy. The assumption of
this model is that males mate at random
among any troops except for their natal troop,
where they are forbidden to mate. To construct the migration matrix for this model
we assume that females are endogamous,
while for males the frequency of migrants
from group j into i is proportional to the size
of j for a l l j except i, for which the probability
is zero. For the Cay0 Santiago situation we
must average the female matrix:
and the male matrix
to yield
which is our random male exogamy migration matrix.
There now occurs an interesting problem.
The vector 3:l:l:l is not a stable vector of this
matrix In other words, this pattern of migration does not lead to the observed distribution of troop sizes. The reason is clear: If male
mating within the natal troop does not occur,
then there is very strong selection against
males from the large troop. This means that
there is also selection against the mothers in
large troops through their sons, and hence
strong selection for fission because of mate
competition induced by the mating rule.
For the sake of clarity, assume that the
troop sizes are exactly 150:50:50:50and that
exactly half of each generation is males and
half females. Then a male born to the large
troop has a pool of 75 females (i.e., the females in the three small troops) that are
potential mates. He has 74 (his troop mates)
plus 50 males (from the two other small
troops) or 124 competitors for the 75 potential mates he has available. Now consider a
male from a small troop. He has 125 potential mates, rather than 75, and there are 124
competitors for 50 of them and 74 competitors for 75 of them. The result of all this is
that mate availability is 751124 for males
from the large troop and 125195 for males
from small troops. The mating rule gives
males from the small troops roughly a two to
one selective advantage over males from the
large ones. This amounts to very strong selection in favor of troop fission.
This mechanical selection imposed by the
mating rule also explains why the random
male exogamy model does not lead by itself
to the stable troop size distribution built into
the model. We will proceed anyway, assuming for the moment that the necessary
amount of selection does occur each generation. The (computed) eigenvalues of the matrix 4 are 1, .4, .4, and .2, and substituting
these values into equation 2 leads to an estimate of effective size of 149, which is intermediate between the estimates generated by
the random allocation of the parent model
and the random male mating model. All
three estimates of effective size are very similar and reasonable, and we have no basis for
distinguishing among these biologically different models.
All three models we evaluated are models
with a great deal of gene flow among groups.
It is clear that this is the state on this island
and that there is very little or no endogamy,
population structure, or restriction to gene
flow among the groups. Further, all three
estimates of effective size are substantially
higher than the rough and ready estimate of
one-third census size often used in human
population studies. There is certainly not as
much polygyny among these monkeys as
some models of social dominance and re-
stricted sexual access to females might imply. If a few males were fathering most of
each generation, the effective size would be
much lower.
We were somewhat surprised to find such
a consistently high estimate of effective size
from these data and from McMillan and Duggleby’s other set (1981) (see below) since the
figure of one-third is widely accepted as a
standard in anthropological genetics. In this
regard it is worth noting that a recent very
careful analysis of effective size in the Gainj
of New Guinea (Wood, 1985) reveals that the
best estimate of their effective size is about
one-half census size, that is, of the same order of magnitude as we find for the macaques. Wood’s analysis is based on demographic and life-history data, while ours is
based on genetic markers.
There is evidence that this open exogamous mating system may have changed since
the capture and removal of a number of
troops from the island in 1972. McMillan and
Duggleby (1981) have subdivided the Cay0
Santiago population into lineages (pooled into
troops in the previous discussion) and reported gene frequency by lineage for both
1972, immediately following depopulation of
the island by capture, and for 1976, after 4
years of rapid population growth. In every
case except one, each lineage in 1976 is more
heterozygous and closer to the overall island
gene frequency centroid than it was in 1972.
This implies that there might have been
more gene exchange among these groups,
which both homogenizes gene frequencies
and raises heterozygosity within groups. This
would lead to the rather startling convergence of gene frequencies, distances, and
overall heterozygosities to the overall mean.
It will be interesting to see whether endogamy increases as population density on
Cay0 Santiago island recovers from the
McMillan and Duggleby (1981)suggest that
this convergence of lineage gene frequencies
may be due simply to the larger sizes of each
lineage in the later sample. The total size
was 255 in 1972 and 441 in 1976. We know
from equation 1 that Ro is almost proportional to the inverse of total effective size.
Estimates, from Duggleby’s biochemical data
(1978) of Ro from the lineages before and
after the four years of population growth are
.124 and .068; these are in the ratio of 681
124 .55, which is close to the ratio of census
sizes 2551441 .58. Duggleby’s suggestion
that the differences in genetic differentiation
in the two samples simply reflect population
size is likely to be correct. On the other hand,
these data are not incompatible with random
mating, and there is no need to invoke lineage-specificmale mating as she does. Under
the random allocation of parents model, for
example, equation 2 is
(2x1 - .124)
(14) = .124,
since there are 15 lineages and thus 14 zero
eigenvalues under random allocation of parents. This provides an effective size estimate
of about 100, approximately 40% of census.
Recall that when troops were the unit of
study the estimate of effective size was about
50%of the census size. It is reassuring that
these two agree as they do: Note that they
are both somewhat greater than the estimate
of one-third often used by human geneticists.
Since the fraction of a primate troop that is
capable of reproduction is larger than the
fraction of a human population in its reproductive years, this estimate is probably quite
It seems clear that, from the viewpoint of
method, we need to know more about effective size. There is a rich elaborate literature
about estimating efyective size from demographic parameters, but this has been of limited use in anthropology because there was
little to be done with the estimates generated
by these methods. But now the rest of the
required theory is catching up, and good demographic inference about effective breeding
size would make the migration theory very
The gene frequency data could not distinguish among three models of mating structure. However, these were all models that
were variants of random mating, at least for
one sex. The data are not compatible with
more than minimal endogamy or restricted
mating structure on this island or with high
differential male reproductive success.
Richard Ward called our attention to the
changes in the Cay0 Santiago genetic structure between 1972 and 1976. We have benefitted from comments and advice from Eric
Devor, Jeffrey Froelich, Alan Rogers, Lisa
Sattenspiel, and Jim Wood.
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