Model Syn Agg Call Ini OMU Sex ratio Swelling size AIC 400 398.02 397.93 395.01 392.25 389.55 388.87 D AICi 11.13 9.15 9.06 6.14 3.38 0.68 0 Primates (2011) 52:373–383 Table 4 Rank of 7 models used to predict success of copulation using Akaike’s information criterion (AIC) 379 Likelihood Akaike’s weight Evidence ratio 0.004 0.010 0.011 0.046 0.185 0.712 1 0.002 0.005 0.005 0.024 0.094 0.362 0.508 261.1 97.0 92.8 21.5 5.4 1.4 1 Presented are AIC, D AICi, Akaike’s weight and evidence ratio (best model in comparison with model i). The best model is the model with the lowest AIC (relative swelling size) and, consequently, with a D AICi of 0 Fig. 3 Best single-variable model: relationship between relative swelling size and predicted probability of successful copulation. Shown are predicted mean values and 95% conﬁdence intervals. Model variables:relative swelling size: b = 0.028 (95% bCI: 0.010–0.046), exp(b) = 1.029 (95% bCI: 1.001–1.048), z = 3.02, p = 0.003; constant = -2.47 (95% bCI: -3.95 - [-0.94]). Random effects variable ‘‘Female identity’’: SD = 1.03 (SE = 0.19) model including sex ratio and relative swelling size has the lowest AIC and therefore best approximates the data set. Comparison of the AIC-related measures shows that none of the other models is truly competitive with the best model. The next two models, which include (a) swelling size and initiation and (b) swelling size alone, both have a D AICi of 9.18 and are less likely to be the best model by a factor of 98.5. According to the best two-variable model, copulation success was positively related to relative swelling size and negatively related to the sex ratio. With relative swelling size constant, the odds of a successful copulation decreased by 0.60 (95% bCI 0.53–0.73) with each unit increase in sex ratio. The odds of a successful copulation increased by 1.03 (95% bCI 1.011–0.1.046) for a 1% increase in relative swelling size, if sex ratio is kept constant. The relationship between the predicted probability of successful copulation and relative swelling sizes is plotted for three sex ratios (2, 3, and 6 females) in Fig. 4. Extra-group copulation Four females from two OMUs were observed to copulate with males other than their leader male on 29 occasions (4.0% of 734 observed copulations). Twenty-four cases involved copulation between juvenile males and four females from two OMUs, and ﬁve involved a subadult male copulating with three females from two OMUs. OMU leader males were never seen to participate in any sexual interaction with females of an OMU other than their own. All extra-group copulation was initiated by females and they occurred on the periphery of the group only, out of the sight of the leader male. Both participants looked fre- quently in the direction of the leader male during the encounter. Of the copulations with juvenile males, 14 were deﬁnitely not successful and in 10 cases the outcome was unknown. In 9 of these 24 cases, the female had a large swelling. One copulation of the subadult male deﬁnitely resulted in ejaculation, three were not successful, and the outcome of the ﬁfth case was unknown. The successful copulation was accomplished when the female had a large swelling. In the other four cases the swellings were small. In 27 (23 juvenile male, 4 subadult male) of the 29 cases, females were members of the OMU with the most female- biassed sex ratio (OMU D which had 6 females); this included the one successful copulation by the subadult male. In none of the subadult male’s copulations and in only 5 of the juvenile male’s copulations was the criterion for ‘‘synchrony’’ fulﬁlled. Discussion Our study is based on two questions about the copulation patterns of hamadryas baboons: 1. what determines the success of a copulation; and 2. does extra-group copulation occur? Results from our AIC model selection approach showed that relative swelling size was the most important single 123