~ ----....;..,-~. -- - ~- -­ ------

161

dcs CHAPTER 15 - '"""':: of ADMIXTURE ESTIMATES AND SELECTION IN by M. H. CRAWFORD, P. L. WORKMAN, C. McLEAN, and F. C. LEES

Estimates of genetic admixture in human Elston (1971), and using the same data sets ~ jpulations, based upon allelic frequencies, he demonstrated that roughly similar results ':"'..:1 be traced back to the original formula­ may be obtained irrespective of the method '::::)l1S of Bernstein (1931). Bernstein's for­ of computation. Chakraborty (1975) has re­ .ula, based upon the proportionate contribu­ cently presented a promising new method for :::)n of one population to the genetic makeup estimating racial admixture based upon the :: the hybrid, may be expressed as follows: probability of gene identity. m=qx-Q, A number of investigators have attempted to detect the action of natural selection by q -Q searching for loci with seemingly anomalous "'here m is the proportion of admixture, Q m values. For example, Workman, Blumberg, ":":'-ld q are the allelic frequencies in two pa­ and Cooper (1963) used 14 polymorphic ~~ntal populations and qx is the frequency of traits from Claxton, Georgia, to show that this :~le same allele in the hybrid population. This approach identified certain loci such as G-6­ :-:'jethod of estimating admixture was first ap­ PD and HbS otherwise believed to be sub­ _ ied by daSilva (1949) and Ottensooser jected to natural selection. Hertzog and 1944) on populations of Brazil; by Glass and Johnston (1968), noting elevated estimates of Li (1953), and Roberts (1955) on Afro­ m utilizing the d allele of the Rhesus system, _\merican groups; and by Matson (1970), concluded that selection is operating against \'agel and Soto (1964), and Saldhana (1968) the D allele and in favor of d. A recent crit­ JI1 Amerindian peoples. These investigations ical re-evaluation of the evidence for selection . ased their estimates of admixture (m) in by Adams and Ward (1973) concluded on a :\.fro-American populations on a number of more cautionary note arguing that errors in :lifferent alleles-including Fy", Ro (cDe), R' estimating the gene frequencies of the paren­ CDe) and more recently the Gmzab haplo­ tal populations may explain many of the ob­ ...11e. Similarly, Dia, brittle cerumen, and served deviations at certain loci. Gm ib have been described as useful markers The purpose of this chapter is four-fold: :hat can be used to distinguish hybrid groups (1) to quantify the rate of gene flow from the ·)f Indian and European ancestry. Spanish into the Mexican Indian gene pools Instead of basing estimates of admixture during the creation of a Mestizo population; 'lpon information from a single locus or allele, (2) to estimate the genetic affinities of two ,~ number of investigators have combined in­ Mexican populations to the surrounding pop­ :onnation from various loci for the compu­ ulations through the use of various genetic :ation of a composite m. Roberts and Hiorns distance measures; (3) to detelmine if the 1962, 1965) proposed a least-squares measure various measures of genetic distance reflect ..f In which assumes p parental populations the estimated proportion of hybridization ex­ "ith known gene frequencies, and no selec­ perienced by a population; (4) to determine ::on or drift. Similarly, Krieger, et al. (1963) if the admixture estimates for Mestizo popu­ ::omputed m for a large triracial hybrid pop­ lations can be employed as indicators of the ·.:l.ation in north-eastern Brazil utilizing a actions of natural selection on the specific loci :c,lximum likelihood solution. These methods controlling the blood groups and proteins. .. ',ore compared, contrasted and modified by The Tlaxcalan Valley was chosen for the 162 PUBLICAnONS IN ANTHROPOLOGY study because of the historically documented If it is further assumed that Spanish gene low rates of gene flow into the Valley. This frequencies are known without error (i.e., was partially the result of a military alliance they represent "true" or parametric values in between the Tlaxcaltecans and the Spanish ancestors), then it can be shown that, ap­ directed against the Aztecs of the adjoining proximately valley, and partially because of the cultural integrity of the populations in the Valley. While the more isolated populations within the Valley experienced little, if any, inter­ mixture with the Spanish, the administrative towns of the state of Tlaxcala underwent con­ siderable miscegenation. In particular it derives from the approximate variance (V) of a ratio: METHODS Vx _ 2 cov. (xy) } The proportion of Spanish admixture with V(r)=r2 _. + the Indians of Tlaxcala was estimated by five { x2 xy different methods. Three of these methods, Roberts and Hiorns', true least squares and where r = x/y maximum likelihood, were analyzed by means of a computer program written by R. C. El­ The covariance (cov.) of x and y is only due ston (1968). Biracial hybridization was also to the appearances of similar terms in x and y. computed through a weighted multiple re­ gression analysis (using assumed parental fre­ In particular, if m qu - qs then quencies) and through the summation of m qr- qs ' values for individual loci weighted by vari­ cov. [(qu - qs), (qr - qs)] = a2s. ance. The regression method assumes that only sampling errors are involved, examines If Spanish values are not subject to sampling 2 Xt = a yX2t + b, and if a is not significantly error, covariance = as = O. vVe use formula different from zero, b provides an estimate of intermixture. These methods are based upon (1) and a 2q = pq for codominant loci 2N . Bernstein's formula which assumes qs = Spani:sh, qr = Indian, and q~f = Mestizo 1- q2 (Tlaxcala-hybrid) gene frequencies. By and 4N for dominant loci. standard method: This method further obtains the weighted qM - qs mean of the estimates mj by X = , where X is the proportion qr - qs of Indian ancestry, and mt ~ Vml qM = Xqr (1 - X) qs = X (qr - qs) qs ml= + + 1 ~ if we assume that: Vmj

qM (1 - qM) and the variance of the weighted mean is 2 a qM=----­ 1 2N M 1 ~ Vmi a2qr=----­ 2Nr Mahalanobis' generalized distances (1936) are computed between pairs of populations in this study using gene frequency data as de­ T:\1BER 7 163

';"'

TABLE 75. Gene frequencies of the TJaxcaltecan, Spanish and African populations used in the calculation of genetic distances (Crawford et al, 1974).

Group 0 A B M N Fya Fy" Dia Vi" Rz R, & Ro+r 1. San Pablo _ 0.9460 0.0500 0.0050 0.7821 0.2179 0.7842 0.2158 0.0560 0.9440 0.0400 0.6020 0.3230 0.0350 2. Tlaxcala 0.8410 0.1150 0.0440 0.6920 0.3080 0.5261 0.4739 0.0760 0.9240 0.0250 0.5770 0.2650 0.1330 ~··ted 3. Spanish" _ 0.64000.29200.0680 0.5256 0.4744 0.3993 0.6007 0.0000 1.0000 0.0000 0.4774 0.1128 0.4042 4. Africa' 0.7077 0.1780 0.1143 0.5805 0.4195 0.0607 0.9393 0.0000 1.0000 0.0008 0.4036 0.1670 0.4006

• Spanish frequencies are based upon Mourant ('53). , African frequencies were compiled by Cavalli-Sforza and Bodmer ('71).

TABLE 76. Estimates of biracial hybridization based upon five different methods.

Number of Percentage of Contribution . i5 Method Alleles· Spanish Indian 1. Multiple regression analysis ..... 39 31.49 68.61 2. Summation of Bernstein's "m", weighted by variance 12 27.32 72.68 3. Roberts and Biorn's 39 31.56 68.44 4. True least squares _... 39 30.92 69.08 5. Maximum likelihood __ .__ .. __ . ._.___ 39 22.64 77.36 ~~36) " With the exception of the "~m" method, hybridization estimates are based upon 15 loci: _::'5 in ABO, Duffy, Kidd, Diego, MNS-CHRM, MN, Rhesus, Kell, Haptoglobin, Group Specific e- Component, Phosphoglucomutase, Acid Phosphatase, Lewis, PTC tasting and Cerumen. 164 PUBLICATIONS IN ANTHROPOLOGY

\lonte as a parental population in a multiple hybridization. This analysis suggested a small regression analysis. The computed m for proportion of African admixture (6.7 percent), Tlaxcala was identical to the value estimated which reduced the estimate of the Caucasian when San Pablo allelic frequencies were used component, but did not affect the Indian con­ to represent the parental Indian population tribution to the Mestizo population (see (qI ). The only detectable difference between Table 78). the two estimates was in the standard devi­ With the exception of the maximum like­ ation, which was .034 when San Pablo was lihood method, which consistently but mildly utilized and .070 when the eight Nahua tribes overestimated the Indian contribution to the were grouped to represent qI' The high Mestizo gene pool, the results of the triracial standard deviation for the composite Nahua analysis, irrespective of methods, were fairly population reflects the heterogeneous nature consistent. Fewer alleles were used to repre­ of the grouping. sent the parental populations in the triracial model because of the paucity of reliable data TABLE 77. Proportion of Indian ancestry in the hybrid on some systems. population presented by locus. One test of the accuracy of each method Proportion Standard of estimating admixture is the degree of Indian Ancestry Deviation agreement of the observed and expected val­ Gene M «(hI) qs·q" ues of gene frequencies in the hybrid group.

Fy' ------­ .679 .0840 .554 This test is accomplished by multiplying the E .730 .1130 .278 estimated contributions from each parental ------­ .221 M .661 .1366 population by the frequency of the gene in 6 ______------­ .643 .1663 .280 p A that population. The sum of the two products ° ------­ .719 .1899 .153 Hp' ------­ 1.053 .2519 .150 in a biracial hybrid (or three in a triracial), C ------­ .518 .3699 .085 a which is the expected frequency of a gene, is Di ------­ 1.357 .3762 .056 then compared with the observed value of Gc' ------­ 1.750 .5028 .072 a Jk ------­ 1.197 .7291 .071 that gene frequency in the hybrid group to PGM' ------­ 1.625 1.5876 .024 form a chi-square statistic. A total chi-square S ------­ 5.750 32.4147 .004 value for all genes is also obtained (Pollitzer 1964). There are no significant differences in Because some African admixture has been the chi-square values between the five meth­ detected in anumber of Mexican populations ods employed. However, Table 78 indicates by Lisker, Zarate, and Loria (1966) and Cor­ that Duffy, Lewis, and the group specific dova, Lisker, and Loria (1967), and because components (GSC) are the most deviant loci, of the elevated presence of the Ro( cDe) while Diego and PTC tasting observed fre­ chromosomal segment, a triracial hybrid anal­ quencies differ slightly from the expected ysis was attempted for Tlaxcala. Spanish, values (at P

TABLE 78. Estimates of triracial hybridization based upon four different methods.

Number of Percentage of Contribution Methods Alleles~ Spanish Indian African 1. Roberts and Hioms .._.. __ .. 26 24.43 66.62 8.95 2. Least Squares ._. __ .._ 26 23.87 67.27 8.86 3. Maximum Likelihood 26 15.93 76.16 7.91 4. Multiple Regression . 23 22.90 70.40 6.70

o Hybridization estimates are based upon nine loci: ABO, Duffy, Kidd, Diego, MNS-CHRM, Mr\, Rhesus, Kell, and Lewis. _~BER 7 165

":::-!. However, the PTC locus, significantly gene flow affect the affinities of geographi­ .~::t in the biracial hybrid, falls within the cally proximal populations. The genetic dis­ ~.c':ed values in the triracial model. In tances, summarized in Table 81, indicate that ::-15t, the Kidd locus does not deviate in a "gross" relationship exists between genetic -criracial model, but does deviate signif­ and geographical distances in Mexican popu­ :\ in the triracial analysis. Most impor­ lations. Two exceptions to this purported re­ : ::1 this analysis is a comparison of the lationship between geography and genetics _ _ of the chi-square values for all loci; appear in San Pablo-Tabasco and Puebla­ .:= in the dihybrid model are almost twice Chiapas. San Pablo population exhibits a _·-alues observed in the trihybrid sum (See closer genetic affinity to that of the State of :-=, 79 and 80). These differences suggest Tabasco than geography would dictate, while : :he trihybrid model better fits these data the Puebla/Chiapas genetic distances suggest =. :he assumption that the Mestizo popu­ populations separated by considerable geo­ ::::: resulted only from the admixture of graphic separation. Deviations from the iso­ ~,,: r,:,h and Indian parental groups. lation-by-distance model can, in part, be ::: :he admixture with the Spanish began accounted for by the various degrees of Span­ ::"-.f \"alley of Tlaxcala at the time of con­ ish and African admixture and the possible ::.,. .-'i.D. 1519, and continued until the pres­ action of genetic drift or similar selective -_. ::"'11e i.e., 1969 when gene frequencies forces (as well as social factors). It is inter­ ..' :1rst calculated for Tlaxcaltecan popu­ esting to note that the Mestizo (Tlaxcala) ::5. then 18 generations of 25 years each population has a genetic distance to the Span­ : have transpired. Assuming that 30% of ish (Caucasian) centroid which is less than _Iestizo gene pool is of Spanish and West one-half the distance to the Indian popula­ -..::n origin and that 18 generations of con­ tion (San Pablo). These distances are in .:.:as hybridization have transpired, then agreement with the admixture estimates, :.lte of gene flow can be computed as which suggest that approximately 30% of the Mestizo gene pool is of "foreign" origin. qM - qs DISCUSSION - ::1)k = 1 - ---, where k is the num­ ql - qs ber of generations The five methods of estimating admixture during which indicate that from 23 to 32% of the Mestizo gene pool is of Spanish and/ or West African c:ure has occurred. Let M = 30%, the origin. The gene flow, which undoubtedly ;::-:bution of Spanish to Hybrid Tlaxcalte­ began with Spanish contact in 1519, contin­ so that m = 1 - I'VI - M. Thus, ued until 1750, the latest recorded date for '"":i: :K = 18 generations, m = 1.96%/ gener­ the influx of Spanish administrators. Spanish However, the period of actual gene gene flow into the Mestizo gene pools prob­ ::)m the Spanish administrators into the ably ceased about 1750, after 230 years or C-:' of Tlaxcala ended in 1750 (Halber­ more than nine generations of admixture. In ::~ Crawford and Nutini, 1973). Thus, light of the small number of Spanish residents -: :.: the gene flow took place in approxi­ in the three administrative centers at anyone =.=-> nine generations followed by a period time, it is surprising to note that close to 30% -:·.~~h the Spanish and African alleles seg­ of the Mestizo gene pool is of Spanish and ;r:,ct throughout the urban Tlaxcalan cen­ West African origin. Several interrelated -_-sing nine generations of gene flow, the demographic factors have been advanced by .- ::E:· generation becomes 3.88% per gener­ Halbertstein, Crawford, and Nutini (1973) to . -."c sizeable rate of gene flow! explain this excessive parental contribution of the Spanish. (1) The Valley of Tlaxcala un­ GENETIC DISTANCES derwent considerable depopulation, from ap­ :::-:-:-.etic distances were computed to de­ proximately 300,000 persons in 1519 to its all -..:: to what extent hybridization and time low of 100,000 in the year 1600. This 166 PUBLICATIONS IN ANTHROPOLOGY

TABLE 79. Biracial analysis: comparison of Chi-square values for different methods of calculating proportions of admixture.

Methods Degrees of Roberts and Least Maximum Multiple ~ Bernstein's Locus Freedom Hiorn's Squares Likelihood Regression M

1. ABO ------2 2.4580 2.5658 5.3137 2.4720 3.4203 2. Duffy ------.-.------1 23.0492° 23.9745° 38.1999° 23.1715° 29.6239" 3. Kidd ---.------.---- 1 1.7398 1.6516 0.7142 1.7242 1.9975 4. Diego ------._------.- 1 5.601P 5.4040° 3.2997 5.5642" 4.3934" 5. MNS-CHRM ---.------_.----- 3 1.3992 1.4283 2.0937 1.4023 1.6494 6. MN ------1 0.1102 0.1538 1.4170 0.1168 0.5397 7. Rhesus ------. 6 6.1570 6.0831 5.2886 6.1390 5.6990 8. Kell ______1 2.7096 2.6193 1.4840 2.6929 2.1170 9. HP ------.------1 3.4146 3.2981 1.9745 3.3929 2.6890 10. GSC ------_._---.------1 10.0738° 9.9659° 8.6103" 10.0469" 9.3673" 11. PGM ------.------1 0.6910 0.6834 0.5878 0.6894 0.6411 12. AP ______2 3.0868 3.0347 2.4833 3.0756 2.7576 13. Lewis ------.------1 20.5930" 20.1450° 14.4676° 20.5017" 17.6495° 14. PTC ------.-.------1 5.1078" 4.8329° 1.9139 5.0590" 3.4158 15. Cerumen ______1 0.9451 1.1101 4.2775" 0.9697 2.2597 Total ______24 5.2610 5.2426 5.4360 5.2527 5.2247

o P < .05. rapid depopulation was accompanied by an The founding population of the City of Tlax­ extensive segregation of foreign genes. (2) cala probably had a high proportion of for­ According to Snow (1969), the precontact eign genes. (3) The settlement patterns of settlements in Tlaxcala were situated on bluffs the Spanish were highly centralized, with and valley walls because of the poor drainage most of the administrators residing in either in the low-lands. The City of Tlaxcala was the City of Tlaxcala, Santa Ana , founded by the Spaniards as an administra­ or (documents from Archivo del tive center after the valley Roor was drained. Estado de Tlaxcala). Thus, while most of the

TABLE 80. Triracial analysis: comparison of Chi-square values for different methods of calculating proportions of admixture.

Methods Degrees of Roberts and Least Maximum Multiple Locus Freedom Hiorn's Squares Likelihood Regression 1. ABO 2 0.9859 1.0838 3.2116 1.8315 2. Duffy .. 1 10.2739" 10.8486" 22.0033" 17.8481° 3. Kidd 1 5.8811" 5.7360° 3.1063 3.2596 4. Diego .. 1 5.6649" 5.4253° 3.5431 5.0147° 5. MNS-CHRM 3 2.0678 2.0803 2.2303 1.7677 6. MN 1 0.0802 0.1222 1.1030 0.2477 7. Rhesus 6 2.6128 2.5303 1.4930 2.1681 8. Kell .. .. 1 1.1384 1.0394 0.5094 1.5756 9. HP .. 1 0.5222 0.4626 0.3418 1.3117 10. GSC 1 5.770P 5.6492" 5.5604° 7.3515" 11. PGM .. 1 0.6189 0.6104 0.5468 0.6284 12, AP . .. 2 2.4747 2.4415 2.2016 2.5576 13. Lewis 1 24.6928" 24.2078" 18.2047" 21.3304" 14, PTC 1 0.9998 0.8432 0.2244 1.9415 15. Cerumen .. 1 0.9106 1.0915 3.7389 1.4888 Total 24 3.5564 3.5212 3.5566 3.7120 o P < .05. =-.OGY )lUMBER 7 167

=:;:tions TABLE 81. Genetic distances (D') from , Tlaxcala, Caucasian and African populations to multivariate centroids representing six Mexican states (Crawford et al, 1974). Populations _·-~2in"s Nayant- Populations San Pablo Tlaxcala Ialisco Vera Cruz Puebla Oaxaca Chiapas Tabasco Caucasian

~j 1. Tlaxcala ______78.705 -'::9° 2. Nayarit-Jalisco __ 24.187 178.514 ~-5 3. Vera Cruz ______11.982 54.485 32.543 : ~;.,-±o -1. Puebla ______16.928 137.842 33.499 37.714 -'-;: :'-± 5. Oaxaca ______51.015 78.044 94.727 49.549 107.193 ::> 6. Chiapas ______15.990 87.869 28.608 13.130 34.953 55.162 ;;,0 7. Tabasco ______19.532 37.022 41.612 11.618 58.970 22.783 12.903 _':""0 . Caucasian ______394.925 143.496 478.020 342.244 491.271 341.628 400.951 289.539 9. African ______543.636 224.626 606.937 448.569 658.665 469.249 537.439 407.379 63.263 :":"-.3 Q -1.:':1 -::-6 Valley experienced little or no admixture with Puebla whose ancestors had interbred ;.;5 0 the Spanish, the gene pool of the administra­ with slaves. .:c5it'i tive cities contained a disproportionate per­ The evidence is strongly in favor of the centage of "Spanish" genes. (4) The Spanish first alternative, because the population is in contact with the City of Tlaxcala lasted for genetic equilibrium for all -23 loci, and be­ :230 years. During eight or nine generations, cause a fitting of the multiple regression constant gene flow of high magnitude could curve for a trihybrid population, when com­ - Tl~'{­ account for 30 percent of the estimated ad­ pared to a bihybrid population, results in a : for­ mixture. A fifth possible cause for the high change in the contribution of the Caucasians ~-..3 of incidence of "Spanish" genes in the Mestizo but not the Indians. However, the presence ith gene pool is assortative mating based upon of eight or nine percent African genes in the ~:ther Spanish morphological features. Individuals Mestizo gene pool is considerable. The dem­ ~pan, with Spanish ancestry may have constituted ographic data suggest that gene flow from .- del preferred mates and thus conbibuted dispro­ outside the valley is a recent phenomenon. If ,:: the portionately to the genetic composition of the the African genes were constantly flowing into hybrids. the community then the equilibrium might . :-!ions On the basis of total chi-square values for be disrupted. the blood loci (see tables 79 and 80), it ap­ Santiago Genoves, who led the formal dis­ pears that the triracial model of hybrid origin cussion at the symposium in City,

~ ="' for the Mestizo gene pool provides a better argued that the African genes probably

- "'j fit than does the biracial model. The sum of flowed into Tlaxcala from Puebla, which had the chi-square values for the various blood a large Mulatto and West African slave pop­ - loci, assuming a triracial origin of the Mes­ ulation. The answer probably lies somewhere tizos, are almost one half the values of the between the two positions, and it is likely -, chi-square totals for the biracial model. These that both hypotheses are correct. values suggest that the Mestizo population Workman (1968) has suggested that if es­ received gene flow from an African compo­ timates of ancestral frequencies are reaSOn­ nent as well as a Spanish parental population. ably accurate, the admixture studies may be Historically, the Spanish conquest of Mexico used to detect the action of natural selection. :" =~ is well documented; however, there is no evi­ He computed admixture estimates "m" (Bern­ 10.-":-: dence for the existence of slave populations stein, 1931) for a number of blood loci in in the highlands of Tlaxcala. The "African" American Black populations and suggested genes may have come into Tlaxcala in one or that the data indicate that selection may be both of the following ways: operating on the Hbs, Hbo, HP, G-6-PD, and 1. With the "Spanish genes," carried by­ Al alleles. Although the hemoglobin and G­ the soldiers of Moorish ancestry, or 6-PD loci were not tested in the present study, 2. By Indians from the coast or from because African admixture was not suspected, 168 PUBLICATIONS IN ANTHROPOLOGY the ABO and haptoglobin loci have been appears that geographic distance and admix­ tested for possible selection. The chi-square ture with the Spanish are the primary factors analysis illustrated in Table 5 and 6, how­ involved in determining the distribution of ever, suggest that selection does not appear the allelic frequencies in Mexico. . to be acting on these loci in the Tlaxcalan population. However, the Duffy locus exhib­ ACKNOWLEDGMENTS its exceptionally high chi-square values, sug­ The authors wish to acknowledge the help of F. gesting the possible action of natural selec­ Gottlieb, Seishi Oka, H. G. Nutini, T. Aidan Cock­ tion. Reed (1969) has suggested that the burn, Roberto Ortega-Espinosa, W. C. Leyshon and K. Brown in various phases of these investigations. Duffy blood group system Fy" gene may be The nursing staffs of the clinics at San Pablo del the best available marker for estimating "m" Monte and the City of Tlaxcala aided us in the colIec­ in American Blacks, but judging from these tion of the blood specimens and in the spread of good data, the Duffy system cannot be recom­ will. The field portion of the study was supported in part mended for calculation of m in Mexican In­ by grants from Wenner-Gren Foundation for Anthro­ dian populations. pological Research and grant CA-69-133FF from the In sum, while there is minor disagreement University Center for International Studies, Univer­ in the results based upon the various methods sity of Pittsburgh. Data analysis was funded by grants from the University of Kansas General Research Fund of calculating admixture, the geographic and #3992-5038 and the Biomedical Research Support genetic distances show some agreement. It grant #4851-5706.