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Calculation of the maximum amount of gene admixture in a hybrid population.

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Calculation of the Maximum Amount of Gene Admixture
in a Hybrid Population
EMOKE J. E.
SZATHMARY
AND
T. EDWARD REED
Department ofAnthropotogy, McMaster University, 1280 Main Street West, Hamilton,
Ontario, Canada, L8S 4L9 and Departments ofZoology and Anthropology,
brniversity of Toronto. Toronto, Ontario, Canada, M5S 1Al
1
KEY WORDS Maximum admixture
Gene flow
.
Canadian Indians
-
Evidence is presented to show that “Caucasian” genes fB, K,
ABSTRACT
Luu, r, AK’, P c , andGm3,5,’1) in hybrid North American Indian populations follow a Poisson distribution. A method of determining the maximum amount of
admixture, given an observed count of Caucasian genes, is developed. Establishment of the upper limit of admixture is suggested as the preferred estimate of
gene flow in situations where absence of specific genes a t particular loci precludes the calculation of a mean admixture estimate.
The estimation of the proportion of genes
obtained from two ancestral populations in a
hybrid sample requires a knowledge of the
gene frequencies of each of the two parental
populations as well as the hybrids. In Amerindian studies the gene frequencies of the
ancestral Indians are unknown, and must be
inferred from the hybrid data. One solution to
this problem is to partition the modern Indian
population under investigation into groups
that differ in their amounts of known nonIndian ancestry (e.g., Pollitzer e t al., ’62). Several different admixture estimation methods,
ranging from least squares (Roberts and
Hiorns, ’621, and maximum likelihood (Krieger e t al., ’65; Elston, ’71) to probability of
gene identity (Chakraborty, ’75) have been
used on such data. Criticism has already been
made about some of these approaches (Reed,
’69; Chakraborty, ’75). A more basic issue is
the nature of the data to which the estimation
techniques are applied. That is, partitioning a
sample by degrees of known ancestry depends
not just on having genealogical records readily available, but on the supposition that these
are of sufficient time depth to be accurate and
are free of recording error.
This is clearly not the case for very many
Amerindian groups. In Canada, for example,
tribal registries listing degrees of Indian
ancestry are not kept because the legal definition of “Indian-ness” does not rest on such
AM. J. PHYS. ANTHROP. (1978)48: 29-34.
information. An alternative approach in such
situations is to dispense with subdividing a
sample into “mixed” and “unmixed’ categories and to consider only those alleles in admixture estimation that were absent in Indian populations prior to non-Indian contact.
There is accumulated evidence from very
many North American Indian groups that
indicates that in these populations at least
eight different alleles are now present as a
consequence of Caucasian Le., European)
gene flow (Szathmary and Reed, ’72). Unfortunately all of these alleles will not always be
found in a hybrid population sample. When
only blood group data are available the gene
most commonly present is r, while either ha
andlor K may be absent.
Such a distribution of Caucasian alleles
poses problems in the determination of the
magnitude of gene flow. Foremost is the fact
that the lack of observation of a specific gene
precludes the calcu.&ation of a mean admixture estimate (MI. M is a weighted mean, the
1
weighting factor being - where siZ is the
si*
variance of the ith admixture estimate
(Szathmary and Reed, ’72; Cavalli-Sforza and
Bodmer, ’71). Some authors get around this
problem by calculating single locus admixture
estimates (M,)
only, without attempting to derive a mean (e.g., Doeblin and Mohn, ‘67);
others select one allele and consider that to be
29
30
EMOKE J. E. SZATHMARY AND T. EDWARD REED
TABLE 1
Frequencies of eight "Caucasian " alleles in
Western Europeans
Allele
Frequency (p) '
A2
0.0647
0.0678
0.0457
0.0356
0.4048
0.0470
0.0500
0.6650
0.1726
B
K
Lua
r
PC
AK
Gm3 5 I 1
Mean frequency of Caucasian alleles
1
Source: (Szathmary and Reed, '72).
indicative of the possible amount of Caucasian gene flow (e.g., Allen and Corcoran, '60).
As very rough estimates of admixture, or as
demonstrations of admixture of undefined
magnitude such methods may be permissible.
However, it would be preferable to be able to
establish with a stated degree of confidence
the range of possible admixture, even if a
mean value cannot be calculated.
This paper suggests a method whereby the
maximum amount of detectable gene flow can
be established & those situations wherein the
calculation of M is impossible.
METHODS AND RESULTS
The occurrence of individual Caucasian
genes in a North American Indian group could
be considered t o be rare events if admixture
has been low. If this is so, their incidence
could be described by the Poisson distribution.
The upper confidence limits for expected
Poisson variables given an observed count are
available (Pearson and Hartley, '621, and
could be used to calculate the upper limit of
admixture in any Indian population.
The fundamental hypothesis in this argument is that Caucasian genes are distributed
in these populations as Poisson variates. To
test this, a sample of 105 Ojibwa (Szathmary
and Reed, '72) from Wikwemikong, Ontario,
Canada, were examined. Each individual was
regarded as a sampling unit within which 0 t o
14 rare events (i.e., Caucasian genes) could occur a t 7 different loci.
This method requires that Caucasian genes
be identifiable in the phenotype. This poses no
AK2 and P c
problems for the genes Gm3.5.11,
which are recognizable, but presents difficulties for their blood group counterparts.
For example, the phenotypes A2, B, Lu(a 1,
+
and K ( + ) could be heterozygous or homozygous in a genotype, respectively, while the
phenotypes A, and CcDEe could containA2 (in
A '/A2)and r (in R Vr), respectively.
To bypass this difficulty calculations were
made to determine the probability of homozygous combinations of each of the Caucasian
genesA2, B, Lu a, K and r and the heterozygous
combinations of A1/A2and RVr. The results
showed (table 2) that none of the alleles were
likely present homozygously; hence each A2,
B, Lu(a+) and K ( + ) phenotype included a
single Caucasian allele, respectively. It further seemed improbable that any of the
CcDEe phenotypes contained r in combination
with R z . Of the A, phenotypes, however, a t
least one was likely to contain a n A 2 allele.
This single A 2 allele in turn could either be
the only, or the second or the third Caucasian
gene in any one individual. Because no known
method exists to distinguish homozygous
from heterozygous forms of Al, it was not possible to determine which A, phenotype containedA2.Since our method demands that the
genes be counted, and because we could not do
so with A2, this allele had to be eliminated
from subsequent calculations.
Once the number of Caucasian genes in
each phenotype was established, the total
number of these genes (B, r, K, Lua, Gm3.5.11,
AK2 and P c ) were counted in each of the 105
sampling units. The mean number of these
genes per unit (i.e., per individual) was 0.83,
and the sample variance was 0.64. The variance test (Snedecor and Cochran, '67) showed
no significant difference between the observed and Poisson variances (x2,04= 80.8, p
> 0.95). To determine goodness-of-fit to the
Poisson distribution, the expected numbers in
classes with 3 counts or more were first pooled
to yield a minimum class value of 5. The fit of
the data to the expected Poisson distribution
was then calculated, and found to be good (xZ3
= 2.85, p > 0.25). These findings support the
basic hypothesis that Caucasian genes in a
hybrid Indian population follow the Poisson
distribution.
The next step in the analysis was to determine the upper limit of the amount of admixture detectable in an Indian population. Since
our approach is meant to be used specifically
in those instances in which 0 Caucasian
alleles occur a t a particular locus, data from
another Indian population had to be employed. For this purpose the Pikangikum
31
CALCULATION OF THE MAXIMUM AMOUNT OF ADMIXTURE
TABLE 2
Probability of hornozygous and heterozygous combinations of specific “Caucasian” blood group
genes in the Wikwernikong Ojibwa
Probability of
genotype
Aliele
Frequency in
Wikwemikong
A=
A‘
B
0.039
0.133
0.044
0.010
0.010
0.100
0.043
K
Lua
r
RZ
Homozygote
Expected no. of
indicated genotype
( N = 105)
Heternzygote
0.00153
-
-
0.01037IA’/A21
-
0.00860(Rzlr)
0.00194
0.00010
0.00010
0.01000
0.1597
1.0920
0.2033
0.0105
0.0105
1.0500
0.9030
-
’
-
The cde frh) phenotype was not observed in the sample.
Ojibwa were selected, for in this group 7 of the
8 Caucasian genes under consideration were
absent. OnlyA2was found, and then only in a
single individual (Szathmary and Reed, ’72).
The use of the Pikangikum data rested on
two assumptions. Firstly, that if 7 Caucasian
alleles were distributed as Poisson variates in
one hybrid Indian population, they would be
so distributed in any such population. Secondly, that if 7 Caucasian genes followed a
Poisson distribution, the eighth possible allele, A2 would behave in similar fashion.
Neither of these assumptions could be tested
directly in the Pikangikum Ojibwa.
For any observed frequency or count of a
Poisson variable, the upper and lower confidence limits of its expectations can be found
(Pearson and Hartley, ’62). The upper 99%
confidence limit for an observed count of 1 is
7.43. Applied to the Pikangikum data, this
meant that for the one observed A2 allele, a s
many as 7.43 Caucasian genes could be expected. The lower 99%confidence limit for an
observed count of 1was given as 0.0253. However, in order to take into account the information from all other loci a t which no Caucasian genes were observed, the lower limit of 0
observed counts (0.0000) should set the
minimum number of foreign genes that have
entered the Pikangikum gene pool. In other
words, in a situation where counts are made
a t some loci but not a t others, one can be 99%
(or 95%, dependent on the confidence limits
desired) sure of the upper boundary since that
depends upon the number of observed genes.
The lower boundary, however, must be set
at 0.
The total number of loci examined for the
presence of Caucasian markers in the Pikangikum Ojibwa was 1,330 (table 3). The ra-
TABLE 3
Total number of genes “examined” in the
Pikangikurn Ojibwa
Allele
Number of persons tested
Number of genes
examined
A=
95
190
96
96
96
91
91
100
192
192
192
182
182
200
1,330
B
r
K
Lua
PC
AK
Gm 3.5 I 1
Total
tio of the maximum expected number of Caucasian genes to the total number of genes examined (7.43/1,330) yielded the maximum
Caucasian gene frequency of 0.0056 in this
population.
The mean gene frequency of the Caucasian
markers used was calculated to be 0.1726
(table 1). By the ratio method (0’0056)
-the max0.1726
imum amount of admixture in the Pikangikum Ojibwa was 3.24%.
DISCUSSION
In the study of the genetic characteristics
of American Indian populations, it is almost
inevitable that some evidence of Caucasian
gene flow will be found. The perplexing question always is the method whereby an estimate of the magnitude of this gene flow can
be made. In the past we have advocated an approach that includes testing for betweenlocus heterogeneity and which considers the
different amounts of information provided by
various loci (Szathmary and Reed, ’72). This
method is still recommended whether or not
32
EMOKE J. E. SZATHMARY AND T. EDWARD REED
TABLE 4
Maximum Caucasian admkfure (M,,&
LIZ several North American indian populations
'
No. of loci at
Population
Mmax
Pikangikum
Ojibwa
Blood
Stoney
Naskapi
Montagnais
0.024
0.308
0.339
0.156
0.123
Caucanian
alleles
found
which Caucasian
alleles could
occur
7
4
4
4
4
A'
B andr
r
B andr
B
' Maximum 18 based on the upper 95%confidence limit (see text)
detailed genealogical information is available
for the population concerned. In the absence
of such data, however, the single locus approach, using only those alleles which were
absent prior to Caucasian contact is the only
estimation procedure possible.
Studies that have used this method in calculating admixture have sometimes reported
the absence of specific Caucasian markers.
When only blood groups were considered, Lu a
andlor K were most often absent while r was
almost always found. This unequal distribution of Caucasian genes has been interpreted
by some as evidence of genetic drift (e.g.,
Allen and Corcoran, '60) or possibly, of natural selection. However, if it is assumed that
gene flow is the only microevolutionary force
affecting gene frequencies, the appearance of
low frequency Caucasian genes (low in the
parental Caucasian population) in a hybrid
sample will be a function of both sample size
and magnitude of admixture. For example,
when gene flow has been low (e.g., 5%)and the
sample size is small (e.g., 75 persons) r and
Gm3 are most likely to be the only Caucasian genes found. At the same level of admixture, but with a sample size of 300 persons,
the expected number of each Caucasian gene
is a t least 1.0.
Unfortunately, samples as large as 300 are
rare in North American Indian genetic studies. Therefore, one should expect studies
which report the absence of one or more low
frequency Caucasian genes in the presence of
r and G m 3 5
Such a distribution of Caucasian alleles
poses problems in determination of the magnitude of gene flow. Foremost is that the
method for the calculation of the mean
amount of admixture does not allow the inclu-
Source
Szathmary and Reed, '72
C h o w and Lewis, '53
Chown and Lewis, '55
Blumberg et al., '64
Blumberg et al., '64
All calculations of M,,
are those of the authors.
sion of 0 value Mi estimates. No satisfactory
approach has been presented to date that
would circumvent this statistical obstacle.
Our method proposes both to take account of
the information provided by the absence of
Caucasian markers at specific loci, and to define the upper limit of the magnitude of
admixture that can be expected to have occurred given the observed data.
I t is worth emphasizing that our method is
most useful when the magnitude of gene flow
has been small. In such situations 0 value Mi
estimates will occur, and low sample size
serves to increase this likelihood. The method
is applicable even when no Caucasian genes
are observed at any locus. By way of illustration of its general utility, table 4 lists five
Canadian Indian populations for which previously no statement could be made about admixture, other than that it had occurred. In
each of these cases, the true amount of gene
flow is probably much less than the maximum
shown. Nevertheless this value gives an indication of the greatest amount of admixture
that may have affected the gene pool of each
of these populations.
LITERATURE CITED
Allen, F. H., and P. A. Corcoran 1960 Blood groups of the
Penobscot Indians. Am. J. Phys. Anthrop., 18: 109-114.
Blumberg, B. S.,J. R. Martin, F. H. Allen, J. L. Weiner, E.
M. Vitaglioni and E. Cooke 1964 Blood groups of the
Naskapi and Montagnais Indians of Schefferville,
Quebec. Hum. Biol., 36: 263-272.
Cavalli-Sforza,L. L., and W. F. Bodmer 1971 The Genetics
of Human Populations. W. H. Freeman and Co., San
Francisco.
Chakraborty, R. 1975 Estimation of race admixture - a
new method. Am. J. Phys. Anthrop., 42: 507-511.
Chown, B., and M. Lewis 1953 The ABO, MNSs, P, Rh,
Lutheran Kell, Lewis, Duffy and Kidd blood groups and
the secretor status of the Blackfoot Indiana of Alberta,
Canada. Am. J. Phys. Anthrop., 11: 369-383.
CALCULATION OF THE MAXIMUM AMOUNT OF ADMIXTURE
1955 The blood group and secretor genes of the
Stoney and Sarcee Indians of Alberta, Canada. Am. J.
Phys. Anthrop., 13: 181-190.
Doeblin, T. D., and J. F. Mohn 1967 The blood ~ ~ O U PofSthe
Seneca Indians. Am. J. Hum. Genet., 19: 700-712.
Elston, R. C. 1971 The estimation of admixture in racial
hybrids. Ann. Hum. Genet., 35: 9-17.
Krieger, H., N. E. Morton, M. P. Mi, E. Azevedo, A. FreireMaia and N. Yasuda 1965 Racial admixture in northeastern Brazil. Ann. Hum. Genet., 29: 113-125.
Pearson, E. S., and H. 0. Hartley 1962 Biometrika Tables
for Statisticians. Cambridge University Press, London.
Pollitzer, W. S., R. C. Hartmann, H. Moore, R. E. Rosen-
33
field, H. Smith, S. Hakim, P. J. Schmidt and W. C.
Leyshon 1962 Blood types of the Cherokee Indians. Am.
J. Phye. Anthrop., 20: 33-43.
Reed, T. E. 1969 Caucasian genes in American Negroes.
Science, 165: 762-770.
Roberta, D. F., and R. W. Hiorns 1962 The dynamics of
racial intermixture. Am. J. Hum. Genet., 14: 261-277.
Snedecor, George W.,and William G. Cochran 1967
Statistical Methods. Sixth ed. Iowa State University,
Ames, Iowa.
Szathmary. E. J. E., and T. E. Reed 1972 Caucasian admixture in two Ojibwa Indian communities in Ontario. Hum.
Biol., 44: 655-671.
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