Group selection models with population substructure based on social interaction networks.код для вставкиСкачать
AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 77:427-433 (1988) Group Selection Models With Population Substructure Based on Social Interaction Networks JAMES M. CHEVERUD, B. DIANE CHEPKO-SADE, MALCOLM M. DOW, AND DONALD S. SADE 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.) KEY WORDS Cay0 Santiago Trait-groups, Grooming, Macaca mulatta, ABSTRACT 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 structures. 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- 0 1988 ALAN R.LISS, INC 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. 428 J.M. CHEVERUD ET AL. 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 thought. MATERIALS AND METHODS The data used here are derived from sociometric records of grooming behavior among all of the adult and juvenile females BETWEEN TRAIT-GROUP GENETIC VARIATION 429 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 Groomer’s rnatrilineage 065 004 AC 073 076 022 members (Chepko-Sade, 1982). The average degree of relatedness of 0 0 065 394 43 16 10 004 52 246 9 4 0 0 groomers t o groomees was measured by first 16 18 3 row normalizing the grooming matrix (P) so 18 12 452 AC 3 14 582 7 18 14 that entries (pi,) represent the proportion of 073 17 516 14 1 11 5 076 0 2 4 10 282 grooming events performed by the row ani022 2 313 mal (i, the source of potential altruism) for 305 513 ,633 562 Totals 478 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 observation. 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 of 430 J.M. CHEVERUD ET AL. 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 G = g'g 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 c? 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 RESULTS 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. 431 BETWEEN TRAIT-GROUP GENETIC VARIATION 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). DISCUSSION 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 ratios. 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 432 J.M. CHEVERUD ET AL. 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. 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