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Group selection models with population substructure based on social interaction networks.

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Group Selection Models With Population Substructure Based on
Social Interaction Networks
DepartmentofAnthropology(J.M.C., B.D.C.-S, M.M.D.,D.S.S.), and
Department of Cell Biology and Anatomy (J.M. C.), Northwestern University,
Euanston, Illinois 60201; The North Country Institute for Natural
Philosophy, Mexico, New York 13114 (B.D.C.-S., D.S.S.)
Cay0 Santiago
Trait-groups, Grooming, Macaca mulatta,
Most models of evolution by group selection assume that
groups have discrete boundaries with homogeneous levels of interaction within
groups and no interaction between groups. While this assumption is analytically useful, it is not an accurate description of groups in nature. We use a
generalization of D.S. Wilson’s (Am. Nut. 111:157-185, 1977; The Natural
Selection of Populations and Communities. Reading, Mass.: BenjamidCummings, 1980) concept of trait-groups, in which groups are defined as sets of
interacting individuals, to estimate the average degree of relatedness among
groomers and groomees, referred to here as grooming-groups. The average
degree of relatedness is an important parameter in models of both kin and
group selection.
Data on grooming among 52 female rhesus macaques drawn from Group F
on Cay0 Santiago were used to represent the pattern and intensity of affiliative
interactions. Degrees of relatedness among individuals and transferrin phenotypes were obtained from demographic and genetic records on the colony. The
average degree of relatedness within grooming-groups was estimated directly
by calculating the average degree of relatedness among interactants (groomers
and groomees),weighted by their frequency of interaction. Average degrees of
relatedness among interactants were also estimated from the subjective frequency of the transferrin C allele.
Our analysis indicates that the average degree of relatedness within grooming-groups is 0.316 when estimated directly and 0.347 when estimated from
the subjective frequency of the transferrin C allele. These values are much
higher than are usually considered for group selection in primate societies and
indicate the relative ease with which altruism may evolve given primate social
Hamilton’s rule (1964) states that more altruistic character states will evolve when
the average degree of relatedness between
the sources and targets of altruism exceed
the ratio of the costs incurred by the sources
to the benefits derived by the targets. Most
of the theoretical research following Hamilton has broadly confirmed his rule using both
single locus (Wade, 1978, 1980; Michod and
Abugov, 1980; Wilson, 1980) and quantitative genetic models (Yokoyama and Felsen-
stein, 1978; Crow and Aoki, 1982; Aoki,
1982a,b;Engels, 1983;Cheverud, 1984; 1985),
although many important refinements have
also been made.
The parameters of these kin and group selection models have only rarely, if ever, been
measured for traits of interest. To some extent this omission is due to the perceived
difficulty in measuring the parameters, and
Received April 9, 1987; accepted December 28, 1987.
to the fact (frequently noted by field workers)
that the assumptions of the theoretical
models only rarely apply in field situations.
In a previous paper, Cheverud (1985) described the parameters necessary to test for
altruistic selection and evolution and the
means by which they can be estimated using
field data. Here we present a refinement of
the methods described by Cheverud (1985)
based on the concepts of trait groups and
subjective gene frequencies as developed by
D.S. Wilson (1977, 1980).This refinement involves estimating the average degree of relatedness between altruists and their targets
in situations where discrete groups, with homogeneous interaction within groups and no
interaction between groups, do not exist. This
is analogous to the consideration of population genetic structure in neighborhood
models in contrast to island models.
Group selection models, such as those developed by Wade (1978, 1980, 1985), often
start with the assumption that a population
is divided into discrete groups of interacting
individuals. lnteractions which a e c t fitness
are assumed to occur randomly or homogeneously within groups and to be absent between groups. This assumption facilitates
theoretical analysis and is quite valid for
groups in which there is no variation in the
degree of genetic relatedness among individuals. However, it is unlikely to be met in
groups of primates, or mammals generally,
as encountered in the field. Groups exist at
many levels in nature and the interactional
boundaries between them are not always discrete. An individual may interact with different sets of conspecifics for different purposes
and may interact preferentially with only a
few members of a group. D.S. Wilson (1977,
1980) defined trait-groups as discrete sets of
individuals within a total deme which interact with one another, thus first using the
interactions among individuals to determine
group membership and then representing
demic substructure as a set of discrete groups.
We will show how the interactions among
individuals can be directly used to represent
demic substructure in group selection models
without the identification of discrete groups.
In this report we will estimate the average
degree of relatedness among interactants
drawn from a rhesus monkey (Macaca mulatta) social group, Group F, on Cay0 Santiago, Puerto Rico (Sade et al., 1985). Social
interactions within the group are structured,
but not in a way which can be accurately
represented by discrete subgroups with ran-
dom, or homogeneous, interactions within
subgroups and no interaction between
subgroups. Grooming is the specific social
interaction which will be investigated here.
Sade (1965,1972b;Sade et al., 1988)and Baxter and Fedigan (1979) have argued that
grooming is the best single class of interaction for revealing the network of social attachments within the group. It is presumed
that altruistic acts would tend to follow the
same patterns as grooming, as has been documented for interactions in which an animal
interferes in a fight on behalf of another individual (Kaplan, 1977).
On Cay0 Santiago, rhesus macaques live
in social groups, operationally defined as
groups of animals consistently found in spatial proximity to one another over long periods of time. The natal portion of a social
group is composed of a set of extended families, or matrilineages, defined as all animals
within the group known to be descended from
a single female. These matrilineages are a
basic unit of social structure, as evinced by
their integrity during group fission events
(Chepko-Sadeand Olivier, 1979;Chepko-Sade
and Sade, 19791, as well as by grooming relations (Sade, 1965, 1972b) and by their role
in determining dominance relations among
females within the group (Sade, 1967,1972a).
Matrilineages in turn, contain overlapping
sets of related families, each composed of a
mother and her offspring. Thus female rhesus monkeys on Cay0 Santiago could be said
to belong to a hierarchy of social units, with
individual animals being members of a family, families being members of a matrilineage, and matrilineages being members of
social groups.
Previous research shows that friendly or
helpful interactions are most frequent among
close relatives (Sade, 1965, 1972b; Kaplan,
1977; Chepko-Sade and Sade, 1983). Therefore, we expect that the average degree of
relatedness among such interactants will exceed that usually found among all social
group members or even among members of a
single matrilineage. Given that friendly interactions are found to follow such a pattern,
the opportunity for evolution of altruistic
character states in such groups would be
much higher than has previously been
The data used here are derived from sociometric records of grooming behavior
among all of the adult and juvenile females
1972. The genealogies were three to four generations deep but only represent the female
line, fathers being unknown. Thus known
genealogical relatedness may underestimate
Groomee’s matri 1ineage
the total degree of relatedness among group
065 004
073 076 022 members (Chepko-Sade, 1982).
The average degree of relatedness of
52 246
0 groomers t o groomees was measured by first
3 row normalizing the grooming matrix (P) so
12 452
14 that entries (pi,) represent the proportion of
10 282 grooming events performed by the row ani022
313 mal (i, the source of potential altruism) for
513 ,633 562
each other animal (j, the targets of potential
altruism) in the social group. Then an average degree of relatedness (ri), or genetic corresident in Group F from September 1 to relation, between sources and targets of
December 31, 1972. Only females were used grooming was calculated for each source ansince they compose the stable core of social imal (i) as follows:
group members (Sade et al., 1985). The parn
ticular length and season of the study period,
4 months in the breeding season, was chosen
in order to limit the demographic turnover
due to births and deaths but still include
sufficient numbers of interactions for relia- where rij is the genetic correlation between
bly measuring the extent of interaction individuals i and j. These individual average
among pairs of individuals. This particular degrees of relatedness (ri) among sources and
period was also one of intensive behavioral targets of grooming were then averaged over
the total sample. This overall degree of relatAll females in Group F (N=52) who were 1 edness is the genetic correlation among group
year old or older by September 1, 1972 are members specified in kin and group selection
included in the sample, except for WT, who models. However, it is derived here without
died soon after September 1. The observer the identification of discrete groups and is
spent approximately 8 hours per day during instead estimated using the level of potenthe study period recording all agonistic, sex- tially altruistic interaction among individuual, and affiliative behavior observed using als (P matrix).
a sampling procedure described by Sade
In analyzing data for groups in which ge(1965; 1972b; 1975). Grooming data were or- nealogical relationships are unknown, the
ganized into a 52 x 52 matrix, including overall degree of relatedness among sources
only the adult and juvenile females of the and targets of altruism can be estimated by
group. Of the 5,140 grooming interactions an alternative method, using the average beobserved during this period, 2,804 were tween-group genetic variance at several inamong these females (an additional 887 were dividual loci. The locus-specific average
between these females and their infants of between-group genetic variance can be estithe year and an additional 2,972 were re- mated using the subjective gene frequency
ceived by natal males; only 1,282 were re- (Wilson, 1977, 1980)of the allele in question,
ceived by non-natal males). Individuals even when discrete groups cannot be identiwithin the matrix were organized according fied. A subjective gene frequency is the avto matrilineage to facilitate comparison of erage frequency of an allele experienced by
amounts of grooming within and between the carriers of that allele in the course of
matrilineages. Table 1 shows a summarized altruistic interactions. This definition is relversion of the grooming matrix. It is appar- atively straightforward in the haploid case
ent from the table that most grooming occurs considered by Wilson, but can also be exbetween members of the same matrilineage. tended to the diploid case with some effort.
The degrees of relatedness among memTo demonstrate this technique, subjective
bers of the grooming network were calcu- gene frequencies were calculated for the
lated from the genealogies in Sade et al. grooming network using alleles at the trans(1985).There were six maternal genealogies, ferrin locus (Buettner-Janusch et al., 1974).
or matrilineages, represented in Group F in We have no expectation that transferrin alTABLE 1. Frequency
grooming among females
within and between Group F matrilineages from
September 1 to December 31, 1972
leles produce variance in altruism, so this
calculation should only be taken as an example of how subjective gene frequencies can
be estimated using field data. It would also
be beneficial to include as many loci as possible in order to increase the accuracy of the
estimated degree of relatedness. Only one
locus is used here by way of example and due
to limits of the sample available. Transferrin
genotypes for each female in the network
were obtained from Sade et al. (1985). For
this example, only the C allele was distinguished from all others (G, D1, D2). Each
female is assigned her appropriate gene frequency (0, .5,or 1)based on the number of C
alleles she carries, thus generating an N X1
vector, g, of individual gene frequencies. An
N x N matrix of genotypic similarity among
pairs of interactants (G) is generated by
The elements of the G matrix represent the
probability that two transferrin alleles, one
drawn randomly from individual i and one
drawn from individual j, are both C alleles.
The subjective gene frequency is then given
by the sum of the elements of the Hadamard
(element by element) product of P with G
divided by N. This subjective gene frequency
is the frequency with which carriers of C
alleles may potentially interact altruistically
with other carriers of C alleles, weighted by
the frequency of the C allele in the source's
and target's genotypes. Weighting by each
individual's C allele frequency generates a
diploid version of the concept Wilson (1977,
1980)defined for the haploid case.
From Wilson (1980)and with the aid of the
subjective allele frequency, the between
grooming-groupgenetic variance (2,)can be
calculated by
p =
P(Ps - P)
where ps is the subjective allele frequency
and p is the total allele frequency. Then,
from Cheverud (1985), the average genetic
correlation between potential altruists and
their targets (r) is
If one considers the natal portion of the
social group as a whole to be the unit for
group selection, (assuming that interaction
among social group members is uniformly
distributed while no interaction occurs between social groups) the average degree of
relatedness within the study group of 52 females is 0.032. Estimates of average withingroup degree of relationship for natal portions of groups, based on allele frequencies
and averaged over groups for the Cay0 Santiago colony as a whole for this period, are
about twice this value (r = 0.059) (Cheverud,
1985; Duggleby 1978; Olivier et al., 1981).
This difference may reflect the effects of unrecognized paternal relatedness, or may be
due to the fact that Group F at this time was
the largest group on the island, having the
largest number of matrilineages (six as compared to the typical two to four matrilineages), and thus contained a much larger
proportion of unrelated pairs of animals than
other groups on the island.
If one considers the matrilineage as the
unit for group selection (assuming uniformly
distributed interaction within matrilineages
and no interaction between members of different matrilineages), the average degree of
relatedness among female matrilineage
members in Group F is 0.19, with a range
from 0.143 to 0.325. This value is a more or
less typical average degree of relatedness
within matrilineages for Cay0 Santiago during the early 1970s,when values ranged from
about 0.05 to 0.25 and averaged 0.17 (Olivier
et al., 1981). Furthermore, this value is consistent with that derived from allele frequencies (r = 0.1581, indicating that paternal
relatedness within matrilineages is likely to
be negligible and that males mate at random
with respect to matrilineage. This observation is in direct contrast to the expectations
of a lineage-specific mating scheme, as proposed for the Cay0 Santiago colony by McMillan and Duggleby (1981).
Finally, if one considers the groominggroup, or trait-group based on grooming interactions, as the unit of group selection,
thereby using the pattern of interactions
themselves to define population substructure
and making no further assumptions, the average degree of relatedness among traitgroup members in Group F is 0.316. This
value is quite high. Thus, when demic substructure is based directly on the interactions among individuals rather than being
based on more arbitrary distinctions of rhesus social structure, the relative additive genetic variance between groups is quite high.
The subjective gene frequency for the
transferrin C allele is 0.66 with a total allele
frequency for those included in the matrix of
0.57. Thus the between grooming-group variance is 0.0514, and the average degree of
relatedness between groomers and groomees
at the transferrin locus is 0.347. This estimate is quite close to the value obtained using the genealogical information and is also
much higher than values obtained between
social groups or matrilineages at the transferrin locus (Buettner-Janusch et al., 1974;
Cheverud et al., 1978; Olivier et al., 1981).
We have provided two different means of
estimating the average degree of relatedness
within substructured demes for which discrete trait-groups do not exist. These methods allow for an exact estimate of average
degree of relatedness with population substructure based directly on actual patterns of
interaction among animals, rather than one
based on an assumption of random or homogeneous interaction within discrete groups.
The first method, based on the degree of relatedness between pairs of interactants, provides an estimate averaged over all alleles
and is most appropriate when many alleles
affect variation in the altruistic trait or when
individual altruistic alleles cannot be identified. However, it requires reliable estimates
of degree of relationship and thus necessitates long term records of individual and population history. The second method, based on
subjective allele frequencies, is most appropriate when a single altruistic allele can be
identified and allelic states measured at the
relevant locus. However, it may also be useful for short-term studies in which blood polymorphisms and behavioral data are collected
in a cross-sectional fashion. In this situation
the between trait group variance can be estimated with subjective allele frequencies for
one or preferably several loci even in the
absence of genealogical data. In the example
given above estimates based on the two
methods were quite similar. This result may
have been fortuitous in that between traitgroup variances at individual loci may often
deviate from the expected value (for an example see Olivier et al., 1981).
A quantitative genetic version of Hamilton’s rule was derived by Cheverud (1985)
indicating that evolution would proceed in
an altruistic direction when
(rKl -r)) >
( 1 Pw 1 / PB)
where r is the average degree of relatedness
within the group, 1 PW1 is the absolute value
of the within-group selection gradient, or the
average within-group linear regression of
relative fitness on the phenotype (Cheverud,
1985; Lande, 1979), and PB is the between
group selection gradient or the linear regression of the relative fitness of the group on its
average phenotype. The selection gradients
measure the strength of within and between
group selection and are analogous to Hamilton’s (1964) costs and benefits respectively.
The situation only relates to altruism when
and PB have opposite signs.
From the results and equation given above,
evolution will proceed in an altruistic direction in this group of macaques when the costbenefit ratio is less than 0.46. This is a
threshold cost-benefit ratio above which altruism will not evolve. In order t o achieve
this level, the benefit to the target, measured
in terms of its relative fitness, must be about
twice the cost of the character to the source’s
relative fitness. This is a much less stringent
condition for group selection in macaques
than has previously been considered and is
nearly equivalent to kin or group selection
with full-sibs. Groups smaller than the one
analyzed here tend to have even higher degrees of relatednesss within groups (Silk,
1984) and may allow the evolution of altruism with correspondingly higher cost-benefit
The maximum cost-benefit ratio at which
altruistic evolution is allowed may often be
quite high if environmental factors affecting
the development of the altruistic character
are randomly distributed across a genetically
substructured deme. The cost-benefit ratio is
equal to
where covw is the average within-group covariance or selection differential, COVBis the
between-group covariance or selection differential, P is the character or phenotype of
interest, WR is relative fitness, and t is the
proportion of phenotypic variance between
groups (Cheverud, 1985). When the environment is randomly distributed among traitgroups, t will be quite small, leading to the
strong possibility that the threshold cost-benefit ratio above which altruism cannot evolve
will be greater than 0.46.For example, with
a heritability for the character of 0.30, the
environment randomly distributed among
groups, and r = 0.316,only about 10% of the
total phenotypic variance will be between
groups and the ratio of within and between
group selection differentials (COVW/COVB) allowing altruistic evolution will be reduced by
a factor of ten. Thus the within-group selection differential could be 4.6 times the between group selection differential and
altruism would still evolve.
By eliminating the assumption of uniformly distributed or homogeneous interaction among group members from considerations of the potential for altruistic evolution through group selection and instead
representing population substructure directly as a network of interacting individuals, we have shown that it should be
relatively easy for altruistic behaviors to
evolve in rhesus macaque social groups. The
average degree of relatedness among interacting animals is quite high, well above the
level of half-sibs but still below the level of
parents and offspring. This result reflects the
observation that most grooming takes place
within a family consisting of a mother and
her daughters and in this context altruistic
behaviors are likely to be directed towards
close kin. We may see here the basic structure of all mammalian societies which are
based on the mother-offspringbond, with the
affiliation founded on this bond being extended to also include maternal siblings.
Once altruistic behaviors have evolved in the
context of close kin, they can be redirected
towards other individuals in appropriate contexts, such as in reciprocal altruism. Thus
the evolution of maternal effects on offspring
phenotypes (Cheverud, 1984) may be the basis for the evolution of much further social
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