Female fertile phase synchrony, and male mating and reproductive skew, in the crested macaque

High social status is the primary determinant of reproductive success among group-living male mammals. Primates living in multimale–multifemale groups show the greatest variation in the strength of this link, with marked variation in reproductive skew by male dominance among species, dependent on the degree of female fertile phase synchrony, and the number of competing males. Here, we present data on two groups of wild crested macaques (Macaca nigra), living in the Tangkoko Reserve, Sulawesi, Indonesia. We investigated male monopolization of fertile females in 31 cycles of 19 females, and genetic paternity of 14 offspring conceived during the study period. We show that female fertile phase synchrony was low, that females had few mating partners in their fertile phase, and that dominant males monopolized a high proportion of consortships and matings, resulting in marked and steep mating and reproductive skew. We conclude that female cycle asynchrony provides the opportunity for strong direct male–male competition in crested macaques, resulting in monopolization of females by dominant males, consistent with their marked sexual dimorphism. Our study provides a test of the underlying factors that determine the relative occurrence and strength of different mechanisms of sexual selection, and the phenotypes that evolve as a result.

Sexual selection theory predicts conflict between members of one sex for reproductive opportunities with the other. For many mammals, this often manifests as competition between males for females, which represent the limiting resource in reproduction 1 . For group-living mammals, social status usually determines access to females during receptive periods, with males of high social status obtaining most sires, a phenomenon often known as reproductive skew (e.g. kangaroos 2 ; coatis 3 ; feral cats 4 ). The degree to which males and females associate, and the extent to which males can monopolize females, are key determinants of the extent of dominant male reproductive success 5 . Given that males may only be able to monopolize one female at a time, it has been suggested that in species living in multi-male multi-female groups with any overlap between females in periods of fertility, males ranked higher in the dominance hierarchy gain access to females before lower ranked males in a sequential Priority of Access (PoA) system 6 .
Non-human primates are a particularly interesting group in which to study the related issues of female cycle synchrony and male reproductive skew, as primate species show an unusually high level of variation in such skew 7,8 . This variation can be attributed to the fact that primate species vary a great deal in the number of females present in groups and mating seasonality (and hence fertile phase synchrony) 9,10 , as well as in the number of males found in social groups (and hence the number of competitors for a dominant male) 7 . This variation is ultimately caused by ecological factors, with seasonality of breeding being determined by seasonality of food resources 11 and number of females (itself determined by within and between group competition 12 ) determining the number of males 13,14 . When females are highly asynchronous in the timing of their fertile phases, highranking males may be able to monopolize these periods, leading to marked reproductive skew. In contrast, when

Results
Female ovarian cycle synchrony. Across both groups, on any one day there was an average of 16.8 ± 0.0 (mean ± STD; range [14][15][16][17][18][19][20] females present during observation at any one time; 3.3 ± 0.1 (range 0-9) females exhibiting a swelling; 1.3 ± 0.1 (range 0-5) exhibiting maximal swelling; and 0.5 ± 0.0 (range 0-3) females being in the fertile phase of their cycle. (See Fig. 1 for an exemplary three months in group Rambo I). Only 0.2 ± 0.4 (range 0-2) females were in the fertile phase of their conception cycle on any one day and only during 3.9% of days in which a female was in the fertile phases of her conceptive cycle was there a second female in the same cycle stage and type. The mean operational sex ratio was 0.06 ± 0.00 (range 0.00-0.33).
Consortships. Females consorted with males a mean 83.5 ± 3.3% of time during the four day fertile phase, compared with 60.1 ± 6.2% of time in the five days preceding the fertile phase, and 28.6 ± 4.4% of time in the five days following the fertile phase. Separating cycles according to whether they were conceptive or not shows that for conceptive cycles these figures were 87.1 ± 4.1% (fertile phase), 58.8 ± 8.7% (pre-fertile phase), and 32.2 ± 7.0% (post-fertile phase), and for non-conceptive cycles were 79.8 ± 5.2% (fertile phase), 61.5 ± 9.3% (pre-fertile phase), and 24.3 ± 6.5% (post-fertile phase). A Linear Mixed Model with zero-inflated Poisson error structure showed that male likelihood of consorting females varied according to cycle phase (β = 1.7231, lower CI = 1.2824, upper CI = 2.1562, p < 0.001), as did the time they spent consorting females (β = − 0.4699, lower CI = − 0.6344, upper CI = − 0.2984, p < 0.001), such that males were more likely to consort in the fertile phase, and consorted females for longer when consorting. However, there were no differences in consort time across all males between conceptive and non-conceptive cycles, both for the zero-inflated (β = − 0.1273, lower CI = − 0.9359, upper CI = 0.6720, p = 0.753) and Poisson (β = − 0.2361, lower CI = − 0.5672, upper CI = 0.0769, p = 0.148) parts of the model. Consorts were strongly skewed by rank both across the whole 14 day period surrounding ovulation, and within the four day fertile phase (top six individuals only; all 14 days, r = − 0.943, p = 0.005; fertile phase r = − 0.943, p = 0.005; Fig. 2a). Alpha-males obtained a mean of 55.7 ± 5.8% of all consort time across the whole 14 day period around ovulation, and a mean of 62.0 ± 6.7% of consort time during the fertile period. Separating cycles according to whether they were conceptive shows that alpha-males obtained 48.1 ± 10.4% of consort time during the fertile period in non-conceptive cycles and 71.6 ± 8.5% of consort time during the fertile period in conceptive cycles (Fig. 3). A Linear Mixed Model with zero-inflated Poisson error structure showed that for alpha-males, the likelihood of consorting females varied according to cycle phase (β = 1.4713, lower CI = 1.0685, upper CI = 1.8724, p < 0.001), as did the time they then spent consorting females (β = − 0.3845, lower CI− 0.6651, upper CI = − 0.0944, p = 0.008), such that alpha-males spent more time consorting females and were more likely to consort in the fertile phase. Unlike for all males, though, alpha-males were in general not more likely to consort females in conceptive than non-conceptive cycles (β = − 0.1041, lower CI = − 0.8661, upper CI = 0.6277, p = 0.782). However, when they did consort with females, they consorted females for longer in conceptive than non-conceptive cycles (β = 0.9630, lower CI = − 1.4611, upper CI = − 0.4723, p < 0.001; Fig. 3).

Maintenance of consortships.
Both males and females maintained consortships, though the majority of consort time was maintained by males. Males maintained consortships 83.6 ± 2.3% of the time during the fertile phase, 78.4 ± 3.8% of the time during the pre-fertile phase, and 64.6 ± 7.7% of the time during the post-fertile phase. As such, females increased their own maintenance of consortships when they were not fertile. Separating these figures for conceptive and non-conceptive cycles shows that in conceptive cycles, males maintained consortships for 86.1 ± 3.1% (fertile phase), 76.5 ± 6.4% (pre-fertile phase) and 65.1 ± 9.3% (post-fertile phase) of the
Mating skew. During the study period we observed 4976 matings during the 14 day period around ovulation, including 2315 matings during the four day fertile period. Almost all matings were from in-group males, with almost no out-group mating. Matings were highly skewed by rank (all 14 days, r = − 0.829, p = 0.042; fertile phase, r = − 1.0, p < 0.001; Fig. 2b). The alpha-male obtained a mean 51.0 ± 5.0% of matings during the whole 14 day period around ovulation, and a mean 63.5 ± 6.0% of matings during the fertile period. Separating cycles according to whether they were conceptive or not shows that alpha-males obtained 56.3 ± 8.8% of matings during the fertile period in non-conceptive cycles and 70.3 ± 8.1% of matings during the fertile period in conceptive cycles. A Linear Mixed Model with zero-inflated Poisson error structure showed that alpha-males were not more or less likely to mate according to cycle phase (β = − 0.4668, lower CI = − 1.1910, upper CI = 0.2160, p = 0.167), but mated at higher frequencies in the fertile phase (β = − 0.5278, lower CI = − 0.6777, upper CI = − 0.3826 p < 0.001). Alpha-males were not more likely to mate in conceptive than non-conceptive cycles (β = 0.6884, lower CI = − 0.7467, upper CI = 2.1814, p = 0.331), and when they did mate, did not mate at higher rates in conceptive cycles (β = − 0.0267, lower CI = − 0.3496, upper CI = 0.3284, p = 0.879). Alpha-males mated less often during the fertile phase (63.5%, see above) than would be predicted (89.8%) from the Priority of Access model based on patterns of female fertile phase overlaps. Similarly, the steepness of observed fertile phase mating skew (r = − 0.733, p = 0.016, see above) was lower than predicted by the Priority of Access model (r = − 0.813, p = 0.004).
Reproductive skew. Male reproductive success was highly skewed towards alpha-males (Table 1). Of the 14 infants conceived during the study period, 12 (86%) were sired by the group's alpha-male. The first infant of a nulliparous female was sired by the group's beta male and a third, the last infant of a very old female, by a low ranking male that had just newly immigrated into the group. Nonacs' B-index for paternity was high and significantly different from a random distribution (B = 0.508, p < 0.001).

Discussion
Our data show that, as predicted, female crested macaques exhibit low fertile phase synchrony, and probably as a direct consequence of this, are heavily monopolized by high-ranking males. They spend 70% of all time during fertile periods of conceptive cycles in consort with the alpha male, and mate with few partners. As a consequence, and consistent with our predictions, mating, and reproductive skew are very high. The factors influencing female fertile phase synchrony in nonhuman primate populations are number of females (often correlated with group size in species living in mulitmale multifemale groups), combined with the degree of breeding seasonality 7,8,10 , with breeding seasonality in turn often thought to depend on seasonality in the environmental. This population of crested macaques lives in an aseasonal environment (Engelhardt et al. unpublished data), which may have a causal role in influencing the lack of breeding seasonality, and creating relatively low fertile phase synchrony. With few females being able to conceive at any one time, and the presence of clear signals of the fertile phase 41 , it is no surprise that female fertile periods can be monopolized by the top ranked males. As a consequence, females undergo reduced partner numbers (lower promiscuity) when they are fertile than in other periods of the cycle, and spend a high degree of their fertile phases in consorts that are especially maintained by males. Given that females signal their fertile phase to males through the presence of sexual swellings and proceptive behaviours 41 , this may indicate that females have been selected to further enable their own monopolization by high ranking males. Consistent with the above, consort and mating skew are marked, and alpha males particularly are able to dominate consort and mating activities during fertile periods, and therefore sire the majority of infants. The combination of strong reproductive skew with high levels of sexual dimorphism 31,32 is consistent with the fact that males usually immigrate into groups from outside and engage in direct contest competition for alpha-male status 37,43 . As such, dominance may be a proxy for male competitiveness and/or quality in crested macaques, such that female preferences for males may coincide with male rank.
Females nonetheless had more than one partner during the fertile period despite theoretical preference for high ranking males among females, and despite high monopolization potential for alpha males. Although it remains unclear how females escape male monopolisation, they may have a selective advantage in obtaining multiple mates even when they have a preferred partner. This may be because it ensures fertilization 21 , induces sperm competition 44 , ensures fertilization by genetically compatible individuals 45 , keeps lower ranking males in the group, who might aid with group defence 40,46 , or reduces the risk of infanticide 21 Infanticide is known to be the number one cause of infant mortality in this study population 38 .
Our data show that mating skew was less steep, and the proportion of matings obtained by the alpha male fewer, than would be predicted from the PoA model 6 . This model has been tested in a number of non-seasonally breeding primate species where female synchrony is low, and has found broad support among such species (e.g. yellow baboons 47 ; mandrills 19 ; chimpanzees 48 , though see 28 for seasonal breeders). Numerous possibilities could explain the lower than expected skew in the present study. One explanation may be our choice of using the fertile periods of females only to calculate the degree of female cycle synchrony for our assessment of the PoA model. The timing of the fertile period is the most biologically important variable for males, but using it to calculate female reproductive overlap inevitably leads to relatively low levels of synchrony compared to assessments so far made on the basis of, for example, observations of all swellings of any size, or of mating in general (e.g. 8,14,21 ). Such a high degree of mating monopolization may also be unfeasible due to biological constraints (e.g. the energetic costs of consort strategies and mating 49 ), or males may choose not to mate with some females of low priority, (e.g. low-ranking females 30 ). Nonetheless, alpha-male paternity was higher and reproductive skew steeper than observed in most other primates living in polygynandrous mating systems (see 10 Suppl. Mat. for alpha-male paternities; see 20,27,50,51 for B-indices). Alpha-male paternity was especially high given the number of males Table 1. Results of the genetic paternity analysis for 14 mother-infant pairs. The table shows the identity of the mother-infant pair, the mother-infant pair's group, the most likely father, his rank at the time of conception, and the paternity likelihood as calculated with Cervus 3.0.

Mother-infant pair
Group Sire Sire rank Number of loci compared www.nature.com/scientificreports/ present in the groups, a parameter so far thought to be one of the most important determinants of alpha-male reproductive success 8,10 . Crested macaque alpha-males thus seem to be able to control reproduction even in the presence of a large number of competitors. The consort data show that alpha males (unlike all males, see Fig. 2) consorted for longer periods in conceptive than in non-conceptive cycle. Our data are consistent with results of some other species, including captive olive baboon males, which appeared more attracted to conceptive than non-conceptive cycles 52 , and wild male chacma baboons who consorted more with females during conceptive cycles 53 . Other analyses of our dataset show that, across all males, there is no difference between mating rates between conceptive and non-conceptive cycles 41 . Given the strong mating skew and limited reproductive opportunities for lower ranked males this could be because all opportunities for mating must be taken by lower ranked males. Another possibility is that due to their domination of consort periods during the fertile phase, alpha males have increased information about female cycle status not available to all males. We have previously suggested that consorting males may have access to signals from close range (e.g. olfactory signals) not available to all males that enable them to refine their estimates of female fertility 54,55 . For example only group resident male chacma baboons consorted more with females during conceptive cycles 53 . Relatively clear signals of the likelihood of conception may thus support experienced, dominant males in making decisions on which female to monopolise at what time, and in this way further increase the advantages of high rank for males.
Our data also provide further evidence for a relationship between social styles and reproductive skew, with a highly despotic male-male competitive regime observed in a socially-tolerant species 56,57 . Further theoretical and empirical work should focus on whether these links may be a product of higher relatedness between individuals in species of high reproductive skew (as suggested by 56,57 ), or whether the correlation may be a product of both systems deriving from related ecological factors, with food resource seasonality influencing both female-female competition and hence social style, and female reproductive synchrony and hence male reproductive skew.

Methods
Data. Data are available and citable from Dryad 58 .

Study site and population. The study was undertaken as part of the Macaca nigra Project at the Tangkoko
Reserve at the north-eastern tip of Sulawesi (1° 34′ N, 125° 14′ E). The reserve was established in 1980, comprises an area of 8867 hectares, with a sea boundary of 12 km, and ranges from sea level to an elevation of 1350 m 59,60 . All research was undertaken between July 2006 and July 2007 on two study groups (Rambo I, Rambo II), which were studied previously by other researchers 61,62 . We re-habituated these groups from April 2006 to July 2006, and identified and named all adult group members according to individual characteristics such as size, gait, cuts, missing digits, scars etc. The home range of both groups overlapped and included primary forest, secondary forest and, for Rambo II, also gardens near the village. During the study period, both groups ranged in size from 65 to 70 individuals, with Rambo I consisting of 10 adult males and 21 adult females, and Rambo II 7 adult males and 15 females, the remaining individuals in both groups being subadults, juveniles and infants.
Male dominance rank. Male dominance ranks varied at times during the study period, including one alpha-male takeover over of one of the groups (R2). Following elsewhere 63 , during each period and for each group separately, we used Elo-ratings to create dyadic dominance interaction. We included agonistic interactions with unambiguous winner and loser and displacement interactions for all adult males present during the given study period. Similar to elsewhere 63 , we included only unidirectional interactions, and did not include conflicts in which there was counteraggression by the loser. Elo ratings were extracted on a given day for analysis, and then males were ranked in order, with those rankings used for analysis.
Female ovarian cycle synchrony. On each day, swelling status of all females was recorded in both groups.
The first day of visible swelling of sex skin was noted by a single observer in close proximity and under excellent observation conditions; maximum swelling size and the beginning of detumescence was also assessed by a single member of the field team. Swellings were categorized as maximal when the area around the anus clearly protruded the rest of the swelling from a side view and when the skin was tight over the entire swelling area. The beginning of detumescence was recognized through wrinkles (re-)appearing on the sex skin followed by rapid deflation of the sex skin tissue.
Behavioural data collection. We collected behavioural data during 31 ovarian cycles (N = 19 adult females), of which 16 were conceptive and 15 were non-conceptive. We classified cycles as conceptive (N = 16) when an infant was born around 6 months later (see 64 ), or when it was the last female cycle (either assessed hormonally, see below, or by the occurrence of anogenital swellings, as M. nigra does not exhibit post-conception swellings, see 64 ; Engelhardt pers. obs.), or when miscarriage was subsequently observed (assessed by female bleeding from the vagina, N = 3). In cases where a cycle was classified as conceptive based on the birth of an infant, the lack of any further cycles with swelling after that conceptive cycle gives us a high degree of confidence that this was indeed the conceptive cycle. Cycles were classified as non-conceptive (N = 15) when they were immediately followed by another cycle (assessed hormonally or by the occurrence of swellings).
Our sampling covered 417 observation days and 2443 h of behavioural data. Data collection was carried out using handheld data recorders (Psion Workabout Pro M, Psion Teklogix) and using focal animal sampling 65 . We attempted to follow focal females every observational day from dawn until dusk, with actual observed time averaging 5.9 ± 0.1 h per observation day and female. We here focus on the two most important sexual behaviours-consortship 15  www.nature.com/scientificreports/ in proximity up to 10 m for at least 10 consecutive minutes and aligning their directions of forward movements (i.e. grooming after mating by one or both mating partners was not categorized as consortship if the two individuals did not move on into the same direction afterwards; see also 41 ). Data on consortship were collected using instantaneous sampling 65 with an interval of one minute and mating was recorded by all occurrence sampling during focal observations. In the case that during a consortship, the female climbed a tree and was not followed by the male, but still closely watched by him, the consortship was noted as continued if there was no other male closer to the female than her partner and if the two individuals continued to stay in proximity once the female returned to the ground. In the case that more than one male stayed in proximity to the female and aligned the direction of movements with her, the highest ranking of the males present was recorded as the main consort partner. In these cases, the lower ranked male was often trailing in the wake of the consort pair, and might be considered to be undertaking the role of a 'follower male' 66 . In order to investigate the extent to which consortship was based on male effort, and thus represented male mate-guarding 16 , we also noted for every minute who was the maintainer of the consortship. The maintainer was defined as the individual following the direction the consort partner is moving into. Whenever consort pairs were not moving, the last maintainer remained as maintainer until the next movement occurred.
Faecal sample collection and hormone analysis. In parallel to behavioural observations, and for analysis of our behavioural data, we collected faecal samples for hormonal analysis opportunistically during the 31 ovarian cycles of the 19 focal females. Sample collection occurred on a daily basis at least during mid-cycle, i.e. the period of maximum anogenital swelling, and the seven following days, to allow ovulation to be timed accurately in each cycle 67 . Only samples uncontaminated by urine were collected directly after the animal had been observed defecating. Samples were placed on ice, and stored frozen (− 18 °C) within 10 h of collection. Overall, 3-7 samples per week were collected per female. From these samples we determined the timing of ovulation based on patterns of immunoreactive faecal progestogen concentrations measured by enzyme immunoassay (EIA). Processing of the samples and their EIA measurement has been described by 41 . Sensitivity of the assay at 90% binding was 20 pg/well. Inter-assay coefficients of variation (CVs) of high and low value quality controls were 15.4% (high) and 15.7% (low), while intra-assay CVs were 7.8% (high) and 9.5% (low). The presumed time of ovulation was determined by counting back from the defined post-ovulatory rise in faecal progestogen concentrations 68 , taking into account the excretion lag time of faecal progestogens 69 . In this way, a two day ovulation window was determined for all 31 cycles as the 2 and 3 days prior to the post-ovulatory rise in progestogens. In all 31 ovarian cycles, this rise was defined as a rise of more than 2 standard deviations above a baseline calculated from the previous 3-5 values, and which was sustained for a minimum of 3 datapoints (as in, e.g. 69 ). We defined a four day fertile period as the 2 day ovulation window plus the previous 2 days (as in, e.g. 69 ), and took the previous 5 days (pre-fertile phase) and the following 5 days (post-fertile phase) for comparison. and all potential sires (N = 53, total 81 subjects) applying the two-step alcohol-silica storage protocol 70 . Potential sires were defined as any adult males present or immigrating into our study groups during our study period. We extracted DNA using 100-150 mg of faeces and the GENIAL all-tissue DNA extraction kit following the manufacturer's instructions with only slight modification. Samples were genotyped on a total of twelve highly variable microsatellite markers (details in 71 ). We used a combination of the multiple tube approach 72,73 and the two-step multiplex PCR to increase the accuracy of the results 74 . Products were analyzed with an ABI PRISM3100 automated sequencer and the ABI peak scanner software. A heterozygous genotype was accepted when both alleles were confirmed at least two times per extract, i.e., a total of four independent PCRs were required for a given individual. A homozygous genotype was assigned when a single allele occurred in six independent PCRs, in order to control for allelic dropout 30,72,73 . In case one heterozygous genotype appeared within the six PCRs, we did up to eleven PCR replications to ensure that we reported a true genotype 72 . Maternity derived from field observations was genetically tested and confirmed for all mother-infant pairs (N = 14) in our study which were subsequently used in the paternity analysis. For paternity assignment, we considered all genotyped males as potential sires for all infants (compare 71 ) and compared an average of 11.36 ± 0.63 markers over the 14 mother-father-offspring trios (Table 1). We used a combination of exclusion and likelihood analyses (compare 71 ) as follows: for 10 infants, all potential males were excluded on at least two loci, with the exception of the assigned sire, who matched the mother-offspring pair at all loci. In 4 cases, the assigned sire had one mismatch with the given infant, while the next likely sires had at least two mismatches. All offspring, paternity assignments were supported at the 95% confidence level by the likelihood method calculated by CER-VUS 3.0 75 (Table 1). Data analysis. Aim 1: Female ovarian cycle synchrony: Using our observations of sexual swellings, we assessed for each group separately, then averaged across the groups, overlap in: females exhibiting any swelling; females exhibiting maximal swelling; females being in the fertile phase of their conceptive cycle as hormonally assessed. The sample size was n = 31 cycles. Aims 2 and 3: Consortships and the maintenance of consortships: To investigate the frequency with which we counted females and males as being in consort, and for analysis of the maintenance of consorts, we carried out Generalized Linear Mixed Models (GLMMs). Dependent count data were zero-inflated, as assessed by comparison of the number of zeros found in each variable compared with the number predicted under the Poisson distribution. This is because behaviours were absent on many days of the cycle. We therefore undertook zero-inflated Poisson models using the R package MCMCglmm 76  www.nature.com/scientificreports/ Male Maintenance Count or Mating Count, with an offset for number of observation counts to account for any differences in observation time. Fixed effects were cycle phase, and cycle type, with Female ID and Group specified as random effects. The models produce two different B values and p values for each variable-one for the Poisson part of the model and the other for the zero-inflated part which models the distribution of the excess zeros. Models were checked for convergence by checking trace plots. Models were carried out for all males and alpha-males separately, except for mating, for which only alpha-males are considered since analyses of how mating from all males relates to ovulatory timing has been already published 41 . When creating mean values for presentation, values were averaged within and then across cycles so that no one cycle exerted undue influence over the presented figures. The sample size was 314 female days from 31 cycles. Aim 4: Number of mating partners across the cycle: To test whether females had more partners according to 'cycle phase' (pre-fertile vs fertile vs post-fertile phases), we carried out repeated-measures ANOVA comparing the number of partners obtained in each cycle for each phase, while also testing for differences between cycles by including 'cycle type' (conceptive vs non-conceptive) in the model. Following this, we carried out post-hoc paired t tests to test each cycle phase against the other. The sample size was n = 31 cycles.
Aim 5: Mating skew: To test for mating and consort skew by dominance rank we carried out Spearman's correlations. As values for rank number 3 onwards were all close to zero or zero (see "Results") we used only data for the first 6 ranks (the minimum number of data points required to undertake a Spearman's correlation) in these analyses.
In order to calculate the predicted mating skew for males of different ranks based on the PoA model, we assessed female fertile period synchrony across all females in the group, with fertile phase determined either by hormonal data where available, or otherwise assessed as the days -5 to -2 prior to the onset of detumescence (day 0; Engelhardt et al. in prep.). On the basis of this, males were assigned a rank-specific probability of mating with a female on each day any female was fertile, where the alpha obtained a probability of 1 and all other males 0 when only one female was fertile, the alpha and beta males probabilities of 0.5 each and all other males 0 when two females were fertile, and so on. These values were then averaged over the observation period to obtain an estimate of the proportion of matings that males of each rank should obtain according to the PoA model. This estimate was then compared to the observed mating data. The sample size was n = 31 cycles.
Aim 6: Reproductive skew: To compare the reproductive skew of our study population with that of other species, we calculated Nonacs' reproductive skew index (B-index 77 ) and tested it for deviation from random distribution using the Skew calculator 2013 (https ://www.eeb.ucla.edu/Facul ty/Nonac s/PI.html). We also calculated the mean proportion of infants that were sired by the two alpha-males as this is a typical measure of reproductive skew in studies on primates (e.g. 10 ). The sample size was n = 31 cycles.