MATING PATTERNS AND GENE DYNAMICS OF A POPULATION
ISOLATE OF NATIVE AMERICANS
JEFFREY
C.
LoNG, FRANCINE
C.
ROMERO, MARGRIT URBANEK, AND DAVID GOLDMAN
Laboratory of Neurogenetics, National Insititute on Alcoholism and Alcohol Abuse,
National Institutes of Health, Park V Building, Room 451, MSC 8/l0,
12420 Parklawn Drive, Bethesda, MD 20892-8/l0 (JCL, FCR, MU, DG)
Department of Anthropology, University of New Mexico, Albuquerque, NM 87131 (FCR)
Department of Human Genetics, University of Pennsylvania School of Medicine,
Philadelphia, PA 19104-6145 (MU)
Mating structure can have important effects on population genetic phenomena, including
inbreeding and genetic drift. However, data necessary to test predictions based on mathematical models or identify sensitivity to simplifying assumptions are difficult to collect.
We used two sources of such data, pedigrees and genotypes, collected in a human-population isolate. The population studied was Native American and located in New Mexico.
It was founded in the mid-19th century by ca. 30 individuals, primarily of Navajo origin,
and its size increased steadily thereafter. A complete tribal pedigree spanning ca. 100 years
(up to 1948) was collected by anthropologists starting in the 1920s. Probabilities of allelic
identity by descent (IBD) within and among individuals were calculated for all generations
directly from the pedigree. Wright's F-statistics were calculated from the IBD probabilities,
and Ne was obtained from the statistic F ST' Genetic typings were performed on blood
samples collected from the population between 1991-1993. A second set of F-statistics
were calculated from genetic typings. Genetic kinship between individuals (FST) and average
inbreeding within individuals (FIT) stabilized after the first two generations. However, FST
was always greater than FIT of the next generation, suggesting that the net effect of social
practices was inbreeding avoidance. In contrast to general expectations for growing populations, Ne increased over generations due to immigration. F-statistics estimated from the
genetic typings were remarkably close to pedigree estimates, suggesting a drift-migration
steady state.
Key words:
human-population isolate, F-statistics, pedigrees, marker typings
Human-population isolates form natural
experiments on effects of genetic drift and
other processes that influence levels and
patterns of genetic variation. They provide
an opportunity to evaluate genetic consequences of phenomena such as mate-exchange systems, founder's effects, and population bottlenecks. These phenomena set
the trajectory of evolutionary divergence in
small populations but become less important and less analytically tractable as populations grow large. We studied a semi-isolated group of Native Americans from the
Navajo tribe. Our analysis of its unique genealogical history and current gene freJournal of Mammalogy, 79(3):681--691, 1998
quencies provide a useful reference for understanding other populations, and we point
to new directions for development and interpretation of population-genetic models.
Isolation and finite population size make
consanguineous matings unavoidable, regardless of mating structure. These constraints result in accumulation of allelic
identity by descent (IBD), which occurs
when two copies of an allele in the population are both copies of an allele that existed as a single copy in an earlier generation (Crow and Kimura, 1970). When two
alleles are IBD within an individual, the
person is inbred. When two IBD alleles ex681
682
JOURNAL OF MAMMALOGY
ist in different people, they share genetic
kinship. Distribution of IBD alleles within
and among individuals is a function of mating structure, while the rate at which IBD
accumulates depends on both mating structure and population size (Cockerham, 1969,
1973). The extent of IBD in a population
and its mating structure can be inferred
from diverse data. We used pedigrees and
genetic markers to estimate probabilities
that randomly drawn genes within and
among individuals from the population
were IBD. Those probabilities were then
analyzed with a population-genetic model.
The model's parameters were F-statistics,
which are functions of IBD probabilities,
and effective population size (Wright, 1951,
1965, 1969). Our basic interest was in how
the mating structure affected evolution and
distribution of genotypes in the population.
Although inbreeding for human isolates has
been determined from pedigrees (Castilla
and Adams, 1990; O'Brien et al., 1988),
this is the first study to use such human data
to compute a full array of F-statistics and
effective population size. It is also the first,
for a human population, to compare pedigree estimated F-statistics with F-statistics
estimated from allele frequencies and incorporate effects of migration, which
played an important role in maintenance of
genetic diversity in this isolate.
POPULATION BACKGROUND
The focal population was founded between 1820-1840 when a few families
moved into westcentral New Mexico where
the town of Ramah is now located. They
are geographically isolated by 40, 80, and
120 km from the three other Navajo communities in the region. This population was
severely disrupted between 1863-1868
while the United States Army held all Navajo people captive at Fort Sumner, New
Mexico (Bosque Redondo). However, the
population re-established at its former location immediately following release in ca.
1870. The founders after incarceration were
primarily Eastern Navajos, but there also
Vol. 79, No.3
were three Chiricahua Apaches, three Mescalero Apaches, and one Walapai Indian.
Population growth by intrinsic increase and
immigration of families and marriage partners followed. By ca. 1890, the population
included 23 men, 30 women and 46 children. After 1890, a Laguna Indian, a Yaqui,
a Zuni, and additional Navajos married into
the population. Immigrants were accepted
as marriage partners, but no new biological
families settled after this time. By 1948,
there were 614 members dispersed in small
groups of nuclear and extended families
over 1,334 km2 • By 1965, the population
numbered ca. 1,100 individuals, and it was
ca. 2,500 by 1990. Traditional Navajo culture predominated until the mid-1960s. It
exists today but there is now more EuroAmerican influence. The culture, demography, and genealogy of the tribe have been
studied extensively (Kluckhohn, 1966;
Morgan, 1973; Spuhler, 1989; Spuhler and
Kluckhohn, 1953).
Social organization and marriage practices of Navajo affect the genetic structure.
For example, mate choice is influenced
heavily by the clan system. Clan membership is matrilineal, and post-marriage residence is matrilocal. Kluckhohn (1966) noted four general clan related prohibitions
concerning appropriate marriage partners:
marriage to members of one's own clan,
marriage to members of their father's clan,
marriage to members of clans linked with
his or her own clan, or marriage to members of clans linked with his or her father's
clan. Nevertheless, violations of these prohibitions occur and clan linkage is ambiguous, even among Navajo (Spuhler and
Kluckhohn, 1953). Other cultural practices
affecting mate choices among Navajo have
potential genetic consequences. Until recent
decades, polygyny (levirate and sororate)
was practiced, and nuclear and extended
families exhibited preferential patterns of
reciprocal marriages. Cross-generational
marriages between older women and younger men also were relatively common. Clan
exogamy, as opposed to random mating,
August 1998
SPECIAL FEATURE-SOCIAL GENE DYNAMICS
will reduce inbreeding, but polygyny and
preferential mate exchanges among nuclear
families and lineages will increase inbreeding. We analyzed the balance between these
opposing forces and their impact on genetic
differentiation and effective population
size.
MATERIALS AND METHODS
Pedigree and demography.-Detailed demographic and genealogical records, unparalleled
in completeness and spanning the period between 1870-1948, were collected by C. Kluckhohn and his associates. A copy of the genealogical chart of Spuhler and Kluckhohn (1953)
was provided to the first author by the late Professor J. N. Spuhler. This chart recorded the
complete genealogy of the population, beginning
with 31 individuals (founders) in 1870 and ending with 614 individuals on 1 September 1948.
In total, there were 1,105 individuals representing 317 fertile unions across seven generations.
Familial relationships among some founding individuals were known and incorporated into subsequent calculations. The genealogical chart
cannot be presented here because of its size and
complexity, but Spuhler and Kluckhohn (1953)
described it in detail and diagrammed some of
the more interesting segments.
Each subject was assigned to a pedigree generation as follows. Pre-founders were assigned
to generation 0 and founders were assigned to
generation 1. Each per~on born to a pedigree
member was assigned to the first generation after
the highest generation occupied by his or her
parents. Migrants were identified as individuals
who contributed offspring to later generations
but could not be linked to the previous generations. All migrants were assumed unrelated to
each other, or to pedigree members, and to be
non-inbred. Migrants were assigned to the generation of their partners.
Genotyping.-Blood samples and summary
demographic infonnation were collected from
adult Native Americans visiting the Albuquerque Indian Hospital, Albuquerque, New Mexico
and other Indian Health Service facilities in New
Mexico between 1991-1993. Thirty-four of
these samples were donated by Navajos from the
focus group. Genomic DNA was extracted directly from blood samples, or from Ebstein-Barr
Virus transfonned lymphoblasts. Genotypings at
683
13 dinucleotide repeat loci located on chromosomes 9, 10, 11 and 20 were perfonned with an
ABD 373a automated DNA sequencer (Applied
Biosystems Division of Perkin Elmer, Foster
City, CA) following PCR amplification using
fluorescent dye labelled primers. Because of
PCR failures and the use of multiplex procedures, the actual number of persons typed per
locus ranged from 15 to 26. Allele frequencies
were determined by direct counting. For comparative purposes, allele frequencies from six
other populations of Native Americans in New
Mexico were used in computing F ST• These included Navajos on the main reservation, a second isolate of Navajos, two populations of
Apaches, and two populations of Pueblos. Allele
frequencies for Pima and Cheyenne tribes and
Finns and Swedes were included for FST calculations. These four latter populations were represented by control samples obtained for studies
on alcoholism and other psychiatric disorders
·(Urbanek et al., 1996).
F-statistics.-The basic quantities considered
were Wright's F-statistics, which were computed
from inbreeding and kinship coefficients. FIT
equaled correlation of alleles within individuals
relative to the founding population. FST equaled
correlation of random alleles within the existing
population, relative to the founding population.
F Is equaled correlation of alleles within individuals, relative to the existing population.
FIT was the average of inbreeding coefficients,
F i • Thus,
(1)
where N was the number of individuals in the
population. FST was the average of genetic kinship coefficients, 9ij'
(2)
where P = lhN(N - 1) was the number of pairs
of individuals in the population. Proof that average probabilities of IBD given above are indeed correlations is given in Table 1. Following
Wright (1951), F IS was obtained by manipulating
the equation (1 - Ffr) = (1 - F sT)(1 - F ls )
where the prime denotes the offspring generation. Thus,
(3)
Vol. 79, No.3
JOURNAL OF MAMMALOGY
684
TABLE
I.-Proof that average probabilities of identity by descent are correlations.
Genic value"
GI
Al
Al
A2
A2
G2
Probability of pair
Al
A2
Al
A2
p2(1
pq(I
pq(1
q2(1
-
<1»
+
G1(X)
p<1>
1
0
1
0
1
<1»
<1»
<1»
G2(Y)
+
q<1>
0
0
X2
y2
XY
0
0
1
0
1
0
1
0
0
0
, We define the genic random variables X and Y for two genes, Gland G2, drawn from the population. If G 1 is of type A I,
then X = 1, otherwise X = 0, and if G2 is of type AI, then Y = I, otherwise Y = O. Let p be the relative frequency of AI
among the founders and unrelated immigrants, and let q be the relative frequency of A2 genes. Let <\> be the probability that G 1
and G2 are identical by descent. The covariance between X and Y, (J'Xy, is E[XY] - E[X]E[Y] = p(l - p)<\>, because E[XY] =
p2(l - <\» + p<\>, and E[X] = E[Y] = p2(l - <\» + p<\> + pq(l - <\» = p. The correlation between X and Y, r" = <\>, because (J"x
= (J'2y = E[X2] - E[X]2 = p(l - pl. When Gl and G2 are drawn from two individuals at random, <\> = F ST• When Gl and G2
are drawn from same individual, <\> = FIT'
1
'2(1
FST and FIT are necessarily positive when measured from a pedigree, but F ls is negative when
FST > F'IT' This condition arises when there is
systematic avoidance of consanguineous mating
(Wright, 1965).
Population-genetic model.-A population-genetic model was developed to evaluate effects of
the mating system. The model assumed a diploid
population with discrete generations and without
self-fertilization. Mating was random, and all individuals had the same expected number of
progeny. The population size was finite but
could change from one generation to the next,
and there was immigration into the population.
The fundamental parameters were Wright's Fstatistics, which were functions of population
size and allelic identity by descent. From basic
principles of probability (c.f., Crow and Kimura,
1970:102; Wright, 1969:291), the transition in
FST across one generation was:
+ FIT)
Ne = ,
- FST
2
(FsTI(1 - m) - F ST )
(5)
•
The effective number defined by equation 5 was
a variance effective size because FST was the
quantity of change (Chepko-Sade et al., 1987;
Crow and Kimura, 1970).
A general formula for FST> at any generation,
(G), since the isolate's formation, was obtained
by applying equation 4 recursively and simplifying,
G-]
2:
Fk~ =
<I>(g, G)
+ C(O, G)
(6a)
g~O
where
<I>(g, G) = (1
+ FW)
(1 - m(g)2
2N(g)
e
x
[TI (1 -~)(1l~g+]
2Ne
m(i)2]
(6b)
and
where the prime denotes FST in the next generation, N was the population size, and m was the
proportion of immigrants. The F-statistics and
their relationships with IBD probabilities were
defined in equations 1-3.
Under the model's assumptions, F'rr = FsT'
That was not be the case with non-random mate
exchange systems and violations of other model
assumptions. For equation 4 to hold, N was replaced by an effective number, N e. Upon replacement with Ne and solving equation 4, the
formula for Ne is
C(O G) = F(O)
,
ST
TI
i~O
G-] (
1 - - 1 ) (1 - m(i)2
N~i)
(6c)
Components of this formula had important interpretations; <I>(g, G) was the IBD contribution
of the earlier generation (g) to the focal generation (G), and C(O, G) was the genetic kinship
of the founders remaining in the focal generation. As such, C(O, G) + <1>(0, G) was a measure
of founder's effect and the <I>(g, G) coefficients
(g > 0) revealed bottlenecking.
Statistical analysis of pedigree.-Using stan-
August 1998
SPECIAL FEATURE-SOCIAL GENE DYNAMICS
TABLE
Generation
2.-Demographic and pedigree derived statistics for the Navajo isolate. a
NB
NM
29
99
264
402
208
14
16
23
14
5
0
2
3
4
5
6
685
*
*
N
31
45
122
278
407
208
14
m
FIT
0.36
0.19
0.05
0.01
0.0000
0.0000
0.0001
0.0057
0.0145
0.0153
*
*
FST
F ls
0.0046
0.0152
0.0293
0.0266
0.0268
0.0292
-0.0154
-0.0301
-0.0214
-0.0127
-0.0143
Ne
NjN
47
9
42
153
159
1.52
0.20
0.42
0.58
0.40
'NB = number born, NM = number of migrants, N = NB + NM = total number, m = NMIN = migration fraction, all other
symbols are introduced in the text.
* = missing data, generation not completed.
dard pedigree methods, inbreeding coefficients
were computed for all individuals in the population. Kinship coefficients were computed for
all individuals in a generation if there were
<1,000 pairs of individuals; otherwise, 1,000
pairs were selected at random and the average
of those coefficients was taken to represent the
generation. The error introduced by forming
those samples was likely to be negligible. For
each pedigree generation, F-statistics were computed according to equations 1-3 and effective
popUlation size was calculated according to
equation 5. lfJ(g,G) estimates were obtained by
using estimated demographic parameters (N~g)
and m(g) in place of the parameters in equation
6b.
Statistical analysis of genotypes.-The three
principal F-statistics were calculated using typings at the 13 dinucleotide repeat loci. F[s for
the focus population was calculated using the
heterozygosity method of Currie-Cohen (1982),
and its standard error was calculated by the jackknife method (Weir, 1990). FST was calculated
for the focus population, and other groups, using
the variable-effects model (Urbanek et aI.,
1996). For this purpose, populations were arranged hierarchically based on historical, linguistic, and geographical considerations (Greenberg et aI., 1986; Spuhler, 1972). The focal isolate of Navajos was clustered with another isolate of Navajos, Navajos on the main
reservation, and the two populations of Apaches.
That was appropriate because the isolate's founders were primarily Navajo and Apache, and
those groups were closely related linguistically.
A second cluster of southwestern Native Americans consisted of Pima and two Pueblo tribes.
Those populations were ancient inhabitants of
the southwest and they spoke Amerind languages. Cheyenne, an Amerind-speaking tribe of
Plains Native Americans, joined all other American Indians. Finally, the two European populations formed a cluster that was linked to the Native Americans at the highest level of nesting.
An F-statistic associated with each branch was
computed from FHL = (J~ - JD/(l - J~) where
J~ was the homozygosity (gene identity-Nei,
1987) associated with the higher node and J~
was homozgosity associated with the lower node
(Urbanek et aI., 1996). The homozygosity associated with each node of the hierarchy was
fitted using maximum likelihood (Cavalli-Sforza
and Piazza, 1975; Urbanek et aI., 1996).
RESULTS
Pedigree analysis.- The basic demographic analysis is given in Table 2. It
should be remembered that the population
grew tremendously between 1870-1948
and the smaller numbers of individuals in
generations 5 and 6 reflected the fact that
those generations were incomplete at the
end of the study period. Population sizes
across generations were observed to be associated inversely with migration rates.
That was expected because marriages between close relatives were avoided and suitable partners were likely to be absent when
total number of individuals was small. Both
FIT and FST rose over the generations sampled (Fig. 1A). FIT is zero until the third
generation, which was due to restrictions
imposed by sexual reproduction (i.e., at
least two generations are required before
Vol. 79, No.3
JOURNAL OF MAMMALOGY
686
.... FiT
A
- FST
0.03
- - F[S
0.02
'"
O.oJ
.~
O+-----r----.----~~--_.----._--_.
.~
.,
-0.01
....
~ -0.02
-0.03
-0.04
2
3
"".... ........... _-
-- --
6
5
4
-,-----
Generation
B
.,
.~
200
s:
0
150
"[
100
r/J
.~
0
.,
j:l.;
.~
~
50
0
i:LI
0
2
4
3
5
Generation
c
t
~
0.Q25
i:LI
...... '"
s:
o 0 0.020
....
~ .~
.9 t O.oJ5
:; 5
:9 "
~ t
8j
:.2'
.S
~
-- --IlJ(O,l)
- . -1lJ(1,l)
_. ·1lJ(2,l)
-1lJ(3,l)
• 1lJ(4,l)
0.010
0.005
S 0.000
....
....
....
t _ .. _ .
- - - - - - - .. -
- .. - ....
_ - .. _
...
..
........................ .
+----,---,-----,---.....,.----,
0
2
3
4
5
Recipient Generation (1)
FIG. I.-Temporal trends in genetic demography of Navajo Isolate computed from extended pedigrees. A) Change in F-statistics over generations, B) change in variance effective population size,
N e , over generations, and C) kinship contributions <I>(t, T) of earlier to later generations.
IBD alleles can form a zygote) and consanguinity avoidance. The tendency toward
consanguinity avoidance was further reflected by negative values of F[s in all generations (Fig. lA). Effective size of the
Navajo isolate rose precipitously over the
early generations (Fig. IB); however, the
change was negligible in the transition from
generation 3 to generation 4. Rise in effective size was directly due to migrants into
August 1998
TABLE
SPECIAL FEATURE-SOCIAL GENE DYNAMICS
687
3.-Estimates of genetic kinship contributions from earlier to later generations, l/> (g,G).
Generation
receiving
(G)a
C(O,G)
0
2
3
4
5
0.0046
0.0045
0.0016
0.0010
0.0009
0.0106
0.0039
0.0025
0.0022
0.0022
Generation contributing (g)
2
0.0228
0.0146
0.0131
0.0127
0.0078
0.0070
0.0068
3
0.0029
0.0028
4
FST
0.0031
0.0152
0.0312
0.0265
0.0262
0.0285
, Each entry is obtained from equation 6b using the data from Table 2.
the Ramah population. Ne exceeded N for
the founding generation at Ramah, despite
the fact that effective sizes are much smaller than actual sizes in most other populations. While the cause for this is uncertain,
founders of a new deme were not a random
sample of people born into the population.
For example, they have escaped childhood
mortality and many have already found
mates.
Analysis of the kinship contributions of
earlier to later generations revealed several
interesting phenomena (Table 3, Fig. 1C).
The founder effects of generation 0 were
greatly diminshed by the high migration
rates in the next two generations. Generation I had the largest overall contribution
4.-Dinuckotide repeat loci analyzed
in the Navajo isolate.
TABLE
and
PIS
Locus
D9S273
D1OS192
D1OS547
DllS935
DllS937
D20S111
D20S114
D20S172
D20S177
D20S186
D20S193
D20S97
D20S171
Average
Number of
different
Sample alleles
Gene
size observed diversity
24
24
15
26
24
20
18
20
21
20
20
20
26
8
6
4
4
10
2
3
4
3
8
4
5
6
F]s
0.615
0.788
0.596
0.589
0.856
0.455
0.573
0.471
0.291
0.696
0.649
0.348
0.396
0.187
0.048
0.216
-0.044
0.027
-0.099
-0.454
0.151
-0.144
-0.221
-0.002
0.282
-0.167
0.563
-0.016
to inbreeding and genetic kinship, due to
the small effective population size at this
generation and low migration rates in later
generations. Finally, a population bottleneck in the transitions from generation 3 to
generation 5 was clear from the flatness of
the <I>(g,G) functions.
Genotypic F-statistics.-The analysis of
F-statistics from recently collected genotypes closely mirrors the pedigree predictions from ca. 40 years earlier. The point
estimate of F[s averaged over the 13 loci
was negative (-0.016) but it was not significantly different from zero (Table 4). FST
for the Navajo isolate relative to other populations of Apaches and Navajos was
0.027, a little less than the final pedigree
value (Table 5).
A graph of the nested popUlation structure (Fig. 2) showed that after the reduction
in heterozygosity leading from Europeans
to Native Americans is accounted for, there
was only a minor tendency for tribes of Native Americans to cluster into genetic supgroups. When the terminal branch lengths
were converted to estimates of FST (Table
5), other populations showed a greater reduction in heterozygosity than was measured for the focal isolate. This suggested
that all tribes are semi-isolates in their own
right.
DISCUSSION
Although the focal population became
more inbred over time, on the balance, the
mating system minimized inbreeding and
may have provided the impetus for much of
TABLE 5.-FsT relative to nearest internal
node of hierarchy (Fig. 2) for individual Native
American and European populations. Navajo
isolate 1 is the focal population of this study.
Population
Navajo isolate 1
Navajo isolate 2
Navajo
Apache 1
Apache 2
Pueblo 1
Pueblo 2
Pima
Cheyenne
Finn
Swede
Vol. 79, No.3
JOURNAL OF MAMMALOGY
688
Gene
diversity
Sample size (average
(average for for 13
13 loci)
loci)
21
26
37
23
26
25
25
123
46
48
38
0.563
0.524
0.603
0.528
0.625
0.638
0.569
0.634
0.573
0.715
0.695
Hierarchical Population Structure
Isolate I
~-- Isolate 2
Navajo
FST
Apache I
0.027
0.090
0.027
0.059
0.024
0.027
0.104
0.059
0.027
0.025
0.038
Apache 2
Pueblo I
Pueblo 2
Pima
Cheyenne
Finn
Swede
0.25
the immigration seen in the early generations when population size was small. The
extent of inbreeding reduction would have
been difficult to deduce by simultaneously
modeling complicated factors such as polygyny, clan avoidance, and reciprocal marriage exchange between families. Also,
mate exchange rules in society are often
broken. Therefore, it is difficult to say how
well an idealized system will predict an actual genetic architecture. Our sample of genotypes provides an F[s value that is close
to the pedigree's. However, a jackknife
standard error for the genotypic estimate is
large, so that the result would have been
equivocal in the absence of the pedigree
analysis. The consequence of this mate exchange pattern is negative F[s values. This
implies an excess of heterozygotes in a contemporaneous sample from the population.
This is observed in other North and South
American tribes (Neel and Ward, 1972;
Workman et aI., 1973). Consanguinity
avoidance has been suggested for these
tribes, but differences in gene frequencies
between sexes and other explanations for
the excess of heterozygotes have been favored. A recent study on the Havasupai, a
neighboring tribe of southwestern Native
I
0.30
I
0.35
I
0.40
0.45
I
0.50
I
I
Homozygosity
FrG. 2.-Hierarchy used for calculating FST of
individual popUlations relative to their base
(closest internal node). Isolate 1 is the focal population of this study. Isolate 2 is another Navajo
isolate. Navajo is represented by a sample from
the main reservation. According to the wishes of
the study participants and tribal authorities, the
exact identities of popUlations of Apaches and
Pueblos are not given. Branch lengths measure
homozygosity (loss of heterozygosity). FST is
calculated from F HL = (J~ - JD/(l - JD where
J~ is the homozygosity (gene identity) associated
with the observed popUlation and J~ is homozgosity (gene identity) associated with its nearest
internal node.
Americans, attributed an excess of heterozygotes at the HLA-A locus to balancing
selection (Markow et al., 1993). In light of
the present findings based on pedigrees and
dinucleotide repeat loci whose dynamics
are regulated by random drift, the balancing-selection hypothesis should be regarded
with caution until a mating structure explanation can be ruled out.
FST measures the divergence of the population from allele frequencies of the foun-
August 1998
SPECIAL FEATURE-SOCIAL GENE DYNAMICS
ders and pre-founders. The pedigree shows
large increases in the first two generations,
followed by an apparent plateau. Estimates
of <I>(g, G) show that after the second generation, the kinship contributed by a generation to its successors ~ently decays, but
the amounts contributed by these generations is relatively small. This stability is unsurprising because equation 4 provides an
eqUilibrium at FST
(1 + Frs)/(4N em + 1)
assuming that the product Nem remains
constant across generations. With random
mating in the population (i.e., Frs = 0), this
reduces to the eqUilibrium for Wright's
(1951, 1965, 1969) island model of population structure. However, a stable FST can
arise for reasons other than a constant Ne
and m. For example, Nem can remain stable
if changes in population size are related inversely to changes in migration rates, as in
the early generations of the study population.
A base population from which genes in
the isolate were drawn is implicit in FST
computed from allele frequencies. We are
fortunate to have sampled an array of populations of Navajos (including another isolate and the main reservation) from which
to construct this base. The analysis of allele
frequencies indicates that FST similar to that
of the pedigree was maintained over the
next 40 years. Interestingly, FST is not extreme in the focal Navajo Isolate as compared with other tribes of Native Americans. In fact, FST in the other Navajo isolate
sampled is nearly three times as great, and
it is considerably higher in large populations of Native Americans such as the
Pima. This assuredly relates to the population disruption and unique histories of exposure to disease and population rebound
that nearly all tribes experienced in the centuries following European contact (Ramenov sky, 1987).
The effective population size, N e, is an
important parameter that bridges complexities of natural populations with predictions
of simplified models. Because several subtly different effective sizes have been de-
=
689
fined (Chesser et al., 1993; Kimura and
Crow, 1963; Sugg and Chesser, 1994), it is
important to point out that we have analyzed the variance effective size. Theory
demonstrates that variance and other effective sizes are usually less, and often much
less, than the actual size of a closed population (Kimura and Crow, 1963). In principle, the long-term effective size of a
closed population that changes in size is approximated by the harmonic mean of population sizes over time. Accordingly, Ne is
dominated by the smallest population size
experienced, and population growth alone
cannot substantially increase it. Nevertheless, the effective size of this Navajo isolate
grew precipitously during the first four generations.
Complexities imposed on Ne by population growth with migration are seen by examining generation 3. At this time, the effective size was 153 individuals which is
only 58% of the total population number.
However, the harmonic average of all effective sizes prior to this generation is only
ca. 20 individuals. Growth of Ne must be
attributed to the addition of independent
genes by migration, but it is apparent that
population growth compounds the effect of
migration. To illustrate the compounding
effect, consider that 53 migrants had joined
this Navajo isolate by generation 3. In addition to the 31 founders, this yields 84 independent genomes, which is only about
one-half of the measured effective size.
These results show that, unless a population
is isolated completely, the harmonic mean
formula can be grossly inadequate for measuring effective size. Thus, Ne should not
be estimated from population size changes
alone (e.g., Chepko-Sade et aI., 1987), unless it can be demonstrated that the population is a complete isolate. This result also
shows the power that can be obtained when
pedigrees are available for analysis. Interestingly, recent theory and application to
prairie dogs (Cynomys) shows that more
complicated hierarchical social structures
also can increase effective population size
JOURNAL OF MAMMALOGY
690
and retard loss of genetic variation (Sugg et
aI., 1996).
Genetic drift in the isolate was only
slightly affected by the mating system. Differentiation of the isolate from the founders,
or a base population, is quantified by FST'
If we take F IS as the degree of non-random
mating, the mating system influences the
rate at which IBD accumulates (equation 4)
through F'IT = 1 - (1 - F Is )(1 - F ST)' This
effect is minimal with the slightly negative
F IS observed. Similarly, equilibrium for FST
== (1 + FIS)/(4Nem + 1) is not appreciably
affected by the observed F IS' However, this
is not to say that the relationship between
the mating system and F IS is unimportant.
Consanguinity avoidance encourages immigration and prevents inbred individuals,
and perhaps genetic deaths, in the early
generations of a newly formed isolate when
population size is smallest and probability
of extinction is highest.
ACKNOWLEDGMENTS
We are indebted to Professor J. N. Spuhler
(deceased) who enabled this study by generously
providing his genealogical information. He also
provided help and encouragement in the early
phases of the project. The authors are responsible for all analyses and interpretations. Data collection for this project was funded in part by
National Science Foundation grant BNS 91
08422.
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