Cohort size and the allocation of social effort by female mountain baboons

Anim. Behav., 1997, 54, 1235–1243

Cohort size and the allocation of social effort by female mountain baboons S. PETER HENZI*, JOHN E. LYCETT* & TONY WEINGRILL† *Behavioural Ecology Research Group, University of Natal †Anthropological Institute, University of Zu¨rich (Received 16 October 1996; initial acceptance 11 December 1996; final acceptance 28 February 1997; MS. number: 5358)

Abstract. Dunbar (1992, Behav. Ecol. Sociobiol., 33, 35–49) argued that constraints on social time limited the size to which savannah baboon, Papio cynocephalus, troops in any given population could grow before fissioning. Since this should be reflected in population structure, we have elsewhere (Henzi et al. 1997a, Anim. Behav. 53, 525–535) constructed a model, based on a rising probability of fission, that fits the observed distribution of troop sizes of mountain baboons, P. c. ursinus, in the Drakensberg mountains of South Africa and which predicts that the probability of fission will rapidly increase once a troop has more than 23 members (or 8.7 females). We test this prediction in this paper. Since Dunbar argued that females will drive fission once they cannot engage in the grooming necessary to sustain alliances, we compared the grooming interactions of adult females from four troops in the Drakensberg mountains. The mean female grooming clique size reached an asymptote at 7.4 females, so that females in cohorts of eight or more no longer attempted to groom all other females, and mean grooming bout length declined as the cohort grew to 7.9 females and then increased again. These values are coincident with the female cohort size predicted by our model of troop growth and fission. We argue that females attempt to groom all other females as well as sustain closer relationships with a few females through longer bouts of reciprocated grooming. When the demands of grooming all other females reduce bout length to a point when no reciprocated bouts are possible, female clique size is capped. As a troop continues to grow, the mechanical difficulties involved in gaining access to grooming partners leads to a reduction in the diversity of grooming relationships. This weakening of the total female network, as cliques become more differentiated, is likely to facilitate fission. We conclude that our data provide the first within-population validation of Dunbar’s hypothesis concerning the mechanism underpinning fission. In the Drakensberg, where there is no advantage to female coalitions, we propose, as an amendment, that females will leave a troop not to escape local competition, but to follow a male with ? 1997 The Association for the Study of Animal Behaviour whom they have a close friendship.

The most comprehensive attempt yet to link individual action with the population structure of a primate species has been that of Dunbar (1992, 1993). This extended van Schaik’s (1983) earlier proposal regarding the costs associated with group living by arguing that increasing troop size eventually leads to fission, not as a direct result of a decline in individual foraging efficiency but because the effort involved in foraging leads to a reduction in the time Correspondence: S. P. Henzi, Department of Psychology, University of Natal, King George V Avenue, Durban 4001, South Africa (email: henzi@ mtb.und.ac.za). T. Weingrill is at the Anthropological Institute, University of Zu¨rich-Irchel, CH-8057 Zu¨rich, Switzerland. 0003–3472/97/111235+09 $25.00/0/ar970520

available for the maintenance of strategic social relationships. Cross-population data on savannah baboons, Papio cynocephalus, indicate that the probability of fission should rise with troop size (Dunbar 1992). This is a consequence of the fact that, while rising competition for resources in larger groups requires larger coalitions, the decreasing amounts of ‘free time’ and an inherently larger number of possible relationships make it less and less likely that the necessary relationships can be serviced. While there are data to suggest that baboons use coping strategies, such as conserving grooming time by cutting back on resting time (Dunbar & Sharman 1984), there will come a point from which a growing troop can be said to be

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‘demographically stressed’ (Dunbar 1992) and can no longer compensate for these increased social demands. Since this point is set by local conditions (inter alia thermal demand, amount and distribution of food and water), testing Dunbar’s hypothesis necessitates work within, rather than between, populations (see also Bronikowski & Altmann 1996). In this regard, chacma baboons, P. c. ursinus, living in the Drakensberg mountains (‘mountain’ baboons) of South Africa offer an excellent opportunity to assess the relationship between ecology, sociality and population events, as the population is large and undisturbed, while the terrain makes it unusually easy to get an estimate of its structure and demography (Henzi & Lycett 1995). Having confirmed that the probability of fission and attempted fission increases with troop size, we have elsewhere used this to model the distribution of troop sizes in the population (Henzi et al. 1997a). The best-fit model makes two predictions: that the smaller of the two troops resulting from fission will be 0.34 times the size of the original troop and that the probability of a troop splitting will rapidly increase as the troop grows from 23 (P~0) to 29 (P~1) members. The first of these predictions has been confirmed (Henzi et al. 1997a) while the second is a focus of this paper. Among mountain baboons, the expression of fission is neither retarded by the threat of predation nor accelerated by any foraging cost associated with growth in troop size (Henzi et al. 1997a,b; see also Henzi & Lycett 1995 for the absence of troop size-related effects on recruitment). There is a sense, then, in which the elimination of these extraneous influences provides sufficient support for Dunbar’s proposal, since neither Wrangham’s (1980) original model, nor van Schaik’s (1983) extension, can be said to predict, as the proximate mechanism affecting group cohesion, a rising probability of fission in the absence of direct nutritional costs to any members of a troop. By the same token, however, Dunbar’s hypothesis is predicated on the assumption that fission is a consequence of the breakdown of coalitionary relationships. Despite the fact that mountain baboon troops are female-bonded (Henzi 1996a), there is, as with other chacma baboon populations (Henzi 1996b), little

indication of alliance formation. Indeed, mountain baboon troops are, as a consequence of the dispersion and size of food items (Henzi et al. 1992), characterized by very low rates of agonism (Barton et al. 1996; unpublished data). Without any foraging costs associated with increasing troop size, and no need for coalitionary relationships, there should be no impetus for fission. Conversely, the absence of predation implies that there should be no need for individuals to remain within a larger troop, an implication confirmed by the independent existence of troops with as few as four members (Henzi & Lycett 1995; personal observation). The fact, therefore, that we observe a rising probability of fission with troop size suggests that, in the absence of ecological variables, social factors must, in some way, influence individual decisions over group membership. Clearly, an explication of the relationship between the allocation of social effort and the emergence of shear forces within a growing troop is necessary if we are to evaluate Dunbar’s argument as it might apply to mountain baboons. One obvious possibility is that there is an intrinsic disinclination or inability on the part of females to pursue, beyond a certain point, the growing number of relationships that accompany an increase in troop size (Dunbar 1984). If this were so, any consequent weakening in the overall linkage of relationships within a group may on its own be sufficient to lead, with time, to fission, should other factors coincide. Accordingly, in this paper, after determining the extent of time budget constraints on female grooming, we test two hypotheses. (1) The diversity of female–female grooming decreases with increasing female cohort size. In other words, we expect the allocation of grooming effort by females to reflect the fact that they will be less able to interact with all potential partners as cohort size increases, because of time budget constraints. (2) There is a limit to clique size (i.e. the number of females that directly interact with one another; Dunbar 1988) linked, presumably, to the decline in grooming bout length that must accompany any increase in the numbers of grooming partners. If social time constraints do underpin fission decisions then, ideally, we would expect that any capping of network size should tie into the specific predictions of our fission model.

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Table I. Details of study troops

Troop

Locality

OT WA1 WA2 FT HT

Giant’s Castle Giant’s Castle Giant’s Castle Cathedral Peak Cathedral Peak

Troop size 10 14 18 27 36

Males

Females

No. timed female grooming samples

2 2 3 4 7

2 3 6 9 12

63 — 222 525 511

(93) (84) (61) (26) (7)

No. days activity data 30 29 57 57 86

Values in parentheses next to the size of each troop indicate the percentage of troops in the population that are larger.

METHODS Study Sites and Subjects We collected data on four habituated baboon troops at two localities in the Natal Drakensberg (see Whiten et al. 1987; Henzi et al. 1992 for detailed descriptions of the habitat). All four troops used the same broad ecological zone (montane grassland, centred on 1800 m above sea level). One of the troops (WA2) had been worked on 11–12 years earlier (with A. Whiten and R. Byrne) and since it was smaller then and had fewer females, we have used activity data collected from it to provide a fifth data set (as troop WA1) in the analyses of grooming as a component of the activity budget. Details of the troops and data sets are provided in Table I. Data Collection We followed the troops on foot and recorded the activity of all visible animals every 30 min, using the procedure outlined in Whiten et al. (1987). Adult activity was considered to fall in one of four mutually exclusive categories: moving, eating, resting and grooming. ‘Grooming’ in this context was always grooming directed at a second animal. In analyses of these data, time is defined as the proportion of scan records allocated to grooming. The low rate of social interaction under conditions of good visibility allowed us to record the majority of the observed grooming encounters. A grooming bout was defined as a continuous period of allogrooming involving the same two animals. A change of identity of one of the animals or a

shift in activity for more than 10 s signalled the end of a bout. For each observed bout, we recorded the identities of the participants (all adults were individually recognizable), the number of role reversals (groomer becomes groomee) during the bout and its duration (to the nearest s). Data Analysis We used the Shannon–Wiener diversity index (H) to measure the proportion of grooming time (s) given by each female to every other female in each of the four groups, using the formula: H= "Ópi (ln pi) where p is the relative proportion of grooming given to the ith female. Note that diversity increases with the increasing value of H. However, since diversity depends not only on the way in which proportions are distributed but also on the number of categories (individuals), the observed values of H are meaningful only in relation to the natural increase in H (HMAX) with cohort size, where: HMAXn(i) =ln n(i). To allow comparison across cohorts we determined the difference between HMAXn(i) and H(i). If this value increases with n(i) it is reasonable to conclude that diversity has decreased. Only the activity data for adult females are used in the analyses. Tests were conducted on the contribution of combined female activity scores to

–0.4

Logit proportion

–0.9 –1.4 –1.9 –2.4 –2.9 –3.4

0700 0900 1100 1300 1500 1700 0800 1000 1200 1400 1600 1800 Time of day (hours)

Figure 1. Mean and 95% confidence limits for the proportion of each hour’s activity budget records contributed by grooming. Transformed data are presented.

the overall proportions of each activity type by month or hour. All percentage data were logit-transformed to normalize distributions for statistical analysis and all tests are two-tailed.

RESULTS Representation of Grooming in the Time Budget Effects of group size Although we know that foraging time is unaffected by group size (Henzi et al. 1997a,b) it is not necessarily the case that the same will hold for grooming. To test this, we correlated grooming time with group size, controlling for the amount of time spent foraging. Foraging time was partialled out as there is a significant relationship between this activity and the amount of time spent grooming (Henzi 1996a). There was no significant relationship between grooming and group size (r= "0.06, N=31, ). For the five troops combined, the overall contribution of grooming to the activity budget was 12%. Diurnal distribution of grooming This was characterized by a small number of individuals engaging in grooming during each hour, so that the overall allocation of time to grooming was relatively evenly spread throughout the 12 daylight hours (ANOVA: F11,47 =1.635, ; Fig. 1).

Mean number of female grooming partners

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12 10 8 6 4 2 0

2 Troop OT

6 Troop WA2

9 Troop FT

12 Troop HT

Number of females per troop Figure 2. The mean number of female grooming partners of females in each of the four study troops. The horizontal line above each bar indicates the number of potential grooming partners (i.e. Nfemales "1).

Grooming Dynamics Diversity of grooming partners Females did not persist in grooming all available partners as troop size grew and the average number of female grooming partners (excluding the groomer) reached an asymptote at around 6.4 females (Fig. 2). As the number of possible dyads in troop FT represented a smaller fraction of the number of female–female bouts (72/375) than did those in troop HT (132/230), it is possible, given stochastic variation, that the number of grooming partners recorded in HT is a consequence simply of the fact that the sample size was too small. To assess this, we compared the cumulative acquisition of new dyads in the two troops. While an asymptote was reached after 120 consecutive bouts in both troops, the asymptotic values were 65% of all possible dyads for FT and 48% for HT (Kolmogorov–Smirnov two-sample test: D=0.57, P<0.05). We conclude that the number of grooming partners in HT does represent an asymptotic value. Individual values of H are plotted in Fig. 3 as is the value of HMAX for each cohort size. The best fit to the data is given by a quadratic model: Y= "1.04+0.54X"0.02X2, where Y is H and X is cohort size. Solving for group size generated a summary value of H for each cohort which was compared with HMAXn(i). This comparison

Henzi et al.: Grooming by female baboons 3.0 [0.6]

[1.0]

H

Bout length (s)

[0.5]

2.0

1.0

0

[0.6]

2 Troop OT

6 9 12 Troop WA2 Troop FT Troop HT

Number of females per troop Figure 3. A comparison of H (/) for each female, with quadratic model fitted, and HMAX (;). The difference between HMAX and the summary value of H for each troop is given in parentheses above the value of HMAX for each troop. H is the observed Shannon–Wiener diversity index, obtained for each cohort and HMAX is the maximum diversity possible for a cohort of that size.

(Fig. 3) also suggests that diversity remains constant until the cohort is larger than 10, after which it declines. Using the median value of H for each cohort gives the same result. Grooming bout length When the lengths of all female–female grooming bouts are compared among the four troops, the data show that grooming bout length drops to a minimum value and then rises again, even though cohort size continues to grow (Fig. 4). Since females contribute a varying number of bouts to the data set and as bout lengths are not normally distributed (see Fig. 6 below), we condensed each female’s bouts into a single value (total time groomed/number of grooming bouts) and tested for differences between groups using the Kruskal–Wallis one-way ANOVA by ranks. Despite restricting the data set in this way, the results nevertheless approach conventional levels of significance (÷23 =6.5, P<0.1). This suggests that there comes a point, associated with a critical cohort size, when the allocation of grooming time is reapportioned. In terms of our hypothesis, this should be linked to the maximum number of females that can form a single grooming clique. Fitting a quadratic model to the full data set yielded the following equation: Y=1010.45" 145.214X+9.139X2, where X is the size of the female cohort and Y is the length of the grooming

1200 1100 1000 900 800 700 600 500 400 300 200 100 0

2 Troop OT

1239

6 9 12 Troop WA2 Troop FT Troop HT

Number of females per troop Figure 4. Mean bout length and 95% confidence limits (N=358 bouts) for female–female grooming in each of the four study troops. The curve indicates the values predicted by the quadratic model.

bout. This equation can be used to predict the number of females present in a troop when the bout length curve reaches its lowest point. Solving for cohort size gives a value of 7.9 females when bout length is at its shortest (433 s). Exactly the same value was given by the quadratic model fitted through the restricted data set (mean bout length per female), although the estimate of minimum bout length shifted upwards to 498 s. Female–male grooming bout length did not differ significantly between groups (Kruskal– Wallis one-way ANOVA: ÷23 =1.82, ). Reversals of direction in grooming As has been observed for other species (Rowell et al. 1991), a proportion of all the bouts in this study were characterized by one or more reversals, where the groomer became the recipient of grooming. Since the regression of the number of such reversals onto bout length was positive in all four troops (rOT =0.66, N=29, P<0.0001; rWA2 =0.67, N=171, P<0.0001; rFT =0.79, N=375, P<0.0001; rHT =0.7, N=230, P<0.0001), it may be that the effect of grooming for group stability lies less with the loss of time as such, but with the loss of opportunity for within-bout reciprocation and the decline in cohesion that this implies (Cheney 1992). Not surprisingly, the proportion of bouts in each troop in which there was at least one reversal

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Proportion

1.0

0.5

0

2 Troop OT

6 9 12 Troop WA2 Troop FT Troop HT

Number of females per troop Figure 5. The proportion of all female–female grooming bouts, for each of the four study troops, in which there was at least one reversal of grooming direction.

of direction mirrored the distribution of mean bout lengths across the four troops (Fig. 5). For the three largest troops, by far the single most prevalent grooming bout was one that involved no reversals. Nevertheless, the distribution of the number of reversals for these troops did not conform to the Poisson model (Fig. 6). Contributions to the overall chi-square indicate that females in each of these troops engaged both in bouts without reversal as well as in bouts of three or more reversals more frequently than expected.

DISCUSSION Our analysis of the activity budgets indicates that our four mountain baboon troops had similar amounts of time available to them for grooming and that this time was used in the same way: short grooming bouts spread evenly across the day. The observed differences in grooming behaviour between our four study troops, and the bearing that these are presumed to have on fission, must, therefore, be a direct consequence of the size of the female cohort. The fact that ‘femalebondedness’ intensified with troop size (Henzi 1996a), together with the observation that female– male bout lengths were similar across groups, makes it likely that female–female relationships underpin the shift in fission probability. In line with this, two of our findings converge to suggest that there is an upper limit to the number

of females that can be adequately linked within a single social clique (sensu Dunbar 1984). The first is that grooming clique size reaches an asymptote at 7.4 females (6.4 partners plus the groomer: Fig. 2); the second is that when bout length is at its lowest, the size of the female cohort was estimated to be 7.9 females. From our population census (Henzi & Lycett 1995) we know that the number of females (F) is strongly correlated with group size (G), such that F= "0.497+0.4G (r28 =0.94, P<0.0001). Using this equation to solve for group size, we find that groups containing at least 7.6 females must have at least 20.2 members (21.2 if we assume eight females). This is sufficiently close to the predicted value for the largest stable troop (N=23; Henzi et al. 1997a), both to satisfy the general terms of our model and to support our argument that fission is a consequence of social constraint. Since the observed upper limit on clique size in our population is smaller than the apparently asymptotic values recorded by Sambrook et al. (1995) for two savannah troops (9.6 and 11.5, respectively) we are clearly not dealing with a fixed constraint, such as might be imposed by cognitive capacity, but with one that is derived from local circumstances. What we need to explain is how local conditions lead to this value and how, in turn, exceeding it can generate fission in a population where there is very little contest competition for resources and where, consequently, coalition formation is absent. We propose that the limit on clique size is an unavoidable consequence of living in an environment where food is scarce and hyper-dispersed (Henzi et al. 1992). Under these circumstances, foraging effort is constant (Henzi et al. 1992, 1997b), so that grooming opportunities must be created on the run, as it were, for short periods, with partners who are likely to be foraging some distance away (Barton et al. 1996; Henzi et al. 1997a). Negotiating grooming is therefore likely to become more difficult as the cohort grows, both because group spread increases linearly (Henzi et al. 1997a), making it more difficult to reach a desired partner if she is not nearby, and because the number of possible relationships is proportional to the square of cohort size, so that the desired partner is increasingly likely to be already engaged in grooming. This means that, even without active competition for access to partners, there will be problems with the

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120 Troop OT 2

χ 2 = 0.7, NS

8

Troop WA2 100

2

χ 2 = 47.9, P < 0.0001

80 6 60 4 40

Frequency

2

0

20

0 1 2 3 4 5 6 7 8 9 10 11

200

Troop FT

0

150

2

Troop HT 2

χ 3 = 74.8, P < 0.001

χ 3 = 109.2, P < 0.0001

160

120

120

90

80

60

40

30

0

0 1 2 3 4 5 6 7 8 9 10 11

0 0 1 2 3 4 5 6 7 8 9 10 11 0 1 2 3 4 5 6 7 8 9 10 11 Number of reversals

Figure 6. Observed frequency distributions of the number of grooming reversals for troops OT, WA2, FT and HT. Observed distributions are compared with those predicted by the Poisson model (——).

coordination of access: with prospective partners either foraging, being too far away, or being groomed by someone else. Such ‘mechanical’ difficulties should induce a reduction in diversity in the distribution of grooming effort as soon as there are more than two females, on the grounds that a partner to hand should be interacted with while she is available. Such bouts will be longer and involve reciprocity. If, as is likely, reciprocated grooming strengthens

relationships, then we should see the emergence of cliques. At the same time, the observation that bout length declines before grooming clique size is capped implies that there is an impetus by females to groom all other females. The data for WA2, a troop for which the model predicts stability, indicate that females can, by and large, still groom all other females, by employing two strategies: engaging mostly in short grooming bouts, with no

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reciprocity, and grooming a few females for longer, reciprocated bouts (troop WA2 in Fig. 6). Doing this results in the maintenance of diversity (Fig. 3) and suggests that the divergence of bouts into very short and long clusters is an attempt by females to solve their social dilemma. As the cohort grows to eight females, bout lengths would decline to a point where reciprocity would not be possible (see Fig. 5, where an extension of the line joining OT and WA2 to the X-axis indicates a cohort size of 7.9 females when grooming bouts contain no reversals), preventing females from satisfying the two conflicting demands of grooming all females while still maintaining a set of close relationships, characterized by longer, reciprocated grooming bouts. Beyond this point, females therefore respond by limiting the size of their grooming cliques, with diversity decreasing and mean grooming bout length rising as a consequence of the greater incidence of long, reciprocated bouts (troops FT and HT in Fig. 6). We might expect all measures of the allocation of social effort to level out at this point, provided that grooming partners forage in the vicinity of one another, simply because we find no increase in inter-individual distance with increasing group size (Henzi et al. 1997a). The fact that they do not is, we argue, due to the intensifying difficulty of coordinating access. So, in much the same way, then, that human conversational cliques may be limited by acoustic constraints rather than strategic concerns (Cohen 1971), the emergence of cliques in mountain baboon troops may be no more than an unavoidable canalization of relationships imposed by local environmental parameters. If similar organizational principles, where simple decision rules operating locally bring about conspicuous patterns on a larger scale (te Boekhorst & Hogeweg 1994), are true of other populations and species then we may have a purely mechanical explanation for the failure to find a relationship either between female grooming diversity and participation in inter-troop encounters, or between the strength of female hierarchies and grooming diversity in femalebonded primates (Cheney 1992). In any respect, this conceptualization of the structural roots of social form has important ramifications (te Boekhorst & Hogeweg 1994) and needs to be investigated empirically in relation, we suggest, to appropriate modelling (see Hogeweg & Hesper 1985).

Lastly, one consequence of rising cohort size is that we see the emergence of a small set of females that is markedly male-bonded (Henzi 1996a). If access to other females becomes increasingly difficult, then some females may find that males offer the best prospect of primary relationships. If a male then leaves a troop, his female grooming partners may therefore accompany him (Henzi & Lycett 1992). This is a realistic option for females in the Drakensberg, where there are no negative consequences to life in small groups. While we will consider elsewhere the relationship between cohort size, linkages among cliques and the emergence of male friendships, our data do indicate that 10 of the 13 fission and attempted fission events recorded during our study have involved a single male. In this way, contrary to Dunbar’s (1992) supposition, fission can occur in populations without contest competition, purely because environmental attributes lead ineluctably to an increasingly rugged social landscape.

ACKNOWLEDGMENTS This study was funded by the National Geographic Society, FRD and URF grants to S.P.H., an FRD fellowship to J.E.L., as well as awards from the Janggen-Poehn-Stiftung, the Marthe Selve-Gerdtzen-Stiftung and the Schweizerische Stiftung fu¨r Alpine Forschungen to A.W. Dr Loulou Barrett eliminated eigenvectors, generated diversity indices and discussed the data at length. We are grateful to an anonymous referee and, especially, to Dr Rene´ te Boekhorst who provided a good natured and invaluable lesson in the use and interpretation of the Shannon–Wiener index. We thank the Natal Parks Board for permission to work in the Drakensberg Park and the Ukuhlamba Steering Committee for allowing us to operate out of the Ukuhlamba Research Centre.

REFERENCES Barton, R. A., Byrne, R. W. & Whiten, A. 1996. Ecology, feeding competition and social structure in baboons. Behav. Ecol. Sociobiol., 38, 321–329. te Boekhorst, I. J. A. & Hogeweg, P. 1994. Selfstructuring in artificial ‘‘chimps’’ offers new hypotheses for male grouping in chimpanzees. Behaviour, 130, 229–252.

Henzi et al.: Grooming by female baboons Bronikowski, A. M. & Altmann, J. A. 1996. Foraging in a variable environment: weather patterns and the behavioural ecology of baboons. Behav. Ecol. Sociobiol., 39, 11–25. Cheney, D. L. 1992. Intragroup cohesion and intergroup hostility: the relation between grooming distributions and intergroup competition among female primates. Behav. Ecol., 3, 334–345. Cohen, J. E. 1971. Casual Groups of Monkeys and Men. Cambridge, Massachusetts: Harvard University Press. Dunbar, R. I. M. 1984. Reproductive Decisions: an Economic Analysis of Gelada Baboon Social Strategies. Princeton, New Jersey: Princeton University Press. Dunbar, R. I. M. 1988. Primate Social Systems. London: Croom Helm. Dunbar, R. I. M. 1992. Time: a hidden constraint on the behavioural ecology of baboons. Behav. Ecol. Sociobiol., 33, 35–49. Dunbar, R. I. M. 1993. Ecological constraints on group size in baboons. Physiol. Ecol. Japan B, 29, 221–236. Dunbar, R. I. M. & Sharman, M. J. 1984. Is social grooming altruistic? Z. Tierpsychol., 64, 163–173. Henzi, S. P. 1996a. Group size and sociality in mountain baboons. National Geographic Society Research Report. Henzi, S. P. 1996b. Copulation calls and paternity in chacma baboons. Anim. Behav., 51, 233–234. Henzi, S. P. & Lycett, J. E. 1992. Male-induced fission as the determinant of mountain baboon population structure. Primate Eye, 48, 7–8.

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Henzi, S. P. & Lycett, J. E. 1995. Population structure, dynamics and demography of mountain baboons. Am. J. Primatol., 35, 155–163. Henzi, S. P., Byrne, R. W. & Whiten, A. 1992. Patterns of movement by baboons in the Drakensberg mountains: primary responses to the environment. Int. J. Primatol., 13, 601–629. Henzi, S. P., Lycett, J. E. & Piper, S. E. 1997a. Fission and troop size in a mountain baboon population. Anim. Behav., 53, 525–535. Henzi, S. P., Lycett, J. E., Weingrill, T., Byrne, R. W. & Whiten, A. 1997b. The effect of troop size on travel and foraging in mountain baboons. S. Af. J. Sci, 93, 333–335. Hogeweg, P. & Hesper, B. 1985. Socioinformatic processs, a MIRROR modelling methodology. J. theor. Biol., 113, 311–330. Rowell, T. E., Wilson, C. & Cords, M. 1991. Reciprocity and partner preference in grooming of female blue monkeys. Int. J. Primatol., 12, 319–336. Sambrook, T. D., Whiten, A. & Strum, S. C. 1995. Priority of access and grooming patterns of females in a large and a small group of olive baboons. Anim. Behav., 50, 1667–1682. van Schaik, C. P. 1983. Why are diurnal primates living in groups? Behaviour, 87, 120–143. Whiten, A., Byrne, R. W. & Henzi, S. P. 1987. The behavioral ecology of mountain baboons. Int. J. Primatol., 8, 367–388. Wrangham, R. W. 1980. An ecological model of femalebonded primate groups. Behaviour, 75, 262–300.