American Journal of Primatology 10: 291-300 (1986) Dominance Index: A Simple Measure of Relative Dominance Status in Primates DORIS ZUMPE AND RICHARD P. MICHAEL Department of Psychiatry, Emory University School of Medicine and The Georgia Mental Health Institute, Atlanta, Georgia A simple measure of relative dominance status (cardinal rank) is described which we have termed the dominance index. Like more familiar techniques for assessing rank order, it is based on the direction of aggressive and submissive b,ehaviors between all possible paired combinations of animals in a social group. Using data from five groups of female rhesus monkeys, it reliably produced the same ordinal ranks as fight interaction matrices. There was also good agreement with the cardinal ranks produced by two additional measures of dominance and with those produced by observer ratings. The dominance index can be calculated when fights have not actually occurred and is largely independent of the frequency of agonistic interactions. It has, therefore, wide application and can estimate dominance during brief sampling periods (one hour) and also in stable groups when agonistic interactions are low. Its application is described in experiments in which the male in a group of females was changed and the hormonal status of the females was altered. Estrogen increased female dominance status relative to other females. Key words: rank, agonistic behavior, social groups, hormones, primates, rhesus macaques, Macaca mulutta INTRODUCTION It is usual to assess the rank order of individuals in social groups of animals on the basis of the direction of their agonistic behavior. The animal that directs aggressive but not submissive gestures toward other group members is considered to be the highest ranking, while the individual directing submissive but not aggressive gestures toward others is judged to be lowest ranking. The intervening ranks are assessed on the basis of consistent wins and losses during agonistic interactions between particular pairs of animals [Schjelderup-Ebbe, 1922; Richards, 1974; Bernstein, 1981; McMahan & Morris, 19841. However, such observations merely assign a rank order (ordinal rank) and do not determine the degree or extent to which a higher-ranking animal dominates the next lower-ranking individual (cardinal rank). Received November 4, 1985;revision accepted January 26,1986. Address reprint requests to Richard P. Michael, MD, Department of Psychiatry, Emory University School of Medicine, 1256 Briarcliff Road, N.E., Atlanta, GA 30306. 0 1986 Alan R. Liss, Inc. 292 I Zumpe and Michael A technique has recently been developed [Boyd & Silk, 19831 that permits the assessment of relative as well as absolute rank in social groups of primates, but it requires the application of a rather complex, iterative computer procedure and a fairly large body of behavioral data. This limits its use with small captive groups in which agonistic interactions may be infrequent and usually do not involve fights. The dominance index described here is very simple to calculate and does not even require the aid of a pocket calculator. It is based on the proportion of aggressive and submissive behaviors between pairs of animals and is largely independent of the absolute number of agonistic gestures made. Relative dominance can therefore be evaluated on a day-by-day basis, and any changes can readily be related to other behavioral or experimental variables. Its application to data from female-female interactions is described here. This index has been informally used in our laboratory for a number of years, and it now seems appropriate to provide sufficient detail to facilitate its use by others. METHODS Animals The behavioral data reported here were obtained from five groups of rhesus monkeys (groups 1-5), each containing four females tested either alone or together with one male. The 18 females and five males were all obtained a s adults from the wild through dealers in North India. Males were intact, and females were ovariectomized several months before their use in a variety of behavioral studies from which the data reported here were obtained. Except during tests, all animals were housed in individual cages in large cage rooms where artificial lighting gave a 14hour day between 0615 and 2015 and temperature was maintained between 20 and 24°C. Food consisted of Purina Monkey Chow supplemented by fruit and vegetables, and water was available ad libitum. Hormone Treatments In some of the behavioral studies, one or more females in a group were treated with ovarian hormones. Details of the hormone treatments are not reported here since they are irrelevant in the present context with the exception of group 4. In group 4,each female in turn was treated first with 10 pg estradiol benzoate subcutaneously (sc)/day alone (EB) and then in combination with 50 mg progesterone sc/ day (EB + P) for five group tests while the other females in the group remained untreated. When all four females had completed the hormone treatments, the male was changed, and the process was repeated with each of three other males. With each male, therefore, each female was observed during 30 tests while she was untreated, during five tests while she received EB, and during five tests while she received EB + P (see Fig. 3). Further details of this study have been given elsewhere [Michael & Zumpe, 19841. Behavioral Tests Observations were made during 60-min behavioral tests conducted five days a week on groups of four female rhesus monkeys, either with or without a male, in a room 4.9 m wide by 4.9m deep by 2.1 m high [Michael & Zumpe, 19821. In addition to social, grooming, and sexual behavior, the following behavioral interactions were routinely scored (1)aggressive behaviors-the total numbers of bites, chews, grabs, pulls, hits, chases, open-mouth threats, and aggressive jerks per test given and received by each individual; (2) submissive behaviors-the total numbers of flees, crouches, submissive presentations, and grimaces per test given and received by each individual; (3) approaches-the total number of approaches to within touching Dominance Index I 293 distance made and received by each individual; (4)departures-the total number of departures (from within touching distance) made and received by each individual in the group. Dominance Index The dominance index is based on the direction of aggressive and submissive behaviors between the two members of all possible paired combinations of animals in a group. It is calculated in four simple steps. Percent aggressive behaviors given. For each pair, the number of aggressive behaviors given by one animal to the other is expressed as a percentage of the total number of aggressive behaviors given by both animals to one another. Thus, if female A gives seven aggressive gestures to female B and if female B gives three aggressive gestures to female A, female A scores 7/10 = 70% aggression given while female B scores the reciprocal, ie, 3/10 = 30%aggression given. Percent submissive behaviors reeeived. For each pair, the number of submissive behaviors received is calculated exactly as described above for percent aggression given. Thus, if female A receives eight submissive gestures from female B and if female B receives two submissive gestures from female A, female A scores 8/10 = 80% submission received while female B scores the reciprocal, 2/10 = 20%submission received. Percent aggression given and submission received per pair. For each pair, the percent aggression given and percent submission received scores are combined for each animal. Thus, female A scores (70% 80%)/2 = 75%, and female B scores (30%+ 20%)/2= 25%.Where there are no aggressive interactions, percent submission received is used, and where there are no submissive interactions, percent aggression given is used. Dominance index. The dominance index is produced by averaging, for each animal, the percent aggression given and submission received scores with all the other animals in the group. Thus, if female A scores 75%with female B, 80% with female C, and 100%with female D, her dominance index for the test would be (75% + 80% + 100%)/3= 85%. Animals not showing any agonistic interactions with others are excluded from the averaging procedure. + Other Behavioral Measures The dominance index was compared with some other behavioral measures, namely: (1) rank order derived from fights unambiguously won and lost, ie, any agonistic interaction in which the recipient of aggression responded with submission toward the aggressor; fight interaction matrices were constructed by ranking animals so a s to minimize the numbers of interactions below the diagonal (see Table I); (2) percent aggression given, calculated as described above and averaged for each female in the group; (3) percent submission received, calculated as above and averaged for each female in the group; and (4)percent approaches made and departures received, calculated like the dominance index but by using approaches and departures instead of aggression and submission; this resembles in some respects the measures used by Hinde and colleagues to study mother-infant proximity interactions [Hinde & Spencer-Booth, 19671. Observer Ratings Many ethological insights originated from unconscious as well as conscious mental processing of somewhat unstructured observations made on animals with which observers were thoroughly familiar [Lorenz, 19811. The dominance index would, in our view, be validated with the greatest level of confidence if it matched 294 I Zumpe and Michael TABLE I. Interaction Matrix for Fights Clearly Won and Lost in a Group of Four Female Rhesus Monkeys (Group 1): Data From 3 Successive Daily 1-Hr Behavior Tests After the Introduction of an Unfamiliar Male No. of fights won by Female A Female L Female E Female I Total No. of fights lost by female A ** 0 0 0 L E I Total 1 3 15 1 20 15 5 35 15 0 55 ** ** 0 0 1 0 0 ** 18 36 TABLE 11. Comparison of Rank Order in Groups of Female Rhesus Monkeys as Determined by Fights Won and Lost and as Determined by Dominance Index (Means SEs for 3 Behavior Tests)* Grauu Group 1t?V = 55) Rank order determined by fights Dominance Index including fights Dominance Index excluding fights Group 2 (N = 12) Rank order determined by fights Dominance Index including fights Dominance Index excluding fights Group 3 (N = 43) Rank order determined by fights Dominance Index including fights Dominance Index excluding fights Group 4 (N = 13) Rank order determined by fights Dominance Index including fights Dominance Index excluding fights Group 5 RJ = 19) Rank order determined by fights Dominance Index including fights Dominance Index excluding fights n Females A 1 267 96 f 2.2 97 100 f 0.0 I 1 88 98 f 2.1 60 98 f 2.1 474 357 189 123 122 56 L 2 90 f 9.0 95 & 5.0 G 2 70 f 15.0 72 k 13.9 E 3 I 4 1 & 0.9 1 f 0.6 H F 3 4 18 f 17.6 6 f 5.6 2 f 2.1 18 f 17.7 P 0 R Q 3 1 2 4 100 f 0.0 89 _+ 11.0 33 f 0.0 0 0.1 100 f 0.0 83 f 16.3 33 +_ 0.0 1 f 0.5 N K J M 2 3 1 4 100 & 0.0 66 f 1.0 22 f 11.1 12 f 12.1 100 f 0.0 66 f 1.2 28 k 14.7 12 f 12.3 C H B D 2 3 4 1 95 f 4.9 52 f 11.3 41 f 22.6 0 f 0.0 92 f 8.4 44 f 5.6 50 f 9.6 0 0.0 34 k 0.8 57 f 21.5 * *N, total number of fights; n, total number of agonistic behaviors used to calculate dominance index. the independent ratings of highly trained observers thoroughly familiar with the animals involved. To this end, the four trained observers who made observations on the animals in group 1 (see Tables I, 111, Fig. 1)also rated the dominance ranks of the females. Each observer was given a ten-inch horizontal line drawn on 0.1-inch graph paper starting with 0% (lowest rank) on the left and ending with 100% (highest rank) on the right. The observers were asked, for each of the four females in the group, to place on the line a mark whose position indicated the dominance rank of each animal with respect to the others. Selection of Tests and Analysis For each group of females (groups 14),three tests were selected that between them provided at least one fight clearly won and lost for each of the six possible Dominance Index I 295 paired combinations of females. The rank order produced by this fight interaction matrix was compared with the dominance hierarchies produced by (1)the mean dominance index per test for each female calculated on the basis of all agonistic behaviors; (2) the mean dominance index per test for each female calculated on agonistic behaviors excluding data from fights clearly won and lost; (3) the means per test for percent aggression given, percent submission received, and percent approaches made and departures received during the same three tests with group 1; and (4) the mean observer ratings for group 1. Mean dominance indices were also calculated for three tests with group 1conducted six months earlier. Finally, mean dominance indices were calculated for the entire study involving group 4 to ascertain if the dominance index would change with changes in the female's hormonal status and with changes in the identity of the male in the group. RESULTS Dominance Index Compared With Fights Won and Lost Although fights between females under our conditions were occasionally rather severe, they generally involved only certain individuals and rarely all combinations of animals. Of the 13 different groups of females observed between 1974 and 1985, in only five groups (groups 1-5) was it possible to construct a n interaction matrix in which a t least one fight (unambiguous outcome) was observed between every pair of females. Table I shows the fight interaction matrix of group 1 females from which the rank order was established. Rank orders were similarly obtained from the fight interaction matrices of the other four groups. In the eight groups remaining, certain individuals occasionally directed aaonistic behavior toward others, but either the recipient failed to respond or, in thecase of fights, the outcome was unclear. Table I1 shows, for each of the five groups for which ordinal ranks could be GROUP 2 GROUP I FIGHTS PER TEST: 20 15 20 - 0-1-x DATE: 6/15 FIGHTS PER-TEST: loo x-x 6/16 6 6/17 O 6 3 4 l0/6 10/11 7/3 10/3 15 3 I 1 *--.-' 0-0 X-X 3/16 7/5 7/6 KEY 0-0 1/19 18 GROUP 5 3 .-a DATE: 21 - ,-, GROUP 4 4 GROUP 3 3 5/11 6/20 6/29 RANK I RANK 2 RANK3 RANK 4 FEMALE FEMALE FEMALE FEMALE 7/6 Fig. 1. The dominance index, for each individual in five groups of female rhesus monkeys, during three behavior tests giving fight interaction matrices. For some females, the dominance index was stable, while for others, major changes in dominance status occurred. 296 I Zumpe and Michael assigned, the rank of every female determined by the fight interaction matrix compared with the mean dominance index per test. There was complete concordance for every group between the dominance hierarchy as assessed by fights and the hierarchy as assessed by the mean dominance index (binomial test, P = .031). From the dominance index data it appeared that the dominance status of certain females was very similar. For example, in groups 1 and 3 there appeared to be little difference between the two highest-ranking females in each group (A and L; 0 and &I. In some cases this reflected a true equality between females, but in others there were rank reversals, which balanced each other, over the time required to fill the fight interaction matrix (Fig. 1). For the purpose of comparison, the dominance index was recalculated by omitting all agonistic behaviors that occurred during fights won and lost. Because of possible changes in dominance from test to test, this procedure was preferred to selecting tests in which fights did not occur. Table I1 shows that, except for group 5, there was complete concordance again between the fight rank order and the dominance index rank order calculated in this way. In group 5, however, there was a rank reversal between females B and C between the second and third tests (Fig. 11, which resulted in large test-to-test variance in dominance indices calculated by both methods. This produced almost identical means per test for both females that were slightly higher for female B when all agonistic interactions were used and slightly higher for female C when fight interactions were excluded. Dominance Index Compared With Other Behaviors and Observer Ratings In order to examine how the dominance index compared with other behavioral measures and with observer ratings of dominance rank, the data from the three tests with group 1were analyzed in greater detail. Table I11 gives, for each female, the means per test for the dominance index and for various other measures of dominance during the same three tests. Also given are the mean observer ratings for each female obtained one week later. There was quite close agreement between the objective and subjective measures of relative dominance but not between these and percent approaches made and departures received. Figure 2 compares the dominance indices of females during each of three tests without a male (left) and during three tests with a male (right) conducted six months later. The dominance index for a given female generally remained quite stable despite large test-to-test variations in the total numbers of agonistic behaviors. However, the relative dominance status of female E was clearly higher during the later sampling time than during the earlier one. Application of the Dominance Index Does the dominance index have any utility? Since it provides a numerical TABLE 111. Comparison of the Dominance Ranks of 4 Female Rhesus Monkeys (Group 1) as Assessed by Dominance Index, Other Behavioral Measures, and Observer Rating (Means SEs for 3 Daily Behavior Tests and 4 Observers) Female A Female L Female E Female I Behavioral measures % submission % approaches made + Observer given received % departures received rating Dominance index % aggression 96 k 2.2 90 k 9.0 34 k 0.8 0.3 k 0.3 91 f 4.4 91 f 6.9 35 k 1.6 0.6 _+ 0.6 100 k 0.0 89 f 11.1 39 f 5.6 0 0.0 * 52 86 41 4 k 13.7 k 2.7 k 8.0 k 4.2 86 81 35 13 f 2.4 k 3.8 f 9.9 k 3.3 Dominance Index I 297 AGONlSTlC BEHAVIORS PER TEST: ./:\26 WITH MALE WITHoUT MALE 66 e 129 100 75 50 25 a 0 Q Q - I 1/15 x-x-x -Female I 1 1/16 1/19 6/15 6/16 6/17 Fig. 2. Comparison of test-to-test changes in the dominance indices of group 1 females during three successive tests without a male Ueft) and during three successive tests with a male (right) conducted six months later. In both situations, the dominance index for each female remained stable, although there were large differences in the numbers of agonistic behaviors occurring in tests. The dominance status of female E was consistently higher in tests with a male than in those without one. measure for every test in which a n individual has any agonistic interactions with others, it can be used to monitor changes in relation to other variables; this is illustrated in Figure 3. The dominance index profiles are shown for the females in group 4 during a long-term experiment reported elsewhere [Michael & Zumpe, 19841, in which the hormonal status of every female and the identity of the male in the group were varied systematically. Female rank order, assessed by the mean dominance index for the whole experiment with each male, remained constant throughout. However, there were marked temporary changes in relative dominance, and even temporary rank reversals; these occurred when the male was changed and when females were treated with hormones. For example, when male 3 was replaced with male 4,the dominance index of female J declined to well below that of female K (both untreated) (Fig. 3, top panel). The dominance index profiles also changed when females were treated with ovarian hormones (Fig. 3, middle and lower panels). When females were given estrogen, the dominance index increased in 12 of 16 cases (sign test on data from four females with each of four males, P = .038). DISCUSSION Like more familiar methods of determining rank order, the dominance index is based on the direction of aggressive and submissive behaviors between the members of all possible paired combinations of individuals in a group. Our data were derived from female-female interactions but could be derived equally well from female-male or male-male behavior. A behavioral index can be validated in terms of other behavioral measures, and one does this by testing for concordance with other, often simpler, behavioral measures. The dominance index was found to be perfectly concordant with fight interaction ranks (Table 111, and with aggression given, submission received, and observer ratings (Table III) in the five groups for which fight matrices could be constructed. The advantages of the dominance index are that it utilizes both aggressive and submissive behavior and that it can be calculated when agonistic interactions are too infrequent to calculate one of the other two measures reliably. There was also good agreement between the dominance index and mean observer ratings. Observers were, however, clearly reluctant to employ the extremes of the rating lines, and this was reflected in a 27% restriction of the range utilized. Percent approaches made and departures received did not agree well with any of the 298 I Zurnpe and Michael MALE : FEMALE: I K J N M 2 3 K J N M K J N M 4 K J N M FEMALE UNTREATED r-l I I h h 0 h N= I 21 28 25 24 20 24 25 6 15 20 20 18 14 24 20 FEMALE GIVEN EB 83 oL N= 5 5 3 5 4 5 5 5 2 3 5 4 1 5 4 5 2 5 FEMALE GIVEN E B + P N* 3 4 1 4 3 5 5 4 4 1 2 3 0 0 Fig. 3. Changes in the dominance index profiles of group 4 females occurring with changes in the identity of the male in the group and with changes in the hormonal status of females. EB = 10 pg estradiol benzoate sciday. EB + P = 10 pg estradiol benzoate and 50 mg progesterone sc/day. N = number of tests for which dominance index could be calculated. Vertical bars give standard errors of means. other measures of dominance; it is obviously affected by many extraneous factors. It was not possible to compare the dominance index described here with the method developed by Boyd & Silk  because the latter cannot be used unless there are values in the cells below the diagonal of the interaction matrix. The dominance index is simple to calculate and offers certain advantages. It can be used to assess dominance in stable groups in which fights are infrequent and in which rank order is maintained by occasional threats or submissive gestures. Such situations are encountered in long-term studies with captive groups and in the wild. Even in our newly formed groups of adult rhesus monkeys, in which aggression frequencies are considerably higher than in stable natural troops, it required up to four months to collect sufficient data to produce a fight interaction matrix (Fig. 1, group 41, and in many groups it was never possible to do so. Consequently, the assessment of ordinal rank by fights ignores temporary (or even permanent) rank reversals during the period of data collection. Such reversals would produce values in the cells below the diagonal of the fight interaction matrix. In contrast, the dominance index gave almost identical values when calculated for tests including or Dominance Index / 299 excluding fight interaction data (Table II), and it was to a large extent independent of the total numbers of agonistic interactions taking place (Fig. 2). Thus, it can be used with data collected during a relatively short time interval (one hour in our case) and helps provide a numerical estimate of short-term changes in dominance. The dominance index gives both a n animal’s position in the dominance hierarchy (ordinal rank) and its dominance status in relation to others (cardinal rank); that is, the index can measure whether a n animal outranks another by a wide or a narrow margin. It also identifies social isolates with regard to agonistic interactions; namely, those animals for which the dominance index cannot be calculated. Finally, the dominance index is very versatile and can be adapted to specific situations. For example, certain agonistic behaviors (eg, contact aggression and flight) may be given greater weight than are others, or depending on the type of information sought, the dominance index may be calculated for a social group as a whole or for specific subgroups, such as matrilines. The dominance index is likely to be most useful in situations in which the method of Boyd & Silk  cannot be conveniently used. These include small groups of animals in which agonistic frequencies are low, situations in which there are insufficient data for the construction of fight interaction matrices, and situations in which there are no reversals during overt fighting. The dominance index does not take the place of other measures of agonistic behavior, such as aggression and submission frequencies, but provides a n additional measure for studies that focus on dominance relationships. This index, like other proportional measures, is not normally distributed, and, as for the majority of behavioral measures, the index of one animal is not completely independent of those of other group members. Despite these shortcomings, it has proven to be a very useful measure of the influence of dominance in our own behavioral work. CONCLUSIONS 1. A dominance index has been developed which is based on the direction of agonistic interactions between all individuals in a social group. It is simple to calculate and is largely independent of changes in the absolute numbers of agonistic interactions. 2. In five groups of female rhesus monkeys, there was complete concordance between rank orders produced by the dominance index and those produced by fight interaction matrices. There was also good agreement with two other measures of agonistic behavior and with observer ratings. The dominance index can, therefore, be considered a reliable measure of both ordinal and cardinal rank. 3. Because the dominance index can be calculated when fights with unambiguous outcomes do not occur, it is suitable for studies with short sampling periods and with stable groups of animals in a wide range of situations. ACKNOWLEDGMENTS This work was supported by USPHS grant MH 19506, and general research support was provided by the Georgia Department of Human Resources. Both are gratefully acknowledged. REFERENCES Bernstein, IS. Dominance:The baby and the Hinde, R.A.; Spencer-Booth, Y.. The behavbathwater. 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