376 1999; Zinner et al. 2004). We therefore measured size to determine the reproductive status of females, using pho- tographs of female swellings taken with a digital video camera on each day of the study period. Relative swelling size was estimated, by use of ‘‘Adobe Photoshop 10.0’’, as the ratio of swelling width (sw) to the maximum length of the ischial callosity (cal) where width was deﬁned as a line from the edge of the swelling at a central position of the ischial callosity to an imaginary central axis through the anal and vaginal oriﬁces (Fig. 1). Relative swelling sizes for each female were calculated as percentages of the biggest swelling of the respective female. Swelling sizes were categorized into two states, deﬁned as follows: small = 0–50% of maximum swelling size of the respec- tive female; large = 51–100% of maximum swelling size of the respective female. Statistical analysis We analysed the data on two sample size levels: 1. sample size based on the number of individual females; and 2. sample size based on the number of copulations. For analyses on the ﬁrst, inter-individual, level we used non-parametric tests (SPSS for Windows, Rel. 12.0; SPSS, Chicago, USA) with alpha set at 0.5. For analyses on the second, intra-individual, level we used multilevel logistic regression, which takes into account repeated observations of individuals by including female identity as a random factor in the model. We estimated the models using mul- tilevel logistic regression analysis with maximum likeli- hood estimation to predict the probability of a successful copulation. Estimates are presented with bias-corrected Fig. 1 Schematic diagram of female hamadryas baboon anogenital swelling depicting sections of measurement used in the analysis: SW, swelling width at callosity midline; cal, ischial callosity length 123 Primates (2011) 52:373–383 accelerated bootstrap conﬁdence intervals (bCI; Efron and Tibshirani 1993), which are robust against possible viola- tion of the assumptions of logistic regression. Additionally, the ﬁnal models were rerun with an interaction between the ﬁxed factors and the random factor ‘‘female identity’’ (random slope). Almost no variance was estimated for these random effects and results changed only marginally. The assumptions of multilevel logistic regression were assessed by plotting predicted values against binned residuals (Gelman and Hill 2007). Similar multilevel linear regression analysis was used for analysis of the duration of copulation. Analyses were done using STATA 10.1 (StataCorp. 2007. Stata Statistical Software: Release 10; StataCorp LP, College Station, TX, USA). We used Akaike information criterion (AIC) model selection to select from our candidate set of models the one that best approximated our data set (Burnham and Ander- son 2002; Claeskens and Lid 2008). The AIC is a measure of the goodness of ﬁt that includes a penalty for the number of variables estimated. AIC selects the best of several competing models as that which predicts best in a new data set. The best model is the one with the lowest AIC. Unlike model selection based on Null-hypothesis testing, AIC model selection enables an evaluation of the quality of other models by assessing AIC-related measures (Delta D AICi, Akaike’s weight and evidence ratio). D AICi is the difference in AIC between model i and the best model. As a rule of thumb, a D AICi value of \2 times the AICi of the best model has substantial support and should be consid- ered with the best model. A D AICi value [4 times the AICi of the best model has substantially less support and models with a D AICi [ 10 times the AICi of the best model can be omitted from further consideration (Burnham and Anderson 2002). Akaike’s weight is an estimate of the probability that model i is the best model among the can- didate set of models. The evidence ratio for a given model i is the ratio of Akaike’s weights of the best model and of model i. Unlike Akaike’s weight, the evidence ratio of two models is independent of other candidate models. Because of the small number of females and observa- tions in our data set, our main model selection analysis is based on single-variable models. In a second step, we used the single best predictor and compared models with this variable and one of the remaining variables. As possible predictor variables, we assessed: synchrony (yes/no), male aggression (yes/no), female copulation calls (yes/no), ini- tiation of copulation (male/female), OMU ID (equal to male ID), sex ratio, and relative swelling size. Model selection was done using the complete case data set (n = 301). The parameters of the ﬁnal best models were estimated using all available data of the selected variables (n = 347). Estimates differed only marginally between the two data sets.