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