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An autocorrelation analysis of genetic variation due to lineal fission in social groups of rhesus macaques.

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AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 67:113-121 (1985)
An Autocorrelation Analysis of Genetic Variation Due to Lineal
Fission in Social Groups of Rhesus Macaques
JAMES M. CHEVERUD AND MALCOLM M. DOW
Departments ofAnthropology (J.M.C., M.M.D.), Cell Biology and Anatomy,
and Ecology and Evolutionary Biology (JM. C,), and Program in
Mathematical Methods in the Social Sciences (M.M.D.), Northwestern
University, Euanston, Illinois 60201
KEY WORDS
Rhesus, Fission, Cay0 Santiago, Autocorrelation
ABSTRACT
Empirical analyses and models of the lineal effects of fission
indicate that considerable genetic differentiation may occur at the time of
group formation, thus confusing the usual positive relationship between historical affiliation and genetic differentiation. We analyze the effects of fission
pattern on variation in highly heritable morphological traits among eight
social groups on Cay0 Santiago. The analysis is performed using general
network autocorrelation methods that quantitatively and directly measure the
amount of variation in social group mean morphology that can be explained
by fission. All of the fission autocorrelation coefficients are strongly negative,
indicating that groups most recently formed by fission are most dissimilar.
Also, most of the variation between groups can be explained by the fission
pattern, indicating that lineal fission is the most important process generating
between-group variation on Cay0 Santiago.
In anthropological genetics, the standing
diversity of sets of locally distributed populations have been interpreted primarily in
terms of the time since divergence from a
common ancestral population and the rate of
migration between them. The more genetically or morphologically similar two populations are, the more recent was their
divergence and/or the higher their rate of
exchange through migration. Conversely, the
more distinct two populations are, the earlier
their time of divergence andor lower their
intermigration. These expectations are
firmly based on population genetic theories
of random drift and migration (Crow and Kimura, 1969). This standard model has been
commonly used in analyses of both modern
and prehistoric groups to infer the historical,
phyletic relationships among populations
given measures of genetic and morphological
variation. O’Rourke and Bach Enciso (1982)
have applied this common interpretative
model to an analysis of genetic variation
among social groups on Cay0 Santiago.
However, this common model will not always be appropriate for interpreting the genetic distances among the subdivisions of a
0 1985 ALAN R. LISS, INC.
regional population. Lineal fission, a process
of population formation in which relatives
nonrandomly assort into the new daughter
groups (Neel and Ward, 1970; Chagnon, 1975;
Chepko-Sade and Sade, 1979), can cause
rather large differences between groups, instantaneously, at the time of their formation
(Neel and Ward, 1970; Duggleby, 1977; Cheverud et al., 1978; Cheverud, 1981; Fix, 1978;
Olivier et al., 1981; Smouse et al., 1981;
Buettner-Janusch et al., 1983; Ober et al.,
1984). This may alter the usual correlation
between time since divergence and genetic
distance among related populations. Buettner-Janusch et al. (1983) interpret their results as indicating that “. . . where lineal
fission of groups [is] common, biological distances among social groups may not reliably
reflect recent historical, phyletic relations”
(p. 352). If the original difference generated
by lineal fission is large enough, it may produce levels of divergence equal to the average divergence represented in a set of
subpopulations connected through migration
Received May 16, 1984; accepted January 21,1985.
J.M. CHEVERUD AND M.M. DOW
114
(Cheverud et al., 1978; Cheverud, 1981;
Smouse et al., 1981; Buettner-Janusch et al.,
1983; Ober et al., 1984). Thus lineal fission
may seriously disrupt the theoretical relationship between genetic divergence and time
since formation from a common ancestral
group. This is especially likely for a small set
of recently differentiated subpopulations.
While work on lineal fissions has increased
greatly over the past 10 years (see above
citations), its effects are not often considered
when anthropologists reconstruct historical
and social relationships among populations
from genetic andor morphological similarity.
We will test the hypothesis that groups
most recently formed from a common ancestral population are more similar to one another than distantly related or unrelated
groups using highly heritable morphological
traits and social groups of rhesus macaques
on Cay0 Santiago. O'Rourke and Bach Encis0 (1982)have recently analyzed allelic variation among social groups on Cay0 Santiago
and interpreted the degree of genetic divergence among groups in terms of the geographical distance separating them on the
40-acre island and the recency of group fission, although there is no evidence for the
effects of geographical separation of migration between groups in the Cay0 Santiago
colony. Previous genetic research on this island population has concentrated on the genetical analysis of individual fission events
(Duggleby, 1977; Cheverud et al., 1978;
Cheverud, 1981; Buettner-Janusch et al.,
1983; Ober et al., 1984). This research has
indicated that lineal fission is a n important
source of genetic variation between social
groups, generally producing moderate to high
levels of differentiation at the time of group
formation, but the overall importance of lineal fission for understanding diversity between social groups has not been measured.
In this paper, we will evaluate the importance of lineal fission for the overall level of
social group genetic differentiation using
Years
I
I
I
r-
A
c
Fig. 1. Fission tree depicting the historical phyletic relationship of social groups on Cay0
Santiago (Sade et al., 1977).
FISSION AUTOCORRELATION
newly developed general network autocorrelation techniques.
MATERIALS AND METHODS
The free-ranging colony of rhesus macaques (Macaca mulatta) on Cay0 Santiago
was founded with 400 animals by C.R. Carpenter in 1938 and 1939. After a period of
relative neglect, Altmann (1962) arrived in
1956, began provisioning on the island, and
identified individual animals. The provisioning led to a large increase in the population
from about 200 in 1956 to 800 animals over
a period of 13 years. Also, during this period
of growth the two original unrelated social
groups, A and B, had divided to form nine
social groups (A, C, E, F, H , I, J, K, and L)
(see Fig. 1).By 1969, the 40-acre island was
overcrowded, so whole social groups A, C, E,
H, and K were removed. Genealogical and
demographic data have been collected and
maintained since 1956. For a more detailed
discussion of the history and management of
the Cay0 Santiago colony, see Sade et al.
(1977).
Animals drawn from the Cay0 Santiago
skeletal collection will be used in this analysis. The nature and history of this collection
has been discussed in Cheverud and Buikstra (1981a) and Cheverud (1981). A total of
287 animals from eight social units are included in the analysis (see Table 1).Animals
were assigned to social groups on the basis of
their lineage's group membership a s of 1971.
Groups H and I did not present sufficient
samples for separate analysis and have
therefore been combined into one group,
which will be referred t o as Group I. These
sister groups were formed by fission about
one generation prior to the ending date of
this analysis.
TABLE 1. Sample sizes for individual social groups of
rhesus macaques on Cay0 Santiago (Animals were
assigned to their natal group)
Group
N
A
23
E
F
I'
22
45
32
19
106
26
287
c
J
K
L
Total
'Group I contains animals from sister groups H and I.
14
115
The traits to be analyzed include five
highly heritable morphological characters
taken from the cranium (Cheverud, 1981).
All five traits were standardized with a mean
of zero and standard deviation of one. Traits
GM1-3 are linear combinations derived from
cranial metric traits (Cheverud, 1982) and
account for 61% of the additive genetic variance in metric cranial morphology (Cheverud, 1981).Their heritabilities ?re 0.77,0.64,
and 0.65 respectively. GN1 and GN2 are linear combinations of 13 cranial nonmetric
traits (Cheverud and Buikstra, 1981a,b;
Cheverud 19811, which together account for
50% of the additive genetic variance in nonmetric cranial morphology. Their heritability estimates are 1.42 and 1.20, respectively.
These heritability estimates are not significantly greater than one and result from
mother-offspring correlations greater than
0.5. It is important to note that there are no
correlations among traits GM1-3 or between
GN1 and GN2.
All five linear combinations were derived
from a procedure specifically designed to produce highly heritable traits containing a significant amount of the total genetic variation
in morphology (Cheverud, 1981).When there
is no phenotypic covariance between traits,
spectral decomposition of genetic and environmental dispersion matrices will generate
the same set of eigenvectors, but these eigenvectors will appear in reverse order when
arranged according to the magnitudes of
their associated eigenvalues. Thus individual components, which explain a large portion of the total additive genetic variance,
will explain only a minor portion of the environmental variance and will thus be highly
heritable (Cheverud, 1981). Lowly heritable
traits showed no significant between-group
variation and are therefore not subjected to
analysis here (Cheverud, 1981).
The hypothesis will be tested using network autocorrelation methods originally derived for the analysis of spatial patterns (Ord,
1975; Cliff and Ord, 1981) and subsequently
generalized to allow the analysis of autocorrelation in any form of network (Dow et al.,
1982; Dow, 1984; White et al., 1981). Sokal
and his colleagues (Sokal and Menozzi, 1982;
Sokal and Friedlaender, 1982) have applied
spatial autocorrelation methods to allelic and
anthropometric data. We will analyze autocorrelation between social groups owing to
their origin from a common ancestral group.
The network autocorrelation approach is su-
116
J.M. CHEVERUD AND M.M. DOW
perior in several ways to previous methods dent variable, y, appears on both sides of the
for testing hypotheses concerning the effects regression equation (Eq. 1).We utilized a pure
of population structure, such as historical re- network effects model (Ord, 1975; Anselin,
lationship or migration, on genetic structure. 1982)that takes the following form:
It allows a specific, quantitative test for the
effects of network structure on the distribu(1)
y = pWy + e
tion of population attributes, such as mean
morphologies. Other means of comparing where y is a n nxl vector (n = number of
population and genetic structures are less individuals) containing normalized and
direct in that they typically involve the deri- standardized values for the trait of interest,
vation of genetic distance matrices or pheno- p is the scalar autocorrelation coefficient
grams displaying genetic similarity and the varying from -1.0 to +1.0, W is the nxn
comparison of these imperfect representa- connectivity matrix describing the network,
tions to distance matrices based on known and e is the nxl residual vector. The analysis
historical and migratory relationships. The is performed on one trait at a time. The elenetwork autocorrelation approach directly ments of the connectivity matrix (W) repremaps the population attributes onto the pop- sent the strength of relationship among the
ulation structure and uses a single number groups. For this analysis, the connectivity
to measure the extent to which the attributes matrix was derived from the fission tree (Fig.
of subpopulations can be explained in terms 1)describing the history of group formation
of their interrelationships. The network au- on Cay0 Santiago. First, a fission distance
tocorrelation coefficient also has a n associ- matrix (Table 2) was derived representing
the number of nodes connecting two groups
ated test for statistical significance.
Essentially, the autocorrelation approach to a common ancestor. If the groups conconsists of a maximum likelihood regression cerned are unrelated, a zero is entered. Also,
model in which the score of any individual all diagonal elements are given a value of
case is predicted by a linear combination of zero. The distance matrix was transformed
the scores of related cases. Maximum likeli- into a connectivity matrix (Table 2) by taking
hood methods are used because the depen- the reciprocal of each nonzero entry. Values
TABLE 2. Fission distance, raw connectiuity, and normulized conn.ectiusty matrices for social groups on
Cay0 Santiago
Groups
A
Fission distance matrix
A
0
K
1
L
1
J
2
F
I
E
C
K
L
1
1
1
2
0
2
0
J
F
I
E
C
0.33
0
0
0
0
0.33
0
0
0
0
0
0
0.4
0.4
0
0.33
0
0
0
0
0
0
0
1
1
2
0
1
0
1
0
C
.___
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0.5
1
0
0
0
1
1
0.5
0.2
0
0.2
0.2
0
0.5
0.5
0
0
0
0
E
2
0
0
0
0
0
I
0
0
0
0
2
2
2
0
0
0
C
0
0
Normalized connectivity matrix
A
0
0.4
K
0.4
0
L
0.4
0.4
E
F
0
0
0
0
1
1
0
2
2
0
0
0
0
0
Raw connectivity matrix
A
0
K
1
I
J
0
0
0
0
0
0
0
0
0
0
0.4
0.4
0.33
0
0
0
0
0
0
0
0.5
0
0.5
0.5
0.5
0
0
0
0
0
0
0
0
0.2
0.2
0
0.4
0.4
0
0.4
0.33
0.4
0
0.33
0.2
0
117
FISSION AUTOCORRELATION
of zero are left unaltered. Finally, the connectivity matrix is row normalized so that each
row sums to 1.0, thus producing the final
connectivity of W matrix (Table 2). Row normalization constrains the autocorrelation
coefficient to p < 1.0. The nxl vector Wy is
also standardizedprior to analysis.
Given a vector of measurementson a single
trait of interest of) and a network matrix of
relatedness (W), a n estimate of the autocorrelation coefficient (p) can be obtained by
maximum likelihood procedures as follows:
Given e
N(0, 211, the likelihood function
[L(e)] for the residuals (el in Equation 1 is
(Mead, 1967)
-
and the autocorrelation coefficient, p, as the
value of p which maximizes
~(y=
) constant
-
N
- In ($1 + In IA/ . (7)
2
Computationally, Equation 7 is extremely
burdensome, since the determinant of matrix
A, i.e., the / A / term, must be evaluated at
each iteration of any search procedure. Ord
(1975) has immensely simplified this problem by noting that
N
/A[
=
C (1 - phi)
i=l
(8)
where X,I X2, As, . . . , A, are the n eigenvalues of the W matrix. Hence, the eigenvalues
of W need to be evaluated only once. Now,
substituting Equations 6 and 8 into Equation 7 and simplifying, we obtain a considerably less burdensome expression that the
maximum likelihood estimate, p, must mini(3) mize (Ord, 1975):
However, since it is the original trait values
(y) that are observed and not the residuals
(el, we require a change of variables. From
Equation 1we note that
e
=
(I - pW)y
=
Ay
where A = (I - pW) and I is a n nxn identity
matrix. Substituting Equation 3 into Equation 2 gives the likelihood function [L(y)] for
the original trait values (y):
where I A J is the Jacobian of the transformation from the residuals re) to the original
trait values (y) (i.e., the determinant of matrix A). Transforming Equation 4 to the analytically more tractable log-likelihood
function [Pof)] gives
Equation 5 must be maximized with respect
to & and p to obtain the maximum likelihood
estimates. After differentiatingthis equation
with respect to each of these parameters and
simplifying, we obtain as the maximum likelihood estimates
The maximum likelihood autocorrelation
coefficients (p) reported below were found using a direct search procedure which minimizes this latter equation. We searched the
-1 < p < 1 interval in steps of .01 for a
minimum.
Once the maximum likelihood p is obtained, v 2 can be easily calculated from
Equation 6 above. With these two estimates
in hand, it is possible to estimate their variance-covariance matrix; thus the usual inferential procedures are possible with respect to
the estimated autocorrelation coefficient (p).
In general, the asymptotic variance-covariance matrix is given by the negative inverse
of the information matrix (Kendall and
Stuart, 1967, p. 55), i.e., the matrix of the
second order partials of the parameters being
estimated by
-1
118
J.M. CHEVERUD AND M.M. DOW
most dissimilar. This is because lineal fission
can have a drastic effect on between-group
variability. If a cluster analysis were to be
performed on intergroup distances derived
V ( 2 , p) =
from these same data (Cheverud, 19811, the
4 N/2
2 tr (B)
phenograms would present a pattern quite
unlike the known historical relationships
[2tr (B)
2 [tr(B'B) + a]
among the groups. Therefore, the data from
Cay0 Santiago indicate that the lineal effects
where
of fission may be extremely important for the
interpretation of genetic and morphological
N
variation among closely related groups.
B = A-' W, (Y = C X;/(l - pXJ2
The results presented here are quite unui=l
sual in network analysis since it is rare that
and t r is the trace operator, which simply phyletic connections between groups would
sums the elements on the main diagonal of produce dissimilarity. The extreme magniits matrix argument. Entering the estimated tude of the autocorrelations is also surprisfI and ?C values into the right-hand side of ing. They are so highly negative that the
Equation 11 and evaluating the resulting lineal effect of fission may be considered the
expression yields the standard deviation of$ major force producing intergroup genetic
as the square root of the (2,2) element of V. variation on Cay0 Santiago. We are espeSince p is asymptotically normally distrib- cially confident in the results, since they are
uted, the usual inferential procedures are repeated for every trait studied and traits
easily applied. Derivationsof all of the above within the GM and GN sets are not correresults are available from the authors upon lated with one another. Thus, we demonrequest. All calculationswere performed with strate that in the case of closely related
the BASIC program MINRH03 written by groups, a population structure analysis
the authors. Since maximum likelihood esti- should regard lineal fission as an important
mation is based on asymptotic results, it is factor, since it may create immediate, gross
biased in any finite sample. Simulation stud- differences between populations in morpholies of the network effects model (see Eq. 1) ogy and its underlying genetic basis.
The fact that Cay0 Santiago is a free-rangstrongly suggest that the bias will be negative in small samples (Dow et al., 1982; An- ing but spatially restricted colony may have
selin, 1982), so that p may be slightly influenced the results presented here. It
underestimatedin our analysisof eight cases. seems clear from analyses of individual group
Therefore, negative autocorrelations will be divisions (Duggleby, 1977; Cheverud et al.,
tested for significant deviations from zero a t 1978; Buettner-Janusch et al., 1983)that linthe more conservative 0.01 level, in addition eal effects can generate significant intergroup differences between daughter groups,
to the standard 0.05 significance level.
although this is the first demonstration of its
RESULTS AND DISCUSSION
overall importance for intergroup variation
The means of the five cranial standardized on Cay0 Santiago. Lineal fission is also likely
traits for each social group are given in Table to be important for feral populations, al3. The fission autocorrelation coefficients (p) though Melnick and Kidd (1983) detected litfor the five highly heritable traits are pre- tle or no genetic variation among daughter
sented in Table 4. All five coeficients are groups formed from a single fission in feral
negative; three of them are significantly less rhesus macaques from Pakistan. In contrast
than zero a t the 0.01 level; and one addi- to unfettered populations, on Cayo Santiago
tional trait (GM2) is significant only a t the newly formed groups cannot disperse to new,
0.05 level. Only GN1 is not significantly dif- geographically distant locations. Thus all
ferent from zero. Spearman rank-order cor- groups, regardless of their historical relarelations between y and Wy are also tionship, may have a more or less equal oppresented. They produce results fully consis- portunity for intermigration. Since intertent with the autocorrelation analysis. These group migration tends to lessen the genetic
results indicate that social groups most differences between groups, we may expect
closely related through a common ancestral unrelated and distantly related groups to be
group are genetically and morphologically more similar to one another on Cayo SanFollowing Ord (19751, this matrix is obtained
from
'
119
FISSION AUTOCORRELATION
TABLE 3. Mean values of five highly heritable linear combinations of cranial metric (GMl-3) and nonm.etric (GNl-2) traits for each social group (Grand means are zero and the variance is one for each trait)
Group
GM1
GM2
GM3
GN 1
GN2
A
K
L
J
F
I
E
C
-0.12
0.36
-0.10
0.04
-0.15
0.29
-0.11
-0.06
-0.19
0.09
0.33
-0.15
0.33
-0.35
-0.52
0.19
-0.63
-0.18
0.62
0.28
0.18
0.35
0.49
-0.72
0.23
-0.33
-0.15
0.19
0.17
0.31
-0.01
-0.17
-0.56
0.31
0.06
-0.40
-0.31
0.36
-0.32
-0.20
TABLE 4. Fission autocorrelation coefficients(p),
standard errors o f p (S.E. [p]), Spearman rank-order
correlations (r$, and heritabilities (h2)for five highly
heritable morphological traits
Trait
P
S.E. (p)
rs
h2
GM1
GM2
GM3
GN1
GN2
-0.86**
-0.56*
-0.68**
-0.40
-0.97**
0.10
0.31
0.23
0.39
0.02
-0.76**
-0.69*
-0.74**
-0.50
-0.93**
0.77
0.64
0.65
1.42
1.20
'Significantly less than zero at the 0.05 level.
**Significantly less than zero at the 0.01 level.
tiago than in a feral situation. Thus, intergroup differences are instantaneously generated by the effects of lineal fission, then,
over time, the homogenizing influence of intergroup migration degrades these differences. Therefore, we may expect a negative
autocorrelation among historically related
groups on Cay0 Santiago. The effects of genetic drift on intergroup variation are likely
to be small owing to the high per lifetime
migration rate exhibited on Cay0 Santiago.
In a feral situation, where correlations between recency of formation by group division, geographical proximity, and migration
rate may exist, the standard model of anthropological genetics, where genetic similarity
indicates historical propinquity, may be more
applicable. However, we feel that the standard model should not be applied uncritically,
without taking into account the social dynamics of the groups concerned, and should
be used with great caution in reconstructing
social and historical dynamics from genetical
and morphological data, as is often done in
studies of recent and prehistoric human
populations.
This analysis has also demonstrated the
usefulness of general network autocorrela-
tion techniques in testing hypotheses relating intergroup variation to population
structure. Similar methods are also being
used to analyze the distribution of allele frequencies relative to social structure in the
Hutterites (O'Brien, n.d.1. Networks of relationship which may be of special interest in
analyzing genetical and morphological variation include phyletic networks, as presented
here and, at the species level, in Cheverud et
al. (19841, migration networks, geographical
networks (Sokal and Menozzi, 1982; Sokal
and Friedlaender, 19821, and linguistic networks (Dow et al., 1984; Dow, 1984). The
method is general, not restricted to geographical or phyletic relationship, and can
be applied to a wide range of problems in
which population structure plays a n important part.
Since lineal fission is important in the production of significant amounts of intergroup
variation, it is a major factor in the evolutionary dynamics of primate populations.
Models of kin and group selection depend
critically on the proportion of genetic variation which occurs between groups (Hamilton,
1964; Wade, 1980; Wilson, 1980; Cheverud,
1985). The higher the intergroup Variation,
the better the chances for evolution in a n
altruistic direction. Also, Wright's shifting
balance theory (Wright, 1978) depends critically on genetic variation between groups
generated by genetic drift and/or founder
effects.
Finally, differences in the level and pattern
of quantitative genetic variation among population subdivisions can greatly influence the
genetic response to selection pressures
(Wright, 1931; Cohen, 1984). Thus populations may diverge genetically even when exposed to similar selection pressures if the
genetic variancelcovariance matrix is different among related populations due to foun-
120
J.M. CHEVERUD AND M.M. DOW
der effects. Since research on Cay0 Santiago
has shown that lineal effects of fission are
important in producing allelic variation
(Duggleby, 1977; Cheverud et al., 1978;
Buettner-Janusch et al., 1983) and the genetic variancelcovariance matrix is affected
by the frequencies of alleles a t loci affecting
morphological traits (Falconer, 19811, we expect that lineal fissions may have a large
effect on the particular level and pattern of
genetic variance available for selection in
any given population. So lineal fission may
have important effects not only on group
means, as demonstrated here, but also on
within-group variances and covariances
(Lande, 1980).
netics of skeletal non-metric traits in the rhesus macaques on Cay0 Santiago. 11. Phenotypic, genetic, and
environmental correlations between traits. Am. J.
Phys. Anthropol. 545-58.
Cheverud, J, Leutcnegger, W, and Dow, M (1984)Phylogenetic autocorrelation and the correlates of sexual
dimorphism in primates. Am. J. Phys. Anthropol.
63:145 (abstract).
Cliff, A, and Ord, J (1981) Spatial Processes. Pion Limited London.
Cohen, F (1984) Genetic divergence under uniform selection. I. Similarity among populations of Drosophila
melanogastcr in their responses to artificial selection
for modifiers of ci’. Evolution 3855-71.
Crow, J, and Kimura, M (1969) An Introduction to Population Genetic Theory. Minneapolis: Burgess Publishing Co.
Dow, M, Burton, M, and White, D (1982) Network autocorrelation: A simulation study of a foundational problem in regression and survey research. SOC.
Networks
4: 169-200.
ACKNOWLEDGMENTS
Dow, M (1984) A biparametric approach to network autocorrelation: Galton’s Problem. Sociol. Methods Res.
We thank Jane Buikstra, Diane Chepko13:201-217.
Sade, Henry Harpending, Alice Martin, CarDuggleby, C (1977) Blood group antigens and the popuole Ober, Elizabeth O’Brien, and Donald Sade
lation genetics of Macoca mulatta on Cavo Santiago.
for illuminating, general discussion of the
11.EffeGts of social group division. Yrbk. Phys. Anthyopol. 20:263-271.
methods and results presented here and comments on a n earlier version of this Falconer, D (1981) lntroduction to Quantitative Genetics. New York: Longman Press.
manuscript.
Fix, A (1978) The role of kin-structured migration in
genetic microdifferentiation. Ann. Hum. Genet.
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