Proc. Nat. Acad. Si. USA Vol. 70, No. 12, Part I, pp. 3311-3315, December 1973
"Private" Genetic Variants and the Frequency of Mutation Among South American Indians (mutation rates/protein variants)
JAMES V. NEEL Department of Human Genetics, University of Michigan Medical School, Ann Arbor, Mich. 48104
Contributed by James V. Neel, June 15, 1973 ABSTRACT Electrophoretic studies were performed on 15 proteins of blood serum and of erythrocytes, from blood specimens from 72 villages of six relatively unacculturated and genetically pure Indian tribes of South America, for a total of 56,237 determinations. At least 10 different "private" variants were encountered, in 131 people. Two previously recognized genetic polymorphisms of these 15 proteins were also encountered. On the assumption that these variants are neutral from the standpoint of natural selection, and that only one-third of amino-acid substitutions in proteins result in electrophoretically detectable variants, the mutation rate is estimated from a formulation of Kimura and Ohta to be about 8 X 10-- per locus per generation. The calculation involves several approximations which can be improved by further investigations; if confirmed, then for this class of mutations Indian mutation rates are roughly an order of magnitude higher than commonly envisioned.
The designation of a genetic variant as "private" was first introduced by serologists, to describe rare inherited antigens limited to a few families. Such variants depend for their recognition on the more or less fortuitous development of specific antisera in the possessors of the variants, often in response to transfusions, sometimes in consequence of isoimmunization, and are quite uncommon. More recently, with the widespread use of electrophoretic techniques to define protein variants, it has become apparent that in addition to inherited biochemical variants occurring in polymorphic proportions, there are also "private" inherited biochemical variants, the counterpart of the private blood factors. Now, however, detection of the variant does not depend on the fortuitous development and discovery of an antiserum; these variants are being recognized with a higher frequency than the serological variants. The ultimate source of these variants is mutation. The variants that result from this process may, in the heterozygous or homozygous state, result in deleterious, neutral, or beneficial phenotypes from the standpoint of survival and reproduction. Both theory and observation suggest that most mutations are deleterious or at best neutral in their effect on the phenotype, with a small fraction beneficial. Fisher (2, 3) first demonstrated the high probability of loss of a mutant gene from a population. Although the probability of loss of a mutant is of course related to its phenotypic effects (deleterious > neutral > favorable), within the range of selection coefficients commonly envisioned in evolutionary processes, there is surprisingly little difference in the probability of mutant loss. For instance, in Fisher's model the probability of loss of a selectively neutral mutant was 0.79 during the 3311
first 7 generations; if the mutant conferred a 1% selective advantage, the probability became 0.78. Fisher's demonstration assumed a population of infinite size. More recently Kimura and Ohta (1) have treated the problem of mutant loss in populations of finite size, and, on the assumption of a stable population size and genetic equilibrium, developed a relationship between the mutation rate to alleles with neutral phenotypic effects (,u) and the frequency and mean extinction time in generations for these mutants. The formulation is I _1 IL  2N lo =
where I = the average number of mutant alleles per locus among the loci sampled, N = the number of individuals in one generation in the population in which I has been determined, and to = the average mutant survival time in generations for those mutants not going to fixation. By definition, I should not include those variants that will ultimately go to fixation, but this presumably very small fraction of the total cannot be excluded from any actual data set. The final formula has an appealing simplicity: on the assumption of equilibrium, the mutation rate is equal to the mean proportion of different variants per locus (I/2N) times the fraction of these variants lost each generation (1/to). However, as we ahall see, there are very real difficulties in the estimation of these parameters for actual populations. The mutational process is, of course, one of the basic processes of all biology. Unfortunately, the study of mutation rates in higher organisms, and especially humans, has for various reasons remained in a most unsatisfactory state (4-7). The recent technical developments with respect to electrophoresis, the ready availability of computers for simulation programs, and the above-mentioned formulations create a new and more basic approach to the study of a very important class of mutations. Over the past 10 years we have been involved in extensive studies of several relatively unacculturated South American tribes (8-10). One aspect of these studies has included a search for electrophoretic variants with respect to a series of serum proteins and erythrocyte enzymes. Simultaneously, through the use of a population simulation program based on the demographic characteristics of one of the tribes studied, the Yanomama Indians, an estimate of to has been generated (11). It is the purpose of this paper to summarize the results of this search, to generate estimates of I and N to accompany the estimate of To, and to
Proc. Nat. Acad. Sci. USA 70 (1973)
TABLE 1. The 13 variants encountered in South American Indians Number 1 2
3 4 5 6 7 8 9 10 11 12 13
System Peptidase A Phosphohexose isomerase Isocitrate dehydrogenase Ceruloplasmin Ceruloplasmin Ceruloplasmin Albumin Albumin Albumin Albumin Albumin Albumin Albumin
Name of variant
Yanomama-1 Macushi-1 Cayapo-1 Yanomama-1 Yanomama-2 Maku' Mak-1 Mak-3 Piaroa Wapishana
(13) (12) (14) (15, 16) (12) (17) (18) (12, 16) (12) (12)
explore cautiously the implication of these data for human mutation rates. Although there is little doubt that the estimate herein generated will be subject to several revisions, the nature and importance of the problem are such that supplementation at this time of past efforts with this fresh approach seems justified. THE DATA
The tribes for which results will be presented are the Yanomama, Makiritare, Piaroa, Macushi, Wapishana, and Cayapo. At the time of study, their acculturation to Western civilization ranged from minimal (Yanomama and Cayapo) to modest (Makiritare, Piaroa, Macushi, and Wapishana). Among 4850 Indians from these six tribes tested for the ABO blood groups in Ann Arbor, only four were not of blood group 0. Three of these "Indians" not of blood group 0 were a Caucasian abducted as a child (now culturally an Indian) and his two children. By this commonly accepted criterion, there has been in these tribes essentially no admixture with non-Indians. In all these tribes the Indians aggregate in small villages of 25-250 persons. When a village was contacted, as many of the villagers as possible were sampled, and the relationships of the individuals sampled to one another were recorded. The 15 serum proteins or erythrocyte enzymes surveyed for the occurrence of variants were the following: 6-phos-
phogluconate dehydrogenase, phosphoglucomutase 1 and 2, lactate dehydrogenase, adenylate kinase, malate dehydrogenase, adenosine deaminase, peptidase A, peptidase B, phosphohexose isomerase, isocitrate dehydrogenase, hemoglobin A, transferrin, ceruloplasmin, and albumin. The sole basis for selection for inclusion in this study was that the protein (enzyme) in question yielded stable, sharply defined "bands" in the appropriate system. Systems with which we have experience but which in our hands, given our field conditions, did not meet these criteria were: haptoglobin, groupspecific component, acid phosphatase, galactose-1-phosphate uridyl transferase, glucose-6-phosphate dehydrogenase, and catalase. The previous occurrence of variants in the laboratories of others was not a basis for selection. Table 1 lists the different rare variants encountered to date. Each of these is presumed to result from a mutation in the
genetic code resulting in an amino-acid substitution in the appropriate polypeptide. The use of the term "different" in this context requires careful definition. The sole criterion for distinguishing among variants in this study was electrophoretic mobility. However, for hemoglobin, a molecule in which detection of an electrophoretic variant is customarily followed by a determination of the precise amino-acid substitution, there are now recognized some 36 different aminoacid substitutions which, because they add one charge to the molecule, have mobilities that are either electrophoretically indistinguishable or distinguishable only when careful comparisons are possible. In the table, we enter separately variants of apparently identical mobilities that occur with quite low frequencies in different tribes. When, later in the paper, we estimate mutation rates, we will however treat these variants as identical, originating from the same mutation, a conservative procedure. In addition to the variants listed in Table 1, in some of the tribes we studied we encountered in one of the 15 systems a variant electrophoretically identical with one known to assume polymorphic proportions in other Indian tribes. Specifically, a transferrin variant with the mobility of Dchi occurred in 17.8% of the Piaroa Indians we studied; a variant with similar mobility was observed in 58% of 91 Yupa Indians from the extreme west of Venezuela (19). The original demonstration of a variant with this mobility was in people of Chinese extraction (Kwantung Province, southern China) residing in New York City (20). It is impossible to state at present whether these are identical variants. We also encountered a phosphoglucomutase polymorphism in all six of these tribes, which we attribute to the presence of the well-known phosphoglucomutase,2 gene. We omit both the presumptive transferrin Dchi and the phosphoglucomutase,2 phenotypes from our enumeration of "private" variants. It is customary before accepting a variant as valid to require its demonstration in other members of the family (although occasionally, because of mutation, one expects negative family studies). Our system of sampling ensures that most individuals found to have variants will have close relatives in the sample. We note that of the 13 variants encountered, in only three cases was there no confirmatory evidence in the form of other affected family members or covillagers (some of the latter have a high probability of relationship, even in the absence of demonstrable family links). However, since in none of these three cases were both parents available for study, they cannot be considered examples of the results of mutation. Among 56,237 system determinations (each, of course, testing two gene products), the 13 private electrophoretic variants were found in 131 people: 2.3 per 1000 tests. If electrophoretically similar variants in different tribes are scored as identical, then the number of different variants is 10. (The Macushi-1 and Cayapo-1 ceruloplasmin variants appear identical; the Piaroa albumin dimer migrates indistinguishably from the Makiritare dimer; and albumin Maku appears identical to the Wapishana variant.) However, as noted, the transferrin and phosphoglucomutase1 loci were also segregating in low frequencies in these tribes for a gene resulting in a variant electrophoretically identical with a known polymorphism. Thus, the minimal number of variants is 12. It is apparent that albumin variants contribute quite disproportionately to the total, comprising half the variants.
Proc. Nat. Acad. Sci. USA 70
Mutation Rates among South American Indians
TABLE 2. Summary of the sampling data for six Indian tribes Estimated total
Tribe Yanomama Makiritare Cayapo Piaroa
Macushi Wapishana Total
population 12,000 1,500 1,500 1,0002,000 4,000 1,000
Total no. of system Approximate N determinations 5,760 37,678 720 8,375 720 4,567 -720 1,897
Average no. sampled per locus 2,512
No. of variants in adults*
558 304 126
268 146 60
4 3 3 4
21 37 20 8
* Includes the transferrin and phosphoglucomutase polymorphism when present.
This is a large molecule (about 575 amino-acid residues), so one can argue that variants of this protein might be exceptionally frequent. On the other hand, no hemoglobin variants were encountered in 3989 determinations [by the starch-gel method of Smithies (21)] whereas Sick et al. (22) reported 10 variants in 8000 determinations on blood samples from Caucasoids. We are repeating the hemoglobin studies, using the cellulose acetate method of Kohn (23), but from time to time during this study my colleagues have experienced no difficulty in demonstrating hemoglobin variants in specimens from populations where these are known to occur in high frequency. The two cistrons of hemoglobin together are composed of 287 amino acids. The data begin to raise the possibility of locus heterogeneity in the frequency of variants. ESTIMATION OF THE PARAMETERS AND THE MUTATION RATE We turn now to estimating the parameters necessary to calculate the mutation rate. In the ideal situation these estimates would be based on the results of complete surveys of closed populations in genetic equilibrium. In fact, no such human population exists, nor has our sampling and demo-
graphic analysis of the various study populations yet approached the completeness necessary to define N with precision. Several approximations will be necessary. Estimation of N. For the purposes of this calculation, we shall define an Indian tribe as a self-contained breeding unit, on which to base an estimate of N. This is not entirely accurate, since there has probably always been, since the peopling of the Americas and the differentiation of the Indian into tribes, some migration across tribal boundaries. Such migration in the present context increases the estimate of N (or, more properly, effective population size, Ne) disproportionately to the numbers involved; no precise estimate of its effect is possible. On the other hand, we have recently argued that because of high infant mortality and a tendency to endogamous mating, for mutant survival in a population structured as the American Indian, the population of reference is primarily that of a single village (11). We assume for now that these opposing factors more or less balance, and we can consider the tribe as a basis of computing N (see Discussion). The numbers of Indians in these six tribes can be very roughly estimated (Table 2). These numbers include representatives of four generations. N in a species with overlapping
generations such as humans refers to the reproducing adult generation. Most of the Indians studied cannot give accurate ages and the Yanomama, who constitute the bulk of the study, lack a counting system and cannot give even approximate ages. From a demographic analysis of the Yanomama now in progress (Neel and Weiss, unpublished) we have developed an age pyramid of estimated ages. This enables us to infer that in our Indian sample, which in general excludes children under 2 years of age, 48% of those sampled are above the age of 14 and below the age of 41. Table 2 also presents an estimate by tribe of the average number of people sampled for each of the 15 loci, and then, by use of the 0.48 conversion factor, an estimate of N and of the average number of people aged 15-40 sampled per locus. In the total material the number of people aged 15-40 can be estimated to be 1799. If this group is considered as the population of reference, the number of locus determinations is reduced to an estimated 26,944, one variant is lost from the series (one of the Yanomama slow albumins, observed only in a girl aged 9), and the total number of private variants becomes nine. Estimation of I/2N. Ideally, the quantity I/2N is based upon a complete sampling of the defined population. Unfortunately, in no instance has the sampling of a tribe approached completeness; the estimate of proportion sampled ranges from 0.05 to 0.37 (Table 2). However, we can from the data develop minimum and maximum estimates of the quantity 1I2N. Although 15 proteins were sampled, two of these (lactate dehydrogenase and hemoglobin A) are composed of two independently elaborated polypeptides, so that the survey involves the products of 17 different cistrons. In the Yanomama, three variants were encountered in the age group 15-40 and the phosphoglucomutase-1 polymorphism was present in a sampling of 21% of the population. Thus, a minimum estimate of I/2N on the assumption that the tribe is the population of reference is (4/17)/(2 X 5760), or 2.0 X 10-5. A similar figure for the Makiritare with two variants and the phosphoglucomutase-1 polymorphism, 37% of whom were sampled, is 12.2 X 10 5. These estimates are regarded as minimum because of the high probability that further sampling of the tribe would have uncovered additional variants. The unweighted average of these two underestimates is 7.1 X 10-5. An overestimate comes from treating the entire sample as if from a single tribe. Now there are nine variants plus the two polymorphisms, and the figure is (11/17)/(2 X 1799), or 18.0 X 10-5. This is surely an overestimate, since the re-
suits of small samples of several tribes are included, whereas in the extensive sampling of a single tribe, the law of diminishing returns set in (the common variants are encountered early, whereas later one finds only the variants restricted to one or a few villages). As a first approximation, we will use as the value of I/2N the average of these two estimates, 12.6 X 1O-5. For the hemoglobin molecule, it can be shown that less than one-third of all possible amino-acid substitutions will result in a charge change. Assuming this is true for all the polypeptides under study, a rough correction of the estimate to include the "silent" variants is achieved by multiplying by a factor of 3, resulting in an estimate of 37.8 X 10-s. Boyer et al. (24) have shown that with respect to primate hemoglobin, the ratio of "silent," nonelectrophoretically detectable substitutions (ascertained by sequence analysis), is substantially higher than the ratio of 2:1 predicted if mutation of all nucleotides is equiprobable and if substitutions were the result of a random genetic process rather than, to some extent, Darwinian selection. This suggests heavier selection against the electrophoretically detectable than the "silent" mutations (or, much less likely, preferential mutation of the type resulting in silent substitutions). If, as a general rule, there is negative selection against the electrophoretically detectable mutants, this will be reason to regard an estimate of mutation rate from these data as conservative. Estimation of to. As noted earlier, to, has been determined by a computer simulation of the survival of a mutant gene introduced into a newborn infant in a population patterned after the Yanomama (11). The mean of 214 "runs" was 2.3 generations. However, the estimate of I/2N just developed is not based on a newborn population, but a population that has survived the vicissitudes of early life, which in the Yanomama include roughly 15% infanticide and 25-35% infant and childhood mortality. We have also estimated to for those mutants whose possessor reaches maturity and reproduces in the first generation; it is 3.7 (11). The fact that the estimate is based upon a population estimated to be expanding at the rate of about 0.5-1.0% annually should bias the estimate upwards, but probably not greatly. Because of certain recognized imperfections in the simulation, we have suggested that to may be underestimated by 1 generation, so that the "corrected" value would be 4.7. Our estimate of to is based upon a simulation of a closed population of four Yanomama villages. An attempted simulation based upon the entire tribe would of course have exceeded the capacity of most existing computers. The question may well be raised, whether by so restricting the numbers involved, we have influenced to. In the 214 determinations of mutation survival, the mutation did not spread beyond the village of origin in 192 runs. In 18 runs it spread to a second village, in three runs to a third, and in two runs it spread to all three of the other villages. The Yanomama tend to be subdivided into clusters of interbreeding villages; our simulation has been patterned after one such cluster. Thus, while to might have been somewhat greater in a simulation involving the entire tribe, our present judgement is that the increase would be relatively small. Calculation of A. The formulations used to estimate , were derived on the assumption that the phenotypes resulting from mutation were selectively neutral. In the present series, aside
Proc. Nat. Acad. Sci. USA 70 (1973) from the two polymorphisms, the remaining variants were usually encountered in the heterozygous state (128 of 131 occurrences). In our simulation program, most mutants were lost without ever occurring in the homozygous state. Thus, by and large the assumption of neutrality for these biochemical variants reduces to neutrality as a heterozygote. Mathematically this assumption of neutrality has high heuristic value, but its introduction into the calculation should not be taken as an endorsement of the concept that all, most, or even a substantial fraction of mutations are neutral in their phenotypic effects. Despite the current interest in the possibility that a high proportion of the mutants that achieve polymorphic proportions and ultimately go to fixation in a species are neutral in their phenotypic effects (25, 26), the experimental evidence continues to suggest that the majority of mutant genes are deleterious, but a small fraction, favorable. To the extent that some of the variants encountered in this study are deleterious, the assumption of neutrality results in a conservative estimate of ,u, since the mutation rate necessary to maintain a given number of mutants in a population is higher if these are deleterious than if they are neutral. However, as pointed out earlier, random loss is the usual fate of even favorable mutants, let alone the unfavorable. On the other hand, we cannot exclude the possibility that some of these variants occur as balanced polymorphisms, or transient polymorphisms, the latter the situation wherein a recent mutation with favorable effects is replacing the type allele; it is assumed these are a distinct minority of the variants encountered in this study. With the assumptions that have been stated and the foregoing estimates of N, I, and to, the estimate of u is 8 X 10-5 per gene per generation. With the various approximations that have entered into this calculation, there is no possibility of attaching a confidence interval to the estimation. On the other hand, we are at this stage in our developing knowledge of human mutation rates concerned with developing an order of magnitude, and this seems reasonably secure. Some might argue that the polymorphisms of transferrin and phosphoglucomutase-1 encountered in this study should not be included in the calculation, because their existence is most probably due to the action of balanced selective forces. If they are omitted from the calculation, ,' _ 6 X 10-. The choice of the population of reference (i.e., N) is clearly a central issue to this estimation procedure. Any species has a hierarchical structure, first the deme, then a group of obviously interacting demes, then a group of infrequently interacting demes, then a group of still less frequently interacting demes, etc. For man, before the upheaval in population structure that civilization caused, this situation is described as village, closely related villages, tribe, ethnic group, and species. The analysis of protein structure reveals, for given proteins, specific amino-acid differences between species that characterize all members of the species and that can only result from the spread of a mutation throughout the entire species. Thus, for genetic phenomena, the ultimate population of reference is the entire species. However, in using the tribe as the reference point for N, we argue both from observation and simulation that the great majority of mutants never escape the boundaries of the tribe within which they arise. If this argument is essentially correct, then taking the tribe as the reference population introduces only a relatively small approximation into the calculation.
Proc. Nat. Acad. Sci. USA 70
On the basis of extrapolation from the study of the frequency of origin through mutation of about a dozen rare phenotypes in civilized Caucasian populations, the rate of mutation in humans is in round figures often given as 10-5 per gene per generation (summary in ref. 4). Reasons have been advanced why this may be an overestimate, and some prefer a figure of 10- (6, 7). Thus, as a general guide line the estimate generated by these data must be regarded as relatively high, especially when it is realized that even with the attempted allowance for mutation resulting in silent amino-acid substitutions, not all mutations are detected by this approach. For instance, mutation resulting in duplication, deletion, or inactivation of a genetic locus would probably go undetected. On the other hand, the reader is again reminded of the extent to which variants of one single protein, albumin, increase the present estimate; only further data will permit a decision as to whether this is a happenstance or whether albumin truly is a more variable protein than most, and has unduly influenced this estimate of average mutation rates. It is clear the present estimate is destined to undergo many refinements. But already it should have served a useful purpose, since to reconcile the present data on variant frequency with a mutation rate of 10- requires for Indian populations a to of 470, a value which because of the size of the population it implies is clearly excessive. Several findings during our studies of these Indian populations should prepare us for the possibility that ultimately the rate of this type of mutation in Indians will be recognized as relatively high. Thus, we have reported evidence for more chromosome breakage in the Yanomama than in urban Caucasians or Japanese (27), and also the findings of high serum and urinary mercury levels in two isolated Indian villages (Hecker, L. H., Allen, H. E., Dinman, B. D., & Neel, J. V., in preparation). Gammaglobulin levels are high in these groups and antibody surveys provide evidence of extensive contact with viral diseases (28). Indian diets contain many exotic foods, and the use of various hallucinogens is widespread (29). There is a more direct approach to the question of the relative frequency of mutation in primitive and civilized populations. This involves a determination of the frequency with which neither parent of an individual with a rare variant is affected, the determination accompanied by appropriate studies to detect extramarital conceptions. Such data are becoming available for these Indians but a meaningful estimate of mutation rates involves a larger sample than is at hand. This is the approach of choice, since it avoids many of the assumptions of the present treatment. The present estimate will undoubtedly undergo several revisions, but it seems clear the methodology is now at hand ultimately to provide much more acceptable estimates of mutation rates in mammals than those based on gross phenotypes whose molecular basis remains poorly understood. These investigations have been supported by grants from the U.S. Atomic Energy Commission and National Science Founda-
Mutation Rates among South American Indians
tion, and constitute one aspect of an Integrated Research Program in the U.S. International Biological Program.
1. Kimura, AI. & Ohta, T. (1969) Genetics 63, 701-709. 2. Fisher, R. A. (1922) Proc. Roy. Soc. Edinburgh 42, 321-341. 3. Fisher, R. A. (1930) The Genetical Theory of Natural Selection (Clarendon Press, Oxford), pp. xiv & 291. 4. Neel, J. V. (1962) in Methodology in Human Genetics, ed. Burdette, W. J. (Holden-Day Inc., San Francisco, Calif.), pp. 203-224. 5. Neel, J. V. (1971) Perspect. Biol. Med. 14, 522-537. 6. Stevenson, A. C. & Kerr, L. B. (1967) Mutat. Res. 4, 339-352. 7. Cavalli-Sforza, L. L. & Bodmer, W. F. (1971) The Genetics uf Human Populations (Freeman and Co., San Francisco, Calif.), pp. xvi & 965. 8. Neel, J. V. & Salzano, F. M. (1964) Culd Spring Harbor Symp. Quant. Bicl. 29, 85-98. 9. Neel, J. V. (1970) Science 170, 815-822. 10. Neel, J., Arends, T., Brewer, C., Chagnon, N., Gershowitz, H., Layrisse, M., Layrisse, Z., MacCluer, J., Migliazza E., Oliver, W., Salzano, F., Spielman, R., Ward, R. & Weitkamp
L. (1972) in Human Genetics, Proc. IV Int. Cong. Hum. Genet., Paris, Sept. 1971 (Excerpta Medica, Amsterdam),
pp. 96-111. 11. Li, F. H. F. & Neel, J. V. (1973) in Computer Simulation in Human Population Studies, eds. Dyke, B. & MacCluer, J. W. (Seminar Press, New York), in press. 12. Tanis, R. J., Neel, J. V., Dovey, H. & Morrow, M. (1973) Amer. J. Hum. Genet., in press. 13. Weitkamp, L. R., Arends, T., Gallango, M. L., Neel, J. V., Schultz, J. & Shreffler, D. C. (1972) Ann. Hum. Genet. London 35, 271-279. 14. Salzano, F. M., Neel, J. V., Weitkamp, L. R. & Woodall, J. P. (1972) Hum. Biot. 44, 443-458. 15. Weitkamp, L. R. & Neel, J. V. (1972) Ann. Hum. Genet. London 35, 433-444. 16. Wietkamp, L. R., Salzano, F. M., Neel, J. V., Porta, F., Geerdink, R. A. & Tdrnoky, A. L. (1973) Ann. Hum. Genet. London 36, 381-392. 17. Weitkamp, L. R. & Chagnon, N. A. (1968) Nature 217, 759760. 18. Arends, T., Weitkamp, L. R., Gallango, M. L., Neel, J. V. & Schultz, J. (1970) Amer. J. Hum. Genet. 22, 526-532. 19. Arends, T. & Gallango, M. L. (1964) Science 143, 367-368. 20. Parker, W. C. & Bearn, A. G. (1961) Ann. Hum. Genet. London 25, 227-241. 21. Smithies, 0. (1965) Vox Sang. 10, 359-362. 22. Sick, K., Beale, O., Irvine, D., Lehmann, H., Goodall, P. T. & MacDougall, S. (1967) Biochim. Biophys. Acta 140, 231242. 23. Kohn, J. (1960) in Chromatographic and Electrophoretic Techniques, ed. Smith, J. (Interscience Press, New York), Vol. II, pp. 84-146. 24. Boyer, S. H., Noyes, A. N., Timmons, C. F. & Young, R. A. (1972) J. Hum. Evol. 1, 515-543. 25. Kimura, M. & Ohta, T. (1971) Nature 229, 467-469. 26. Kimura, M. & Ohta, T. (1971) Theoretical Aspects of Population Genetics (Princeton University Press, Princeton, N. J.), pp. ix & 219. 27. Bloom, A. D., Neel, J. V., Tsuchimoto, T. & M\eilinger, K. (1973) Cytogenet. Cell Genet. 12, 175-186. 28. Neel, J. V., Andrade, A. H. P., Brown, G. E., Eveland, W. E., Goobar, J., Sodeman, W. A., Jr., Stollerman, G. H., Weinstein, E. D. & Wheeler, A. H. (1968) J. Trop. Med. Hyg. 17, 486-498. 29. Chagnon, N. A. (1968) Yanomamo: The Fiei cc People (Holt, Rinehart & Winston, New York), pp. xiv & 142.