~ ----....;..,-~. -- - ~- -­ - - --- -- - 161 dcs CHAPTER 15 - '"""':: of ADMIXTURE ESTIMATES AND SELECTION IN TLAXCALA 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 <ribed in Crawford et al. 1974. The rationale lation. Significant differences in the estimates :LJf utilizing the method of Mahalanobis of hybridization can also result from the use 1936) is described by Crawford et al. 1974. of particular loci and alleles. It is probably .:J.Ielic frequencies used in the computation for this reason that the ~m method described .Jr genetic distances between pairs of Mexican in this chapter provides an estimate inter­ _Dpulations were compiled from various pub­ mediate between the extreme results found by :ications. The frequencies of the Tlaxcalte­ maximum likelihood, and the similar methods ~} ~n, Spanish, and Ahican populations used in based upon least squares and multiple re­ -'­ - he calculation of the D2 are summarized in gression. :able 75 (Crawford et al. 1974). Table 77 contains the proportions of In­ dian ancestry, standard deviations, and differ­ _~ilte RESULTS ences in Spanish and Indian gene frequencies Table 76 summarizes the proportion of by locus. Using all 12 alleles and the formula Spanish admixture with the Indians of Tlax­ ~ 2 cala estimated by five different methods, four (xJa x .) m= 2 ' ~ ) of them using 39 different alleles and the ~m (l/a xj -} method described above utilizing 12 alleles. the proportion of Indian ancestry m, is com­ Three of the methods, multiple regression, puted to be .7268 ± .0517. The standard de­ Roberts and Hioms', and least squares, pro­ viation is calculated as the square root of the vide the most similar estimates of hybridiza­ variance (a2Xi) ::.ue tion. This is not surprising, since the last two ...~;Ij y. methods are based upon a least squares solu­ -1 tion to the problem of the estimation of pa­ ~ ~ r ] = 0.0026749. rental contribution using random sets of in­ l (J Xi dependently assorting loci. In contrast to Elston's (1971) finding, maximum likelihood A composite Nahua population, based ';"'<T estimates differ most from the other methods upon the gene frequencies from eight Indian "'-"0 even when all alleles are used in the formu­ tribes, was substituted for San Pablo del -~-=-.ula 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.