Bioassay of Kinship in Micronesia NEWTON E. MORTON AND J. M. LALOUEL Population Genetics Laboratory, University of Hawaii, 241 1 Dole Street, Honolulu, Hawaii 96822 KEY WORDS Bioassay . Kinship Micronesia. ABSTRACT Phenotype bioassay agrees with clan isonymy, anthropometrics, and migration in estimating the mean kinship within a Micronesian population, relative to large distances, as 0.05. Various calculations of occupancy for the Eastern Carolines from ethnohistory, kinship, and glottochronology average around 1,000 years. Estimates of isolation by distance are in agreement for different indicators of population structure. Problems of kinship bioassay are discussed. Kinship is both a correlation between gametes and, if expressed relative to founders, probability of identity by descent. Information about observed and expected variation of gene frequencies among populations is summarized in a square, symmetrical matrix of pairwise kinship which may be predicted from genealogy or migration and estimated (bioassayed) from phenotypes, metrics, or isonymy. Recent reports on genetic systems in the Eastern Carolines (Yamamoto and Fu, '72; Morton and Yamamoto, '72; Steinberg and Morton, '72) had as their goal to compare estimates of kinship from bioassay with predictions from migration and genealogy (Morton et al., '71a,b). Here we give those results. A final paper in this series on the population structure of Micronesia will consider topology of kinship (Morton and Lalouel, '72). nkih = 2Nihqkih Here q k i h is the maximum likelihood estimate of the frequency of the kth allele in the ithpopulation, Ah is the totd number of alleles for the hth system, Nih is the sample size in the it" population, 2 and nkih i Qkh = 35-K i is the frequency of the kth allele in the array of populations. A subroutine of BIOKIN applies the program ALLTYPE (Yasuda, '69; Miki et d . , '69) to determine the amount of information per individual (kh) furnished by the hth genetic system about @ = 0 at known gene frequencies Qkh (table 3). Finally, BIOKIN estimates an optimum weight w such that Phenotype bioassay The current status of kinship bioassay (Morton et al., '71c) has recently been summarized (Morton, '72a). With the FORTRAN IV program BIOKIN for the O L W L l , CDC 3100 computer, we used the data of tables 1 and 2 on phenotype frequencies in the weight assigned to the estimate of Micronesia to estimate kinship for the hth 0 r l h is system as h h = Ah z [k=l q k j h q k j h / Qkli -1 1 /(Ah - 1) i # j AM. J. PHYS.ANTHROP., 38: 709-720. (1) 1 PGL Paper 85. This work was supported by grant GM 17173 from the U. S. National Institutes of Health. 709 3 f 1 Simmons et al., 1965. Simmons et al., 1953. Boyd, 1939. Boyd. 4 Platdet Plato et al.. al., 1966. 5 Hainline et al., 1969. 6 Hainline, 1965. Pingelap MOM Kusaie Ponape Yap TotalPonapedistrict Total Population Pingelap Mokil Kusaie Ponape Kapingamarangi Palau Saipan Chamorros Saipan Carolinians Yap Yap outer islands Truk Mortlocks Marshalls Gilberts Total Ponape district Total Population BA 256 92 200 136 248 684 932 B 418 110 144 249 171 3 18 17 69 15 TABLE 2 2-1 PGMi 2 B 0 0 953 52 953 52 Miller, R. E., 1953. 0 0 0 0 350 29 184 10 245 3 174 10 _ 228 121 184 136 1- 391 669 391 669 _ 181 86 70 54 1+ Inv '72: '72; Morton and' and Yamamoto. Yamamoto, '72: 72; Steinberg and Morton, '72). 13 Blumberg and Gentile, 1961. 14 This study (Yamamoto a?d and Fu. Fu, If BA - - - A 6-PGD 354 117 200 105 776 776 1.33 13,14 38 55 34 67 194 194 13.5, 13,14,21 12 3 9 25 25 1 1.21 11 11 - 3 6 0 2 18 153 66 13 7 4 24 2 5 5 2 4 1 8 12 0 cF6E 4 4 0 0 1 3 1,5,6,21 Gm 6 19 2 0 0 1 0 0 2 2 2 0 3 3 4 0 ?& 1,2,21 181 843 292 46 48 54 111 26 10 17 8 32 118 282 42 42 60 22 15 26 31 52 2 RlRz CcDE 55 26 13 23 1 31 35 5 0 RIR, CcD Phenotype frequencies in Micronesia. Isozymes and immunoglobulins 367 12 0 158 35 1 160 80 8 132 45 7 - - 817 172 16 817 172 16 1 54 Simmons et al.. al., 1952. 10 Douelas Douglas et al.. al., 1961. 11 Grafdon Graydon et a]:, al., 1953. 9 219 109 99 514 169 71 15 54 936 129 174 156 26 277 RiRi CCD 1421 3683 27 224 56 24 29 62 57 44 62 55 131 211 63 220 78 314 28 1007 222 100 463 82 42 212 97 31 174 0 44 17 156 5 333 115 90 27 139 70 5 162 14 257 M N S + S - 940 1131 305 174 154 1217 732 201 1900 4171 3110 1443 515 675 2838 2302 374 4121 45 31 78 59 30 25 21 15 0 2 4 21 35 25 30 30 19 34 28 68 143 36 58 0 126 89 44 176 690 282 147 93 5 157 22 55 277 N 475 173 233 740 224 359 254 149 265 201 611 207 128 608 A B M B 410 222 288 236 221 485 235 187 132 92 238 171 100 242 A 437 107 112 161 123 508 282 223 610 0 '8 Plato and Cruz, 1966. Sussman et al., 1959. 15 32 40 1 44 32 166 9 131 41 297 1 3 4 A AcP 1.3;7 3;8;9,13 10,ll 14 14 3,14 3. 14 2;12 1,2,3 Reference TABLE 1 Phenotype frequencies in Micronesia. Blood groups and haptoglobins 23 23 - 6 12 4 1 1A5, 6,13,14 329 581 2 18 30 59 51 19 19 54 - 233 23 44 29 Hpl-1 6 2 13 4 25 25 1,2,3,5, 13,14,21 480 1191 37 63 76 83 111 155 104 143 78 67 66 208 Hp2-1 2 2 2 0 0 0 1.5.13. 14,21 250 780 33 43 54 31 72 26 82 60 82 56 59 182 Hp22 71 1 MICRONESIAN BIOASSAY OF KINSHIP m ln 9 and the variance of 2 m @,I = wiih @ u h 2 W u h h ? 0 9 0 I -8 a Q) around the Malkcot expectation for isolation by distance is minimal. The Malecot expectation is = (@,, - L ) / ( 1 - L) = ae-bdij (3) where d,, is the geographic distance between populations i and j . Since w is optimized, the final weight Wllh need not be highly dependent on the estimated amount of information kh, which may more simply be taken as the number of factors in the phenotype system on one less than the number of alleles, the generally most efficient estimate being unknown. The value w = 0 corresponds to k, = 1 for all h . Kinship relative to indefinitely large distances and indefinitely remote founders is Random kinship is defined as or qIR' where = -L I-L @R ~ N; = Z N;h w h h For O R we find - .0001, SO that OR' = - L. There is a function of kinship called hybridity, defined a s (5) which measures the excess of heterozygosity in an F, relative to an F, between a pair of populations : its expected value + '( 'IJ) 2 qkt2 2 qkj2 - 2 2 qkiqki k k k = 4 - 2 q k ? - 2 qk]* - 2 2 q k l q k , k k k is thus independent of regional gene frequencies. More generally, e is invariant under the transformation 0 -+ ( 0 - L ) / ( 1 - L). The limits of hybridity are 0 (for two populations with the same gene frequencies and one (for two populations 712 NEWTON E. MORTON AND J. M. LALOUEL fixed for different alleles) and so hybridity is a measure of the mean number of allelic substitutions per locus. Its MalCcot expectation is Since 8 increases monotonically from zero for i = j to a n asymptote at a/2, it is proportional to measures of genetic distance proposed by Sangvhi and others (Morton, '72a), but differs in having a simple genetic interpretation and in allowing comparison and combination of estimates. Fitting Eq. 6 to the values of (3 in table 4, we find simultaneous estimates 1, w=o a = 0 0552 2 0.0060 b E 0.0023& 0.0012 Lacking phenotypic data on the Eastern Carolines, Imaizumi and Morton ('70) estimated the mean kinship within a Micronesian population as 0.05. For Pingelap and Mokil, the same value was estimated from clan isonymy and anthropometrics (Morton and Greene, '72), and predicted from migration (Morton et al., '71b). The various methods to study kinship are in substantial agreement. Anthropometrics For anthropometrics kinship is a function of heritability (Morton and Greene, '72). If simultaneous estimation is not feasible, it is still possible to bioassay kinship with anthropometrics, providing a n independent estimate is available of mean kinship 9 , defined as 6 = Z N, 6,J Z N, i (7) i = (Xih - Ph) (Xjh - Ph) (i # j ) where x z h is the mean v d u e of the hth metric in the ithsample of size N, with intrapopulation variance Vh, and fih = ,P Ni X i h / i The mean value of Eh Enh = Z N, Z N, i (8) is [nh/ i Z i NL (9) By letting @rib (@/Eh) Euh (10) we eliminate heritability differences, providing the environment is randomly distributed among populations. On this critical assumption, estimates of @,,,, from anthropometrics can be treated just as estimates from a single locus. Choice of a weight kh is more delicate. Equal weights are commonly taken in numerical taxonomy, but it may be more reasonable to consider metrical correlation. Let R h be the multiple correlation coefficient when xh is regressed on the other metrics. Then we may take kh = 1 - Rh2 (11) in applying Eq. 2. Data for the same samples except Gilbertese and Carolinians of Saipan were available from Hasebe ('39) on eight metrics: stature, head length, head breadth, nose height, nose breadth, face height, face breadth, and chest girth. They were assigned by weighted regression according to Eq. 11, the weights 0.216, 0.247, 0.076, 0.173, 0.197, 0.104, 0.329, and 0.082, respectively. The variances Vh were taken as L(N, - 1 ) ~ 2 h , / ~ ( N1l) . With i i as 0.045 and the above weights, the @I,, e,, were computed and fitted to Eq. 3 and Eq. 6, respectively (table 5 ) . Fitting the @,I, we get the simultaneous estimates. a= 0.0569 & 0.0084 b = 0.0016I 0 0 0 6 L = - 0.0133 ? 0.0064 0 estimated from phenotype bioassay and, fitting the e,, a = 0.06342 0.0069 b = 0,00372 0.0033 The determinants of anthropometrics appear to have the same parameters of systematic pressure and drift a s the polymorphisms, supporting the hypothesis that polygenes and polymorphs are different perceptions of essentially similar alleles (Morton, '69). Chronology Simulation of population structure from a migration matrix leads to prediction of kinship in successive generations (Malkcot, '50; Morton, '69). Let $J' be a matrix (or submatrix) derived by bioassay, and Q ~ be~ ) Population Pi Mo Ku Po Ka 0.0334 0.0112 0.0664 Kapingamarangi (Ka) Palau ( P a ) Saipan Chamorros ( S a ) Saipan Carolinians ( C a ) 0.0273 0.0429 0.0561 0.0298 0.0318 0.0176 0.0410 Yap (Ya) Yap outer islands ( Y o ) Truk (Tr) Mortlocks (Mt) Marshalls (Ma) Gilberts (Gi) 0.0087 0.0255 0.0163 0.0072 0.0447 0.0267 0.0444 0.0306 0.0076 0.0897 0.0292 0.0621 Ponape (Po) Pa 0.0108 0.0156 Mt -0.0267 0.0173 -0,0087 -0.0113 -0.0223 0.0191 0.0226 0.0045 0.0191 -0.0017 0.0261 0.0124 0.0015 -0.0097 0.0302 - 0.0003 - 0.0471 0.0053 0.0075 0.0004 0.0032 0.0046 0.0018 - 0.0041 0.0259 Ma Gi -0.0070 - 0.0027 0.0182 0.0356 0.0231 -0.0114 0.0174 0.0204 0.0132 0.0082 0.0076 0.0258 0.0226 0.0103 0.0166 0.0360 0.0363 0.0769 0.0786 0,0435 0.0418 0.0288 0.0167 0.0629 0.0249 0.0314 0.0102 0.0124 0.0368 0.0127 0.0191 0.0153 0.0311 0.0527 0.0040 0.0141 0.0096 0.0205 0.0050 0.0098 - 0.0241 - 0.0162 0.0079 -0.0068 0.0243 -0.0432 -0.0057 -0.0142 0.0003 - 0.0021 0.0257 0.0113 - 0.0259 0.0013 0.0041 - 0.0121 - 0.0006 - 0.0007 - 0.0248 0.0144 TI 0.0079 0.0108 0.0128 Yo - 0.0250 0.0117 0.0106 Ya 0.0542 0.0247 0.0353 Ca 0.0099 -0.0158 -0.0198 -0,0034 -0,0109 -0,0172 -0.0192 0.0199 0.0332 0.0225 0.0635 Sa 0.0077 -0.0476 -0.0320 -0.0212 -0.0456 -0.0160 -0.0158 0.0059 I0.0160 -0.0125 -0.0017 0.009510.0263 0.0247 I 0.0607 -0.0156 -0.0012 -0.0163 -0.0206 ‘0.03331 0.0378 0.0122 0.0110 -0.0479 Kusaie (Ku) Mokil ( M o ) Pingelap ( P i ) TABLE 4 Matrices of kinship @ (upper trimat) and hybridity 0 (lower trimat) f r o m phenotype bioassay NEWTON E. MORTON AND J. M. LALOUEL a prediction in generation t. The norm of the matrix @’ - act) is o a m a l m m c - m a ~ ~ a v m m m m m m - m m o o o o - m - ~ o 0 0 ~ 0 0 0 0 0 0 0 0 0 0 I I 0 0 I 0 0 0 0 I m m ( 9 c - a 0 8 $ 8 t - - m 0 0 - m a 9 9 9 ? ? ? 0 0 0 rt 0 a m 9 9 9 ? ? ? 0 9 0 0 0 0 0 0 I I I l l z (a9l m9 3 s e 0 0 9 % El% m o m 0 0 0 P - d a l 9 9 9 9 9 9 9 9 9 0 0 I ~ m m c - m - m m 0 0 0 0 m 9 9 9 0 0 I I 0 % % k m - 0 9 9 9 0 0 0 I %m Zm %9 9 9 9 0 0 0 c ~ m m m - m 9 0 3 m m m t m m 3 - 4 - 0 0 0 m m m z m 0 3 9 - 9?? 0 0 0 0 0 0 ~ m 0 0 0 ~ O ( 0 0 9 0 0 0 0 9 a l w m m m m m o m 0 0 0 0 3 0 0 0 0 0 0 0 9 - 0 3 m m - o a l m 888 I y T F 0 3 o m a l t - o t - 0 3 m o m ~ m r - 0 3 ( 9 9 m m - 4 u t0 - 09 m 0 0 0 0 ? ? 9 0 0 0 ._ M 2 m W fi M ma.5 $7 z C 4 Z & (12) The matrices 0’ and @ c t ) are said to be congruent if t is the integer for which rt is a minimum. Then t is an estimate of the duration of the system, as the number of generations since the population was founded. This estimate is of course no more reliable than the migration matrix from which it was generated. Similarly, the matices 0 and Wt) are congruent if t is the integer for which 3 2 8 0 I I I a l m o m m m a m m m o d = z z (@,I’ - @,,“’)2 j i I 0 0 0 0 0 0 is a minimum. A program CHRONIX determining congruence was applied to predictions of @ c t ) by the program OBELIX from a migration matrix corresponding to seven Micronesian populations (Morton et al., ’71a, table 3). The long-range migration rate was taken to be 0.00584 for Pingelap, 0.01923 for Mokil, and the mean of these (0.01254) for the five remaining populations. The vector of local effective population sizes N was determined as follows. From table 5 of Morton et al. (’71a) the ratio of assumed to evolutionary size was estimated as 1.08 for Pingelap and 1.21 for Mokil, the excess over unity being due to immigrants. Evolutionary sizes were estimated as 87 and 82, respectively (Morton et al., ’71b). Therefore we aslsumed a local effective size of 87/1.08 = 81 for Pingelap and 82/1.21 = 68 for Mokil. The ratio of the effective to census sizes of the atolls is 149/1208 = 0.123. This fraction of the census size was assumed for the other populationis, or 450 for Kusaie, 754 for the Mortlocks, 5020 for the Gilberts, 1518 for Ponape, and 2250 for the Marshalls. Estimates of duration for this system are given in table 6, with a mean of 34 generations. Morton et al. (’71b) estimated a mean generation time of 29.1 years, and calculated from the ethnohistory that the occupancy of Pingelap extended between 25 generations and 1,000 years. From kinsihip we calculate t = (34)(29.1) = 1000 years, in good agreement. An independent estimate is provided by glottochronology (Swadesh, ’52; Hymes, MICRONESIAN BIOASSAY OF KINSHIP 715 '60). If C = 0.708 is cognate frequency between Pingelap and Ponape, duration in years is approximately log '708 = 800 yrs. log ,805 t = 500 by a formula based on large, continental populations. Isolation by distance Our analysis has provided five kinds of data for study of isolation by distance: phenotypes, metrics, migration, cognates, and clan isonymy, of which the latter is not available for all Micronesia (table 8). Estimates of a and b are in close agreement for phenotypes and anthropometrics. Migration gives a lower estimate of a, because predictions of kinsihip in generation 34 are considerably less than observed for the Mortlocks, Marshalls, and Gilberts. This may be due in part to nonrandom sampling of bhese archipelagoes, but probably a more important factor is the settlement pattern: if chance settlers of one atoll spread subsequently to the others, the number of founders was much smaller than 12.3% of the present census size, as extrapolated from Pingelap and Mokil. Some support for the conjecture that archipelagoes had small numbers of founders was provided by Pollock et al. ('72). Her migration data for Namu atoll in the Marshalls predicted kinship for two random Marshallese of 0.003 after 30 generations, which is far less than indicated by bioassay. Even her prediction of 0.02 for random kinship on Namu after 30 generations is less than half the value from bioassay. Presumably the number of Marshallese founders was smaller than the present effective size of Namu atoll. The estimate of b from migration is greater than from bioaslsay. In MalCcot's theory of isolation by distance, b = V 2m/ci, where m is the (linearized) systematic pressure and c2 is the variance of (shortrange) migration. Perhaps the short-range migration rate was greater, and/or the long-range migration rate smaller, in prehistoric times. However, this discrepancy is reduced when only pairs of populations involving Pingelap or Mokil, which alone have reliable migration estimates, are considered (table 9). 716 NEWTON E. MORTON AND J. M. LALOUEL TABLE 7 Prediction of kinship (upper trimat) and hybridity (lower trimat) at generation t = 34 Pingelap Pi Mo Ku PO Mt Ma Gi 0.0804 0.0211 0.0013 0.0008 0.0013 0.0002 0.0004 0.0404 0.0005 0.0008 0.0007 0.0007 0.0004 Kusaie 0.0250 0.0150 0.0002 0.0002 Ponape 0.0219 0.0116 0.0000 0.0000 Mortlocks 0.0234 0.0134 o.oooo o.oooo Marshalls 0.0216 0.0111 0.0048 0.0000 Gilberts 0.0209 0.0105 Mokil 0.0054 0.0023 I 0.0017 0.0040 0.0022 TABLE 8 Isolation by distance in Micronesia. Kinship Source Phenotypes 1 Anthropometrics Migration ( t = 34) Cognates 1 2 L a Ua b - 0.0081 0.0463 0.0083 0.0023 - 0.0133 0.0569 0.0084 0.0016 0.0006 0 0.0244 0.0012 0.0065 0.0014 0.00 - 0.0029 0.0005 0.00 0.1531 2 X I for parameter not iterated 1 ub - 0.17 - Since simultaneous estimation failed to converge, b = 0.0023 was taken from hybridity. From the lower trimat of table 5, Imaizumi and Morton, 1971. TABLE 9 Isolation by distance of Pingelap and Mokil with other populations. Kinship Source Phenotypes L 1 Anthropometrics Migration ( t = 34 ) Clans 1 x z for parameter not iterated 0.0069 - 0.86 0.0069 0.0041 - 0.0120 0.0010 0.08 0.0111 0.0099 - 0.0014 0.09 Ua -0.0103 0.0565 0.0132 -0.0021 0.0884 0.0222 0.0606 0.0015 0.0540 0.0161 - 0.0045 0 -0.0121 Cognates Ub a 0.3440 1 b Since simultaneous estimation did not converge, b = 0.0069 was taken from anthropometrics. Imaizumi and Morton ('70) obtained a similar value of b by phenotype pair bioassay (0.0014 0.0005) which agrees closely with the present results. Agreement is even better if Pingelap is omitted, because it is the most highly differentiated of the Micronesian samples and was not included by Imaizumi and Morton. Then estimates of b in table 8 are reduced to 0.0017 i 0.0007 for phenotypes and 0.0015 2 0.0007 for anthropometrics. Although Imaizumi and Morton estimated 0.0508 for random kinship within * populations, their estimate of a was 0.0328 2 0.0058. This confmns Morton ('72a), who showed that the method of phenotype pair bioassay underestimates a by one-third but gives an unbiased estimate of b. Pollock et al. ('72) predicted b = 0.0005 from migration in the Marshalls, corresponding to greater internal migration than for the Carolines. All of these values of b are smaller than have been found for continental populations, and very much smaller than for continental isolates 717 MICRONESIAN BIOASSAY OF KINSHIP (Morton, '69; Friedlaender, '71 ; Imaizumi and Morton, '70), reflecting greater displacement of migrants. The value of a is higher than for all reported populations except slash-and-burn agriculturalists (Friedlaender, '71; Imaizumi and Morton, '70; Roisenberg and Morton, '70; Chapman and Jacquard, '71), which also have small effective size and low systematic pressure. When only pairs of populations including Pingelap or Mokil are considered, estimates of a and b increase (table 9). There is no longer any marked discrepancy between bioassay and predictions from migration. Clan isonymy agrees well with other estimates. Previously we found a lower value of b from cognates than migration (Morton, '72b). This is still apparent but less striking, since the value of L is significantly positive. Cognates present much more acutely than other indicators the problem of variable retention rate, so that decline of cognate frequencies is more rapid at small than large distances. When only small distances are considered (by simultaneous estimation of L ) , migration appears to be about as effective for cognates as genes. Thus our earlier suggestion that migration is less effective for cognates must be restricted to large distances, and therefore to different linguistic groups. DISCUSSION Except for test data from Papago Indians, this is the first analysis of population structure ulsing a new method for phenotype bioassay (Morton et al., '71c). There seems little to choose among various estimates of kinship. Even the method called biased, because it includes errors of gene frequency estimation, gives w = l a = 0.04772 0.0078 b = 0.00162 0.0010 which, despite a much M e r e n t value of w, is in good agreement with the first line of table 8. Chdoe of the weight w does not appear to be critical. Although Eq. 2 is not fully efficient, it seems satisfactory. The parameter L has excited controversy (Harpending, '72; Morton, '72a). Its estimation can be avoided by using Eq. 6 for hybridity instead of Eq. 3 for lunship. However, estimates of kinship will not then be strictly comparable to predictions from migration or genealogy. We have two alternatives : to introduce L into estimates of kinship, retaining the concept of identity by descent; or to express predictions from migration i n terms of gametic correlation, as F,, - @IJ - @R 1- @R This has the major disadvantage that unless genealogy covers the whole region, it will not yield estimates of rl,. We therefore prefer to retain the concept of identity by descent and with it the parameter L. In principle we could estimate a,, bi, and L, for each population and its pairs with all others. Highly differentiated populations will tend to give above-average estimates of a, b, and ( L ( .I n table 8 and 9, although a and b are larger for pairs including Pingelap or Mokil than for all Micronesia, n o tendency is observable for L. Unless populations differ greatly in size or migration pattern, it seems preferable to avoid the convergence problems and multiplicity of estimates for a,, b,, and LI, and to take a, b, and L as parameters characterizing the region or a subset of interest (here, Pingelap and Mokil). In the first attempts at studying isolation by distance, the MalBcot equation was written as 6' = ae-wd-c, where c was called dimensionality. The justification for this was that a n equation of this form had been derived in the limit for large distances in one and two dimensions ( c = 0 and 0.50, respectively). However, it was found in real populations (Morton, '69), i n simulations of simple structures (Imaizumi et al., ' 70), and finally proven by MalBcot ('72) that under local panmixia this equation can be simplified by taking c = 0 for distances small enough so that kinship is measurable. Thus the parameter L has replaced c in population structure theory, a positive value of L signifying a positive value of c, but not conversely. A positive value of L for pedigree inbreeding has been taken to indicate preferential mating with relatives at large distances, due to restricted contacts with strangers (Azevedo et al., '69). 718 NEWTON E. MORTON AND J. M. LALOUEL ABO, Rh and MNS blood typing results and We have interpreted a positive value of L other biochemical traits in the people of the for cognates as due to variable retention Yap Islands. Archaeol. Phys. Anthrop. Oceania, rates within a word list. Migration and 4: 64-71. genealogy have L = 0. All bioassays are Hainline, L. J. 1965 Blood typing data, ABO and Rh(D), collected from hospital records in expected to have negative values of L. An Yap and Saipan: a brief note. Human Biol., advantage of formulations in terms of L 37: 174-177. (rather than c ) is that the value of b gives Harpending, H. 1972 !Kung population strucdecline with small distances, over which ture. In preparation. selection is likely to be uniform and less Hasebe, K. 1939 The natives of the South Sea Archipelago. Jinruigaku Senshigaku Koza, 1 : important than migration, so that inter1-35. pretation is simplified. Hymes, D. H. 1960 Lexicostatistics so far. CurMuch of the variation in kinship is due rent Anthrop., l: 3-44. to errors of estimation and nonisotropic Imaizumi, Y., and N. E. Morton 1970 Isolation by distance in New Guinea and Micronesia. migration, with selective clines at large Arch. Phys. Anthrop. Oceania, 5: 218-235. distances. Perhaps the Malkcot equation Imaizumi, Y., N. E. Morton and D. E. Harris would give a better fit if distance were not 1970 Isolation by distance in artificial popumeasured i n a straight line, but in some lations. Genetics, 66: 569-582. other way. Unfortunately, no one has yet Malecot, G. 1950 Quelques schemas probabilistes sur l a variabilitb des populations natureldevised a n algorithm that would make les. Ann. Univ. Lyon Sci. Sec. A, 13: 37-60. such an attempt more than an exercise in 1972 Structure geographique et variasolipsism, with subjective weighting of all bilite d u n e grande population. Proc. IV. Int. Cong. Human Genet. In preparation. possible routes and travel times. The justification of Euclidean distance is not that Miki, C., S. Yee, N. Yasuda and N. E. Morton 1969 ALLTYPE. In: A Genetics Program migration is “as the crow flies,” but that Library. N. E. Morton, ed. University of Hawaii other measures of distance are arbitrary Press, Honolulu, pp. 24-27. and not comparable among populations. Miller, R. E. 1953 Health report on Kapingamarangi. Atoll Res. Bull., 20: 1-42. Estimation of kinship is not a n alternaN. E. 1969 Human population structive to principal component analysis or Morton, ture. Ann. Rev. Genet., 3: 53-73. construction of dendrograms. On the con1972a Kinship bioassay. In: Genetic trary, such procedures are more closely reDistance. J. F. Crow, ed. In preparation. 1972b Clans and cognate frequencies. lated to genetics if the data are a kinship Amer. J. Hum. Gen., 24: 290-298. matrix rather than a n arbitrary index of Morton, N. E., and D. L. Greene 1972 Pingelap similarity (Morton and Lalouel, ’72). and Mokil atolls: anthropometrics. Amer. J. LITERATURE CITED Azevsdo, E , N. E. Morton, C. Miki and S. Yee 1969 Distance and kinship in northeastern Brazil. Amer. J. Hum. Genet., 21: 1-22. Blumberg, B. S., and Z. Gentile 1961 Haptoglobins and transferrins of two tropical populations. Nature, 189: 897-899. Boyd, W. C. 1939 Blood groups. Tabulae Biologicae, 17: 113-240. Chapman, A. M., and A. Jacquard 1971 Un isolat d’Amerique Centrale: les Indiens Jicaques du Honduras. In: Genetique et Populations, Travaux et Documents Cahier No. 60, Institut national d’etudes demographiques. Presses Universitaires de France, Paris, pp. 163-185. Douglas, R., J. Jacobs, J. Sherliker and J. M. Stavely 1961 Blood groups, serum genetic factors, and haemoglobins in Gilbert Islanders. New Zeal. Med. J., 60: 146-152. Friedlaender, J. S. 1971 The population structure of South-Central Bougainville. Am. J. Phys. Anthrop., 35: 13-26. Graydon, J. J., R. T. Simmons, N. M. Semple and M. G. W. Ingram 1953 Blood groups in the Gilbertese. Med. J. Austral., 2: 245-247. Hainline, L. J., P. Clark and R. J. Walsh 1969 Hum. Genet., 24: 299-303. Morton, N. E.,and J. M. Lalouel 1972 Topology of kinship in Micronesia. In preparation. Morton, N. E., and M. Yammamoto 1973 Blood groups and haptoglobins in the Eastern Carolines. Am. J. Phys. Anthrop., 38: 695-698. Morton, N. E., D. E. Harris, S. Yee and R. Lew 1971a Pingelap and Mokil atolls: migration. Amer. J. Hum. Genet., 23: 339-349. Morton, N. E., I. Roisenberg, R. Lew and S. Yee 1971b Pingelap and Mokils atolls: genealogy. Amer. J. Hum. Genet., 23: 350-360. Morton, N. E., S. Yee, D. E. Harris and R. Lew 1971c Bioassay of kinship. Theor. Pop. Biol., 2: 507-524. Plato, C. C., and M. Cruz 1966 Blood group and haptoglobin frequencies of the Trukese of Micronesia. Act. Genet. Stat. Med., 16: 74-83. Plato, C. C., D. L. Rucknagel and L. T. Kurland 1966 Blood group investigations on the Carolinians and Chamorros of Saipan. Am. J. Phys. Anthrop., 24: 147-154. Pollock, N., J. M. Lalouel and N. E. Morton 1972 Kinship and inbreeding on Namu atoll. Human Biology, 44: 459-474. Roisenberg, I., and N. E. Morton 1970 Population structure of blood groups in Central and MICRONESIAN BIOASSAY OF KINSHIP South American Indians. Am. J. Phys. Anthrop., 32: 373-376. Simmons, R. T., D. C. Gajdusek and P. Brown 1965 Blood group genetic variations in natives of the Caroline Islands and in other parts of Micronesia. Oceania, 36: 132-170. Simmons, R. T., J. J. Graydon and N. M. Semple 1953 A further blood genetical survey in Micronesia; Palauans, Trukese and Kapingas. Med. J. Austr., 2: 589-596. Simmons, R. T., J. J. Graydon, N. M. Semple, J. B. Birdsell, J. D. Milbourne and J. R. Lee 1952 A collaborative genetical survey in Marshall Islanders. Am. J. Phys. Anthrop., 10: 31-54. Steinberg, A. G., and N. E. Morton 1973 Im- 719 munoglobulins in the Eastern Carolines. Am. J. Phys. Anthrop., 38: 699-702. Sussman, L. N.,L. H. Meyer and R. A. Conrad 1959 Blood groupings in Marshallese. Science, 129: 644-645. Swadesh, M. 1952 Lexico-statistic dating of prehistoric ethnic contacts. Proc. Amer. Phil. SOC.,96: 452-463. Yamamoto, M., and L. Fu 1973 Red cell isozymes in the Eastern Carolines. Am. J. Phys. Anthrop., 38: 703-708. Yasuda, N. 1969 Estimation of the inbreeding coefficient and gene frequency from mating type frequency. In: Computer Applications in Genetics. N. E. Morton, ed. University of Hawaii Press, Honolulu, pp. 87-96.

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