Ségolène Delaitre
email: segolene.delaitre@cefe.cnrs.fr

Claire Doutrelant

Samuel P Caro

Whoever their partner, female blue tits breed the same

Keywords: reproduction, mate preference, birds, laying date, clutch size

Do females modify their reproductive investment if they do not succeed to pair with a male that matches their preference? In a two-year experiment, we asked female blue tits (Cyanistes caeruleus) to select among six males, and then successively paired them with their preferred and their most avoided male. We monitored female reproductive investment through nest building activity, timing of breeding, size and number of eggs, number of fertilised eggs, and brood sex-ratio. We found that females preferred males with a chromatic coloration (blue UV chroma of the head crown) that matched their own, but also that they preferred males with a lower achromatic coloration (less bright color of the cheeks and head crown). Although females paired with their preferred males tended to build heavier nests during the breeding season, we found no evidence for an effect of the pairing treatment on timing of breeding, or any other aspects of female reproductive investment. We however found that laying dates, clutch sizes, egg sizes and brood sex-ratio were significantly repeatable within females between the two years, despite the opposite pairing treatments. These findings show that in female blue tits, the males with which they are paired do not substantially alter their reproductive decisions.

Introduction

Mate choice is a major component of sexual selection in the animal kingdom [START_REF] Andersson | Sexual selection[END_REF][START_REF] Cotton | Sexual selection and condition-dependent mate preferences[END_REF][START_REF] Höner | Female mate-choice drives the evolution of male-biased dispersal in a social mammal[END_REF][START_REF] Locatello | Context-dependant evaluation of prospective mates in a fish[END_REF]. Individuals can derive benefits for themselves in the present generation, or for their offspring in the following generation, from carefully choosing a mate [START_REF] Andersson | Sexual selection and mate choice[END_REF][START_REF] Jones | Mate choice and sexual selection: What have we learned since darwin?[END_REF][START_REF] Kokko | The evolution of mate choice and mating biases[END_REF]. They can consequently be expected to evaluate traits indicating partner condition, characteristics and quality. Animals might use physical characteristics to select their mate, like coloration [START_REF] Baube | The mechanisms of colour-based mate choice in female threespine stricklebacks: hue, contrast and configurational cues[END_REF][START_REF] Rowland | Video playback experiments on stickleback mate choice: female motivation and attentiveness to male colour cues[END_REF][START_REF] Pryke | The relative role of male vs. female mate choice in maintaining assortative pairing among discrete colour morphs[END_REF][START_REF] Gomez | Support for a role of colour vision in mate choice in the nocturnal European treefrog (Hyla arborea)[END_REF] or size [START_REF] Mckaye | Mate choice and size assortative pairing by the cichlid fishes of Lake Jiloá, Nicaragua[END_REF][START_REF] Howard | Mate choice and mate competition influence male body size in Japanese medaka[END_REF][START_REF] Shine | Pick on someone your own size: Ontogenetic shifts in mate choice by male garter snakes result in size-assortative mating[END_REF][START_REF] Romero-Pujante | Tail length and mutual mate choice in bearded tits (Panurus biarmicus)[END_REF][START_REF] Hoefler | Male mate choice and size-assortative pairing in a jumping spider, Phidippus clarus[END_REF]. They can also use behavioral traits such as song characteristics [START_REF] Searcy | Song repertoire and mate choice in birds[END_REF][START_REF] Wagner | The importance of calling song and courtship song in female mate choice in the variable field cricket[END_REF][START_REF] Byers | Female mate choice and songbird song repertoires[END_REF][START_REF] Riebel | Chapter 6 Song and Female Mate Choice in Zebra Finches: A Review[END_REF][START_REF] Caro | Female Lincoln's sparrows modulate their behavior in response to variation in male song quality[END_REF][START_REF] Iglesias | The role of courtship song in female mate choice in South American Cactophilic Drosophila[END_REF], courtship behaviors [START_REF] Zuk | The role of male ornaments and courtship behavior in female mate choice of red jungle fowl[END_REF][START_REF] Sargent | Courtship and mate choice in fishes: integrating behavioral and sensory ecology[END_REF][START_REF] Kallman | Excitation and inhibition onto central courtship neurons biases drosophila mate choice[END_REF][START_REF] Ota | Tap dancing birds: The multimodal mutual courtship display of males and females in a socially monogamous songbird[END_REF], personality [START_REF] Van Oers | Personality is associated with extrapair paternity in great tits, Parus major[END_REF][START_REF] Schuett | Do female zebra finches, Taeniopygia guttata, choose their mates based on their "personality[END_REF][START_REF] Bierbach | Personality affects mate choice: Bolder males show stronger audience effects under high competition[END_REF][START_REF] Chen B Jian | Personality differentially affects individual mate choice decisions in female and male Western mosquitofish (Gambusia affinis)[END_REF][START_REF] Delaitre | Female great tits (Parus major) reproduce earlier when paired with a male they prefer[END_REF] or cognitive abilities [START_REF] Boogert | Mate choice for cognitive traits: A review of the evidence in nonhuman vertebrates[END_REF][START_REF] Kavaliers | Social cognition and the neurobiology of rodent mate choice[END_REF]. Even the chooser's own phenotype, such as its condition, coloration or size [START_REF] Hunt | Female mate choice as a condition-dependent lifehistory trait[END_REF][START_REF] Holveck | Low-quality females prefer low-quality males when choosing a mate[END_REF]Riebel et al. 2010;[START_REF] Rueger | Size matters: Male and female mate choice leads to size-assortative pairing in a coral reef cardinalfish[END_REF][START_REF] Caro | Mutual mate preferences and assortative mating in relation to a carotenoid-based color trait in blue tits[END_REF], can play a decisive role at the time they decide with whom to mate. All those criteria can be used separately or in combination (Burley 1981a;[START_REF] Candolin | The use of multiple cues in mate choice[END_REF].

Females, historically considered the choosing sex [START_REF] Jones | Mate choice and sexual selection: What have we learned since darwin?[END_REF][START_REF] Davies | An introduction to behavioural ecology[END_REF], were initially assumed to reach a consensus about who is the most attractive male, and inter-individual variation in female preference and in the optimal male phenotype were therefore expected to be low [START_REF] Real | Search Theory and Mate Choice . I . Models of Single-Sex Discrimination[END_REF][START_REF] Jennions | Variation in mate choice and mating preferences: A review of causes and consequences[END_REF]. However, in some species, mating preferences seem largely individual-specific, suggesting that they might rather target genetic or behavioral compatibility [START_REF] Jennions | Variation in mate choice and mating preferences: A review of causes and consequences[END_REF][START_REF] Widemo | Beauty is in the eye of the beholder: Causes and consequences of variation in mating preferences[END_REF][START_REF] Brooks | Female guppies agree to differ: Phenotypic and genetic variation in mate-choice behavior and the consequences for sexual selection[END_REF][START_REF] Forstmeier | Repeatability of mate choice in the zebra finch: Consistency within and between females[END_REF][START_REF] Cotton | Sexual selection and condition-dependent mate preferences[END_REF][START_REF] Rosenthal | Sexual selection and the ascent of women: Mate choice research since Darwin[END_REF].

Beyond the difficulty of understanding mate selection processes and targets, the impact of partner selection on female reproductive timing, investment, and physiology is also not easy to predict [START_REF] Burley | The differential-allocation hypothesis: an experimental test[END_REF][START_REF] Frank | Sex allocation theory for birds and mammals[END_REF][START_REF] Penn | The evolution of mating preferences and major histocompatibility complex genes[END_REF][START_REF] Mays | Choosing mates: Good genes versus genes that are a good fit[END_REF][START_REF] Gowaty | The hypothesis of reproductive compensation and its assumptions about mate preferences and offspring viability[END_REF][START_REF] Bolund | Compensatory investment in zebra finches: Females lay larger eggs when paired to sexually unattractive males[END_REF]. Two main, non-mutually exclusive hypotheses have been proposed to explain why females would invest differently depending on their preference for their partner.

First, the differential allocation hypothesis states that an individual adjusts its investment in its current reproductive effort according to the perceived attractiveness, or overall quality of its partner (Burley 1986;[START_REF] Burley | The differential-allocation hypothesis: an experimental test[END_REF][START_REF] Sheldon | Differential allocation: Tests, mechanisms and implications[END_REF][START_REF] Haaland | Differential allocation revisited: When should mate quality affect parental investment?[END_REF]. A higher number of offspring and of higher quality are consequently expected when females are paired with a male of higher perceived quality [START_REF] De Lope | Female reproductive effort depends on the degree of ornamentation of their mates[END_REF][START_REF] Gil | Male attractiveness and differential testosterone investment in zebra finch eggs[END_REF][START_REF] Cunningham | Egg investment is influenced by male attractiveness in the mallard[END_REF][START_REF] Gowaty | Male house mice produce fewer offspring with lower viability and poorer performance when mated with females they do not prefer[END_REF][START_REF] Limbourg | Female blue tits adjust parental effort to manipulated male UV attractiveness[END_REF][START_REF] Velando | Pigment-based skin colour in the bluefooted booby: An honest signal of current condition used by females to adjust reproductive investment[END_REF]Anderson et al. 2007;[START_REF] Gowaty | The hypothesis of reproductive compensation and its assumptions about mate preferences and offspring viability[END_REF][START_REF] Walling | Do female association preferences predict the likelihood of reproduction?[END_REF]. For example, female zebra finches lay on average 0.5 eggs more when paired with their preferred males, which produce songs of longer duration and faster rate, and are consequently considered higher quality males [START_REF] Balzer | Do female zebra finches vary primary reproductive effort in relation to mate attractiveness?[END_REF]. In mallards (Anas platyrhynchos), females mated with a less-preferred male produce smaller eggs and therefore lower quality offspring [START_REF] Cunningham | Egg investment is influenced by male attractiveness in the mallard[END_REF][START_REF] Bluhm | Social constraints on female mate preferences in mallards, Anas platyrhynchos, decrease offspring viability and mother productivity[END_REF].

Second, the sex-allocation theory predicts that, when the fitness of sons and daughters differs, parents should adjust the sex-ratio of their brood [START_REF] Charnov | The theory of sex allocation[END_REF][START_REF] Frank | Sex allocation theory for birds and mammals[END_REF][START_REF] Booksmythe | Facultative adjustment of the offspring sex ratio and male attractiveness: a systematic review and meta-analysis[END_REF]. Consequently, when sons inherit from their fathers some traits that determine their own attractiveness, females are expected to adjust their brood sex-ratio depending on the qualities of the male with which they are paired (Burley 1981b;Burley 1986;[START_REF] Hardy | Sex ratios concepts and research methods[END_REF][START_REF] Saino | Offspring sexual dimorphism and sex-allocation in relation to parental age and paternal ornamentation in the barn swallow[END_REF][START_REF] West | Constraints in the evolution of sex ratio adjustment[END_REF][START_REF] Sato | Female control of offspring sex ratios based on male attractiveness in the guppy[END_REF][START_REF] Bowers | Cross-fostering eggs reveals that female collared flycatchers adjust clutch sex ratios according to parental ability to invest in offspring[END_REF][START_REF] Booksmythe | Facultative adjustment of the offspring sex ratio and male attractiveness: a systematic review and meta-analysis[END_REF]. Females are therefore predicted to produce more sons when mated to a male of higher quality. Great tit (Parus major) females have for example been suggested to produce more sons when they are paired to larger males [START_REF] Kölliker | Offspring sex ratio is related to male body size in the great tit (Parus major)[END_REF].

Studies investigating the traits used in mate choice and its consequences on reproductive investment have usually been conducted in the wild [START_REF] Bonneaud | Complex Mhc-based mate choice in a wild passerine[END_REF][START_REF] Foerster | A spatial genetic structure and effects of relatedness on mate choice in a wild bird population[END_REF][START_REF] Eriksen | Interspecific cross-fostering affects song acquisition but not mate choice in pied flycatchers, Ficedula hypoleuca[END_REF][START_REF] García-Navas | Heterozygosity-based assortative mating in blue tits (Cyanistes caeruleus): Implications for the evolution of mate choice[END_REF][START_REF] Fargevieille | Assortative mating by colored ornaments in blue tits: space and time matter[END_REF]). The drawback is that it is often impossible to control, and even know, all the factors that influence mate choice and its subsequent effects on reproduction. The pairings observed in the wild are indeed the result of a series of events mixing mate preferences, competition with other females for males and territories, male availability, and finally mate choice [START_REF] Jennions | Variation in mate choice and mating preferences: A review of causes and consequences[END_REF][START_REF] Widemo | Beauty is in the eye of the beholder: Causes and consequences of variation in mating preferences[END_REF][START_REF] Edward | The description of mate choice[END_REF][START_REF] Scauzillo | Factors that affect non-independent mate choice[END_REF]. Disentangling the respective roles of the different mate choice components may therefore request experiments in controlled conditions, which artificial characteristics may in turn hamper the expression of natural behaviors. In the case of mate preference studies, many have only offered binary choices between two potential partners [START_REF] Amundsen | On the function of female ornaments: Male bluethroats prefer colourful females[END_REF][START_REF] Witte | Sexual imprinting on a novel adornment influences mate preferences in the Javanese Mannikin Lonchura leucogastroides[END_REF][START_REF] Romero-Pujante | Tail length and mutual mate choice in bearded tits (Panurus biarmicus)[END_REF][START_REF] Tomaszycki | Experimental alteration of male song quality and output affects female mate choice and pair bond formation in zebra finches[END_REF][START_REF] Burley | Variation in female choice of mates: condition influences selectivity[END_REF][START_REF] Rutstein | Evaluating mate choice in the zebra finch[END_REF][START_REF] Reparaz | Mate preference of female blue tits varies with experimental photoperiod[END_REF][START_REF] Kniel | Novel mate preference through mate-choice copying in zebra finches: Sexes differ[END_REF][START_REF] Caro | Mutual mate preferences and assortative mating in relation to a carotenoid-based color trait in blue tits[END_REF], or have only manipulated one phenotypic trait and not the overall signaling value of an individual [START_REF] Clayton | Mate choice and pair formation in Timor and Australian Mainland zebra finches[END_REF][START_REF] Bennett | Ultraviolet vision and mate choice in zebra finches[END_REF][START_REF] Waas | Female zebra finches prefer symmetrically banded males, but only during interactive mate choice tests[END_REF][START_REF] Caro | Mutual mate preferences and assortative mating in relation to a carotenoid-based color trait in blue tits[END_REF][START_REF] Cantarero | Mate choice is affected by parasite infestation rate of the choosing individual as well as of potential mating partners[END_REF], which may lead to unnatural contrasts among the sexual signals conveyed [START_REF] Caro | Mutual mate preferences and assortative mating in relation to a carotenoid-based color trait in blue tits[END_REF]).

In the present study, we adopted an intermediate approach mixing the advantages of wild and captive studies, to test the two hypotheses described above. We first investigated mate preferences of blue tits (Cyanistes caeruleus) in captivity by offering females the choice between six, unmanipulated, males. In particular, we evaluated whether male body size, personality and color traits explain the preference patterns expressed. We then paired half of the females with their preferred male and the other half with their most avoided one. We conducted this experiment over two years, so that each female was paired with its preferred male in one year and with its most avoided male in the other. Thus, each female acted as her own control. In line with the differential allocation hypothesis and the sex allocation theory, linking reproductive investment to mate preference, we hypothesised that females paired with their favorite male would lay more and larger eggs, and would produce more fertilised eggs (differential allocation hypothesis), and more sons (sex allocation theory). In addition, we also hypothesised that females paired with their favorite male would build heavier nests and lay earlier in the season. Indeed, nest-building activities of females are stimulated by the presence of a male [START_REF] Hinde | The effect of male song on an estrogen-dependent behavior pattern in the female canary (Serinus canarius)[END_REF], and males can stimulate female gonadal development and hormone secretions through social interactions [START_REF] Erickson | Effect of Castration of Male Ring Doves upon Ovarian Activities of Females[END_REF][START_REF] Hinde | The effect of male song on an estrogen-dependent behavior pattern in the female canary (Serinus canarius)[END_REF][START_REF] Hinde | The Influence of Daylength and Male Vocalizations on the Estrogen-Dependent Behavior of Female Canaries and Budgerigars, with Discussion of Data from Other Species[END_REF][START_REF] Silverin | Influence of the opposite sex on photoperiodically induced LH and gonadal cycles in the Willow tit (Parus montanus)[END_REF][START_REF] Stevenson | Effects of social cues on GnRH-I, GnRH-II, and reproductive physiology in female house sparrows (Passer domesticus)[END_REF][START_REF] Perfito | Social cues regulate reciprocal switching of hypothalamic dio2/dio3 and the transition into final follicle maturation in European starlings (Sturnus vulgaris)[END_REF], which can result in earlier laying [START_REF] Adkins-Regan | Monogamy on the fast track[END_REF][START_REF] Griffith | Constrained mate choice in social monogamy and the stress of having an unattractive partner[END_REF][START_REF] Crino | Divorce in the socially monogamous zebra finch: Hormonal mechanisms and reproductive consequences[END_REF][START_REF] Delaitre | Female great tits (Parus major) reproduce earlier when paired with a male they prefer[END_REF].

Methods

Ethical note

Blue tits were trapped and maintained under licenses 2018-s-11 issued by the Direction Régionale de l'Environnement, de l'Aménagement et du Logement Languedoc-Rousillon; and 15-XIX-116 issued by the Direction Départementale de la Protection des Populations de l'Hérault. Experiments were run under the license 2017-XIX-075 from the Direction Départementale de la Protection des Populations de l'Hérault, and approved by the Ethical committee N°036 with reference APAFIS#2021120712067677 #34249 v2.

Birds and general procedures

Blue tits originated from the long-term studied population of La Rouvière (43.621°, 3.733°) at Montarnaud near Montpellier. They were born in the wild in 2019, collected as chicks (10 days old) in nest-boxes, and subsequently hand-raised in captivity until independence (35 days old), following the procedure described in [START_REF] Reparaz | Mate preference of female blue tits varies with experimental photoperiod[END_REF] and [START_REF] Caro | Mutual mate preferences and assortative mating in relation to a carotenoid-based color trait in blue tits[END_REF].

Birds were kept in large outdoor aviaries (27 m 3 ) as standard housing. They were fed with cake made of sunflower seed grease, eggs, sugar, wheat flour and high-protein pellets (Show 1+2 crumble, Versele-Laga, Deinze, Belgium), supplemented with minerals, vitamins, amino-acids and carotenoids (Nutribird A21, Versele-Laga, Deinze, Belgium; Nekton-S, Günter Enderle, Pforzheim, Germany; Yel-Lux, Versele-Laga, Deinze, Belgium) and mealworms. Food and water were provided ad libitum.

Preference test Experimental subjects and housing

The experiment took place at the CEFE in Montpellier, France, for two consecutive years. We used 24 female and 29 male blue tits the first year and 23 females and 23 males the second year. All birds used in the second year had already been used the first one, in such a way that each female acted as its own control (see below). Birds were moved from aviaries to individual cages (0.8 x 0.4 x 0.35 m) on 8 th December 2020 and on 11 th January 2022, across 3 indoor rooms. Females and males were housed in separate rooms. Windows in rooms allowed birds to be exposed to natural light, and supplementary artificial lightning was provided from 15min after natural sunrise until 15 min before sunset to respect the natural increase and decrease of light intensity every day. Windows were left open to expose birds to natural fluctuations of temperature.

Experimental setup

Females were tested in a carrousel-shaped six-choice chamber inspired by [START_REF] Zandberg | Direct fitness benefits explain mate preference, but not choice, for similarity in heterozygosity levels[END_REF] (figure 1, figure S1) from 12 th to 21 st December 2020 for the first year and from 19 th to 24 th February 2022 for the second year. We ran the preference tests a bit later in 2022 compared to 2021 in order to be a bit closer to breeding. All tests took place in a test room (4.0 x 2.4 x 2.5 m) with white walls, and high-frequency fluorescent lights. In the six-choice setup, each female could see all stimulus male birds from the central platform, but when in the choice zone of a stimulus male, she could not see the other males (figure 1). The males were visually isolated from each other. Before being tested, each female was given 15 min to habituate to this new environment. In the meantime, the six stimulus males were transferred from their home cage to six individual mobile cages (47 x 28 x 26 cm) in an adjacent room. At the end of the 15 min habituation period, each male cage was placed into one of the six compartments of the carrousel. Each female was tested once with one group of six stimulus males during 90 minutes.

The experimenter left the room at the beginning of the test, which was video-recorded using three GoPro cameras (GoPro, Inc., USA) affixed above the test chamber. After each test, all birds were returned to their individual home cages. Videos were analysed soon after the end of each test and, depending on the treatment to which the female was assigned for the breeding experiment (see below), the male with which she spent the most time (hereafter called the preferred male) or the lowest amount of time (hereafter called avoided), was pulled out of the pool of available males for the next females to be tested. Stimulus males could not belong to the family of the female tested and their positions in the setup were randomised for each test. Females were tested for their preference in a six-choice setup for 90 min. From the hexagonal central platform, the focal female could observe all stimulus male birds, whereas only one stimulus male was visible from the perch in the choice zone. The stimulus male birds could not see each other. Time spent in the choice zone of each male was inferred as a proxy for preference. At the end of each test, videos were analysed and, depending on the treatment assigned to the female, the preferred (or avoided) male was pull out of the pool of available males for the next females tested. Positions of the stimulus male birds were randomised for each test.

Video analysis

Videos were analysed using Behavioral Observation Research Interactive Software (BORIS) [START_REF] Friard | BORIS: a free, versatile open-source event-logging software for video/audio coding and live observations[END_REF] version 7.9.7-14/01/2020 (https://www.boris.unito.it/). The time spent by the females in the choice zone of each stimulus male bird was extracted from each video, and used as a proxy for mate-choice [START_REF] Gonçalves | Time spent close to a sexual partner as a measure of female mate preference in a sex-role-reversed population of the blenny Salaria pavo (Risso) (Pisces: Blenniidae)[END_REF][START_REF] Witte | Time spent with a male is a good indicator of mate preference in female zebra finches[END_REF].

All females visited the choice zone of each male at least once during the 90 min of the test.

Neither the males nor the females showed any clear solicitation of mating behavior. The time spent by the female in the choice zone of the male was consequently the most appropriate and direct method for estimating female preference.

Phenotypic trait measurements

To identify on which criteria females choose their mate, a set of phenotypic traits was measured on each male and female tested, ahead of the preference tests each year. We measured an achromatic trait, brightness (i.e. the area under the reflectance curve divided by the width of the interval from 300-700 nm, and that can be defined as the total amount of light reflected from the measured surface [START_REF] Saks | How feather colour reflects its carotenoid conntent[END_REF])) for the white of the cheek, the yellow of the breast and the UV-blue of the head crown, and a chromatic trait, chroma (i.e. the proportion of the total reflectance falling in the color range) for UV-blue of the head crown (R300-400 / R300-700) and yellow of the breast (Rmax 500-700 -R450 / R300-700) [START_REF] Fargevieille | Assortative mating by colored ornaments in blue tits: space and time matter[END_REF]). Higher UVchroma values correspond to a stronger UV signal, and higher yellow chroma values are associated with higher levels of carotenoids in the plumage [START_REF] Isaksson | Sex and age differences in reflectance and biochemistry of carotenoid-based colour variation in the great tit Parus major[END_REF]). We measured coloration of each bird with a spectrophotometer (AVASPEC 2048, Avantes, Apeldoorn, the Netherlands) equipped with an AVALIGHT-DHS deuterium-halogen lamp (Avantes, Apeldoorn, the Netherlands) and a 200 µm optical probe (FCR-7UV200-2-45-ME, Avantes, Apledoorn, the Netherlands) whose tip contained a 45° quartz window. Reflectance was calculated in relative terms, via comparison with a black and a white reference (WS1, Ocean Optics, Dunedin FL, USA). We also took morphological measures, including body mass, tarsus, beak and wing lengths. Ahead of the present study, a personality score was derived from exploratory behavior trials in a novel environment, following the protocol described in [START_REF] Charmantier | Urbanization is associated with divergence in pace-of-life in great tits[END_REF] and [START_REF] Dubuc-Messier | Environmental heterogeneity and population differences in blue tits personality traits[END_REF]. Briefly, each bird was released separately in a novel environment, which consisted of an exploration cage equipped with 2 perches (0.6 × 0.4 × 0.4 m). Once the bird entered the cage, its movements were observed for five minutes. Birds were given an exploration score on a continuous scale based on the total number of movements between the perches, as well as hops up and down and flights. Scores ranged from 47.5 to 260.5, with higher scores indicating faster exploration, and lower scores indicating slower exploration. This kind of measurement has been used to measure exploration behavior in great tits [START_REF] Stuber | Slow explorers take less risk: A problem of sampling bias in ecological studies[END_REF]) and blue tits [START_REF] Mutzel | Parental provisioning behaviour plays a key role in linking personality with reproductive success[END_REF][START_REF] Charmantier | Urbanization is associated with divergence in pace-of-life in great tits[END_REF][START_REF] Dubuc-Messier | Environmental heterogeneity and population differences in blue tits personality traits[END_REF], and provides repeatable exploratory scores [START_REF] Dingemanse | Repeatability and heritability of exploratory behaviour in great tits from the wild[END_REF][START_REF] Stuber | Slow explorers take less risk: A problem of sampling bias in ecological studies[END_REF].

Breeding experiment Pair formation and housing of birds

Before the first preference test, females were randomly distributed across two groups: 12 females paired with the male with which they spent the most time and 12 (11 in 2022) females paired with the male they avoided most. On the second year, we reversed the groups, i.e. a female that had been paired with its preferred male the first year, was paired with its most avoided male the second year. That way each female was used as its own control. Females and males were released simultaneously in outdoor aviaries (2.5 x 3 x 3 m). Pairs were moved in aviaries on 4 th January 2021 and on 28 th February 2022. Nesting materials consisting of moss and dog, horse and donkey hair were provided from early March.

Reproduction monitoring

Starting from mid-March, we monitored nest building and egg laying activities, first once a week, then twice a week as birds were closer to lay [START_REF] Dufva | Blood parasites , health , reproductive success , and egg volume in female Great tits Parus major[END_REF]. The date the first egg was found was recorded as the pair laying date. Tits usually lay one egg every 24 hours [START_REF] Perrins | The timing of birds' breeding seasons[END_REF], so if more than one egg was found in the nest at the day of checking, we back calculated the laying date. All eggs were measured to the nearest 0.05 mm with a calliper (Ecotone Measy DG), marked with a fine point marker, and replaced in the nest until clutch completion. After at least five days of incubation, nest and eggs were collected, and eggs were candled to identify if an embryo was developing. Eggs were then wiped with paraffin oil and stored at -20°C until further analyses (see below). Nests were dried in an oven at 40°C for 48h and then weighted to the nearest 0.1 g (Precisa, France).

Egg analyses

Germinal disc observation 127 eggs the first year and 177 eggs the second year were collected and preserved in a freezer. Eggs were candled when they were collected, but this method does not enable to distinguish between an unfertilised egg and a fertilised egg in which the embryo died at an early stage of development. We thus examined the germinal disc (GD) following the method described in [START_REF] Birkhead | Unhatched eggs: Methods for discriminating between infertility and early embryo mortality[END_REF] to identify if an egg was fertilised or not (figure S2). In short, we opened the eggs, discarded the albumen, placed the yolk in a small Petri dish and examined the aspect of the GD under a binocular dissecting microscope (Optika, Italy). Photos of the observed GD was taken with a camera (OPTIKA C-B5), and the OPTIKA PROview software (version x64, 4.11.18914.20210510,https://www.optikamicroscopes.com/optikamicroscopes/).

Embryo sexing

107 out of the 127 eggs collected the first year and 117 out of the 177 eggs collected the second year contained an embryo and we succeeded to sex 105 and 114 of those embryos the first and second year, respectively. We sampled between 5 and 20 mg of embryo tissue and extracted the DNA using the DNeasy Blood & Tissue Kit (Ref 69506,QIAGEN). DNA extraction products were analysed by agarose gel electrophoresis (1% in TBE) and visualized under UV light after staining with ethidium bromide, using a molecular size marker of a 1 kb Plus ''ladder'' type (Quick-Load, N0469S, New England BioLabs Inc.). The sex identification test employs the P8 (5'-CTCCCAAGGATGAGRAAYTG-3') and P2 (5'-TCTGCATCGCTAAATCCTTT-3') primers [START_REF] Griffiths | A DNA test to sex most birds[END_REF]) and PCR amplification was carried out in a total volume of 20 µL. For each individual, reaction conditions were as follows:

1µL Buffer 10X (Eurogentec, Belgium); 1.5 µL MgCl2 25mM; 1 µL dNTP Master mix 20mM total (Eurogentec, Belgium); 1µL P2 10µM (Eurogentec, Belgium); 1µL P8 10µM (Eurogentec, Belgium); 0.2µL 0.15 units of Red diamond Taq DNA polymerase (Eurogentec, Belgium), 12.3µL H2O; 1µL DNA. PCR was performed in a thermal cycler (Eppendorf AG, Hamburg, Germany). An initial denaturing step at 94 °C for 5 min was followed by 30 cycles of 48 °C for 45 s, 72 °C for 45 s and 94 °C for 30 s. A final run of 48 °C for 1 min and 72 °C for 5 min completed the program. PCR products were analysed by agarose gel electrophoresis (3% in TBE) and visualized under UV light after staining with ethidium bromide, using a molecular size marker of a 100 bp ''ladder'' type (Quick-Load, N0467S, New England BioLabs Inc., USA).

Statistical analyses

All the analyses were performed in R version 4.2.2 (R Core Team 2022). Linear mixedeffects models and generalized linear mixed-effect models were conducted using the lme4 version 1.1.31 [START_REF] Bates | Fitting linear mixed-effects models using lme4[END_REF] and glmmTMB version 1.1.5 [START_REF] Brooks | glmmTMB balances speed and flexibility among packages for zero-inflated generalized linear mixed modeling[END_REF] packages. P-values were obtained with the lmerTest package version 3.1.3 in the case of mixed-model analyses [START_REF] Kuznetsova | lmerTest Package: Tests in Linear Mixed Effects Models[END_REF]. Plots were created with the ggplot2 version 3.4.0 [START_REF] Wickham | ggplot2: Elegant Graphics for Data Analysis[END_REF]) and ggeffects version 1.1.5 [START_REF] Lüdecke | ggeffects: Tidy Data Frames of Marginal Effects from Regression Models[END_REF] packages. Models were simplified using backward elimination of the nonsignificant terms, starting with the higher-order interactions [START_REF] Crawley | The R book[END_REF], we set α=0.05. Correlations were calculated and plotted with the Hmisc version 4.7.2 [START_REF] Harrell | Hmisc: Harrell Miscellaneous[END_REF]) and corrplot version 0.92 [START_REF] Wei | R package "corrplot": Visualization of a Correlation Matrix[END_REF]) packages, respectively.

Principal component analyses were run with FactoMineR version 2.7 [START_REF] Husson | Package FactoMineR[END_REF]) and factoextra version 1.0.7 (Alboukadel and Mundt 2017) packages. Repeatability was measured using the rptR package version 0.9.22 [START_REF] Stoffel | rptR: repeatability estimation and variance decomposition by generalized linear mixed-effects models[END_REF].

Preference test

We ran a linear mixed-effect model with the time (in seconds) spent by the female in the choice zone of each male as response variable. Explanatory variables consisted of each male trait, alone and in interaction with the female corresponding trait. These included brightness (white of the cheek, yellow of the breast, UV-blue of the head crown), chroma (yellow and UVblue), body mass, tarsus, wing and beak size and exploration score. As we had an important number of variables on a relatively restricted number of individuals, we first checked correlations between variables (figure S3). Principal Component (PC) were used for body size to decrease the number of variables to add in the model. It included body weight and tarsus and wing length (figure S4). Identification of the female and year were added as crossed random intercepts, to account for the fact that each female occurred six times in the dataset (once for each six different males) and that females were used in both years of experiment. The response variable (i.e. the time spent in the choice zone of the males) was weighted by the "interest" of the female to allow more statistical weight to the females that spent more time evaluating the males during the test rather than staying in the neutral zone [START_REF] Reparaz | Mate preference of female blue tits varies with experimental photoperiod[END_REF][START_REF] Caro | Mutual mate preferences and assortative mating in relation to a carotenoid-based color trait in blue tits[END_REF]. "Interest" thus depicts the overall motivation of the female to visit the males during the experiment by indicating the proportion of time that the female spent close to the six stimulus males (i.e. not in the central neutral zone), and was calculated as follows [START_REF] Reparaz | Mate preference of female blue tits varies with experimental photoperiod[END_REF][START_REF] Caro | Mutual mate preferences and assortative mating in relation to a carotenoid-based color trait in blue tits[END_REF] :

𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 = 𝑇𝑖𝑚𝑒 𝑠𝑝𝑒𝑛𝑡 𝑤𝑖𝑡ℎ (𝑚𝑎𝑙𝑒 1 + 𝑚𝑎𝑙𝑒 2 + 𝑚𝑎𝑙𝑒 3 + 𝑚𝑎𝑙𝑒 4 + 𝑚𝑎𝑙𝑒 5 + 𝑚𝑎𝑙𝑒 6) 𝑇𝑜𝑡𝑎𝑙 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑡𝑒𝑠𝑡 (90𝑚𝑖𝑛)

Breeding experiment

Out of the 47 pairs that were formed across both years, 4 pairs had to be removed from the statistical analyses (because a member of the pairs died or was injured before or during the experiment), we thus analysed the reproductive behavior of 43 pairs.

We first used binomial tests to compare the number of females that (i) built a nest and

(ii) laid at least one egg, between females paired with their preferred and avoided male, as well as (iii) the total number of eggs laid by all the females on the whole breeding season between the two groups.

We tested the effect of the pairing treatment on female reproductive parameters. We performed linear mixed-effect models on (i) nest weight, (ii) lay date, (iii) egg measures (PC1, see below) and generalized linear mixed-effect models with Poisson distribution on (iv) clutch size and with binomial distribution on (v) the proportion of fertilised egg and on (vi) the proportion of male chicks produced by each female during the breeding season. PC were used for egg measured because egg length, breadth and volume were correlated. The PC1 axis explained 80.6% of the variability in the data (figure S5). In all models, the treatment (preferred vs. avoided) and the year (2021 vs. 2022) were included as explanatory variable. Female ID was included as random effect to account for the fact that the same females were used in both years, and that a same female laid several eggs. As 11 females laid on both years, we measured repeatability of the female identity for each model using the rpt function.

Results

Preference test

Females spent more time close to males with a blue UV chroma of the head crown that was similar to their own (p = 0.036, Table 1, figure 2A). That's the only phenotypic traits for which females referred to their own phenotype, all the other interactions between male and female characteristics were non-significant (Table 1). Females also spent more time close to males with a duller blue head (p = 0.007, Table 1, figure 2B) and tended to prefer males with duller white cheeks (p = 0.084, Table 1, figure 2C). We did not find that females were attracted by any other male phenotypic trait, including body size (PCA body size: p = 0.544, beak length: p = 0.707, Table 1) and exploration score (p = 0.514, Table 1). A: Females prefer male with blue UV chroma of the head crown similar to their own (F1,118.13 = 4.51, p = 0.036). The lines represent the predicted values of the model. Although female blue UV chroma was treated as a continuous variable in the statistical model, for graphical purpose they were split into three categories corresponding to the 25% (i.e. low, orange), 50% (medium, green) and 75% (high, red) quantiles. This graphical representation suggests that the interaction could be mostly driven by females with low blue UV chroma preferring males with low blue UV chroma. Female blue tits prefer males with duller (B) blue head crown (F1,123.12 = 7.55, p = 0.007) and (C) tended to prefer males with duller white cheeks (F1,123.07 = 3.03, p = 0.084). Lines and dotted lines represent the predicted values of the model, with the 95% confidence intervals. On all graphs, points depict individual data and their size represents the overall interest of females for males, with bigger points depicting a higher interest for males during the preference test.

Breeding experiment

Females built a nest in 36 out of 43 occasions (18 in 2021, 18 in 2022, Table 2), but counts were identical in both treatments (18 in the preferred treatment vs. 18 in the avoided treatment; binomial test, p = 1, Table 2). Similarly, the 26 clutch initiations (12 in 2021, 14 in 2022, Table 2) were evenly distributed between the two treatments (13 females in each group; binomial test, p = 1, Table 2), and females produced a similar total number of eggs in each treatment (165 eggs in total in the preferred male group vs. 162 eggs in the avoided group, binomial test, p = 0.91). However, comparing the total number of eggs between treatments for each year separately, revealed that there were more eggs produced in the preferred than in the avoided group in 2021 (p = 0.001, Table 2), while this was the opposite in 2022 (p = 0.007, Table 2). As females were exposed to opposite treatments over these two years, this result suggests that it is not the preference for the male that influences the number of eggs laid by the females.

Table 2. Counts of number of nests built, clutch initiations and total number of eggs laid per year and treatment. Each female was used as its own control, i.e. a female that had been paired with its preferred male the first year was paired with its most avoided male the second year. Females laid more eggs in 2021 with the preferred males while they laid more eggs with the avoided one in 2022. At the individual level, females tended to build heavier nests when paired with their preferred male (n = 36, F1,33 = 3.56, p = 0.068, Table 3, figure 3A), but they did not lay earlier (n = 26, F1,12.24 = 0.03, p = 0.874, Table 3, figure 3B), nor lay larger clutches (n = 25, z = -0.07, p = 0.944, Table 2, figure 3C). Mean egg size was also similar between groups (n = 320, F1,306.78 = 2.23, p = 0.137, Table 3). Finally, we did not find any difference in the proportion of fertilised eggs between the two groups (n = 282, z = -0.03, p = 0.977, Table 3, figure 3D), nor in the proportion of male chicks (n = 219, z = -0.55, p = 0.580, Table 3, figure 3E).

Being paired with a preferred or an avoided male therefore does not seem to make much of a difference in female blue tits. This is further supported by our analyses of the repeatability of the traits we monitored during the breeding season. Laying date (R = 0.413, p = 0.048, Table 3), clutch size (R = 0.87, p <0.001, Table 3), egg size (R = 0.75, p <0.001, Table 3) and proportions of sons (R = 0.758, p =0.017, Table 3) were indeed significantly repeatable within females over the two years of experiment, showing that females are relatively consistent in these decisions, whatever the male with which they are paired. Nest weight and proportions of fertilised eggs were not repeatable (Table 3).

Discussion

We found assortative preference of female blue tits for blue UV chroma of the head crown, a relationship that might have mostly been driven by females with low blue UV chroma selecting males that also presented low levels of blue UV chroma (figure 2A). We also found that females expressed a general preference for males with duller blue head crown and tended to prefer males with duller white cheeks. Contrary to our hypotheses however, we found no effect of female preference on reproductive timing and investment. Although females paired with their preferred male tended to build heavier nests, they did not lay earlier, more or bigger eggs, and they did not produce more fertilised eggs or more sons, compared to females paired with the male they avoided during the preference test. Females however showed significant repeatability for laying dates, clutch sizes, egg sizes, and egg sex-ratio, despite the fact that they each had been paired with both their preferred and most avoided males.

A first finding of our experiment is that female blue tits expressed preferences for males that had values of blue UV chroma similar to their own, but at the same time they also preferred males with duller blue heads and tended to prefer males with duller white cheeks. All three signals (blue UV chroma, blue and white brightness) have been suggested to be linked to individual quality [START_REF] Pärt | Badge size in collared flycatchers predicts outcome of male competition over territories[END_REF][START_REF] Keyser | Structurally based plumage coloration is an honest signal of quality in male blue grosbeaks[END_REF][START_REF] Mennill | Achromatic color variation in black-capped chickadees, Poecile atricapilla: Black and white signals of sex and rank[END_REF][START_REF] Alonso-Alvarez | Ultraviolet reflectance affects male-male interactions in the blue tit (Parus caeruleus ultramarinus)[END_REF][START_REF] Ferns | Immaculate tits: Head plumage pattern as an indicator of quality in birds[END_REF][START_REF] Siefferman | Evidence for sexual selection on structural plumage coloration in female eastern bluebirds (Sialia sialis)[END_REF][START_REF] Delhey | Seasonal changes in blue tit crown color: Do they signal individual quality?[END_REF][START_REF] Galván | The cheek plumage patch is an amplifier of dominance in great tits[END_REF][START_REF] Rémy | Mediating male-male interactions: The role of the UV blue crest coloration in blue tits[END_REF][START_REF] Midamegbe | Female-female aggressiveness is influenced by female coloration in blue tits[END_REF][START_REF] Doutrelant | Evolution of female coloration: What have we learned from birds in general and blue tits in particular[END_REF][START_REF] White | Structural colours reflect individual quality: A meta-analysis[END_REF]. For example, in the blue Grosbeak (Guiraca caerulea), blue brightness indicated male ability to hold large territories with more resources [START_REF] Keyser | Structurally based plumage coloration is an honest signal of quality in male blue grosbeaks[END_REF], and in the great tit (Parus major), males with more immaculate white cheek patches had significantly greater access to feeding sites and produced heavier chicks [START_REF] Ferns | Immaculate tits: Head plumage pattern as an indicator of quality in birds[END_REF]. UV coloration has also been suggested to reflect genetic quality [START_REF] Brown | A theory of mate choice based on heterozygosity[END_REF][START_REF] Foerster | Females increase offspring heterozygosity and fitness through extra-pair matings[END_REF][START_REF] Kempenaers | Mate Choice and Genetic Quality: A Review of the Heterozygosity Theory[END_REF][START_REF] García-Navas | Heterozygosity-based assortative mating in blue tits (Cyanistes caeruleus): Implications for the evolution of mate choice[END_REF][START_REF] Ferrer | Multiple sexual ornaments signal heterozygosity in male blue tits[END_REF]. Female preference for males with similar blue UV chroma to their own could therefore select a male with the same level of quality than themselves [START_REF] Jennions | Variation in mate choice and mating preferences: A review of causes and consequences[END_REF][START_REF] Tregenza | Genetic compatibility, mate choice and patterns of parentage: Invited review[END_REF][START_REF] Cotton | Sexual selection and condition-dependent mate preferences[END_REF]. This is in line with several studies showing assortative mating in blue tits in the wild [START_REF] Andersson | Ultraviolet sexual dimorphism and assortative mating in blue tits[END_REF][START_REF] Hunt | Preferences for ultraviolet partners in the blue tit[END_REF][START_REF] Fargevieille | Assortative mating by colored ornaments in blue tits: space and time matter[END_REF]. A closer look at figure 2A suggests that it is particularly females with low blue UV chroma that prefer males with low blue UV chroma. In captivity, more colored individuals might be more aggressive [START_REF] Senar | Color displays as intrasexual signals of aggression and dominance[END_REF], and pairing with an aggressive partner may lead to reproductive failure [START_REF] Caro | Non-photoperiodic factors and timing of breeding in blue tits: Impact of environmental and social influences in semi-natural conditions[END_REF]). High blue UV chroma males might therefore be more aggressive toward females. Consequently, females with higher blue UV chroma levels, assumed to be more aggressive, would be less choosy because they would be better able to defend themselves, contrary to low blue UV chroma females, which could explain why low blue UV chroma females seem to express clearer preference than higher blue UV chroma females. Females also surprisingly preferred males with duller, and not brighter, blue heads and white cheeks. [START_REF] Caro | Mutual mate preferences and assortative mating in relation to a carotenoid-based color trait in blue tits[END_REF] also found preference for individuals with paler chest plumage in captive blue tits. Consequently, our females would select duller individuals based on blue and white brightness to avoid aggressive individuals in a restricted environment [START_REF] Caro | Mutual mate preferences and assortative mating in relation to a carotenoid-based color trait in blue tits[END_REF].

Surprisingly, besides nests that tended to be bigger with their preferred males, female blue tits did not adjust any other reproductive traits to the male with which they were paired. If females were to match their reproductive decision to the differential allocation hypothesis (Burley 1986;[START_REF] Burley | The differential-allocation hypothesis: an experimental test[END_REF][START_REF] Sheldon | Differential allocation: Tests, mechanisms and implications[END_REF][START_REF] Haaland | Differential allocation revisited: When should mate quality affect parental investment?[END_REF], which predicts that male attractiveness should modulate female reproductive investment [START_REF] Cunningham | Egg investment is influenced by male attractiveness in the mallard[END_REF][START_REF] Gowaty | Male house mice produce fewer offspring with lower viability and poorer performance when mated with females they do not prefer[END_REF][START_REF] Limbourg | Female blue tits adjust parental effort to manipulated male UV attractiveness[END_REF][START_REF] Anderson | Experimental constraints on mate preferences in Drosophila pseudoobscura decrease offspring viability and fitness of mated pairs[END_REF][START_REF] Walling | Do female association preferences predict the likelihood of reproduction?[END_REF], we expected females to lay earlier, more and larger eggs and more fertilised eggs when paired with their preferred male. For example, female zebra finches and barn swallows (Hirundo rustica)

paired with an attractive male lay larger clutches [START_REF] De Lope | Female reproductive effort depends on the degree of ornamentation of their mates[END_REF][START_REF] Balzer | Do female zebra finches vary primary reproductive effort in relation to mate attractiveness?[END_REF], and we recently showed that female great tits lay earlier when they are paired with a male they prefer [START_REF] Delaitre | Female great tits (Parus major) reproduce earlier when paired with a male they prefer[END_REF]. None of this happened with our blue tits, which therefore do not seem to match the differential allocation hypothesis. Alternatively, we hypothesized that if females were to match the sex-allocation theory, those paired with their preferred male would produce more sons [START_REF] Charnov | The theory of sex allocation[END_REF][START_REF] Frank | Sex allocation theory for birds and mammals[END_REF][START_REF] Booksmythe | Facultative adjustment of the offspring sex ratio and male attractiveness: a systematic review and meta-analysis[END_REF].

For example, the proportion of sons increases with the intensity of the sexual characters of the mate in barn swallows [START_REF] Saino | Offspring sexual dimorphism and sex-allocation in relation to parental age and paternal ornamentation in the barn swallow[END_REF]. In tits, brood sex-ratio has been related to male quality, with females producing more sons when paired with a high-quality male [START_REF] Svensson | Mate quality affects offspring sex ratio in blue tits[END_REF][START_REF] Kölliker | Offspring sex ratio is related to male body size in the great tit (Parus major)[END_REF][START_REF] Sheldon | Ultraviolet colour variation influences blue tit sex ratios[END_REF][START_REF] Griffith | Correlations between ultraviolet coloration, overwinter survival and offspring sex ratio in the blue tit[END_REF]; but see [START_REF] Limbourg | Parental care and UV coloration in blue tits: Opposite correlations in males and females between provisioning rate and mate's coloration[END_REF]). However, our female blue tits were significantly repeatable in their brood sex-ratio (see below), whatever the pairing treatment. They therefore did not produce more sons when paired with their preferred male, which does not support the sex-allocation theory.

Consequently, none of the two hypotheses has been verified.

Females thus express preferences for certain males without adjusting their breeding decisions according to whether or not their pairing matched their preferences. One possibility is that females may have expressed a social, instead of a sexual preference in our preference testing. Females were indeed not fully photostimulated at the time of testing, and therefore not sexually active yet [START_REF] Dawson | Photoperiodic control of seasonality in birds[END_REF]). Stimulating females with long photoperiods, or exogenous oestradiol capsules, would have ensured sexual responses to males [START_REF] Byers | Female mate choice and songbird song repertoires[END_REF][START_REF] Reparaz | Mate preference of female blue tits varies with experimental photoperiod[END_REF][START_REF] Caro | Mutual mate preferences and assortative mating in relation to a carotenoid-based color trait in blue tits[END_REF]), but at the cost of interfering with the reproductive experiment that followed the preference testing. Furthermore, in the wild, tits are often seen in pairs as early as February (Caro, pers. obs.) and can be found roosting in nestboxes close to the one in which they will reproduce much later in the season [START_REF] Salis | Manipulation of photoperiod perception advances gonadal growth but not laying date in the great tit[END_REF]).

Finally, using the same mate preference testing apparatus, we recently showed that the more time female great tits had spent close to the male with which they were then paired in aviaries, the earlier they reproduced [START_REF] Delaitre | Female great tits (Parus major) reproduce earlier when paired with a male they prefer[END_REF]. This strongly suggests that we effectively captured sexual preferences during the mate preference tests, and that our experimental set-up cannot itself explain the absence of an effect of the female preferences on their reproductive decisions.

We must also remember that we used captive birds with unlimited food access.

Consequently, environmental constraints might not be harsh enough for females to adapt reproductive decisions with respect to the quality of their mate the same way they would have done it in the wild. Captivity can however not be the only explanation for the results obtained here, given that among the studies described above to illustrate each of the hypotheses, many were similarly conducted in captivity (Burley 1981b;[START_REF] Balzer | Do female zebra finches vary primary reproductive effort in relation to mate attractiveness?[END_REF][START_REF] Gil | Male attractiveness and differential testosterone investment in zebra finch eggs[END_REF][START_REF] Bolund | Compensatory investment in zebra finches: Females lay larger eggs when paired to sexually unattractive males[END_REF]). In fact, another hypothesis seems to emerge from our results, supporting that female blue tits are consistent in their main reproductive decisions, whatever their preference for the male with which they are paired.

Males seem to play a minor role in the major breeding decisions in blue tits. Females were indeed consistent in several of their reproductive decisions across the two years, despite the fact that they were paired with males that were at the opposite ends of their preference rankings. We found relatively high repeatability for laying date, clutch size, egg size, and proportion of sons, suggesting that females were consistent whatever the pairing treatment to which they were assigned. For example, in 2021, females paired with their preferred male laid more eggs (Table 2). While this was totally in line with our initial hypothesis, in 2022, we found the opposite pattern, with more eggs laid in the group of females paired with the male they avoided most. Since we reversed the treatment for each female between the two years, each female was acting as its own control. Females that laid numerous eggs in 2021 with the preferred male were thus the same females that laid numerous eggs in 2022 with the avoided male. This result was confirmed by the significant repeatability of laying dates and clutch sizes within females. This accessorily also shows the importance of repeating experiments over multiple years to avoid confounding effects of unidentified environmental variables, which in our case seem to be that the preferred group of 2021 contained females investing more in reproduction, regardless of the treatment applied to these females. There are other passerine species, like the collared flycatcher (Ficedula albicollis) [START_REF] Sheldon | Natural selection and inheritance of breeding time and clutch size in the collared flycatcher[END_REF] or the European starlings (Sturnus vulgaris) [START_REF] Cornell | Experimentally increased prebreeding male social behaviour has no effect on female breeding phenology and performance[END_REF], in which male quality does not influence female laying dates or clutch sizes. In zebra finches, a study found no evidence of a difference in reproductive timing and investment between females that were force-paired and those that were free to choose their partner [START_REF] Griffith | Variation in reproductive success across captive populations: methodological differences, potential biases and opportunities[END_REF]. Earlier studies on blue tit populations from the Mediterranean region have shown that males play little role in reproductive phenology.

In Corsica, male blue tits from two distinct populations indeed start developing their reproductive system at the same time in late winter, despite the fact that their females lay more than one month apart [START_REF] Caro | Endocrine correlates of the breeding asynchrony between two corsican populations of blue tits (Parus caeruleus)[END_REF][START_REF] Caro | Simultaneous pituitary-gonadal recrudescence in two Corsican populations of male blue tits with asynchronous breeding dates[END_REF]. Further quantitative genetic analyses revealed that the timing of breeding was solely driven by the females, with no evidence for an additive genetic male effect on laying dates [START_REF] Caro | Local adaptation of timing of reproduction: Females are in the driver's seat[END_REF]). Finally, reproductive experiments crossing males and females from different populations suggested that the timing of laying matched the origin of the females and not the origin of the males [START_REF] Caro | Non-photoperiodic factors and timing of breeding in blue tits: Impact of environmental and social influences in semi-natural conditions[END_REF].

Interestingly however, although there is evidence for a higher heritability and repeatability of laying dates in female than male great tits (van [START_REF] Van Noordwijk | Genetic variation in the timing of reproduction in the Great Tit[END_REF][START_REF] Van Der Jeugd | Effects of spatial autocorrelation, natal philopatry and phenotypic plasticity on the heritability of laying date[END_REF][START_REF] Noordwijk | Heritability of Ecologically Important Traits in the Great Tit[END_REF], we recently found that female great tits paired with a male they preferred during a preference test laid their first clutch earlier [START_REF] Delaitre | Female great tits (Parus major) reproduce earlier when paired with a male they prefer[END_REF].

Contrary to the present study however, all those female great tits were paired with one of their favorite males, and none with the male they avoided most. In any case, our results highlight the fact that female investment in reproduction might be species, and potentially even populationspecific.

To conclude, this study suggests that although females have expressed preferences for some ornamental traits in males, based in part on their own phenotype, the male with which they are paired does not alter their reproductive decisions. The fact that females lead most reproductive decisions has already been shown in earlier studies in the wild on Mediterranean blue tits [START_REF] Caro | Non-photoperiodic factors and timing of breeding in blue tits: Impact of environmental and social influences in semi-natural conditions[END_REF][START_REF] Riebel | Chapter 6 Song and Female Mate Choice in Zebra Finches: A Review[END_REF]. In this species, males might thus be primarily used for providing genes and for helping rearing offspring. Consequently, females breeding with a male that does not match their selection criteria, either because their preferred male was already mated with another female, or because they only encounter less-preferred males, will not prevent them from breeding. This could be an adaptive strategy in such a short-living bird that, on average, has only two breeding seasons over its lifetime [START_REF] Olioso | Les mésanges: description, répartition, habitat, moeurs, observation[END_REF].

Figure 1 .

 1 Figure1. Experimental mate preference test setup. Females were tested for their preference in a six-choice setup for 90 min. From the hexagonal central platform, the focal female could observe all stimulus male birds, whereas only one stimulus male was visible from the perch in the choice zone. The stimulus male birds could not see each other. Time spent in the choice zone of each male was inferred as a proxy for preference. At the end of each test, videos were analysed and, depending on the treatment assigned to the female, the preferred (or avoided) male was pull out of the pool of available males for the next females tested. Positions of the stimulus male birds were randomised for each test.

Figure 2 .

 2 Figure 2. Female preferences for male color traits.A: Females prefer male with blue UV chroma of the head crown similar to their own (F1,118.13 = 4.51, p = 0.036). The lines represent the predicted values of the model. Although female blue UV chroma was treated as a continuous variable in the statistical model, for graphical purpose they were split into three categories corresponding to the 25% (i.e. low, orange), 50% (medium, green) and 75% (high, red) quantiles. This graphical representation suggests that the interaction could be mostly driven by females with low blue UV chroma preferring males with low blue UV chroma. Female blue tits prefer males with duller (B) blue head crown (F1,123.12 = 7.55, p = 0.007) and (C) tended to prefer males with duller white cheeks (F1,123.07 = 3.03, p = 0.084). Lines and dotted lines represent the predicted values of the model, with the 95% confidence intervals. On all graphs, points depict individual data and their size represents the overall interest of females for males, with bigger points depicting a higher interest for males during the preference test.

Figure 3 .

 3 Figure 3. Effect of the preference of the females on their reproductive parameters. Females tended to build heavier nests when paired with their preferred male (p = 0.068; panel A), but they did not lay earlier (p = 0.874; panel B) or larger clutches (p = 0.944; panel C). They also did not produce more fertilised eggs (p = 0.977; panel D) or male chicks (p = 0.580; panel E). Large dots and error bars represent mean ± SE, smaller dots depict raw data.

Figure S3 :

 S3 Figure S3: Correlation matrix of the traits of male and females. A: Correlation of male traits for 2021 and 2022 together B: Correlation of female traits for 2021 and 2022 together C: Correlation of male traits for 2021 D: Correlation of male traits for 2022 E: Correlation of female traits for 2021 F: Correlation of female traits for 2022 Number in the coloured square are the Pearson correlation coefficients. Non-significant correlation (p>0.05) are crossed out.

Figure S4 :

 S4 Figure S4: Biplot of the PCA ran for body size. A: 2021 for males B: 2022 for males C: 2021 for females D: 2022 for females Each point depicts an individual.

Figure S5 :

 S5 Figure S5: Biplot of the PCA ran for egg size. (n = 320) High value of the first axis represents bigger eggs.

Table 1 . Results from a linear mixed effect model, exploring the variables that influence the time spent by the females in the choice zone of the males during the 90 minutes of the test (n = 47 females).

 1 Variables in bold had a significant effect on the response variable (p<0.05), italicized variables depict trends (p<0.10). Variables in light grey were removed during the reduction of the model, and presented in the reverse order in which they were removed.

	Explanatory variable	Estimate S.E	df	F	p-
					value	value
	Intercept	213.07	77.21
	PCA Body size male	15.74	25.87	124.11	0.37	0.544
	Beak length male	11.95	31.75	125.91	0.14	0.707
	Exploration score male	13.88	21.21	121.49	0.43	0.514
	White brightness male	-48.04	27.62	123.07	3.03	0.084
	Blue brightness male	-64.34	23.42	123.12	7.55	0.007
	Yellow brightness male	-17.89	29.12	123.22	0.38	0.540
	Yellow chroma male	25.18	26.10	122.01	0.93	0.337
	Blue UV chroma male	-29.97	34.67	124.15	0.75	0.389
	Blue UV chroma female	-8.35	33.37	38.74	0.06	0.804
	Blue UV chroma male*Blue UV chroma	47.86	22.5	118.13	4.51	0.036
	female
	Blue brightness female	-10.68	29.22	71.79	0.13	0.716
	Blue brightness male*Blue brightness	10.96	17.51	117.85	0.39	0.533
	female
	Exploration score female	-19.70	42.29	18.42	0.22	0.647
	Exploration score male*Exploration score	-17.49	26.96	105.03	0.42	0.518
	female
	Beak length female	-38.65	39.77	18.54	0.34	0.344
	Beak length male*Beak length female	11.38	25.26	100.09	0.20	0.653
	Yellow brightness female	-53.27	29.79	71.49	3.19	0.078
	Yellow brightness male*Yellow brightness	11.75	26.63	103.70	0.19	0.659
	female
	Yellow chroma female	-6.77	43.12	28.08	0.02	0.876
	Yellow chroma male*Yellow chroma	4.53	19.27	97.42	0.06	0.815
	female
	White brightness female	36.89	42.08	50.88	0.77	0.385
	White brightness male*White brightness	9.23	34.71	98.74	0.07	0.791
	female
	PCA Body size female	22.00	49.44	16.51	0.19	0.662
	PCA Body size male* PCA Body size	1.33	21.69	96.29	0.004	0.951
	female

Table 3 . Results from generalized linear mixed effect models and linear mixed effect models exploring the variables that influence nest weight, laying date, clutch size, egg size and proportion of fertilised eggs and male chicks.

 3 Repeatabilities of female identity have been measured with the rpt function. Bold writing depicts significant results (p<0.05), italicized depicts trends (p<0.10). Est.: Estimate, S.E: Standard Error, R: Repeatability, CI: 95% Confidence Interval.

			Nest weight		Laying date		Clutch size
	Fixed effects Est.	S.E	p	Est.	S.E	p	Est.	S.E	p
	Treatment	2.36 1.25	0.068 0.38	2.32 0.874 -0.01 0.15	0.944
	Year	1.91 1.25	0.137 -0.52 2.33 0.828 0.19 0.15	0.191
	Repeatability R	CI	p	R	CI	p	R	CI	p
	Female	0	0-	1	0.413 0-	0.048 0.87 0.657-	<0.001
	identity		0.601			0.87			0.981
			Egg size		Prop. fertilised eggs	Prop. male chicks
	Fixed effects Est.	S.E	p	Est.	S.E	p	Est.	S.E	p
	Treatment	-0.16 0.10	0.137 -0.05 1.59 0.977 -0.50 0.91	0.580
	Year	-0.38 0.10	<0.001 0.93	1.62 0.568 -0.29 0.91	0.742
	Repeatability R	CI	p	R	CI	p	R	CI	p
	Female	0.75 0.564-	<0.001 0	0-	1	0.758 0.398-	0.017
	identity		0.85			0.826			0.975

Acknowledgments

The authors would like to thank Marie-Pierre Dubois for her help for DNA extraction and PCR sexing and Nicola Hemmings for her advices and help to identify fertilised germinal discs. We thank Lies Zandberg, Elise Huchard, Marcel Visser and Anne Charmantier for discussions about the experimental design. We also thank Jean-Marc Donnay for taking care of the birds and Annick Lucas, Christophe de Franceschi, Samuel Perret, Nicolas Silva, Constance Blary, Pablo Giovannini, and David Lopez Idiaquez for helping with catching birds in aviaries.

Funding

This work was funded by a grant from the Agence Nationale de la Recherche awarded to SPC (grant number ANR-15-CE02-0005-01).

Supplementary material

Whoever their partner, female blue tits breed the same.

Figure S1: Pictures of the experimental setup for the mate preference test.

A: Picture of the carrousel-shaped six-choice chamber. The roof can be moved to introduce the female into the setup. B: Screenshot of the video of a test, the female is in the choice zone of the male 6. The males are not visible on the video.

.

Figure S2: Fertile germinal disc (GD) showing an early stage developed embryo (circle).

Embryos that have died at early stages of development cannot be identified by simply candling the egg. This can be done by opening the egg and analysing the germinal disc. For more information on the procedure, see: https://www.zsl.org/science/bringing-threatened-speciesback-from-the-brink-of-extinction/practical-resources-for.