Alice Baniel
email: alice.baniel@gmail.com

Guy Cowlishaw

Elise Huchard

Authors Affiliations

Male violence and sexual intimidation in a wild primate society

Keywords: sexual conflict, sexual coercion, intersexual aggression, coercive mateguarding, intimidation, promiscuous mating, injury

Sexual violence occurring in the context of long-term heterosexual relationships, such as sexual intimidation, is widespread across human populations [1][2][3]. However, its evolutionary origins remain speculative because few studies have investigated the existence of comparable forms of sexual coercion in animals [4,5], where repeated male aggression towards a female provides the aggressor with delayed mating benefits [6]. Here, we test whether male aggression towards females functions as sexual coercion in wild chacma baboons (Papio ursinus). We found support for all three main predictions of the sexual coercion hypothesis

) is costly and represents the main source of injuries for cycling females, and (3) increases male mating success with their victims in the future. Detailed analysis of chronological sequences between aggression and matings ruled out other coercive mechanisms, such as short-term harassment and punishment, by showing that aggression and matings are temporally decoupled. This decoupling may explain why some forms of sexual violence have been largely overlooked in well-studied animal populations despite their likely impact on the fitness of both sexes. Finally, we found no support for alternative hypotheses such as a female preference for aggressive males [8,9]. This new, detailed study of the forms and intensity of sexual intimidation in a wild primate suggests that it may be widespread across mammalian societies, with important implications for understanding the evolution of mate choice and sexual conflict in mammals, as well as the origins of human sexual violence.

RESULTS

Animal studies of sexual conflict have focused on its more conspicuous forms, including infanticide [10,[START_REF] Lukas | The evolution of infanticide by males in mammalian societies[END_REF], forced copulations [START_REF] Emlen | Forced copulations and intra-specific parasitism: two costs of living in the white fronted bee-eater[END_REF][START_REF] Knott | Orangutans in perspective: forced copulations and female mating resistance[END_REF], and sexual harassment [START_REF] Clutton-Brock | Mate retention, harassment and the evolution of ungulate leks[END_REF][START_REF] Connor | Patterns of female attractiveness in Indian Ocean bottlenose dolphins[END_REF][START_REF] Cappozzo | Sexual harassment and female gregariousness in the South American sea lion, Otaria flavescens[END_REF]. Pioneering studies exploring more discreet forms of sexual coercion, such as sexual intimidation in chimpanzees (Pan troglodytes), have reported that males who direct repeated aggression towards cycling females are more likely to mate with them around ovulation [START_REF] Muller | Male coercion and the costs of promiscuous mating for female chimpanzees[END_REF][START_REF] Muller | Sexual coercion by male chimpanzees shows that female choice may be more apparent than real[END_REF][START_REF] Feldblum | Sexually coercive male chimpanzees sire more offspring[END_REF][START_REF] Kaburu | Trading or coercion? Variation in male mating strategies between two communities of East African chimpanzees[END_REF]. Besides this work and some anecdotal reports [7,[START_REF] Enomoto | Male aggression and the sexual behavior of Japanese monkeys[END_REF][START_REF] Goodall | The chimpanzees of Gombe: patterns of behaviour[END_REF], the prevalence and evolutionary importance of sexual intimidation in wild primates remain largely unknown. Here, we investigate the occurrence and forms of sexual coercion in wild chacma baboons (Papio ursinus). Chacma baboons live in stable multimale-multifemale groups, where females are philopatric while males disperse and compete for reproductive opportunities [START_REF] Bulger | Dominance rank and access to estrous females in male savanna baboons[END_REF]. Females develop perineal swellings during their oestrus cycle and mate with multiple males [START_REF] Huchard | Can fertility signals lead to quality signals? Insights from the evolution of primate sexual swellings[END_REF], but are often mateguarded by a dominant male when approaching ovulation [START_REF] Weingrill | Male consortship behaviour in chacma baboons: the role of demographic factors and female conceptive probabilities[END_REF], which increases their likelihood of paternity [START_REF] Alberts | Queuing and queue-jumping: longterm patterns of reproductive skew in male savannah baboons, Papio cynocephalus[END_REF][START_REF] Alberts | Sexual selection in wild baboons: from mating opportunities to paternity success[END_REF]. First, we tested the three main predictions of the sexual coercion hypothesis [7]: (1) cycling females face higher rates of aggression from males than non-cycling females ('cycling' refers to all cycling females, with and without swellings), (2) aggression directed by males to cycling females translates into a higher rate of injury, and (3) males achieve higher mating success with those females toward whom they are more aggressive. Second, we characterized the forms of coercion by investigating chronological associations between aggression and matings, in order to differentiate between short-term sexual harassment (where mating immediately follows aggression), punishment (where mating with a rival is immediately followed by aggression), and sexual intimidation (where matings and aggression are temporally decoupled). Finally, we also tested an alternative hypothesis to sexual coercion, postulating that the association between male aggression and mating is driven by a female preference for aggressive males, which may provide direct or indirect fitness benefits to females [8,9].

Does male aggression target cycling females?

We investigated whether the reproductive state of females, defined as swollen (sexually receptive), non-swollen (non-sexually receptive, the non-fertile phase of the cycle), pregnant, or lactating, influenced their chances of receiving aggression from males using a generalized linear mixed model ('GLMM', see Experimental Procedures and Table S1). We found that males preferentially targeted cycling females [swollen: mean±standard deviation: 0.13±0. [START_REF] Feldblum | Sexually coercive male chimpanzees sire more offspring[END_REF] time per hour, i.e., once every 8h; non-swollen: 0.12±0.19, 1/9h] and directed much less aggression towards non-cycling females [pregnant: 0.03±0.08, 1/32h; lactating: 0.03±0.08, 1/32h] (Table S2, Figure 1a). Cycling females could also attract male aggression if they generate frequent conflicts because males regularly intervene in conflicts [5,[START_REF] Smuts | Sex and friendship in baboons[END_REF]. However, cycling females do not initiate more aggression towards other group members than noncycling females (Appendix 1 and Table S3).

Are cycling females likely to be injured by male aggression?

Of the few female injuries with an observed cause, 78% were inflicted by adult males (N=17/22). We tested whether the risk of injury is higher in cycling than non-cycling females using a GLMM (see Experimental procedures and Table S1). Daily rates of female injury varied across the reproductive cycle, and mirrored the rate of male aggression: swollen females received most injuries (0.014±0.022 injuries per day, i.e., 1 injury every 73 days), followed by non-swollen females (0.009±0.016, 1/115), lactating females (0.005±0.010, 1/191), and pregnant females (0.005±0.009, 1/208) (Table S4, Figure 1b). We also found that, within a given cycle, females that faced higher rates of aggression from males suffered more injuries (Table 1, Fig. 2a,b).

Does aggression by males increase their likelihood of mating with the recipient? 3a. Do males use short-term sexual harassment?

To test whether a male was more likely to copulate with a female within 5, 10, 15 or 20 minutes of assaulting her, we used a matched-control analysis [START_REF] De Waal | Reconciliation and redirected affection in rhesus monkeys[END_REF]. We tested the difference in the proportion of observations containing copulations with the aggressor in the postaggression ('PA') and matched-control ('MC') (no aggressive event) observations, using

McNemar's Chi-squared tests (see Appendix 2). We found no support for short-term sexual harassment: the probability of copulation did not increase in the 5-20 minutes following male aggression, for either unguarded (Table S5a) or mate-guarded females (Table S5b).

3b. Do males use punishment?

We used a similar approach to investigate whether the probability of females receiving male aggression increased within 5, 10 or 15 minutes after copulating with a rival male. We tested the difference in the proportion of aggression received from males who had not mated with the focal female in the post-copulation ('PC') and MC (no copulation) observations (see Appendix 3). We found no evidence for punishment either by non-mated males for unguarded females (Table S5a) or by the consort male for guarded females (Table S5b).

3c. Do males use sexual intimidation?

We tested whether a male's probability of mate-guarding a female at her peak fertility (i.e., during her peri-ovulatory period, called 'POP') increased as a function of the mean hourly rate of aggression received by the female from this male prior to her POP, during the same oestrus cycle (calculated using focal observation data). We found that a female who received more aggression from a male throughout her cycle was more likely to be mate-guarded by him during her ovulatory window at the end of that cycle (Table 2, Fig. 2c,d). Overall, females received aggression through their cycle from their future male consort at a rate of 0.04±0.09 times/h compared to 0.01±0.05 times/h from other males. Similar results were found when estimating the rate of male-female aggression using ad libitum data (Table S6).

Do females prefer aggressive males?

This last set of results could possibly result from a female preference for aggressive males, rather than from sexual coercion [8,9]. Under this scenario, we would expect some males to express aggressive phenotypes, and females to express a preference for these aggressive phenotypes. To test this alternative hypothesis, we included an additional fixed effect in the GLMM described above, a proxy of male general propensity to aggression, estimated as the ad libitum daily rate of male aggression initiated toward any individual of the group per year.

In contrast to the dyadic rate of aggression received by a female from a male during an oestrus cycle, a male's general rate of aggression was not found to influence his probability of mate-guarding that female (Table 2, Table S6) .

DISCUSSION

Our study extends previous work on sexual coercion in mammals in three ways. First, our results present new evidence supporting the use of sexual intimidation by wild chacma baboons. Such behaviour, previously reported only in chimpanzees [START_REF] Muller | Male coercion and the costs of promiscuous mating for female chimpanzees[END_REF][START_REF] Muller | Sexual coercion by male chimpanzees shows that female choice may be more apparent than real[END_REF][START_REF] Feldblum | Sexually coercive male chimpanzees sire more offspring[END_REF][START_REF] Kaburu | Trading or coercion? Variation in male mating strategies between two communities of East African chimpanzees[END_REF], may therefore occur in a wider range of primates and strengthens the case for an evolutionary origin of human sexual intimidation [2,3]. Earlier work in baboons has underlined the importance of conditioning aggression by male hamadryas baboons, typically expressed when females leave their spatial proximity [START_REF] Kummer | Social organization of hamadryas baboons: a field study[END_REF][START_REF] Swedell | Sexual coercion in primates and humans: an evolutionary perspective on male aggression against females[END_REF][START_REF] Polo | Behavioural processes in social context: female abductions, male herding and female grooming in hamadryas baboons[END_REF], and has also reported higher rates of male aggression against cycling (versus non-cycling) females in chacma baboons [START_REF] Cheney | Behavior of adult and immature male baboons during intergroup encounters[END_REF][START_REF] Cowlishaw | Behavioural patterns in baboon group encounters: the role of resource competition and male reproductive strategies[END_REF][START_REF] Kitchen | Contextual factors meditating contests between male chacma baboons in Botswana: effects of food, friends and females[END_REF][START_REF] Kitchen | Sexual coercion in primates and humans: an evolutionary perspective on male aggression against females[END_REF]. Our results further link male-female aggression to mating rates, in support of a core prediction of the sexual coercion hypothesis. By attacking females repeatedly in the weeks preceding ovulation, males appear to increase their chances of monopolizing sexual access to females around ovulation, which in turn increases their probability of successful reproduction [START_REF] Alberts | Queuing and queue-jumping: longterm patterns of reproductive skew in male savannah baboons, Papio cynocephalus[END_REF][START_REF] Alberts | Sexual selection in wild baboons: from mating opportunities to paternity success[END_REF]. Although we cannot demonstrate the causality of this link using correlative data, our analyses rule out several alternative hypotheses, including the proposal that cycling females receive more male aggression than non-cycling females because they are more aggressive, and the proposal that females prefer to mate with aggressive males.

Second, we conducted a detailed characterization of the mechanisms of sexual coercion through an analysis of behavioural sequences that reveals the temporal decoupling between aggression and matings. Our results suggest that direct coercion is more important than indirect coercion (i.e., males attempt to increase their own mating rates rather than to decrease those of others), by showing that males rarely punish females who mate with rivals, although it may not be possible to fully disentangle these effects because one aggressive act may simultaneously encourage a female to mate and discourage her to leave.

Third, our study points to important fitness costs of sexual intimidation for females.

Previous evidence has been limited to the finding that fertile female chimpanzees experience higher stress levels than non-fertile females [START_REF] Muller | Male coercion and the costs of promiscuous mating for female chimpanzees[END_REF]. Here we show that sexual violence is an important source of injuries for fertile females, which can compromise their survival (Fig 2b).

Our study may therefore offer an evolutionary explanation for the co-variation between female injury rates and fertility cycles that has been reported from a range of mammals [START_REF] Boeuf | Sexual behaviour of male northern elephant seals: I. Lethal injuries to adult females[END_REF][START_REF] Szykman | Rare male aggression directed toward females in a femaledominated society: baiting behavior in the spotted hyena[END_REF][START_REF] Linklater | Stallion harassment and the mating system of horses[END_REF][START_REF] Hohmann | Intra-and inter-sexual aggression by bonobos in the context of mating[END_REF][START_REF] Manson | Male aggression: a cost of female mate choice in Cayo Santiago rhesus macaques[END_REF][START_REF] Réale | Female-biased mortality induced by male sexual harassment in a feral sheep population[END_REF], including baboons [START_REF] Archie | Costs of reproduction in a long-lived female primate: injury risk and wound healing[END_REF][START_REF] Maccormick | Male and female aggression: lessons from sex, rank, age, and injury in olive baboons[END_REF].

Several factors may favour the use of sexual intimidation in baboons and chimpanzees, including the coexistence of males and females in large groups for long periods of time, their sexual dimorphism in body size and armaments, and long-term memory of previous interactions [START_REF] Cheney | Baboon metaphysics -The evolution of a Supplemental References[END_REF]46]. Sexual intimidation may occur in other mammals sharing these traits, but could have easily gone undocumented due to the temporal decoupling between aggression and matings [6]. Recognizing the importance of discreet forms of sexual coercion, by examining their taxonomic distribution and fitness consequences, should become an important focus for future research. The widespread use of sexual intimidation by males may help to explain core aspects of reproductive strategies with consequences for the evolution of mate choice, social structure and sexual dimorphism [47,48].

EXPERIMENTAL PROCEDURES (a) Study site and population

We studied wild chacma baboons at Tsaobis Nature Park, a semi-arid environment in Namibia [49]. We collected data on two habituated groups. Group composition and periods of data collection are given in Table S7. Only adults were included in the study (see Table S7 for definition), and all were recognizable. Dominance ranks were based on both focal and ad libitum observations of approach-avoid and agonistic interactions (see Appendix 4).

(b) Female reproductive state & mate-guarding patterns

Female reproductive state was recorded daily as pregnant (determined a posteriori) if a female gave birth within six months after the day of observation, lactating if she had a dependant infant and had not yet resumed cycling, swollen if she was sexually receptive with a perineal swelling, and non-swollen otherwise. For each cycle, we defined the POP as the 5day period preceding the day of swelling detumescence, during which ovulation generally occurs [50,51]. Mate-guarding episodes were monitored ad libitum.

(c) Behavioural data

We conducted one-hour focal animal samples on all adults. We conducted 3439 focal observations on 53 females distributed across reproductive states (Table S8) during which we recorded 222 chases or attacks led by males. Supplants, displacements, and threats were excluded because they are likely to be less stressful for females. We also recorded 520 focal observations of 25 adult males, with 79 chases or attacks towards adult females. In addition, we recorded ad libitum agonistic interactions, with 1579 chases or attacks involving an identified adult male/female.

(d) Observations of injuries

From 2013 onwards, injuries were recorded daily, including the date, type of wound (open cuts, punctures of the skin, abnormal skin swelling, limps), freshness (presence of wet/dry blood), and likely cause when known. We recorded 101 injuries on 31 adult females. For analyses, we omitted injuries inflicted by adult females and juveniles where known (N=5/22).

(e) Statistical analysis

We ran a combination of GLMMs (summarized in Table S1), described below, and matchedcontrol analyses (described in Appendix 2 and 3). For technical details on GLMM procedures, see Appendix 5.

Male aggression and female reproductive state

A binomial GLMM with a logit link function was run, using the probability that a female receives male aggression during a one-hour focal observation (yes/no) as the response variable. Reproductive state was fitted as a fixed factor together with the following control variables: female dominance rank, female parity (nulliparous or parous), group sex ratio (the number of adult females divided by the number of adult males, in case females receive more male aggression when the sex ratio is more male-biased), year, and group identity. Random factors comprised female identity and the date of focal sampling.

Male aggression and rate of injury

The number of injuries received by a female in a given reproductive state was modelled as a GLMM with a Poisson error structure. The number of days spent in each reproductive state was log-transformed and included as an offset variable. Fixed effects comprised: female reproductive state, dominance rank, parity, group sex ratio, year, and group identity. Female identity was included as a random effect.

To test whether females who experience more male aggression during their oestrus cycle suffer more injuries, we ran a second GLMM with a Poisson error structure using the number of injuries received in a given cycle as the response variable. The log-transformed number of days spent in each cycle was fitted as an offset variable. The mean rate (number per hour) of aggressive acts received from any adult male by the female throughout her cycle (calculated using female focal observations) was fitted as a fixed effect. Other fixed and random effects were similar to the previous model, except that the operational sex ratio (the number of cycling females divided by the number of adult males) was fitted instead of the group sex ratio. We included a cycle only if we had >5 focal observations for a female in that cycle.

Sexual intimidation and male mating success

We ran a binomial GLMM using the probability that each resident male mate-guards the female during her POP (yes/no) as the response variable. Fixed factors comprised the mean rate of aggression received by the female from the male during the entire cycle, but prior to her POP, calculated as the total number of aggressive acts received during focal observations divided by the number of observation hours, prior to her POP; female dominance rank and parity; male dominance rank (to control for increased access of dominant males to receptive females); operational sex ratio; year; and group identity. To test the alternative hypothesis of female preference for aggressive male phenotypes, we included an additional fixed effect: the rate of male aggression toward any individual of the group (total number of ad libitum aggressive acts initiated by a male per year divided by the time spent in the group that year and by the number of individuals in the group to control for differences in group size).

Random effects comprised the female and male identities, and cycle identity. Only cycles for which we had >5 focal observations of a given female were included.

This analysis was replicated using ad libitum records of male-female aggression to ensure our estimated rates of aggression reliably captured variation across dyads. We ran the same model as above but calculating the mean daily rate of aggression received by the female from the male during her entire cycle, but prior to her POP, as the total number of ad libitum aggressive acts received divided by the number of days observed in the cycle. We only Distribution of the (a) mean rate of male aggression against females (related to Table S2) and (b) mean rate of female injuries (related to Table S4) across female reproductive states. Boxplots are drawn from the raw individual means per year (represented by black dots). The bottom and top of the box respectively represent the 25th and 75th quartiles, and the bold horizontal line the median. Whiskers include the interquartile range. Open squares represent the mean of the distribution. Note that the boxes representing the rate of aggression received by pregnant and lactating females are not visible because the median, the 25 th and 75 th quartiles are equal to zero. Comparisons are denoted by "*" if significant and by "ns" otherwise. (a) Partial residual plot of the number of injuries incurred by cycling females during a cycle in relation to the mean rate of male aggression received during the same cycle (calculated from focal observations). Black dots represent partial residuals of the GLMM, the black line is the model prediction, and the grey area the confidence intervals. The prediction line is drawn holding all other fixed effects constant, using the median for numeric variables and most common category for factors (i.e., for a multiparous female, of rank 0.6, cycling over 38 days, in L group, when there were 9 adult males present, in 2014). Related to Table 1. (b) A female injured three times by her mate-guarding male on the head, who died for unknown reasons 6 months later. (c) Partial residual plot of the probability of establishing a mate-guarding episode with a male in the POP of a cycle in relation to the mean rate of aggression received from him throughout the cycle (calculated from focal observations). The prediction line is drawn for a multiparous female, of rank 0.5, a male of rank 0.5 and an overall rate of aggression of 0.005 time/day, in L group, in 2014. Related to Table 2. (d) A male directs aggression towards a female. Photo credit: Alecia Carter.

included
Rate of aggression received from males (number/h) q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q qq qq q q qq q q q q q q q q q q q q q q q q qq q q q q qq q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q qq q qq q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q Non-swollen Swollen Pregnant Lactating qq q qq q q q q q q q qq q q q qq q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q Non-swollen Swollen Pregnant Lactating 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 Female reproductive state

Response to Reviewers

Supplemental Tables Table S1 Matched control analysis comparing the probability of copulation of a male-female dyad after the male has attacked or chased the female vs in the absence of such aggression 8 Table S5 3b. Males use punishment -unguarded SW -guarded SW Matched control analysis comparing the probability of aggression of a male-female dyad after the female has copulated with another male vs in the absence of such a copulation 6 S5. Results of the matched-control analyses testing for sexual harassment and punishment from (a) any male for unguarded females and (b) male consorts for mateguarded females. For sexual harassment, we tested the difference between the proportion of copulations during post-aggression (PA) and matched-control (MC) observations using McNemar's Chi-squared tests for 4 different time periods. For punishment, we tested the difference between the proportion of aggressive acts during post-copulation b Number of PC observations where aggression was received from a non-copulating male after a copulation (for punishment).

c Number of MC observations with a copulation (for harassment) or with an aggressive act (for punishment). Table S6. Influence of the mean daily rate of aggression received from a male by an unguarded female throughout her oestrus cycle but prior to her peri-ovulatory period (POP) (calculated from ad libitum data) on the same male's probability of mate-guarding her during her subsequent POP. Parameters and tests are based on 78 cycles, 309 male-female aggressive acts, 2240 total aggressive acts from males, distributed among 34 females (number of days of observation per cycle: mean±sd:29.0±14.1, number of mate-guarding males per cycle: 1.10±0.69, range: [0-4]),) and 39 males, and performed using a GLMM controlling for female identity, male identity and cycle identity (fitted as random factors). Significant variables appear in bold. SE: Standard Error, LRT: statistic of a likelihood ratio test, df: degrees of freedom. LRT tests are used to test for the significance of each variable, while the confidence intervals are used to test for the significance of each level of the qualitative variables. Related to main-text results, section 3c. a Males are considered adult when they reach eight years of age [2].

Response

b Females are considered adult when they reach menarche [3].

c Males are considered subadult between 4 and 8 years old, and juveniles below 4 years old [2]. Adult males 520 25 20.8±8.9 ;

FIGURES LEGENDSFigure 1 .

 1 FIGURES LEGENDS

Figure 2 .

 2 Figure 2. Male-female aggression predicts future mating success for males and risk of injury for females.

  injury (number/day)

  Figure 1.

Figure 2 .

 2 Figure 2.

d

  Number or PA-MC or PC-MC pairs available for the test. e McNemar's Chi-squared test.

Table 1 .

 1 cycles for which >10 days of group observations were available. social mind (Chicago: The University of Chicago Press). 46. Stumpf, R.M., Martinez-Mota, R., Milich, K.M., Righini, N., and Shattuck, M.R. (2011). Sexual conflict in primates. Evol. Anthropol. Issues, News, Rev. 20, 62-75. 47. Caizergues, A., and Lambrechts, M.M. (1999). Male "macho" mammals exploiting females versus male "Don Juan" birds exploited by females: the opposite-sex exploitation (OSEX) theory. Ecol. Lett. 2, 204-206. 48. Pradhan, G.R., and van Schaik, C.P. (2009). Why do females find ornaments attractive? The coercion-avoidance hypothesis. Biol. J. Linn. Soc. 96, 372-382. Influence of the mean hourly rate of male aggression received by females (calculated from focal observations) on their daily rate of injury. Parameters and tests are based on the observation of 30 injuries and 119 aggressive acts, distributed among 64 cycles of 30 different females (number of focals per cycle: mean±sd:11.2±5.0). Significant variables appear in bold. SE: Standard Error, LRT: statistic of a likelihood ratio test, df: degrees of freedom. Reference category: 2013. Injuries were only collected in 2013 and 2014.

						95%
	Response					confidence
	variable	Fixed factors	Levels	Estimate	SE	interval	LRT	df	P-value
	Number of	Rate of male aggression during cycle	2.53	1.11	[0.36 ; 4.70] 4.74	1	0.029
	injuries received in a given cycle a	Female rank Female parity b	1.04 nulliparous 0.35	0.57 [-0.08 ; 2.17] 3.51 0.4 [-0.45 ; 1.14] 0.70	1 1	0.061 0.402
		Operational sex ratio		0.15	1.28 [-2.36 ; 2.66] 0.01	1	0.905
		Group c	L	-0.64	0.57 [-1.76 ; 0.48] 1.31	1	0.253
		Year d	2014	-0.38	0.53 [-1.43 ; 0.66] 0.52	1	0.470
	a The number of days of the cycle observed fitted as an offset fixed factor, which modelize a daily rate of injury

49. Cowlishaw, G. (1997). Refuge use and predation risk in a desert baboon population. Anim. Behav. 54, 241-53. 50. Higham, J.P., Heistermann, M., Ross, C., Semple, S., and MacLarnon, A. (2008). The timing of ovulation with respect to sexual swelling detumescence in wild olive baboons. Primates 49, 295-299. 51. Daspre, A., Heistermann, M., Hodges, J.K., Lee, P.C., and Rosetta, L. (2009). Signals of female reproductive quality and fertility in colony-living baboons (Papio h. anubis) in relation to ensuring paternal investment. Am. J. Primatol. 71, 529-538. b Reference category: parous c Reference category: J group d

Table 2 .

 2 Influence of the mean hourly rate of aggression received from a male by an unguarded female throughout her oestrus cycle but prior to peri-ovulatory period (POP) (calculated from focal observations) on the same male's probability of mate-guarding her during her subsequent POP. Parameters and tests are based on 58 cycles and 74 male-female aggressive acts, distributed among 30 females (number of focal observations per cycle: mean±sd:16.07±12.00, number of mate-guarding males per cycle: 1.20±0.72, range: [0-4]), and 39 males, and analysed using a GLMM. Significant variables appear in bold. SE: Standard Error, LRT: statistic of a likelihood ratio test, df: degrees of freedom. LRT tests are used to test for the significance of each variable, while the confidence intervals are used to test for the significance of each level of the qualitative variables. Reference category: 2005. LRT tests are used to test for significance of the whole variable "Year", while the confidence intervals are used to test for significance of each level of the variable.

	Response					95% confidence
	variable	Fixed factors	Levels	Estimate SE	interval	LRT df P-value
	Probability that	Rate of male-female aggression during cycle		5.22	2.03	[1.24 ; 9.19]	7.47 1	0.006
	a male mate-guards a female during her POP	Rate of male aggression toward all individuals Female rank		47.44 50.35 [-51.25 ; 146.13] 0.85 1 -0.87 0.48 [-1.81 ; 0.06] 3.37 1	0.356 0.066
	(0/1)	Female parity a	nulliparous -0.96	0.43 [-1.80 ; -0.12] 5.82 1	0.016
		Male rank		2.30	0.63	[1.06 ; 3.54]	12.01 1	0.001
		Operational sex ratio		0.89	0.99	[-1.05 ; 2.84]	0.83 1	0.364
		Group b	L	0.24	0.38	[-0.50 ; 0.98]	0.39 1	0.533
		Year c	2006	0.61	0.61	[-0.57 ; 1.80]	8.41 3	0.038
			2013	-1.10	0.78	[-2.63 ; 0.43]
			2014	-0.80	0.75	[-2.26 ; 0.66]
	a Reference category: parous
	b Reference category: J group

c

.

  Summary of the statistical analyses explained in the Experimental Procedures. SW: swollen, NSW: non-swollen, P: pregnant, L: lactating

	Predictions	Females included Response variable	Model	Fixed factors	Random	No of	Tables & Figures
				type		factors	models
	1. Males target	-all	Probability of	Binomial -Reproductive state (NSW, SW, P, L)	-Female ID	1	Table S2
	cycling females		receiving male		-Female rank	-Date of		Fig 1a
			aggression during a		-Female parity	focal
			focal observation		-Group sex ratio	observation
					-Group & Year
	2a. Cycling	-all	Number of injuries	Poisson -Reproductive state (NSW, SW, P, L)	-Female ID	1	Table S4
	females are at		received in a given		-Female rank			Fig 1b
	higher risk of		reproductive state		-Female parity
	injury				-Group sex ratio
					-Group & Year
					-Number of days in reproductive state (offset)
	2b. Cycling	-cycling	Number of injuries	Poisson -Mean hourly rate of aggression received by males	-Female ID	1	Table 1
	females	(SW+NSW)	received in a given		throughout the cycle using focal observation data			Fig 2a
	experiencing		oestrus cycle		-Female rank
	more aggression				-Female parity
	from males				-Operational sex ratio
	suffer more				-Group & Year
	injuries				-Number of observation days of the cycle (offset)
	3a. Males use	-unguarded SW
	harassment	-guarded SW

Table S2 .

 S2 Influence of female reproductive state on the probability that she receives male aggression during a one-hour focal observation. Parameters and tests are based on 3439 focal observations (including 172 observations with aggression) distributed among 53 females. Significant variables appear in bold. SE: Standard Error, LRT: statistic of a likelihood ratio test, df: degrees of freedom. LRT tests are used to test for the significance of each variable, while the confidence intervals are used to test for the significance of each level of the qualitative variables. Related to main-text results, section 1.

	Supplemental Data
							95%
		Response variable	Fixed factors	Levels	Estimate	SE	confidence	LRT	df	P-value
							interval
		Probability of	Reproductive state	Swollen (ref: non-swollen)	-0.14	0.21 [-0.55 ; 0.28] 32.53	3	<0.001
		receiving aggression from males (0/1)		Pregnant (ref: non-swollen) Lactating (ref: non-swollen)	-1.02 -1.26	0.27 [-1.56 ; -0.48] 0.31 [-1.86 ; -0.65]
				Swollen (ref: pregnant)	0.89	0.25 [0.41 ; 1.37]
				Swollen (ref: lactating)	1.12	0.28 [0.57 ; 1.67]
				Pregnant (ref: lactating)	0.23	0.32 [-0.39 ; 0.86]
			Female rank		0.08	0.28 [-0.47 ; 0.63] 0.08	1	0.778
			Female parity a	nulliparous	0.13	0.21 [-0.28 ; 0.54] 0.37	1	0.541
			Sex ratio		-0.04	0.21 [-0.46 ; 0.38] 0.03	1	0.853
			Group b	L	-0.13	0.21 [-0.55 ; 0.29] 0.36	1	0.551
			Year c	2006	-0.42	0.35 [-1.10 ; 0.26] 74.41	3	<0.001
				2013	-1.00	0.45 [-1.88 ; -0.12]
				2014	1.14	0.29 [0.57 ; 1.71]
		a Reference category: parous
		b Reference category: J group c Reference category: 2005							Table S5
	3c. Males use	-cycling	Probability of mate-	Binomial -Mean rate of aggression received from a given	-Female ID	2	Table 2 (focal)
	sexual	(SW+NSW)	guarding a given	male prior to POP throughout the cycle using focal	-Male ID		Fig 2c (focal)
	intimidation		female during her	observation data or ad lib data			-Cycle ID		Table S6 (ad lib)
			POP	-Mean rate of aggression emitted by the male toward
				all individuals using ad lib data
				-Female rank
				-Female parity
				-Male rank
				-Operational sex ratio
				-Group & Year

Table S3 .

 S3 Influence of female reproductive state on the probability of initiating aggression toward any individual of the group during a one-hour focal observation. Parameters and tests are based on 3439 focal observations (including 843 observations with aggression) distributed among 53 females. Significant variables appear in bold. SE: StandardError, LRT: statistic of a likelihood ratio test, df: degrees of freedom. LRT tests are used to test for the significance of each variable, while the confidence intervals are used to test for the significance of each level of the qualitative variables. Related to main-text results, section 1.

	Response variable	Fixed factors	Levels	Estimate	SE	95% confidence interval	LRT	df P-value
	Probability of	Reproductive state	Swollen (ref: non-swollen)	0.03	0.14	[-0.25 ; 0.30]	7.39	3	0.060
	initiating an		Pregnant (ref: non-swollen)	0.33	0.15	[0.03 ; 0.62]
	aggression toward any individual (0/1)		Lactating (ref: non-swollen) Swollen (ref: pregnant)	0.09 -0.30	0.15 0.12	[-0.22 ; 0.39] [-0.54 ; -0.06]
			Swollen (ref: lactating)	-0.06	0.13	[-0.30 ; 0.19]
			Pregnant (ref: lactating)	0.24	0.13	[-0.02 ; 0.50]
		Female rank		2.30	0.18	[1.95 ; 2.64]	70.10	1 <0.001
		Female parity a	nulliparous	0.19	0.13	[-0.06 ; 0.44]	2.13	1	0.145
		No of individuals in group		-0.02	0.01	[-0.04 ; -0.01]	9.05	1	0.003
		Group b	L	-0.15	0.13	[-0.40 ; 0.10]	1.31	1	0.252
		Year c	2006	0.46	0.18	[0.11 ; 0.81]	101.47 3 <0.001
			2013	1.12	0.26	[0.61 ; 1.63]
			2014	2.19	0.27	[1.67 ; 2.71]
	a Reference category: parous
	b Reference category: J group
	c Reference category: 2005

Table S4 .

 S4 Influence of female reproductive state on the daily rate of injury. Parameters and tests are based on the observation of 96 injuries distributed among 39 females. Significant variables appear in bold. SE: Standard Error, LRT: statistic of a likelihood ratio test, df: degrees of freedom. LRT tests are used to test for the significance of each variable, while the confidence intervals are used to test for the significance of each level of the qualitative variables. Related to main-text results, section 2. The number of days spent in the reproductive state was fitted as an offset fixed factor, which modelize a daily rate of injury Reference category: 2013. Injuries were only collected in 2013 and 2014.

	Response variable Number of female injuries a a Table	Fixed factors Reproductive state Swollen (ref: non-swollen) Levels Pregnant (ref: non-swollen) Lactating (ref: non-swollen) Swollen (ref: pregnant) Swollen (ref: lactating) Pregnant (ref: lactating) Female rank Female parity b nulliparous Sex ratio Group c L Year d 2014	Estimate 0.46 -0.73 -0.37 1.19 0.83 -0.36 -0.37 0.04 -0.26 0.43 0.40	SE 0.29 0.34 0.33 0.31 0.3 0.31 0.48 0.40 0.67 0.32 0.28	95% confidence interval [-0.11 ; 1.03] [-1.39 ; -0.07] [-1.01 ; 0.27] [0.59 ; 1.79] [0.24 ; 1.42] [-0.98 ; 0.25] [-1.31 ; 0.58] [-0.74 ; 0.82] [-1.57 ; 1.06] [-0.20 ; 1.06] [-0.15 ; 0.95]	LRT 15.85 0.59 0.01 0.15 1.75 2.08	df 3 1 1 1 1 1	P-value 0.001 0.442 0.928 0.701 0.186 0.150

b Reference category: parous c Reference category: J group d

(

  PC) and MC observations using McNemar's Chi-squared tests for 3 different time periods. Significant p-values are set at 0.007 due to Bonferroni correction. Related to main-

	text results, section 3a&b.
				(a) Unguarded females				(b) Mate-guarded females
			N.	N.	Sample	X 2 df	P-	Median	N.	N.	Sample	X 2	df	P-	Median
			cop in PA a /	cop/agg	size d		value e	time of	cop in PA a /	cop/agg	size d			value e	time of
			agg in PC b	in MC c				observation	agg in PC b	in MC c				observation
		05 min	1	3	52	0.25 1 0.617	5	9	3	45	3.13 1	0.077	5
	Harassment	10 min 15 min	1 2	2 0	52 51	0.00 1 1.000 0.50 1 0.480	10 15	10 11	4 9	45 43	2.08 1 0.08 1	0.149 0.773	10 15
		20 min	2	1	47	0.00 1 1.000	17	12	10	41	0.08 1	0.773	20
		05 min	2	8	1334 2.50 1 0.114	5	1	0	31	0.00 1	1.000	5
	Punishment 10 min	3	8	1062 1.78 1 0.182	10	1	0	31	0.00 1	1.000	10
		15 min	4	14	771 5.06 1 0.024	13	1	0	31	0.00 1	1.000	15
	a Number of PA observations including a copulation with the male aggressor (for harassment)

Table S7 .

 S7 Demography of J and L groups in the study periods: June-December 2005, May 2006-January 2007, June-October 2013 and May-November 2014. Demography varies due to migrations, births, disappearances, and life-history transitions (i.e. from juvenile to adulthood). Age was estimated from a combination of known birth dates and dental patterns of tooth eruption and wear, examined during prior captures[1]. Related to main-text Experimental Procedures.

		Year	Number of adult males a	Number of adult females b	Number of subadults and
										juveniles c
			J group	L group	J group	L group	J group	L group
	variable	Fixed factors 2005	6-9	3		Levels 17	9	Estimate SE 26	95% confidence interval 5-9	LRT df	P-value
	Probability that a	Rate of male-female aggression during cycle 2006 4-5 4-5	17	10.65 9-11	2.39 [5.96 ; 15.34] 36 18	27.02 1 <0.001
	male mate-guards a female during her POP (0/1)	Rate of male aggression toward all individuals 2013 7-10 9-11 Female rank 2014 7-8 9	17 18	5.54 18-19 -0.66 17-19	29-32 44.77 [-82.21 ; 93.29] 0.01 1 0.907 31-33 0.43 [-1.50 ; 0.19] 2.31 1 0.128 35 29
		Female parity a			nulliparous		-0.88	0.36 [-1.58 ; -0.18]	6.77 1 0.009
		Male rank						2.34	0.60 [1.17 ; 3.52]	13.75 1 <0.001
		Operational sex ratio					0.40	0.73 [-1.03 ; 1.83]	0.30 1 0.583
		Group b				L		0.34	0.36 [-0.36 ; 1.05]	0.91 1 0.34
		Year c				2006		0.81	0.64 [-0.43 ; 2.06]	11.69 3 0.009
						2013		-1.10	0.69 [-2.46 ; 0.26]
						2014		-0.49	0.71 [-1.88 ; 0.90]

a Reference category: parous b Reference category: J group c Reference category: 2005

Table S8 .

 S8 Sample size of behavioural focal observations. Related to main-text, Experimental Procedures.

		Reproductive state	Number of focal	Number of	Number of focal
			observations	individuals	observations per individual
					(mean±sd ; [min-max])
	Adult females	Lactating	884	45	19.6±10.5 ; [1-45]
		Pregnant	714	47	15.2±9.7 ; [1-46]
		Non-swollen	469	36	13.0±9.7 ; [1-40]
		Swollen mate-guarded	491	32	15.3±14.5 ; [1-53]
		Swollen unguarded	881	39	22.6±21.5 ; [1-81]

Response to Reviewers

ACKNOWLEDGMENTS

We are grateful to the Tsaobis Baboon Project volunteers in 2005-6 and 2013-14 for help in the field, and three anonymous reviewers for comments on the manuscript. Permission to work at Tsaobis Nature Park was granted by the Ministry of Lands and Resettlement and the Tsaobis beneficiaries. Thanks also to the Gobabeb Research and Training Centre for

AUTHOR CONTRIBUTIONS

A.B. and E.H. collected the data and designed the study, A.B ran the analyses, and all authors contributed to draft the manuscript. affiliation, and the Ministry of Environment and Tourism for research permits, as well as to the Snyman and Wittreich families for permission to work on their land. A.B. benefitted from a financial support from the ANR Labex IAST, the 'Ministère de l'Education Nationale, de l'Enseignement Supérieur et de la Recherche', and the Primate Society of Great Britain. The authors declare that they have no conflict of interest.

Appendix 1. Description of the analysis testing the influence of female reproductive state on the probability that females initiate aggression toward any individual of the group

We investigated whether the reproductive state of females influenced their propensity to initiate aggression. A binomial GLMM with a logit link function was run, using the probability that a female initiates aggression towards any group member during a one-hour focal observation (yes/no) as the response variable. In this model, we include any type of aggression (supplant, displacement, threat, chase and attack). Reproductive state (nonswollen, swollen, pregnant, or lactating) was fitted as a fixed factor together with the following control variables: female dominance rank, female age, the number of individuals in the group (since females may be more likely to initiate aggression when more individuals are present), year, and group identity. Random factors comprised female identity and the date of focal sampling. Results of this model are given in Table S3.

Appendix 2. Description of the matched-control analysis of sexual harassment

Using both male and female focal observations, we tested whether an adult male was more likely to copulate with a female after he attacked her across 4 different time intervals (x=5, 10, 15 and 20 minutes). We did not have enough matched-control observations to investigate longer time intervals. After each incidence of malefemale aggression during a focal follow, we selected the x following minutes of observation, hereafter the postaggression (PA) observation, and assessed whether a copulation occurred with the male aggressor (no: 0; yes: 1).

To each PA observation, we matched an observation of the same length of time for the same female, where no male aggression occurred during the previous x minutes, hereafter the matched-control (MC) observation, and assessed whether she copulated with the male aggressor of the PA observation. We compared the difference in the proportions of observations including copulations between the post-aggression (PA) and matched-control (MC) observations using McNemar's Chi-squared tests.

Matched control (MC) observations corresponding to a particular post-aggression (PA) observation

were chosen from 60-minutes focal observations of (1) the same female, who was (2) in the same consortship status as in the PA observation (unguarded, or guarded by the same male), and (3) in the same cycle and located less than 7 days apart from the PA observation. For PA observations that had several possible MC observations, we paired MC and PA observations in a way that minimized the number of times each MC observation was reused. For models investigating periods of x minutes post-aggression (x taking a range of values from 5 to 20, with increments of 5), the first x minutes of each MC observation were discarded in case an event of malefemale aggression occurred immediately before the start of the focal. Within suitable 60-minutes MC observations, the time period selected as an MC sample (which was less than the duration of the entire focal observation) was chosen randomly. Some focal observations were used to draw more than one MC sample (for example, minutes 15-20 and then minutes 45-50 of a 60-minutes focal observation). In such cases, we attempted to sample non-overlapping time periods within the 60-minutes observation. When this was not possible (e.g. the same 60-minutes observation was used to draw three MC samples for the dataset looking at intervals of 20 minutes), we randomly deleted some PA observations relying on this 60-minutes observation in order to keep only independent PA/MC pairs. In the PA samples, when the x minutes were incomplete (e.g. when a second incidence of male-female aggression occurred within the same time interval or when the focal observation finished before the end of the time interval), we reduced the time interval of the matched MC sample accordingly so that the matched PA and MC samples are of similar duration. However, we only kept aggressive acts that were followed by at least 1 minute of observation (see Table S4 for the median observation time after aggressive acts for each analysis). Note that across the 4 different datasets (i.e. 5, 10, 15, 20 min), the same PA-MC pairs were kept but the random sampling of MC samples within 60-minutes observations was rerun for each dataset (in order to optimize the sample size in each dataset).

We ran these analyses separately for unguarded and mate-guarded females, since we may expect different coercion strategies from males not involved in mate-guarding or from male consorts (who already have sexual access to females and may not benefit from harassment).

Appendix 3. Description of the matched-control analysis of punishment

We tested whether an adult male was more likely to attack a female after she has copulated with a rival using a similar matched-control analysis across 3 different time intervals (x=5, 10, 15 minutes). We did not have enough matched-control observations to investigate longer time intervals. After each copulation, we determined whether the female received aggression from a male who was not involved in the copulation, within a given time interval.

For these post-copulation (PC) observations, we selected MC observations, without a copulation event, as described in the Appendix 2. Although this analysis focuses on adult male aggression, we included copulations with juvenile males because adult males may punish females who mate with juveniles.

We similarly ran these analyses separately for unguarded and mate-guarded females, to test for punishment both from any male for unguarded females and from the male consort for mate-guarded females.

Extra-pair copulations during mate-guarding are rare in chacma baboons, but still occur in 4% of cases in our dataset (31 out of 726 copulations).

Appendix 4. Dominance ranks of males and females

Individual ranks were assessed through focal and ad libitum observations of approach-avoid interactions (supplants, when one animal actively displaces another to take its place, and displacements, when one animal passes close to another and makes it move away) and agonistic interactions: attacks (any agonistic physical contacts including hits, bites, or grabbing movements), chases (when one animal chases another for a distance of at least 3 m) and threats (including staring, head bobbing, and ground sweeping while oriented toward the targeted individual).

Our approach to the female dominance hierarchy was contingent upon the demographic stability of the study period. In 2005-2006 there were few demographic changes, so a single hierarchy was calculated by pooling the aggression matrix across years. In 2013-14 there were several demographic changes, so a separate hierarchy was calculated for each year. We used Matman 1.1.4 (Noldus Information Technology 2003) in all cases. The female dominance hierarchies were always linear (interactions in group L: N05-06 = 1190, N13 = 367, N14 = 1259; interactions in group J: N05-06 = 1173, N13 = 590, N14 = 978; Landau's linearity index h: P<0.05 in all cases). All analyses presented here use the female's relative rank (a standardization of absolute rank between 0 and 1), to control for differences in group size. This was calculated using the formula: 1-((1-r)/(1-n)), where r is the absolute rank of an individual (ranging from 1 to the group size, n).

In contrast to the female hierarchy, the male hierarchy was much less stable [4]. Thus, male ranks were established for each study period using an Elo-rating procedure implemented in the R package EloRating (version 0.43) [5] which gives a score for each individual on each day of observation. Compared to dyadic interaction matrices where ranks are calculated over a given time period, an Elo-rating procedure allows the continuous updating of ranks according to the temporal sequence of interactions [5,6]. To obtain comparable ratings across the entire study period, we derived a daily standardized rank by scaling the Elo-rating score of each individual proportionally between 0 (corresponding to the minimal score and thus the lowest ranking male) and 1 (corresponding to the maximal score and the highest ranking male).

Appendix 5. General details on GLMMs procedures

GLMMs were run using the glmer function of the lme4 package [7] in R version 3.3.1 [8]. The significance of the fixed factors was tested using a likelihood ratio test, LRT (assuming an asymptotic chi-square distribution of the test statistic), using the full model (to avoid problems arising from stepwise model selection procedures: [9]).

We further computed the 95% confidence intervals of fixed factors (for multilevel categorical variables, confidence intervals were used to test the significance of each level of the variable by checking that they did not cross zero). To test for pairwise differences between multiple levels of a categorical variable (e.g., "reproductive state") we changed the reference category sequentially [10]. To validate models, we checked the distribution of residuals (i.e., plotted the residuals against the continuous predictors and checked that the residuals were normally distributed).