In the analysis of social dominance in groups of animals, linearity has been used by many researchers as the main structural characteristic of a dominance hierarchy. In this paper we propose, alongside linearity, a quantitative measure for another property of a dominance hierarchy, namely its steepness. Steepness of a hierarchy is defined here as the absolute slope of the straight line fitted to the normalized David's scores (calculated on the basis of a dyadic dominance index corrected for chance) plotted against the subjects' ranks. This correction for chance is an improvement of an earlier proposal by de Vries (appendix 2 in de Vries, Animal Behaviour, 1998, 55, 827-843). In addition, we present a randomization procedure for determining the statistical significance of a hierarchy's steepness, which can be used to test the observed steepness against the steepness expected under the null hypothesis of random win chances for all pairs of individuals. Whereas linearity depends on the number of established binary dominance relationships and the degree of transitivity in these relationships, steepness measures the degree to which individuals differ from each other in winning dominance encounters. Linearity and steepness are complementary measures to characterize a dominance hierarchy.

Estrone conjugates (E1C), pregnanediol glucuronide (PdG), and estriol (E3) in urine, and immunoreactive E1C, E3, pregnanediol (Pd), and progesterone (P4) in feces were determined along with records of perineal sex skin swelling throughout 7 nonconception cycles and 3 full-term pregnancies of 4 adult female bonobos (Pan paniscus). A typical preovulatory urinary E1C surge and postovulatory increase in urinary PdG were seen during the menstrual cycles. Fecal progestin levels were significantly correlated with those of PdG in urine in all cycles, while E1C measurements in feces were significantly correlated with those in urine in only 3 cycles. On the basis of hormone profiles, a variable follicular phase of 17-40 days and a relatively constant luteal phase of 11-15 days was found, resulting in cycle lengths of 31-51 days. All urinary and fecal hormones were markedly elevated during pregnancy. Measurement of E1C in both urine and feces was most useful for early pregnancy diagnosis, while E3 was of value in confirming pregnancy and assessing fetal viability. The period of perineal swelling during the cycle comprised on average 66.3% of cycle length, half of which was associated with a phase of maximum tumescence. Ovulation usually occurred within the maximum swelling phase, but timing of ovulation within this period was highly variable and was more closely associated with the end rather than the onset of maximum tumescence. The data presented here are of great practical value in the captive breeding management of bonobos and offer new opportunities for investigating basic questions of bonobo reproductive biology both in captivity and in the wild.

Bonobos have a reputation as a female-dominated and egalitarian species. We examined the 2 aspects of dominance in 6 captive bonobo groups. Females do not consistently evoke submission from all males in all contexts. Though females occupy the highest-ranking positions in the dominance hierarchy, there are in each group males that obtain rather high ranks and are able to dominate ≥1 female. Thus female dominance is not complete and hierarchies can be better described as nonexclusive female dominance. We studied egalitarianism by measuring linearity and steepness of dominance hierarchies. The hierarchies of all groups are highly linear. Hierarchies among males are steeper than among females. On average, male bonobos are more despotic than females, but females too can have despotic relations, both with other females and with males. Hence one can call bonobos in captivity semidespotic rather than egalitarian.

Based on previous research in captivity, bonobos, Pan paniscus, have been called a female-bonded species. However, genetic and behavioural data indicate that wild females migrate. Bonding between these unrelated females would then be in contradiction with socio-ecological models. It has been argued that female bonding has been overemphasized in captive bonobos. We examine patterns of proximity, grooming and support behaviour in six well established captive groups of bonobos. We find that female bonding was not a typical characteristic of all captive bonobo groups. In only two groups there was a trend for females to prefer proximity with other females over association with males. We found no evidence that following or grooming between females was more frequent than between males and unrelated females or between males. Only in coalitions, females supported each other more than male-female or male-male dyads. We also investigated five mother-son pairs. Grooming was more frequent among mothers and sons than in any other dyad, but sons did not groom their mothers more than males groomed unrelated females. Mothers groomed their sons, or provided more support to them than females groomed or supported unrelated males. Thus, while bonds between females were clearly present, intersexual relations between males and either unrelated females or their mothers are of more, or equal importance.

We investigated dyadic grooming relationships in a captive group of bonobos (Pan paniscus) and questioned what social function grooming fulfils in the 'market of services and favors'. Hereto we examined which of two theoretical models - grooming for support (Seyfarth, 1977, 1980) or grooming according to the similarity principle (de Waal & Luttrell, 1986) - best accounted for the observed grooming distribution. Similarity in traits did not correlate with increased grooming or close proximity among the individuals. Therefore, the similarity hypothesis was rejected. Seyfarth's model of rank-related grooming was largely confirmed. The animals distributed their grooming according to the rank of the receivers. We found an exchange between grooming and receipt of support. There was more grooming up than down the hierarchy. However, not all predictions about rank-related competition over grooming were confirmed. We found that dyadic grooming reciprocity indeed increased with decreasing rank distance. Yet, there was no increase of grooming within the dyad with decreasing rank distance and high ranking individuals were not competed over at the highest rates. The observed correlation between grooming and support received represents an important fit with Seyfarth's prediction, but does not allow for conclusions about underlying causal processes. Other causal explanations, besides the 'groom to receive support' hypothesis, that could explain a similar correlation are discussed.

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We studied sex differences in the nature of aggression and dominance behaviour in two newly formed groups of 1-year-old Icelandic horses. One herd contained nine geldings, the other nine mares. The groups were matched with regard to dominancedetermining traits such as age, weaning age, composition of native herd, social experience, genetic origin, body condition and maternal dominance status. Highranking individuals of both sexes were more aggressive, high-ranking males were older, and high-ranking females had a better body condition. Frequencies of aggressions were similar in both groups. The mares reacted significantly more by showing submission upon an aggression rather than by not responding or by escalating the aggression. For the geldings, this difference was not observed due to a lower tendency to submit. A linear dominance hierarchy was found in both groups. David's scores provided additional information regarding cardinal rank distances and were used to calculate steepness of hierarchies. The female hierarchy was somewhat steeper compared to the male hierarchy, suggesting somewhat lower despotism among males. This was mainly a consequence of the lower unidirectionality in male submission. Male contests occurred predominantly between dyads at top and mid positions, suggesting a low degree of acceptance of the hierarchy.

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