Lucie Rigaill

James P Higham

Sandra Winters

Cécile Garcia

D P Watts

The redder the better? Information content of red skin coloration in female Japanese macaques

Keywords: Skin coloration, Sexual communication, Signal content, Reproductive status, Macaca fuscata 38 39

Primates appear unusual among mammals in the expression of female colorful ornaments in the absence of sex role reversal.

Most studies of female ornamentation in primates have focused on the sexual signaling function of female exaggerated anogenital swellings in female-female competition and male attraction, but other female colorful ornaments, such as red skin coloration, may also contain information about reproductive status and individual characteristics. We analyzed variation in facial and hindquarter coloration (redness and luminance) according to the timing of the fertile phase (intra-cycle variation), the cycle number, whether the cycle was conceptive or non-conceptive (inter-cycle variation), and in relation to individual characteristics (social rank, parity, and body mass) in 12 captive female Japanese macaques (Macaca fuscata). While facial and hindquarter coloration did not accurately indicate the timing of the fertile phase, variation in hindquarter luminance signaled perceptible differences between pre-and post-ovulation stages. Hindquarters became less red, and faces were lighter as the number of consecutive cycles increased. Hindquarters were redder during non-conceptive cycles compared with conceptive ones.

Individual variation in skin redness and luminance appeared perceptible under good light conditions. Higher-ranking females had darker hindquarters. We also found that variation in female skin coloration may contain information about differences in body mass but not in parity. Female skin coloration in Japanese macaques may thus be more indicative of inter-cycle variation and various specific female characteristics than the timing of the fertile phase. Our study provides insight into the potential information content of this signal and demonstrates the characteristics that males might be selecting for should males prefer redder females.

Significance statement

Primates are the most colorful group of mammals. Females of some primate species display red skin color that is suggested to play a role in mate attraction by reflecting reproductive status or individual characteristics. In Japanese macaques, a species lacking accurate behavioral and auditory indices of the probability of ovulation, female red skin coloration (face and hindquarters) may influence mating activity. Our study shows that this colorful trait does not contain information about the timing of the fertile phase and parity but may indicate inter-cycle differences and some female characteristics. Our findings add to a growing body of research on the possible roles and functions of female colorful ornaments in animal sexual communication.

U N C O R R E C T E D P R O O F Introduction 40
In a wide range of animals, both sexes express secondary 41 sexual traits such as colorful signals, with males often 42 exhibiting exaggerated trait expression relative to females 43 [START_REF] Darwin | The descent of man, and selection in relation to sex[END_REF][START_REF] Andersson | Sexual selection[END_REF]). Sex differences in reproduc-44 tive costs are thought to result in selection pressure on males to 45 express traits that attract females (reviewed in Clutton-Brock tion that may influence male mate choice in primates. There is 94 already some evidence that males show mating preferences 95 based on female characteristics, such as age or parity 96 [START_REF] Anderson | Female age: male preference and reproductive suc-666 cess in primates[END_REF][START_REF] Muller | Male chimpanzees prefer mating with old females[END_REF]Setchell and Wickings 97 2006) and social rank (Setchell and Wickings 2006;Garcia 98 et al. 2009;[START_REF] Rigaill | Multimodal sexual signaling and mating behavior in olive baboons (Papio anubis)[END_REF]. Some colorful traits exhibited 99 by female primates also appear to be attractive to males, suggesting a role for sexual selection (sexual swellings: [START_REF] Deschner | Female sexual 709 swelling size, timing of ovulation, and male behavior in wild West 710 African chimpanzees[END_REF]; but see [START_REF] Fitzpatrick | Exaggerated sexual swellings and male mate choice in primates: testing the reliable indicator hypothesis in the Amboseli baboons[END_REF]skin coloration: Waitt et al. 2006;Higham et al. 2011;[START_REF] Pflüger | Colour and contrast of female faces: attraction of attention and its dependence on male hormone status in Macaca fuscata[END_REF]. Female primates exhibit a range of colorful signals that could be related to a variety of signaling functions [START_REF] Bradley | The primate palette: the evolution of pri-688 mate coloration[END_REF]), yet the majority of research in this area has focused on sexual swellings as indicators of fertility status or female fitness (e.g., [START_REF] Nunn | The evolution of exaggerated sexual swellings in primates and the graded-signal hypothesis[END_REF][START_REF] Zinner | Significance of pri-1008 mate sexual swellings[END_REF][START_REF] Deschner | Female sexual 709 swelling size, timing of ovulation, and male behavior in wild West 710 African chimpanzees[END_REF]Setchell and Wickings 2004a;Setchell et al. 2006a;Higham et al. 2008;[START_REF] Fitzpatrick | Exaggerated sexual swellings and male mate choice in primates: testing the reliable indicator hypothesis in the Amboseli baboons[END_REF][START_REF] Street | Exaggerated sexual swellings in female nonhuman primates are reliable signals of female fertility and body condition[END_REF]. Nevertheless, other colorful female signals could also play a role in reproductive signaling. Red skin coloration is linked to changes in concentrations of circulating estrogens, which bind to estrogen receptors in the skin, modulating blood flow (luminance: how dark or light the skin appears) and the amount of oxygenated blood (redness: at least partially reflecting the color of the blood itself) in the skin [START_REF] Rhodes | Effects of administration of testosterone, dihydrotestosterone, oestrogen and fadrozole, an aromatase inhibitor, on sex skin colour in intact male rhesus macaques[END_REF]. Female red skin coloration may thus indicate reproductive status. For instance, female facial coloration varies between follicular and luteal phases in mandrills (Setchell et al. 2006b), cycling and pregnancy periods in Japanese macaques (Macaca fuscata: [START_REF] Rigaill | Multimodal advertisement of pregnancy in free-ranging female Japanese macaques (Macaca fuscata)[END_REF], and indicates ovulation timing in rhesus macaques [START_REF] Dubuc | Sexual skin color contains information about the timing of the fertile phase in freeranging Macaca mulatta[END_REF][START_REF] Higham | Color signal information content and the eye of the beholder: a case study in the rhesus macaque[END_REF]. Female skin coloration may also correlate with some individual characteristics.

There is evidence that female skin coloration correlates with parity or age, which are usually correlated, with females having more infants being darker or redder (Setchell et al. 2006b;Higham et al. 2008;Dubuc et al. 2014b; but see [START_REF] Rigaill | Testing for links between face color and age, dominance status, parity, weight, and intestinal nematode infection in a sample of female Japanese macaques[END_REF]. While social rank often correlates with skin coloration in males, previous studies have found no such relationship in female mandrills (Setchell and Wickings 2004a;Setchell et al. 2006b), olive baboons (Papio anubis: Higham et al. 2008;[START_REF] Rigaill | Multimodal sexual signaling and mating behavior in olive baboons (Papio anubis)[END_REF], and Japanese macaques [START_REF] Rigaill | Testing for links between face color and age, dominance status, parity, weight, and intestinal nematode infection in a sample of female Japanese macaques[END_REF]. Female condition, often indexed using body mass, may also affect a female's ability to cope with the energetic costs associated with reproduction, mating, and signaling, thus potentially influencing the likelihood of conception (Japanese macaques [START_REF] Mori | Analysis of population changes by measurement of body weight in the Koshima troop of Japanese monkeys[END_REF][START_REF] Garcia | Energetic consequences of seasonal breeding in female Japanese macaques (Macaca fuscata)[END_REF]olive baboons: Bercovitch 1987;mandrills: Setchell and Wickings 2004b). However, the relationship between female body mass and skin coloration is still unclear for these species (Setchell and Wickings 2004a;Setchell et al. 2006b;[START_REF] Rigaill | Testing for links between face color and age, dominance status, parity, weight, and intestinal nematode infection in a sample of female Japanese macaques[END_REF].

In Japanese macaques, both males and females express red coloration of the face and hindquarters that peaks during the mating season along with concentrations of sexual hormones [START_REF] Fooden | Systematic review of Japanese macaques, Macaca fuscata (Gray, 1870)[END_REF]. Males show increased attention toward intensely colored female faces, suggesting that skin coloration could play a role in mate attraction and could have a signaling function [START_REF] Pflüger | Colour and contrast of female faces: attraction of attention and its dependence on male hormone status in Macaca fuscata[END_REF]. Adult females do not exhibit sexual swellings or obvious behavioral or auditory indicators of ovulation (proceptive behaviors, estrus and copulation calls, O' Neill et al. 2004;[START_REF] Garcia | Relationship between sexual interactions and the timing of the fertile phase in captive female Japanese macaques (Macaca fuscata)[END_REF]

. While U N C O R R E C T E D P R O O F
skin coloration may influence mating activity, it is unclear what may be signaled by variation in this trait. One hypothesis is that female skin coloration might indicate intra-cycle variation in the likelihood of ovulation. While a previous study found that variation in female facial coloration signals early gestation [START_REF] Rigaill | Multimodal advertisement of pregnancy in free-ranging female Japanese macaques (Macaca fuscata)[END_REF], it is still unclear whether skin coloration contains information about the timing of the fertile phase [START_REF] Fujita | Hormone profiles and reproductive characteristics in wild female Japanese macaques (Macaca fuscata)[END_REF]. Female skin coloration might also signal inter-cycle differences. Female Japanese macaques tend to conceive during their first menstrual cycles in a given mating season [START_REF] Fujita | Hormone profiles and reproductive characteristics in wild female Japanese macaques (Macaca fuscata)[END_REF][START_REF] O'neill | Relationship between ovarian cycle phase and sexual behavior in female Japanese macaques (Macaca fuscata)[END_REF][START_REF] Fooden | Systematic review of Japanese macaques, Macaca fuscata (Gray, 1870)[END_REF][START_REF] Garcia | Relationship between sexual interactions and the timing of the fertile phase in captive female Japanese macaques (Macaca fuscata)[END_REF]). The underlying behavioral and hormonal mechanisms leading to a decrease in conception probability (and possibly in hormonal concentrations) after the first cycles are unknown, although energetic costs related to reproduction and thermoregulation may play a role [START_REF] Fooden | Birth-season variation in Japanese macaques, Macaca fuscata[END_REF][START_REF] Garcia | Energetic consequences of seasonal breeding in female Japanese macaques (Macaca fuscata)[END_REF][START_REF] Takeshita | Environmental, biological, and social factors influencing fecal adrenal steroid concentrations in female Japanese macaques (Macaca fuscata)[END_REF]. Skin coloration may correlate with inter-cycle differences of the likelihood of conception or in hormonal concentrations, with coloration during conceptive or first cycles being redder/ darker than during non-conceptive or following cycles.

Another non-mutually exclusive hypothesis is that female skin coloration is potentially informative about individual condition and characteristics such as social rank, age or parity, and body mass. In a previous study, we found no relationship between female face coloration and individual characteristics in a wild population of Japanese macaques [START_REF] Rigaill | Testing for links between face color and age, dominance status, parity, weight, and intestinal nematode infection in a sample of female Japanese macaques[END_REF]). However, this study focused on facial coloration only with a small number of females from a population under high energetic constraints, which may have led to inconclusive results. Additional data from a more controlled environment and a larger sample size would thus help to further investigate the possible signaling functions of female skin coloration in Japanese macaques.

Our study aims to identify the potential information content of female Japanese macaque faces and hindquarters in a mating context, to determine whether skin coloration (redness and luminance) is informative about intra-cycle variation (timing of the fertile phase), inter-cycle variation (number of consecutive cycles, conception probability), and individual characteristics (social rank, body mass, and parity or age).

1. Intra-cycle variation. If female skin coloration is related to changes in reproductive hormones across the menstrual cycle, and thus to the timing of the fertile phase within a cycle, we predict that faces or hindquarters will be darker/ redder (i.e., stronger signal) during the fertile phase compared with the pre-and post-fertile phases. were analyzed for pregnanediol-3-glucuronide (PdG) using 273 enzyme immunoassays as described by [START_REF] Garcia | Relationship between sexual interactions and the timing of the fertile phase in captive female Japanese macaques (Macaca fuscata)[END_REF].

Inter

274

The presumed day of ovulation and the periovulatory period We extracted reflectance spectra from these areas using ColourWorker software (Chrometics Ltd. available at http:// www.chrometrics.com). The extraction of reflectance spectra was done by a technician who was not involved in data collection and blind to subject characteristics. We converted these spectra into quantal catches, i.e., the stimulation of Japanese macaque photoreceptors. We measured quantal catches for the red (longwave (LW)) and green (mediumwave (MW)) photoreceptors using equations and macaque cone ratio and spectral sensitivity values given elsewhere [START_REF] Stevens | Studying primate color: towards visual system-dependent methods[END_REF][START_REF] Higham | Color signal information content and the eye of the beholder: a case study in the rhesus macaque[END_REF]. In trichromatic primates, such as Japanese macaques, chromatic (wavelength of light) and achromatic (light vs. dark) variations in color are perceived based on relative photoreceptor simulation [START_REF] Stevens | Studying primate color: towards visual system-dependent methods[END_REF]). Based on the quantal catch data for both facial and hindquarter coloration, we calculated chromatic variation in redness based on the red-green opponency channel ((LW -MW) / (LW + MW); higher values indicate a redder color) and achromatic variation based on the luminance channel ((LW + MW) / 2; higher values indicate a lighter color) [START_REF] Osorio | Photoreceptor sectral sensitivities in terrestrial animals: adaptations for luminance and colour vision[END_REF]. We used the receptor noise model [START_REF] Vorobyev | Receptor noise as a determinant of colour 984 thresholds[END_REF]) and the quantal catch data to determine how discriminable two different colors are likely to appear to the macaque visual system by calculating just noticeable differences (JNDs), which scale color distances by the minimal amount by which stimulus intensity must be changed in order to produce a perceptible difference in color. JND values below 1 indicate that differences between two colors are not perceptible, values between 1 and 3 indicate perceptible differences under good light conditions, and values > 3 indicate perceptible differences even when light conditions deteriorate [START_REF] Siddiqi | Interspecific and intraspecific views of color signals in the strawberry poison frog Dendrobates pumilio[END_REF]). We measured intra-cycle (i.e., for each cycle, each data point is compared with that cycle's least red/dark image) and interfemale (i.e., each female data point is compared with the least red/dark value in the data set) perceptible differences in face and hindquarter coloration. We refer to opponency channel calculations as "redness" and "luminance" and JND calculations as "intra-cycle JND redness/luminance" and "inter-female JND redness/luminance."

Data analysis

We used face and hindquarter images from the pre-, post-, and fertile phases of 12 females for color analyses (24 menstrual cycles in total, 6.2 images per cycle per female in average, 292 images in total). Examples of images are given in Figs. 1 and 2. Our statistical approach was designed to test whether female skin coloration was related to cycle phase, the conceptive nature of the cycle (hereafter "conception"), the number of consecutive menstrual cycles, age, social rank, parity, and body mass prior to the mating season. We ran general linear We then performed LRTs comparing each of the four full fitted models to their respective null models in which the predictor variables were removed but the random effect structure was maintained. If a full model outperformed its respective null model, we then tested the statistical significance of each predictor variable using LRTs, comparing the full model to reduced models in which single predictors were removed in order to get the overall effect of this predictor. We also report estimates and pairwise comparisons across all factor levels of each full model for a better interpretation of our results. We report parameter estimates with their respective 95% confidence intervals. Our statistical approach forces comparisons of all categorical predictor levels against a baseline intercept term (here: the fertile phase by default for cycle phase). To obtain pairwise comparisons across all factor levels, we releveled this factor (setting the pre-fertile phase as the baseline) and re-ran models as necessary. We did not further report on parameter estimates of full models that did not outperform their respective null models. We ensured that all relevant model assumptions were met by visually inspecting histograms of phase compared with the pre-fertile phase, but there were no 434 differences between the fertile phase and the other two cycle 435 phases (Table 1). Figure 1 presents examples of intra-cycle 436 variation in hindquarter luminance. Intra-cycle variation in 437 hindquarter luminance may be perceptible to males under 438 good light conditions: averaging across JND comparisons to the lightest value for each female across cycle phases shows that cycle phases differ in coloration by about 1 JND (Fig. 3).

Inter-cycle variation

Models including cycle number better explained the observed color variance in hindquarter redness and facial luminance (LRTs, respectively: χ 2 = 5.90, Δdf = 1, P = 0.015; χ 2 = 6.29, Δdf = 1, P = 0.012). Hindquarters became significantly less red and faces lighter as the number of consecutive menstrual cycles increased (Tables 2 and3). Models including conception better explained the observed color variance in hindquarter redness (LRT: χ 2 = 5.20, Δdf = 1, P = 0.023).

Hindquarters were significantly redder during nonconceptive cycles compared with conceptive ones (Table 2).

Female characteristics

Models including social rank better explained the observed color variance in hindquarter luminance and redness (LRTs, respectively: χ 2 = 6.45, Δdf = 1, P = 0.011; χ 2 = 4.71, Δdf = 1, P = 0.030). High-ranking females had significantly darker hindquarters and exhibited a trend for redder hindquarters (Tables 1 and2, Fig. 4). Female hindquarters or facial coloration were not related to parity (LRT, all P > 0.10). Models including body mass better explained the observed color variance in hindquarter redness and facial luminance (LRT, respectively: χ 2 = 5.09, Δdf = 1, P = 0.024; χ 2 = 3.92, Δdf = 1, P = 0.048). Heavier females exhibited a trend for redder hindquarters and lighter faces (Tables 2 and3). Differences in skin coloration between females are highly perceptible for luminance (mean ± SD JNDs; face 26.74 ± 3.84; hindquarters 21.62 ± 4.99); chromatic variation was less perceptible (mean ± SD JNDs; face 1.52 ± 0.85; hindquarters 1.93 ± 1.28), but mean color differences would still be discriminable in good lighting conditions (i.e., they differ by about 1 JND). Figure 2 presents examples of individual variation in facial luminance.

U N C O R R E C T E D P R O O F 474
All factor-level differences not reported here were non-475 significant (see Tables 1, 2 and3). behavior to determine whether this information influences male mate choice decisions.

Previous studies have showed that female skin coloration or the size of the colorful trait can indicate reproductive status or ovulation timing in some primate (Setchell et al. 2006b;[START_REF] Dubuc | Sexual skin color contains information about the timing of the fertile phase in freeranging Macaca mulatta[END_REF][START_REF] Higham | Color signal information content and the eye of the beholder: a case study in the rhesus macaque[END_REF][START_REF] Burriss | Changes in women's 692 facial skin color over the ovulatory cycle are not detectable by the 693 human visual system[END_REF] and lizard species [START_REF] Galán | Females that imitate males: dorsal coloration varies with reproductive stage in female Podarcis bocagei (Lacertidae)[END_REF][START_REF] Weiss | Reproductive signals of female lizards: pattern of trait 995 expression and male response[END_REF]Jessop et al. 2009). However, we found that female skin coloration does not accurately indicate the timing of the fertile phase in Japanese macaques. This suggests that females in this species either conceal or do not advertise ovulation, at least through the multiple traits that have been measured, including skin coloration, proceptive behaviors, estrus, and copulation calls [START_REF] O'neill | Relationship between ovarian cycle phase and sexual behavior in female Japanese macaques (Macaca fuscata)[END_REF][START_REF] Garcia | Relationship between sexual interactions and the timing of the fertile phase in captive female Japanese macaques (Macaca fuscata)[END_REF]). However, we found that hindquarter luminance may signal pre-vs. post-ovulation periods. Changes in skin coloration could be a by-product of changes in the concentration of circulating hormones over the course of the cycle, but they may also serve a signaling function if males attend to this signal. Females may benefit from Comparison between cycle phases JNDs hindquarter luminance 1 3 Fig. 3 Intra-cycle variation in hindquarter luminance, measured as just noticeable differences (JNDs). JNDs below 1 are not perceptible; differences between 1 and 3 are perceptible under good light conditions, and differences greater than 3 JNDs are perceptible across all lighting conditions. Plot shows the median (black horizontal line), the first and third quartiles (top and bottom of the box), the maximum and minimum JND values (top and lower whiskers), and outliers (points) the relationship between hindquarter redness and the probability of conception across cycles may be due to the fact that females happened to conceive in early cycles in this species, rather than because of a direct relationship between skin study, we found coloration and conception. In our previous that female face luminance varied between pre-and post-conception months [START_REF] Rigaill | Multimodal advertisement of pregnancy in free-ranging female Japanese macaques (Macaca fuscata)[END_REF]. The fact that in the present study only hindquarter redness was related to conception is t3:1 2003), fishes [START_REF] Barlow | Competition between color morphs of the polychro-676 matic Midas cichlid Cichlasoma citrinellum[END_REF][START_REF] Barlow | Colour and levels of aggression in the 679 Midas cichlid[END_REF][START_REF] Volpato | Eye color as an indicator of social rank in the fish Nile tilapia[END_REF], and lizards [START_REF] Thompson | Throat colour reliably signals status in male tree lizards, Urosaurus ornatus[END_REF]Martín and López 2009). Our study is the first to report this relationship for females in a primate species, with higher ranking females having darker and redder hindquarters.

t2:1
However, these differences in skin coloration may potentially be more related to female lineage than social rank per se. In this species, females typically acquire ranks just below those of their mothers, meaning that all females of a given matriline have similar social ranks (Koyama 1967). There is evidence that skin coloration is heritable in another macaque species (rhesus macaques: Dubuc et al. 2014b). Therefore, the apparent effect of social rank on skin coloration could instead be due to genetic inheritance, in which females inherit both higher dominance and redder/darker hindquarters from their mother. Regarding the relationship between female condition and coloration, we hypothesized that females who were heavier prior to the mating season would be redder and darker; however, our results do not fully support this prediction. The relationship between skin coloration and body mass is still equivocal in female (Setchell and Wickings 2004a;Setchell et al. 2006b;[START_REF] Rigaill | Testing for links between face color and age, dominance status, parity, weight, and intestinal nematode infection in a sample of female Japanese macaques[END_REF]) and male [START_REF] Rigaill | Multimodal sexual signaling and mating behavior in olive baboons (Papio anubis)[END_REF] primates, and further studies compiling larger datasets are needed to investigate this particular question. We found that variation in female skin coloration did not correlate with parity, in agreement with our previous results from another population of Japanese macaques [START_REF] Rigaill | Testing for links between face color and age, dominance status, parity, weight, and intestinal nematode infection in a sample of female Japanese macaques[END_REF]. Our results differ to previous findings from other primates (mandrills: Setchell et al. 2006b;olive baboons: Higham et al. 2008;rhesus macaques: Dubuc et al. 2014b), birds [START_REF] Amundsen | Why are female birds ornamented?[END_REF][START_REF] Pilastro | Male rock sparrows adjust their breeding strategy according to female ornamentation: parental or mating investment?[END_REF]Jawor et al. 2004;[START_REF] Doutrelant | Female coloration indi-716 cates female reproductive capacity in blue tits[END_REF][START_REF] Griggio | Female ornamentation and directional male mate preference in the rock sparrow[END_REF], lizards [START_REF] Weiss | Reproductive signals of female lizards: pattern of trait 995 expression and male response[END_REF][START_REF] Weiss | Ornamentation, age, and survival of female striped 998 plateau lizards, Sceloporus virgatus[END_REF][START_REF] Weiss | Female-specific ornamen-1000 tation predicts offspring quality in the striped plateau lizard, 1001 Sceloporus virgatus[END_REF]insects (LeBas et al. 2003) in which female colorful traits correlate with indices of fecundity.

While skin coloration may reflect different female characteristics across species, the larger data sets of the previous primate studies may have also provided better statistical power to highlight the link between female skin coloration and parity.

In long-lived and social species, group-member males may not need a visual signal of female characteristics, as these males may have accumulated knowledge about female social

  251 parity (total number of infants born divided by the 252 number of years post-adulthood, defined as 5 years old) prior to the beginning of the mating sea-254 son (as measured on 18 October 2011) were provided by 255 the Center for Human Modeling Research of KUPRI. 256 Hormonal analyses and determination of ovulation 257 dates 258 To determine each female's reproductive status, we collected 259 an average of 29.31 ± SD 3.17 fecal samples per female (to-260 tal = 381, range per female = 24-34). Because female 261 Japanese macaques do not display obvious signs of ovulation 262 such as sexual swellings, the fecal samples could not be asso-263 ciated a priori to a cycle phase thus limiting any bias in our 264 determination of the reproductive status. We collected fecal 265 samples in their entirety immediately after voiding, with most 266 samples collected between 8:00 a.m. and 12:00 p.m. We 267 bagged and labeled fecal samples and stored them on ice until 268 transfer to a freezer 0-2 h later. All samples were then stored at 269 -20 °C until processing. We collected samples on average 270 every 1.59 days (range = 0-4 days) to accurately assess the 271 ovarian cycle (Hodges and Heistermann 2011). Fecal samples 272

275

  of each ovarian cycle were determined using fecal PdG pro-276 files. The fertile phase was defined as a period of 5 days (cov-277 ering a 2-day window for ovulation plus three preceding days 278 to account for sperm longevity in the reproductive tract 279 (humans: Wilcox et al. 1995)); the 5-day period preceding this 280 phase represented the pre-fertile phase, while the 5 days fol-281 lowing the fertile phase were defined as the post-fertile phase. 282 We observed a total of 24 ovarian cycles (mean ± SD per 283 female = 2.0 ± 0.83, range = 1-3), and the majority of these 284 cycles were non-conceptive (19/24). Hormonal profiles 285 showed that one of the 13 females had abnormal hormonal 286 variations and failed to cycle for the entire duration of the 287 study. This non-cycling female was subsequently excluded 288 of female faces and hindquarters in the morn-292 ing between 11:00 a.m. and 12:00 p.m. every 2 days. We used 293 a Canon EOS 350D camera with an 8-megapixel CMOS cen-294 sor and an EF 28-135 mm f/3.5-5.6 IS USM lens. We stan-295 dardized images by daily manual setting of the white balance 296 using an X-Rite White Balance Card (GretagMacbeth 297 ColorChecker) and then by taking a picture of a Gretag X-298 Rite Color Checker (24 colored squares of known and varying 299 reflectance) in the exact same conditions as those for the sub-300 ject (i.e., camera settings and distance, orientation from the 301 camera). We assessed color from the whole face and hindquarter areas excluding the eyes, nose, forehead, and tail.

  models (LMMs) fitted by maximum likelihood 354 to examine variation in female facial and hindquarter colora-355 tion separately using nlme (Pinheiro et al. 2014) and lmerTest 356 (Kuznetsova et al. 2017) packages in R version 3.3.3. We 357 checked for correlations between our predictor variables to 358 avoid potential confounding effects of multi-collinearity. 359 Female parity did not correlate with body mass (r s = -0.49, 360 P = 0.10, N = 12) or rank (r s = -0.24, P = 0.45, N = 12). 361 Female body mass was not correlated with rank (r s = -0.03, 362 P = 0.94, N = 12). 363 We first investigated whether facial and hindquarter red-364 ness and luminance co-varied by constructing two LMMs 365 for both facial and hindquarter coloration as follows: response 366 variable: redness; predictor variable: luminance; random fac-367 tors: cycle number nested into female identity. We compared 368 the fitted models with their respective null models in which 369 the predictor variable was removed but the random effect 370 structure was maintained via a likelihood ratio test (LRT). 371 To analyze variation in female redness and luminance, we 372 constructed four LMMs in which the response variable was either facial redness, facial luminance, hindquarter redness, or hindquarter luminance. Inspection of the cumulative distribution functions of each response variable revealed good fits to the lognormal distribution, so each variable was logtransformed prior to model fitting. For all four models, we constructed a full model which included cycle phase (three categories: pre-fertile, fertile, and post-fertile phases), conception (two categories: conceptive and non-conceptive cycles), cycle number (continuous), social rank (continuous), parity (continuous), and body mass (continuous) as fixed effects and female identity as a random effect. All continuous predictors were scaled and centered prior to model fitting to facilitate interpretation of the parameter estimates (effect size of the predictors).

Fig. 1

 1 Fig. 1 Images of one female hindquarters across different cycle phases of one menstrual cycle: pre-fertile phase (left), fertile phase (middle), and postfertile phase (right)

428 1 .

 1 Intra-cycle variation 429 Models including cycle phase better explained the ob-430 served color variance in hindquarter luminance only (LRT: 431 χ 2 = 6.53, Δdf = 2, P = 0.038). Hindquarters became signifi-432 cantly lighter (i.e., higher luminance) during the post-fertile 433

  biologically valid measures of colora-478 tion, our results show that information regarding inter-cycle 479 differences and specific female characteristics relevant to mate 480 choice is potentially indicated by variation in Japanese ma-481 caque skin coloration. Our study demonstrates that female 482 skin (face and hindquarter) coloration (redness and lumi-483 nance) does not convey reliable information about the timing 484 of the fertile phase, as perceived by the Japanese macaque 485 visual system. Our results instead show that female skin col-486 oration is linked to the number of consecutive cycles, the 487 probability of conception across cycles, female social rank, 488 and potentially body mass prior to the mating season, but 489 not to parity. Observed variation in female coloration is likely 490 perceptible under good light conditions, lending biological credibility to these results. Future research should assess male

  timing. Concealing the timing of ovula-513 tion could reduce monopolization by higher-ranking males 514 while increasing the pool of potential mates, therefore simul-515 taneously confusing paternity across males and decreasing the 516 risk of infanticide (van Schaik 2000; van Schaik et al. 2000, 517 2004). In species with polygynandrous mating and relatively 518 high reproductive synchrony, males are less able to monopo-519 lize access to all fertile females and multiple fertile females 520 may be competing for the same males. This can result in an 521 increase in intra-sexual competition (in both females and 522 males) and in selection for the trait to be informative about 523 differences between females. Males that chose between fe-524 males based on their hindquarter coloration would benefit if 525 such signals indicate a female's reproductive value. This is 526 consistent with the promiscuous nature of Japanese macaques 527 mating activity, with females having multiple partners, active-528 ly discriminating between mates, and engaging in sneak cop-529 ulations, and with the alpha male not being able to monopolize 530 all conceptions (Huffman 1992; Inoue et al. 1993; Soltis et al. 1997; Hayakawa 2007; Inoue and Takenaka 2008; Fujita 2010). Female hindquarters were redder during non-conceptive cycles and became less red as the number of consecutive cycles increased. This color change across cycles may be a signal indicating the probability of conception that could be used by males to optimally allocate mating efforts to the first menstrual cycle. However, in our sample, females conceived during the beginning of the mating season (November-December) from their first (N = 2 females) or second cycle (N = 3 females), such that being the first or second cycle, and being the conceptive cycle, are confounded. As such,

605

  rank or reproductive history across breeding years (Sheehan 606 and Bergman 2015), yet such a signal may be of interest for 607 newly immigrant and peripheral males. Extra-group copula-608 tions are not rare in mammals, including in primates (Isvaran 609 and Clutton-Brock 2007; Mitani et al. 2012). In the absence of 610 clear ovulatory signaling, "naïve" males may thus use female 611 skin coloration to make their mating decisions and copulate 612 with females which are more likely to conceive (i.e., discrim-613 inating across cycles and among females). Face coloration 614 could therefore play a role in modulating female and male 615 reproductive success through intra-sexual competition. 616 Our study adds to the growing evidence that female 617 coloration may serve different signaling functions across 618 species by showing that sexual skin color can signal 619 inter-cycle variation and some female characteristics in 620 a primate species lacking obvious ovulatory signaling. 621 Future studies should investigate more deeply the role 622 of female skin coloration in driving mating strategies 623 and sexual communication by examining the relation-624 ship between sexual behaviors, skin coloration, repro-625 ductive status, individual characteristics, and indices of 626 quality (e.g., heritable traits). Such research would help 627 answer outstanding questions in this system, such as the 628 following: does female coloration correlate with herita-629 ble traits associated with higher reproductive success? 630 Do males prefer redder/darker females? Does female 631 coloration co-vary with behavioral, auditory, and olfac-632 tory traits to signal inter-and intra-cycle variation? 633 Studies addressing these questions will help to clarify 634 if and why males and females attend to this colorful 635 trait in Japanese macaques. Ultimately, this research 636 helps to clarify the underlying mechanisms leading to 637 the development of female colorful traits.

  Results of LMM examining the relationship between female hindquarter luminance and the tested predictors. For each categorical comparison, the first level indicates the baseline

	t1:2 Predictors	Lower CI	Upper CI	Value	Std. error	t	P
	t1:3 Cycle number	-0.013	0.158	0.072	0.045	1.626	0.106
	t1:4 Rank	-0.208	-0.029	-0.118	0.040	-2.955	0.018
	t1:5 Parity	-0.192	0.021	-0.086	0.047	-1.805	0.109
	t1:6 Body mass	-0.135	0.063	0.036	0.044	-0.810	0.441
	t1:7 Non-conceptive vs. conceptive	-0.141	0.182	0.020	0.084	0.243	0.809
	t1:8 Fertile vs. post-fertile phases	-0.020	0.252	0.116	0.071	1.657	0.102
	t1:9 Fertile vs. pre-fertile phases	-0.197	0.079	-0.059	0.072	-0.818	0.415
	t1:10 Pre-vs. post-fertile phases	0.038	0.312	0.175	0.071	2.462	0.015

t1:1 Table

1

Table 2

 2 Results of LMM examining the relationship between hindquarter redness and the tested predictors. For each categorical comparison, the first level indicates the baseline

	t2:2 Predictors	Lower CI	Upper CI	Value	Std. error	t	P
	t2:3 Cycle number	-0.165	-0.018	-0.091	0.038	-2.385	0.019
	t2:4 Rank	-0.003	0.122	0.060	0.028	2.128	0.066
	t2:5 Parity	-0.105	0.052	-0.027	0.035	-0.760	0.469
	t2:6 Body mass	-0.001	0.146	0.072	0.033	2.211	0.058
	t2:7 Non-conceptive vs. conceptive	-0.279	-0.021	-0.150	0.067	-2.237	0.027
	t2:8 Fertile vs. post-fertile phases	-0.126	0.123	-0.002	0.065	-0.024	0.981
	t2:9 Fertile vs. pre-fertile phases	-0.184	0.069	-0.057	0.066	-0.869	0.387
	t2:10 Pre-vs. post-fertile phases	-0.069	0.181	0.056	0.065	0.856	0.394

Table 3

 3 Results of LMM examining the relationship between female facial luminance and the tested predictors. For each categorical comparison, the first level indicates the baseline

	t3:2 Predictors	Lower CI	Upper CI	Value	Std. error	t	P
	t3:3 Cycle number	0.020	0.157	0.088	0.035	2.492	0.014
	t3:4 Rank	-0.142	0.049	-0.047	0.043	-1.102	0.303
	t3:5 Parity	-0.064	0.150	0.043	0.048	0.897	0.396
	t3:6 Body mass	-0.005	0.192	0.093	0.044	2.119	0.067
	t3:7 Non-conceptive vs. conceptive	-0.041	0.243	0.101	0.074	1.365	0.175
	t3:8 Fertile vs. post-fertile phases	-0.092	0.107	0.007	0.052	0.144	0.886
	t3:9 Fertile vs. pre-fertile phases	-0.092	0.111	0.010	0.053	0.185	0.853
	t3:10 Pre-vs. post-fertile phases	-0.102	0.098	-0.002	0.052	-0.045	0.964

JrnlID 265_ArtID 2712_Proof# 1 -25/06/2019

(or age) influences skin coloration, we predict that fe-

Acknowledgments We thank Amélie Chimènes for her help with the 639 preparation of the digital photography. We also thank The Center for


Lucie Rigaill
email: lucie.rigaill@gmail.com

Michel Raymond

J Duboscq

C Garcia

Fine-scale variation in lip and cheek colour according to the timing of ovulation in women

Keywords: Red skin colour, Information content, Ovulation, Lips, Human, Primate

Various animal species have evolved a sexual communication system with females displaying and males discriminating information about the timing of ovulation through sexual signals. More research is now investigating the potential ovulatory signalling function of female red skin colour in human and non-human primates. However, to date it is still challenging to draft satisfying hypotheses about the evolution and function of female red skin colour, due to methodological discrepancies between human and non-human primate studies. The present study used a within-individual design and objective methods to analyse the relationship between fine-scale variation in cheek and lip colour (luminance and redness) and the estimated day of ovulation in 15 cycling women. I found weak evidence that intra-cycle variation in lip luminance only may be less modulated by inter-individual variation, with lips getting slightly darker around ovulation. However, day to day variation in lip luminance is likely imperceptible, meaning that lip luminance may not act as an ovulatory signal in humans. This study adds to the growing research and discussion on the role and evolution of female red skin colour of human and non-human primates in the context of sexual signalling and mate attraction.

Introduction

Do females display visual information about their reproductive status that can modulate mate attraction and mating strategies? This question is central to sexual selection theory. The number of offspring a female can have is constrained by physiological factors such as menstrual cyclicity, gestation and post-partum amenorrhea, as well as reproductive senescence. Reproduction is usually more costly for females due to the production of larger gametes, extended maternal care, and male monopolization [START_REF] Galef | Costs and benefits of mammalian reproduction[END_REF]; [START_REF] Gittleman | Energy allocation in mammalian reproduction[END_REF]. Thus, in several species, females appear to have evolved traits which are attractive to males and can act as probabilistic signals of ovulation to maximize reproduction while balancing its associated costs. Across human and non-human primates (hereafter, primates), there is evidence that female traits influence male behaviours, suggesting common evolutionary pathways and underlying mechanisms for sexual signalling [START_REF] Campbell | Primate sexuality and reproduction[END_REF][START_REF] Dixson | Primate sexuality: comparative studies of the prosimians, monkeys, apes and human beings, 2nd edn[END_REF]).

Among the different female traits, there is a growing interest in the potential role of red skin colour in primate sexual communication. Intra-cycle variation in oestrogens induces ovulation and also affects some chromatic (redness) and achromatic (luminance) parameters of skin colour [START_REF] Rhodes | Effects of administration of testosterone, dihydrotestosterone, oestrogen and fadrozole, an aromatase inhibitor, on sex skin colour in intact male rhesus macaques[END_REF][START_REF] Thornton | The biological actions of estrogens on skin[END_REF].

Circulating oestrogens bind to receptors in the skin, causing an increase in blood flow and consequently a decrease in the perceived skin luminance (i.e., darkening of the skin) [START_REF] Thornton | The distribution of estrogen receptor β is distinct to that of estrogen receptor α and the androgen receptor in human skin and the pilosebaceous unit[END_REF][START_REF] Pelletier | Localization of sex steroid receptors in human skin[END_REF]. Increase in blood flow can modulate the ratio of oxygenated/deoxygenated blood in the skin vessels which may influence perceived redness. Primate studies provide evidence that facial skin colour varies across the cycle in mandrills [START_REF] Setchell | Signal content of red facial coloration in female mandrills (Mandrillus sphinx)[END_REF], contains information about the probability of ovulation in rhesus macaques [START_REF] Dubuc | Sexual skin color contains information about the timing of the fertile phase in free-ranging Macaca mulatta[END_REF][START_REF] Higham | Color signal information content and the eye of the beholder: a case study in the rhesus macaque[END_REF], and advertises pregnancy but not ovulation in Japanese macaques [START_REF] Rigaill | Multimodal advertisement of pregnancy in free-ranging female Japanese macaques (Macaca fuscata)[END_REF][START_REF] Rigaill | The redder the better? Information content of red skin coloration in female Japanese macaques[END_REF]. Moreover, red skin colour appears to be attractive to males suggesting a role in mate attraction, at least in macaques [START_REF] Higham | Color and mate choice in non-human animals[END_REF].

Cheek and lip colour also correlate with female attractiveness in human [START_REF] Stephen | Lip colour affects perceived sex typicality and attractiveness of human faces[END_REF]Re et al. 2011;Young 2015;[START_REF] Pazda | Women's facial redness increases their perceived attractiveness: Mediation through perceived healthiness[END_REF]. Skin colour may thus be involved into human mate attraction, although the colour of the stimuli was artificially manipulated in previous studies, which may impair the ecological validity of the results. Studies of the potential signalling function of red skin colour in women yielded mixed results. [START_REF] Oberzaucher | The myth of hidden ovulation: Shape and texture changes in the face during the menstrual cycle[END_REF] described that cheeks were redder around ovulation compared to the end of the cycle while [START_REF] Samson | Does a woman's skin color indicate her fertility level? Preliminary findings[END_REF] could not replicate these findings. Recently, Burris et al. (2015) found no intracycle variation in cheek colour. Interpretation of the informative role of skin colour in ovulatory signalling is however constrained by some methodological limitations. While most studies used photography to analyse skin colour, which provides accurate measurements, they did not always correct lighting conditions across photography sessions using colour standards, which may have altered measurements (White et al. 2015;[START_REF] Rowland | Human colour in mate choice and competition[END_REF]. Human studies usually rely on a restricted data set to assess intra-cycle difference: e.g. 2 samples from mid and late cycle, which can underestimate or overestimate cycle effects (but see [START_REF] Burriss | Changes in women's facial skin color over the ovulatory cycle are not detectable by the human visual system[END_REF]. Finally, human studies often failed to confirm ovulation with sex hormone profiles (with the exception of Burriss et al. 2015, ovulation tests), especially when studying perceptions of intra-cycle variation. Taken together, these methodological limitations constrain our understanding of the potential role of female red skin colour in sexual signalling in humans.

To determine if women display a colourful trait that may play a role in ovulatory signalling, there is a fundamental need for more studies of the relationship between fine-scale variation in trait expression and the probability of ovulation. Such studies would benefit from objective and quantitative methods, inspired by primate studies, using standardized photography, regular biological sampling, and hormonal estimation of the ovulation date [START_REF] Bergman | A simple method for measuring colour in wild animals: validation and use on chest patch colour in geladas (Theropithecus gelada)[END_REF][START_REF] Stevens | Studying primate color: towards visual system-dependent methods[END_REF][START_REF] Hodges | Field endocrinology: Monitoring hormonal changes in free-ranging primates[END_REF]White et al. 2015).

Following this premise, this study aims at investigating whether cheek and lip colour contain information about intra-cycle variation in the probability of ovulation in women. If cheek or lip colour is related to the timing of ovulation within a cycle, I predict that cheeks or lips will be darker/redder around this timing.

Methods

Participants

In total, 18 women participated in the study (mean age = 28.3 ± SD 4.3 years, "Asian" = 11, "Caucasian" = 7, additional information on the supplementary material). All participants were naturally cycling and not taking hormonal contraceptives for at least 3 months prior to and during the study. I collected digital photographs and saliva samples every two days, excluding weekends and national holidays, for the duration of one complete menstrual cycle (i.e., from the beginning of their menstruations until the next ones) between September 2018 and June 2019, to limit the effect of tanning. Sampling occurred at a fixed time of the day for each participant to control for possible diurnal variation in sex hormone concentrations [START_REF] Bao | Diurnal rhythm of free estradiol during the menstrual cycle[END_REF]. I collected a total of 204 photographs and saliva samples (mean par participant = 11.3 ± SD 1.5, range = 8-13). It was not possible to record and analyse data blind, because a single experimenter performed data collection and analyses.

Assessment of cheek and lip colour

Participants removed face and lip make-up a minimum of 30 min before sampling. A single female experimenter photographed the participants (LR), as the sex of the photographer can influence participant facial temperature and potentially skin colour [START_REF] Hahn | Hot or not? Thermal reactions to social contact[END_REF]. Sampling was conducted in a unique location, i.e., an office room with closed curtains, ceiling lights turned on, and a constant 24° C temperature. Participants sat in front of a beige background and adopted a neutral expression. The camera was placed 2m from the participant's chair and held at the same height as the participant's face. The experimenter used a Nikon 5000D camera with a 12.3 megapixel CMOS sensor and a Nikon AF-S NIKKOR 18-55mm f/3.5-5.6G lens. Photographs were collected in NEF format, i.e., Nikon's RAW format, with the flash disabled, the shutter speed and aperture size determined automatically by the camera, and a 55mm focal to limit distortion (Třebický et al. 2016). The experimenter standardised photographs by manual setting the white balance using a X-Rite White Balance Card (GretagMacbeth ColorChecker) and by photographing the participant's face along with a Gretag X-Rite Color Checker (colour standards). This technique standardizes photographs such that colour measurements are comparable across all photographs [START_REF] Bergman | A simple method for measuring colour in wild animals: validation and use on chest patch colour in geladas (Theropithecus gelada)[END_REF][START_REF] Stevens | Studying primate color: towards visual system-dependent methods[END_REF]White et al. 2015). Photographs were converted to uncompressed 16-bit TIFF files. Cheek colour was measured from a pair of points located on the area described in [START_REF] Burriss | Changes in women's facial skin color over the ovulatory cycle are not detectable by the human visual system[END_REF]. Lip colour was measured from the whole lip skin (supplementary material, Fig. S1). CIELAB values were extracted using Colourworker software (Chrometics Ltd. available at: http://www.colourworker.com/) which provided luminance (L*) and red-green ratio (a*, hereafter redness) values calculated from the estimated reflectance spectrum according to the standard CIE (Commission Internationale de l'Éclairage) equations (Vorobyev et al. 1997).

Determination of the estimated ovulation

Participants followed the sampling guideline recommended by Salimetrics (Salimetrics, LLC, USA). Samples were collected during the photo session, labelled and stored within 15 min at -80°C until analyses at KUPRI. Saliva samples were analysed for oestradiol (17ß-estradiol) and progesterone (4-pregenene-3,20-dione) using Salimetrics enzyme immunoassays kits. The oestradiol assay had a sensitivity of 0.1 pg/ml with an intra-assay coefficient of variation (CV) of 6.2 % and inter-assay CV of 10.8 %. The progesterone assay had a sensitivity of 5 pg/ml with an intra-assay CV of 6.6 % and inter-assay CV of 9.7 %.

The onset of the luteal phase was defined as the sample with a progesterone concentration at least 2 standard deviations greater than the mean of the 2-3 preceding baseline values [START_REF] Hodges | Field endocrinology: Monitoring hormonal changes in free-ranging primates[END_REF].

Ovulation was considered to have occurred when a mid-cycle peak of oestradiol was detected around the onset of the luteal phase. Because sampling occurred every 2-3 days, I considered the day of peak oestradiol as the most likely day of ovulation and labelled it as day 0. The day directly preceding the estimated ovulation day was labelled as day -1, the day directly following it as day +1, and so on. Ovulation could not be determined (i.e., abnormal hormone variations) for 3 out of the 18 participants.

Statistical analyses

I used photographs of 15 participants showing ovulatory cycles to analyse intra-cycle variation in cheek and lip luminance and redness (N = 165 photographs, mean per participant = 11.0 ± SD 1.4, range = 8-13). Although this sample appears small, it is within the range of previous studies of fine-scale intra-cycle variation in skin colour in both human [START_REF] Samson | Does a woman's skin color indicate her fertility level? Preliminary findings[END_REF][START_REF] Burriss | Changes in women's facial skin color over the ovulatory cycle are not detectable by the human visual system[END_REF] and non-human primates [START_REF] Dubuc | Sexual skin color contains information about the timing of the fertile phase in free-ranging Macaca mulatta[END_REF][START_REF] Higham | Color signal information content and the eye of the beholder: a case study in the rhesus macaque[END_REF][START_REF] Rigaill | The redder the better? Information content of red skin coloration in female Japanese macaques[END_REF]. That said, the sample size warrants cautious reading of the results. This study tests for a possible quadratic effect of the days relative to ovulation on cheek and lip colour: higher effect toward the estimated ovulation and lower effect toward the beginning and end of the cycle. I thus constructed general linear mixed-effects models (LMMs) for cheek and lip colour (luminance and redness respectively) which included the linear (DAY) and quadratic (DAY 2 ) effects of the days relative to the estimated ovulation as fixed effects, and fitted by maximum likelihood using lme4 [START_REF] Bates | Fitting linear mixed-effects models using lme4[END_REF] and lmerTest [START_REF] Kuznetsova | lmerTest package: Tests in Linear Mixed Effects models[END_REF]) packages in R version 3.6.0 (R Core Team 2019). Inspection of the cumulative distribution functions revealed good fits to the normal distribution for luminance variables and to the lognormal distribution for redness variables [START_REF] Harrison | A brief introduction to mixed effects modelling and multi-model inference in ecology[END_REF]. Prior to modelling, the days relative to the estimated ovulation were standardized to mean = 0 and SD = 1 to improve model performance and interpretability [START_REF] Harrison | A brief introduction to mixed effects modelling and multi-model inference in ecology[END_REF]). On one hand, we can expect that the relationship between the timing of ovulation and colour would be similar across participants; I thus constructed random intercept models (RIM) with random intercepts for participant identity. On the other hand, this relationship may vary between participants; I thus constructed uncorrelated random slope models (RSM) with random slopes for the linear and quadratic terms. I also constructed the respective RIM and RSM null models in which the predictor variables were removed but the random effect structure was maintained. This resulted in 4 candidate models for each colour/skin combination: RIM-full, RIMnull, RSM-full, and RSM-null. I ensured that all relevant model assumptions (homogeneity of the residuals and stability of estimates) were met by visually inspecting histograms of the residuals and plots of residuals against fitted values, and performing Kolmogorov-Smirnov, deviation, and outliers tests (all P > 0.05, except the KS test for the RIM-full for cheek luminance: P = 0.042) using the functions simulateResiduals and testResiduals of the DHARMa package [START_REF] Hartig | DHARMa: Residual Diagnostics for Hierarchical (Multi-Level / Mixed) Regression Models[END_REF]). I used an information-theory approach to objectively compare and rank the 4 candidate models in terms of how well they fitted the existing data thus assessing the likelihood that one or more models among the candidates is/are best supported by the data [START_REF] Burnham | AIC model selection and multimodel inference in behavioral ecology: Some background, observations, and comparisons[END_REF][START_REF] Symonds | A brief guide to model selection, multimodel inference and model averaging in behavioural ecology using Akaike's information criterion[END_REF]. I used the function model.sel of the MuMIn package [START_REF] Bartoń | MuMIn: Multi-Model Inference[END_REF] to rank models based on the Akaike's information criterion corrected for small sample size (AICc values). I reported the weight of the models which indicates to what extent one candidate model is more likely than another to provide a reasonable explanation of the variance in the data, along with the evidence ratio (ER) which indicates the extent to which the higher-ranked model is better than another candidate model. I also reported the marginal (fixed effects alone) and condition (fixed effects and random structures) coefficients of determination (R 2 m and R 2 c) of all models using the function r.squaredGLMM [START_REF] Nakagawa | A general and simple method for obtaining R 2 from generalized linear mixedeffects models[END_REF]. I extracted weighted parameter estimates (β), standard errors (SE), and 95% confidence intervals (95% CIs) of model intercepts and predictors from conditional averaging of the 4 candidate models (function model.avg).

Data availability

All data analysed during this study are provided in the electronic supplementary material.

Results

RIMs generally performed better and had between 5.3-37.5 times more empirical support than the competing RSM models (Table 1).

Concerning cheek colour, the RIM-null provided better explanation of the variance in the luminance data than its respective RIM-full (weight = 0.75, ER = 5.4, Table 1). RIM-full provided slightly better explanation of the variance in the redness data than its respective RIM-null (weight = 0.51, ER = 1.4, Table 1). Participant identity explained most of the observed variance in cheek luminance and redness data (R 2 cs around 80 %).

Concerning lip colour, the RIM-full provided slightly better explanation of the variance in the luminance data than its respective RIM-null (weight = 0.53, ER = 1.8). The RIM-null provided slightly better explanation of the variance in the redness data than its respective RIM-full (weight = 0.60, ER = 2.1). Participant identity explained most of the variation in lip redness data (R 2 cs = 82 %) and around half of the variation in lip luminance data (R 2 cs around 50 %).

The timing of ovulation explained none of the variance in cheek luminance or redness (R 2 ms = 0%, Table 1, Fig. 1). The timing of ovulation explained very little of the variance in lip luminance only (lip redness: R 2 m = 0%; lip luminance: R 2 m = 2% but with only 1.8 times more empirical support than the null hypothesis, Table 1).

Lips became darker around ovulation, with a slight decrease / increase in luminance of 0.21 units on average each day 2 to / from the day of ovulation (ß = 0.21 ± 0.09 SE, 95% CI = 0.03; 0.39, Table 2, Fig. 2).

Discussion

Using objective methods to analyse fine-scale and intra-individual changes in cheek and lip colour according to the timing of ovulation, I found a weak evidence for a relationship between lip luminance, but nor redness, and the timing of ovulation in women. Cheek colour may not be related to the timing of ovulation in agreement with a previous study [START_REF] Burriss | Changes in women's facial skin color over the ovulatory cycle are not detectable by the human visual system[END_REF].

Overall, variation in colour data was mostly explained by inter-individual differences (up to 80% of the variance explained). However, when considering lip luminance only, intra-cycle variation appeared to be less modulated by participant identity, which effect dropped around 50%, and slightly more susceptible to the timing of ovulation (around 2%, which is undeniably small but yet twice as much as its effect on any other colour variable analysed). This may suggest that lip luminance respond differently to intra-and inter-individual effects than other colour variables. The luminance of lip skin may be more susceptible to variation in blood flow as a result of its higher vascularization and finer cellular layers [START_REF] Crouzet | Anatomy of the arterial vascularization of the lips[END_REF] or due to tissue-specific differences in oestrogen receptor expression or sensitivity. The latter has already been suggested to explain the differential effect of cycle phase on facial and hindquarter colour in Japanese macaques [START_REF] Rigaill | The redder the better? Information content of red skin coloration in female Japanese macaques[END_REF]. Further studies on tissue-specific expression and sensitivity of oestrogen receptors would help to clarify this question. Alternatively, skin colour changes, and especially redness, may be more condition-dependent and related to individual effects such as health or heritability (Re et al. 2011;[START_REF] Dubuc | Sexually selected skin colour is heritable and related to fecundity in a non-human primate[END_REF][START_REF] Pazda | Women's facial redness increases their perceived attractiveness: Mediation through perceived healthiness[END_REF][START_REF] Thorstenson | Facial redness increases men's perceived healthiness and attractiveness[END_REF].

Lip luminance varied of roughly 0.21 units each day 2 to / from ovulation. Day to day and overall intracycle variation in lip luminance don't achieve a change of more than 2.2 units, i.e., the threshold of colour discrimination in humans [START_REF] Brainard | Color appearance and color difference specification[END_REF]. Therefore, variation in lip luminance is likely imperceptible (at least in this sample), which is not really surprising since we may have noticed this about our own species. While lip luminance is unlikely an ovulatory signal it could still play a role in mate attraction and mating decision, if darker lips are attractive regardless of being informative about the timing of ovulation. Further studies should assess men and women responses toward inter-individual variation in lip colour to determine if this is the case. However, caution should be used when designing such experiments. Studies should avoid using composite stimuli from different participants and should control for the reproductive stage and sex hormones levels associated with the tested stimuli. Studies should also collect and test multiple samples per individual in order to detect fine-scale variation, and confirm ovulation using hormonal data or at minimum with ovulation detection kit. Such experimental design should reduce the risk of over-or under-estimating a potential cycle effect. However, whether variation in this trait is detectable under "optimal" conditions, i.e., artificial environments and controlled settings, does not necessarily entail consequences on human sexual communication and mate preferences since laboratory studies can have low ecological validity.

It should be noted again that the timing of ovulation explained only 2% of the variance in the data, which is quite a weak effect. This could suggest a correlation effect without causation between lip luminance and the timing of ovulation. However, a biological relationship does exist between skin luminance and variation in circulating oestrogens in humans, although presently weak in this sample, as in non-human primates [START_REF] Rhodes | Effects of administration of testosterone, dihydrotestosterone, oestrogen and fadrozole, an aromatase inhibitor, on sex skin colour in intact male rhesus macaques[END_REF][START_REF] Thornton | The biological actions of estrogens on skin[END_REF]. Thus, humans could have inherited the biological bases and mechanisms of expression for female red skin colour from a primate ancestor. This doesn't necessarily imply that lip luminance plays or does not play an active role in concealing ovulation or in mate choice in our species, i.e., the expression of red skin could have been maintained because it does not impose costs on women. However, investigating the possible different forms (traits) and functions (e.g., signalling/concealing the timing of ovulation) of female red skin colour in human and non-human primate species is necessary to better understand their evolution, i.e., to unveil the different socio-ecological constraints on sexual communication and mate choice.

The differences in red skin traits (face, lips, and sexual skin) and signalling functions probably result from the different socio-environmental constraints on mating across species. Concealing the reproductive status may have evolved in species facing higher male monopolization or pair-bonding, lower intra-sexual competition, and higher costs on signalling; while higher infanticide risks and intra-sexual competition, limited mating opportunities, and lower costs on signalling may have favoured exaggerated or multimodal signalling [START_REF] Fitzpatrick | The evolution of male mate choice and female ornamentation: a review of mathematical models[END_REF][START_REF] Rooker | On the evolution of visual female sexual signalling[END_REF]. However, these proposed effects do not appear to fully explain the inter-species differences observed in female red skin colour functions, as species with similar socio-ecology express traits that may be involved in signalling or not signalling ovulation [START_REF] Higham | Color signal information content and the eye of the beholder: a case study in the rhesus macaque[END_REF][START_REF] Rigaill | The redder the better? Information content of red skin coloration in female Japanese macaques[END_REF]). More studies using longitudinal and ecologically valid designs are needed to better understand the possible evolutionary pathways and underlying mechanisms leading to the evolution of female red skin colour in primate species including humans. Researches duplicating the present study design with a greater sample size would especially help to clarify the link between lip luminance, ovulation, and potentially mate choice in humans. Table 1 Characteristics of candidate models for cheek and lip redness and luminance. AICc: corrected Akaike's information criterion, weight: model probabilities, ER: evidence ratios, R 2 m -R 2 c: marginal and conditional coefficients of determination. For each colour variable, candidate models are presented from higher-ranked to lower-ranked ones Table 2 Model averaged parameters estimates (ß) ± standard errors (SE) and confidence intervals (95% CIs) from conditional averaging of all candidate models. Result for which CI does not include zero are presented in bold

Compliance with ethical standard

Fig 1 Fig 2

 12 Figure captions Fig 1 Relationship between cheek (a) luminance and (b) redness and the days relative to the estimated ovulation. Raw data are presented as grey circle. The red line presents the global model prediction; the black lines show prediction for each participant

Research Institute for permission to conduct my research. I would like to sincerely thank C. Neumann for his MacIntosh for their comments on earlier versions of the manuscript, and to K. Mouri for her general support in the lab.

Funding information. This work was supported by the Japanese Society for the Promotion of Science (project 18H05810 JSPS).

Data availability. The data set generated and analysed during the current study is available in the supplementary material.