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Bioassay of kinship in Micronesia.

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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.
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1972b Clans and cognate frequencies.
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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.
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