Aurélie Quinard

Frank Cézilly

Sébastien Motreuil

Jean-Marc Rossi

Clotilde Biard
email: clotilde.biard@upmc.fr

Zenaida Dove

Zenaida Aurita Aurélie Quinard

Reduced sexual dichromatism, mutual ornamentation, and individual quality in the monogamous Zenaida dove Zenaida aurita

Keywords: female ornamentation, heterozygosity, plumage color, sexual selection, iridescence, melanin, Zenaida aurita

ccepted Ar ticle Introduction Among bird species, a high inter-individual variation can be observed in adult plumage colour. Part of this variation can be accounted for by the existence of sexual dichromatism, i.e. a difference in color patterns between the two sexes [START_REF] Badyaev | Avian sexual dichromatism in relation to phylogeny and ecology[END_REF]. Ever since [START_REF] Darwin | The descent of man, and selection in relation to sex. -D. Appleton and Company. Dechaume[END_REF], it has been assumed that the extent of sexual dichromatism partly reflects variation in mating system and the intensity of sexual selection [START_REF] Andersson | Sexual selection[END_REF]; but see [START_REF] Gluckman | Pathways to elaboration of sexual dimorphism in bird plumage patterns[END_REF]. Accordingly, comparative studies have shown that, overall, the extent of avian sexual dichromatism is much reduced in socially monogamous species compared to polygamous ones [START_REF] Scott | Mating systems, parasites and plumage dimorphism in waterfowl[END_REF][START_REF] Owens | Sexual dimorphism in birds: why are there so many different forms of dimorphism?[END_REF][START_REF] Dunn | Mating systems, sperm competition, and the evolution of sexual dimorphism in birds[END_REF], and increases with the intensity of sexual selection [START_REF] Figuerola | The evolution of sexual dimorphism in relation to mating patterns, cavity nesting, insularity and sympatry in the Anseriformes[END_REF]. There are, however, several exceptions to this rule [START_REF] Owens | Sexual dimorphism in birds: why are there so many different forms of dimorphism?[END_REF]Hartley 1998, Badyaev and[START_REF] Badyaev | Avian sexual dichromatism in relation to phylogeny and ecology[END_REF], and, in particular, some monogamous species initially classified as sexually monochromatic based on human vision, have later been found to be sexually dichromatic in UV wavelengths [START_REF] Andersson | Ultraviolet sexual dimorphism and assortative mating in blue tits[END_REF][START_REF] Hunt | Blue tits are ultraviolet tits[END_REF][START_REF] Mahler | Objective assessment of sexual plumage dichromatism in the Picui Dove[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] Mays | Sexual dichromatism in the yellow-breasted chat Icteria virens: spectrophotometric analysis and biochemical basis[END_REF][START_REF] Eaton | Human vision fails to distinguish widespread sexual dichromatism among sexually "monochromatic" birds[END_REF].

In addition to sexual dichromatism, continuous or discrete variation in adult plumage colour may also exist between individuals within each sex. Such variation can be under the influence of both genetic and environmental factors [START_REF] Roulin | Condition-dependence, pleiotropy and the handicap principle of sexual selection in melanin-based colouration[END_REF]Dijkstra 2003, Reudink et al. 2015), and is often associated with fitness differences in terms of survival [START_REF] Hõrak | Viability selection affects black but not yellow plumage colour in greenfinches[END_REF] or reproductive success [START_REF] Kruger | Lifetime reproductive success in common buzzard, Buteo buteo: from individual variation to population demography[END_REF]Lindstrom 2001, Brommer et al. 2005). In addition, inter-individual variation in plumage coloration, through being an honest signal of phenotypic and/or genetic quality, may have a signaling function during social interactions and mate choice.

Both sexual dichromatism and within-sex variation in bird plumage coloration can correspond to variation in structural ultraviolet or visible coloration [START_REF] Cuthill | Plumage reflectance and the objective assessment of avian sexual dichromatism[END_REF][START_REF] Shawkey | The anatomical basis of sexual dichromatism in non-iridescent ultraviolet-blue structural coloration of feathers[END_REF], iridescence [START_REF] Osorio | Spectral reflectance and directional properties of structural coloration in bird plumage[END_REF], or pigment-based coloration of feathers mainly due to carotenoids [START_REF] Badyaev | Evolution of sexual dichromatism: contribution of carotenoid-versus melanin-based coloration[END_REF], psittacofulvins [START_REF] Ccepted Ar Ticle Taysom | The contribution of structural-, psittacofulvin-and melanin-based colouration to sexual dichromatism in Australasian parrots[END_REF], porphyrins [START_REF] Negro | Porphyrins and pheomelanins contribute to the reddish juvenal plumage of blackshouldered kites[END_REF], or melanin [START_REF] Ccepted Ar Ticle Meunier | Eumelanin-based coloration and fitness parameters in birds: a meta-analysis[END_REF], the latter being the most common mechanism of color production in birds [START_REF] Mcgraw | How feather colour reflects its melanin content[END_REF][START_REF] Hubbard | Vertebrate pigmentation: from underlying genes to adaptive function[END_REF]. Whereas carotenoid-based coloration in feathers is generally considered to be a reliable signal of the quality of an individual [START_REF] Møller | Carotenoid-dependant signals: Indicators of foraging efficiency, immunocompetence or detoxification ability ?[END_REF][START_REF] Macdougall | Assortative mating by carotenoid-based plumage colour: a quality indicator in American goldfinches, Carduelis tristis[END_REF][START_REF] Peters | Condition-dependence of multiple carotenoid-based plumage traits: an experimental study[END_REF][START_REF] Murphy | Carotenoid-based status signaling by females in the tropical streak-backed oriole[END_REF], the condition-dependence and signaling function of structural colors and melanin-based plumage ornaments remain debated [START_REF] Siefferman | Ornamental plumage coloration and condition are dependent on age in eastern bluebirds Sialia sialis[END_REF][START_REF] Griffith | Melanin-versus carotenoid-based sexual signals: Is the difference really so black and red?[END_REF][START_REF] Korsten | Is UV signalling involved in male-male territorial conflict in the blue tit (Cyanistes caeruleus)? A new experimental approach[END_REF], Maia and Macedo 2010, Murphy and Pham 2012, Piault et ccepted Ar ticle al. 2012[START_REF] Parker | What do we really know about the signalling role of plumage colour in blue tits? A case study of impediments to progress in evolutionary biology[END_REF][START_REF] D'alba | Melanin-based color of plumage: role of condition and of feathers' microstructure[END_REF][START_REF] Musgrove | Condition-dependent expression of carotenoid-and melaninbased plumage colour of northern flicker nestlings revealed by manipulation of brood size[END_REF] for recent reviews, see Guindre- [START_REF] Parker | What do we really know about the signalling role of plumage colour in blue tits? A case study of impediments to progress in evolutionary biology[END_REF]Love 2014, Roulin 2016).

Sexual dichromatism and inter-individual variation in plumage coloration have been studied in a wide range of species (i.e. [START_REF] Badyaev | Avian sexual dichromatism in relation to phylogeny and ecology[END_REF][START_REF] Eaton | Human vision fails to distinguish widespread sexual dichromatism among sexually "monochromatic" birds[END_REF][START_REF] Bókony | Testosterone and melanin-based black plumage coloration: a comparative study[END_REF][START_REF] Galván | Pheomelanin-Based Plumage Coloration Predicts Survival Rates in Birds[END_REF]. However, although the family Columbidae includes about 310 species that show a large variation in both plumage coloration and the extent of sexual dichromatism [START_REF] Del Hoyo | Handbook of the Birds of the World[END_REF], only a few studies have provided quantitative measurements of plumage coloration in pigeons and doves, essentially focusing on feral pigeons [START_REF] Mcgraw | Multiple UV reflectance peaks in the iridescent neck feathers of pigeons[END_REF][START_REF] Yin | Iridescence in the neck feathers of domestic pigeons[END_REF][START_REF] Yoshioka | Origin of two-color iridescence in rock dove's feather[END_REF]; but see [START_REF] Dyck | Structure and light reflection of green feathers of fruit doves (Ptilinopus spp.) and an imperial pigeon (Ducula concinna)[END_REF]. One noticeable exception, however, is the study by [START_REF] Mahler | Objective assessment of sexual plumage dichromatism in the Picui Dove[END_REF] on the Picui dove, Columbina picui, showing the existence of an ultraviolet sexual dichromatism.

The socially monogamous Zenaida dove, Zenaida aurita, is a Caribbean endemic columbid species [START_REF] Bond | A field guide to the birds of the West Indies[END_REF], characterized by a cinnamon-brownish plumage, with light buff-brown chest and underparts, metallic pink-purple gloss on lateral and lower portions of hind necks, and dark iridescent blue streaks above and below ear coverts [START_REF] Del Hoyo | Handbook of the Birds of the World[END_REF]. The overall brownish coloration of this granivorous dove is presumably due to melanin pigmentation, as carotenoid pigmentation is rare among columbids and strictly limited to frugivorous species [START_REF] Mahler | Objective assessment of sexual plumage dichromatism in the Picui Dove[END_REF]. The Zenaida dove has been reported as being sexually dichromatic according to plumage hue in identification guides and in the literature [START_REF] Wiley | Ecology and behavior of the Zenaida dove[END_REF][START_REF] Del Hoyo | Handbook of the Birds of the World[END_REF][START_REF] Gibbs | Pigeons and Doves: A Guide to the Pigeons and Doves of the World[END_REF][START_REF] Sol | Ecological mechanisms of a resource polymorphism in Zenaida Doves of Barbados[END_REF]. It has been in particular claimed that female Zenaida doves can be readily distinguished from males by their duller and less reddish plumage, and by the absence or reduced size of the iridescent pink-purple patches on the neck [START_REF] Wiley | Ecology and behavior of the Zenaida dove[END_REF][START_REF] Del Hoyo | Handbook of the Birds of the World[END_REF][START_REF] Gibbs | Pigeons and Doves: A Guide to the Pigeons and Doves of the World[END_REF][START_REF] Sol | Ecological mechanisms of a resource polymorphism in Zenaida Doves of Barbados[END_REF]). However, it has been more recently argued that such differences are not quite obvious, such that the sexing of Zenaida doves by plumage color might not be a reliable method [START_REF] Monceau | Territoriality versus flocking in the Zenaida dove (Zenaida aurita): resource polymorphism revisited using morphological and genetic analyses[END_REF].

Through the detailed analysis of plumage reflectance spectra in the Zenaida dove, we i) present here the first assessment of sexual distinguishability of plumage coloration considering the avian visual system in a Columbidae, and ii) investigate the relationship between plumage color and individual quality. Focusing on presumably melanin-based and iridescent plumage areas, we first estimated both the extent of sexual dichromatism, and the extent of variation in plumage coloration within each sex, using reflectance spectrometry over the UV and visible range of light spectra, combined with molecular sexing.

We then evaluated to what extent the observed variation could be perceived by the avian visual system.

Finally, we considered the potential signaling function of coloration through its relationship with body ccepted Ar ticle size (wing chord), body condition, territorial status, and level of heterozygosity (as a measure of genetic quality that might be reflected in plumage coloration; [START_REF] Bolund | Inbreeding depression of sexually selected traits and attractiveness in the zebra finch[END_REF] as potential signals of individual quality.

Methods

Study species, study sites and sample size

The Zenaida dove is a granivorous columbid species characterized by long-term pair-bonding and yearround breeding and territoriality (Wiley 1991, Quinard andCézilly 2012). The species shows a slight sexual dimorphism, with males being on average 2-5% larger than females, although size distribution shows a large overlap between sexes [START_REF] Monceau | Territoriality versus flocking in the Zenaida dove (Zenaida aurita): resource polymorphism revisited using morphological and genetic analyses[END_REF]. Juveniles can be distinguished from adults based on morphological characteristics (plumage development and bill morphology, [START_REF] Wiley | Ecology and behavior of the Zenaida dove[END_REF][START_REF] Del Hoyo | Handbook of the Birds of the World[END_REF][START_REF] Gibbs | Pigeons and Doves: A Guide to the Pigeons and Doves of the World[END_REF], but age cannot be ascertained when birds are first captured as adults.

The data presented here come from a long-term study of the Barbados (West Indies) population of Zenaida doves. There, individuals may either actively defend, alone or in pairs, a territory against conspecifics, or feed with very little aggression towards conspecifics in large aggregations at specific sites where food availability is particularly high (Dolman et al. 1996, Carlier andLefebvre 1996). Individuals feeding in flocks are significantly smaller than territorial individuals, and are presumably floaters or poorly competitive individuals that have not yet obtained access to a territory [START_REF] Sol | Ecological mechanisms of a resource polymorphism in Zenaida Doves of Barbados[END_REF][START_REF] Monceau | Territoriality versus flocking in the Zenaida dove (Zenaida aurita): resource polymorphism revisited using morphological and genetic analyses[END_REF]). On the other hand, once individuals have become territorial, they tend to remain so for the rest of their life, even after having lost their mate through death or divorce (Quinard 2013, F. Cézilly unpubl. data). As in other parts of the range of the species [START_REF] Wiley | Ecology and behavior of the Zenaida dove[END_REF], breeding occurs year-round, but with a peak in breeding activity during the "high" breeding season, i.e. from January to April (F. Cézilly unpubl. data.). Territorial individuals were caught using clap-net traps in the Sunset Crest residential area and the Folkestone Park, both located near Holetown (13°10'60N, 59°38'60W). Non-territorial individuals feeding in large groups were trapped at Roberts Manufacturing Co. Ltd. (13°8'6N, 59°34'48N), a pet and livestock food factory. On each capture, wing chord was measured with a ruler (accuracy: ±1 mm), and tarsus length with a digital caliper (accuracy: ±0.2 mm). Individuals were weighed using a digital scale (accuracy: ±0.1 g). In addition, a blood ccepted Ar ticle sample (40 µl) was taken on each ringed bird by puncturing the brachial vein and stored in 800 μL of storage buffer (70% ethanol and 30% Tris-EDTA buffer pH 8) [START_REF] Monceau | Territoriality versus flocking in the Zenaida dove (Zenaida aurita): resource polymorphism revisited using morphological and genetic analyses[END_REF]. Finally, color was measured on different areas of the plumage (see below) before releasing the bird at the site of capture. Only adults were considered in this study. Sex of individuals was later identified using molecular markers (see Monceau et al. 2011 for details).

Data were collected during both the high breeding season (from 1 March to 9 April 2012 and from 18 February to 19 March 2013) and the low breeding season (from 12 November to 2 December 2012). Data were obtained for a total of 122 individuals, 73 caught at the Sunset Crest and Folkestone areas and 49 caught at the Roberts site. Of these, 60 were females and 62 were males. Two birds were captured twice during two different sessions. For these individuals, we used the data recorded during the first session.

Microsatellite genotyping and individual heterozygosity

We genotyped 122 individuals across 11 polymorphic microsatellite markers developed especially for the Zenaida dove by [START_REF] Monceau | Twenty-three polymorphic microsatellite markers for the Caribbean endemic Zenaida dove, Zenaida aurita, and its conservation in related Zenaida species[END_REF] using the LI-COR Genotyping System (see [START_REF] Monceau | Twenty-three polymorphic microsatellite markers for the Caribbean endemic Zenaida dove, Zenaida aurita, and its conservation in related Zenaida species[END_REF] for a full description of the genotyping method). Tests for linkage disequilibrium (LD) and Hardy-Weinberg equilibrium (HWE) were computed using GENEPOP (v. 4.1.4.;[START_REF] Rousset | Genepop 4.1 for Windows/Linux/Mac OS X[END_REF] and were found to be non-significant. We also found no evidence for identity disequilibrium (ID), i.e. a correlation in heterozygosity and/or homozygosity across loci [START_REF] Szulkin | Heterozygosity-fitness correlations: a time for reappraisal[END_REF]. As an estimate of individual heterozygosity, we computed the multilocus heterozygosity coefficient (MLH) as recommended by [START_REF] Szulkin | Heterozygosity-fitness correlations: a time for reappraisal[END_REF]. MLH corresponds to the proportion of heterozygous loci within an individual, replacing missing values by the locus population mean. MLH varies between 0, when all loci are homozygous, and 1, when all loci are heterozygous.

Plumage color measurements

The dorsal plumage of Zenaida doves varies from brownish to cinnamon, while ventral plumage is light vinaceous to white, with black spots on the wings. The outer secondary feathers and the outer tail feathers ccepted Ar ticle bear white tips. The sides of the neck are characterized by an iridescent pink/violet patch and two dark violet-blue streaks which appear black from a distance (Fig.1a, b;[START_REF] Wiley | Ecology and behavior of the Zenaida dove[END_REF][START_REF] Bond | A field guide to the birds of the West Indies[END_REF].

Compared to humans, birds possess an additional cell cone type in the retina, receptive to ultraviolet light (UV, 300-400nm) above 340nm [START_REF] Chen | The ultraviolet receptor of bird retinas[END_REF]. Columbidae species appear to possess the "VS" rather the "UVS" cone type [START_REF] Ccepted Ar Ticle Romeski | Psychophysical studies of pigeon color vision-II. The spectral photochromatic interval function[END_REF][START_REF] Cserháti | Four cone types characterized by anti-visual pigment antibodies in the pigeon retina[END_REF][START_REF] Ccepted Ar Ticle Ödeen | The phylogenetic distribution of ultraviolet sensitivity in birds[END_REF], more details in Supplementary material), indicating that their maximum light absorption ranges between 402 and 426 nm rather than between 355 and 380 nm. It is therefore likely that the Zenaida dove's vision is also sensitive to UV light, with, presumably, a "VS" visual system.

Feather coloration was assessed in the field using a JAZ-EL200 spectrometer, supplied with a Jaz PX pulsed short arc Xenon lamp module and a 400 μm fibre-optic probe (Ocean Optics, IDIL Fibres Optiques, Lannion, France), kept at a constant distance and a constant angle (90°) from the plumage surface, following a previously published protocol [START_REF] Andersson | Quantification of coloration[END_REF]; details in Supplementary material).

Reflectance was measured for each bird on six body regions, namely the crown, mantle, breast, belly (between the legs), iridescent patch and lower dark streak on both sides of the neck. Reflectance of each body region was recorded three times at the same point, removing the spectrometer probe between each measurement. All measurements were made by the same person (AQ).

The crown, mantle, breast and belly reflectance spectra were characterized by a peak in the UV, followed by a slow increase in reflectance towards the red wavelengths (Supplementary material Fig. A1a, b, c, andd, respectively). Dark streaks on the neck also showed reflectance spectra characterized by a peak in the UV-blue, albeit less important and flatter than for other body regions, while the rest of the spectra was almost flat (Fig. A1e). Finally, iridescent patches on the lower neck typically showed multiple peaked spectra [START_REF] Mcgraw | Multiple UV reflectance peaks in the iridescent neck feathers of pigeons[END_REF], with a first peak in the UV-blue wavelengths, a second peak in the blue-green wavelength, and a third peak in the red wavelengths (Fig. A1f).

Upon observation of reflectance spectra for all body regions, and based on previously published methods [START_REF] Montgomerie | Quantifying colors[END_REF], different parameters were chosen to describe reflectance spectra, and calculated using the Color Project 1 software (version 4.3) developed by JMR. For all body regions, brightness, the total intensity of light reflected by feathers, was calculated as the integral of reflectance ccepted Ar ticle over [300,700] nm (e.g. [START_REF] Endler | On the measurement and classification of color in studies of animal color patterns[END_REF][START_REF] Andersson | Ultraviolet sexual dimorphism and assortative mating in blue tits[END_REF]. For the crown, mantle, breast and belly, UV chroma was calculated as the relative proportion of the total reflectance in the ultraviolet part of the spectrum visible to birds (R 340-400 / R 300-700 ) (spectral purity, e.g. [START_REF] Andersson | Ultraviolet sexual dimorphism and assortative mating in blue tits[END_REF]. We also calculated yellow-red chroma as the relative proportion of the total reflectance within a range from 550 nm to 700 nm of the spectrum (R 550-700 / R 300-700 ). For the crown, mantle, breast and lower belly, we additionally assessed hue as an angle value (0°: red -90°: yellow) that is correlated with the wavelength of maximum slope, and calculated the sign of this slope using the Endler's segment classification [START_REF] Endler | On the measurement and classification of color in studies of animal color patterns[END_REF]. Although this parameter does not take into account the UV part of the spectrum to which birds are sensitive and is adapted to trichromatic vision only, hue was used in order to compare our data to previously reported variation in color as assessed from the human eye (see Introduction). Finally, ultraviolet, blue-green, and red peaks of the iridescent patch were described by their spectral position (spectral position of maximum reflectance e.g. [START_REF] Delhey | Age differences in blue tit Parus caeruleus plumage colour: withinindividual changes or colour-biased survival?[END_REF] and their chroma (wavelength of maximum reflectance, and relative proportion of reflectance in the ranges [340,400], [390,550] and [550, 700] nm, respectively). Mean and s.d. values for each color parameter are given in Supplementary material Table A1.

Correlations among color parameters

Correlations among variables describing plumage color of the four brown areas on the one hand and of the iridescent patch on the other hand, were investigated using non-parametric correlation matrices based on Spearman's rank method. For the crown, mantle, breast and lower belly, correlation matrices were computed separately for hue, brightness, yellow-red chroma and UV chroma. Correlations among the variables describing the color of the iridescent patch were computed separately (Supplementary material Table A2). Hue values for the mantle, crown and breast were moderately correlated (from R S = 0.12, P = 0.08 to R S = 0.36, P < 0.001). Belly hue was positively correlated to breast hue (R S = 0.28, P = 0.002), but not to crown or mantle hue (P > 0.05). Brightness values for the mantle, crown and breast were significantly and positively correlated between themselves, as were yellow-red chroma values (0.40 < R S < 0 .67, P < 0.001) and UV chroma values (0.34 < R S < 0.83, P < 0.001). For the iridescent patch, most parameters were correlated (-0.37 < R S < 0.87, 0.001 < P < 0.93; see Supplementary material Table A2 for details).

ccepted Ar ticle

Differences in color parameters between sessions An exploratory analysis using ANOVAs combined with Tukey multiple comparisons revealed that most mean values of color parameters were different between our three ringing sessions (Supplementary material Table A3). This was mainly due to the fact that data from the high breeding season in 2012 significantly differed from those from the low breeding season in 2012 and high breeding season in 2013, which generally did not differ from each other. However, the proportions of territorial and non-territorial individuals did not differ between sessions (χ² = 0.19, df = 2, P = 0.91), nor did the proportions of females and males (χ ² = 3.56, df = 2, P = 0.17). In addition, body condition, wing chord and heterozygosity did not significantly differ between the three capture sessions. Before further analysis, color variables were therefore centered and scaled across ringing sessions (see Supplementary material for a discussion of this seasonal effect).

Avian color discrimination of sexual dichromatism and of variation in plumage colour among individuals of the same sex

To quantify sexual dichromatism and to estimate whether individuals perceive variation in plumage color among potential mates from the avian visual perspective, we computed the chromatic contrast of the reflectance spectra (ΔS, [START_REF] Vorobyev | Tetrachromacy, oil droplets and bird plumage colours[END_REF]) both between sexes, and within each sex, using the mean spectrum for the three measures (or six, for the right and left iridescent patches and dark streaks) per individual. We used the pavo package [START_REF] Maia | pavo: an R Package for the analysis, visualization and organization of spectral data[END_REF] developed for the R software (v. 2.101; R Core Team 2011) to run these analyses. We created a visual model (vismodel function) using the spectral sensitivity data from the Rock pigeon (Columba livia, [START_REF] Bowmaker | Visual pigments and oil droplets from six classes of photoreceptor in the retinas of birds[END_REF]) -i.e. λ max = 409 nm, 453 nm, 507 nm and 568 nm for wavelength of maximum absorbance for each cone, and λ cut = 445 nm, 513 nm, 539 nm and 570 nm for "cut-off" wavelength of oil droplets of C-, Y-(ventral retina form), Y-(dorsal retina form) and R-type cones, respectively. The illuminant considered was an ideal white one, default option of the R function. The coldist function was used to estimate distances (ΔS) between (i) all pairs of male/female and (ii) all pairs of individuals within each sex for each measured body part. Following [START_REF] Vorobyev | Tetrachromacy, oil droplets and bird plumage colours[END_REF], we used the tetrachromatic photoreceptor ccepted Ar ticle densities ratio 1:1:1:2, and 0.1 as the Weber fraction. The distance in avian color space ΔS is expressed in just noticeable difference (jnd), with ΔS = 1 considered as the threshold of color discrimination. When ΔS < 1, two colors are indistinguishable. Above that threshold, the higher the value, the more discernible the two colors, discrimination being barely accurate under ideal conditions for low values above one jnd [START_REF] Siddiqi | Interspecific and intraspecific views of color signals in the strawberry poison frog Dendrobates pumillo[END_REF]. Analyses were also conducted on each session separately (Supplementary material Fig. A5 andA6), without any marked discrepancy with the results of the global analyses presented below.

Statistical analyses

Analyses were carried out using the R software (v. 2.101; R Core Team 2011). Correlation analyses used Pearson product-moment correlations or Spearman rank-order correlations. The relationship between body condition and feather coloration was tested by computing the scaled mass index proposed by [START_REF] Peig | New perspectives for estimating body condition from mass/length data: the scaled mass index as an alternative method[END_REF], using tarsus length as a linear body measurement of individuals. Each group of correlated color variables were tested for differences related to sex, territorial status, heterozygosity level, wing chord and body condition, as well as two-way interactions, through performing backward stepwise MANOVAs. Interactions were included to account for the fact that relationships between heterozygosity level, body size (wing chord) and condition tend to differ according to the sex and social status of individuals [START_REF] Quinard | Pairing patterns in relation to body size, genetic similarity and multilocus heterozygosity in a tropical monogamous bird species[END_REF]. To that end, we used the manova function with the Wilks test option, followed by the corresponding ANOVAs using the aov function. The assumptions of ANOVAs and MANOVAs (multivariate normality, homogeneity of variances, equality of covariance matrices, absence of outliers) were generally fulfilled on the raw variables (few minor deviations to normality and homogeneity of variances) and checked on residuals of the models. Because Bonferroni correction is a highly conservative method of significance level adjustment [START_REF] Narum | Beyond Bonferroni: Less conservative analyses for conservation genetics[END_REF], we used the modified false discovery rate (BY-FDR correction) proposed by [START_REF] Benjamini | The control of the false discovery rate in multiple testing under dependency[END_REF] when conducting MANOVAs and ANOVAs.

Results

An overall slight sexual dichromatism was found for hue, with crown and breast being more reddish in males than in females (Table 1, Supplementary material Fig. A2). There was also an effect of the ccepted Ar ticle interaction between sex and wing chord on hue (Table 1), with females with longer wing chord being significantly more reddish on the crown (slope estimate = -0.10, ± s.e. = 0.02, t = -5.13, P < 0.001, Fig. 2a), whereas no significant relationship between hue and wing chord was found in males for the crown (slope estimate = -0.01, ± s.e. = 0.01, t = -0.88, P = 0.38, Fig. 2b). There was also a significant overall effect of territorial status on hue: individuals feeding in groups at Roberts were more reddish on the mantle and slightly more reddish on the crown, and tended to be less reddish on the breast (Table 1) than territorial individuals from Holetown. In addition, territorial individuals were overall brighter (for the crown, breast and belly, and marginally for the dark streak, Table 2, Supplementary material Fig. A3) and relatively brighter in the UV part of the spectra (for the breast and belly, Table 3), whereas they were relatively less bright in the yellow-red part (for the breast and belly, Table 4). There was also a tendency for an effect of the interaction between sex and heterozygosity on yellow-red chroma (Table 4) with more heterozygous males being significantly relatively brighter in the yellow-red part of the spectra on the mantle (slope estimate = 2.19, ± 1.05, t = 2.09, P = 0.04, Fig. 2k) and the belly (slope estimate = 2.49, ± 1.00, t = 2.48, P = 0.02, Fig. 2m), but not females (mantle, slope estimate = -1.57, ± = 0.96, t = -1.63, P = 0.11; belly, slope estimate = -0.34, ± 1.01, t = 0.33, P = 0.74; Fig. 2l). Crown brightness varied according to body condition as well (Table 2, Fig. 2c), with brighter individuals being in slightly better body condition (linear regression: slope estimate = 0.01, ± s.e. = 0.006, t = 2.67, P = 0.009).

Both wing chord and the interaction between territorial status and body condition had a significant overall effect on the color parameters of iridescent patches, which did not differ between the sexes (Table 5). Larger individuals were brighter and tended to have greater UV and blue chromas, whereas they tended to have a lower red chroma (Table 5, Fig. 2d, e, f and g), i.e. they were relatively brighter in the UV and blue parts of the spectrum than in the red. The iridescent patch of territorial individuals tended to be brighter with increasing body condition (slope estimate = 0.02, ± s.e. = 0.008, t = 2.27, P = 0.03, Fig. 2h), whereas the reverse was observed in non-territorial individuals (slope estimate = -0.02, ± s.e. = 0.008, t = -2.70, P = 0.009, Fig. 2i).

Finally, the avian color discrimination analyses highlighted that Zenaida doves are unable to perceive sex-related differences in brown plumage, as means and standard deviations are under or close to the threshold of discrimination ΔS = 1 (Supplementary material Table A4, Fig. 3).

Although the difference between males and females for both dark streaks and iridescent patches was more pronounced (Supplementary material Table A4, Fig. 3), it appeared slightly distinguishable with values < ccepted Ar ticle 4 jnds [START_REF] Siddiqi | Interspecific and intraspecific views of color signals in the strawberry poison frog Dendrobates pumillo[END_REF]). From a sexual selection perspective, color discrimination analyses also showed that individuals are able to discriminate among potential mates on the basis of their plumage color for the iridescent patch, but not for the other colors assessed in this study (Supplementary material Table A4). This was the case for both females and males (Supplementary material Fig. A4a andb, respectively).

Discussion

Our study of the plumage colour of Zenaida doves in Barbados detected a slight sexual dichromatism in the pigment-based colored areas when considering hue, brightness and yellow-red chroma, but not in the iridescent patches for brightness, chroma or spectral position of the peaks. However, when taking avian vision into account, it appeared that individuals should not be able to perceive between-or within-sex differences in pigment-based colored plumage, but should be able to discriminate between individuals based on their iridescent colorations. In addition, variation in the plumage colour of Zenaida doves was found to be associated with several variables, suggesting that it may function as an indicator of individual quality in both males and females.

Spectrometry revealed an overall minor sexual dichromatism for hue in the pigmented plumage, with males being on average slightly more reddish than females. However, there was an extensive overlap between males and females, such that, contrary to what has been suggested in field guides and in the literature [START_REF] Wiley | Ecology and behavior of the Zenaida dove[END_REF][START_REF] Del Hoyo | Handbook of the Birds of the World[END_REF][START_REF] Gibbs | Pigeons and Doves: A Guide to the Pigeons and Doves of the World[END_REF][START_REF] Sol | Ecological mechanisms of a resource polymorphism in Zenaida Doves of Barbados[END_REF], sexing by the human eye is definitely unreliable, as previously suggested by [START_REF] Monceau | Territoriality versus flocking in the Zenaida dove (Zenaida aurita): resource polymorphism revisited using morphological and genetic analyses[END_REF]. In addition, our assessment of the difference between male and female plumage coloration using a visual model indicates that birds should not be able to distinguish the sex of their conspecifics based on the overall pigment-based coloration of the plumage.

Our results also tend to invalidate the claim made by some authors [START_REF] Wiley | Ecology and behavior of the Zenaida dove[END_REF][START_REF] Del Hoyo | Handbook of the Birds of the World[END_REF], that females exhibit no or much reduced iridescent patches. Indeed, we found that, at least in the Barbados population of Zenaida doves, chroma and spectral position of the different peaks and brightness of iridescent patches did not differ significantly between sexes. Although we did not measure the actual size of iridescent patches, they did not appear to differ remarkably between males and females when observing tagged individuals of known sex in the field. However, because we measured birds in the field, our results may have to be confirmed by more precise measurements (see [START_REF] Meadows | Quantifiying iridescent coloration in animals: a method for improving repeatability[END_REF]). Yet, taking into account the avian visual abilities, the spectral variation of iridescent patches appeared to be ccepted Ar ticle distinguishable by birds, albeit slightly. To our knowledge, only two studies assessed the degree of sexual dichromatism for iridescent plumage in Columbidae. Similarly to our results, both the black-bluish stripe on the Picui dove's wing coverts [START_REF] Mahler | Objective assessment of sexual plumage dichromatism in the Picui Dove[END_REF] and iridescent neck feathers in pigeons [START_REF] Leclaire | Feather bacterial load affects plumage condition, iridescent color, and investment in preening in pigeons[END_REF] appear to be similar or only slightly different between sexes to the human eye, while the analysis of reflectance spectra shows significant differences between males and females spectra with an overlap between sexes. In addition, male pigeons were found to be unable to recognize the sex of conspecifics and to court every individual [START_REF] Burley | The evolution of sexual indistinguishability[END_REF]. Interestingly, our results and these observations might explain why both male and female Zenaida doves chase all intruders, irrespective of their sex, during territorial defense [START_REF] Quinard | Sex roles during conspecific territorial defence in the Zenaida dove, Zenaida aurita[END_REF].

The absence of strong differences between sexes for ornaments such as iridescent colorations is open to alternative explanations. Female ornamentation in Zenaida doves may have evolved to become similar to that of males. The mutual selection hypothesis suggests ornamentation in monogamous species is the result of selection for its expression in both sexes [START_REF] Johnstone | Mutual mate choice and sex differences in choosiness[END_REF][START_REF] Johnstone | The tactics of mutual mate choice and competitive search[END_REF]) through three possible processes: (i) mate choice and mate competition, (ii) competition for other resources than mates and (iii) sexual selection for sexual mimicry. In particular, [START_REF] Burley | Sexual selection for aesthetic traits in species with biparental care[END_REF] predicted that mutual sexual selection should appear in monogamous species with biparental care. Accordingly, Zenaida doves maintain long-term monogamous pair-bonds and show shared territorial defense [START_REF] Quinard | Sex roles during conspecific territorial defence in the Zenaida dove, Zenaida aurita[END_REF], joint anti-predatory vigilance [START_REF] Cézilly | Vigilance and food intake rate in paired and solitary Zenaida Doves Zenaida aurita[END_REF] and bi-parental care (Wiley 1991, F. Cézilly unpublish. data,). In addition, [START_REF] Owens | Sexual dimorphism in birds: why are there so many different forms of dimorphism?[END_REF] evidenced a positive relationship between dichromatism for structural coloration and frequency of extra-pair paternity in monogamous bird species, which could be consistent with the very low, if any, level of extra-pair copulation observed in our population (FC, personal observations).

Alternatively, similarity in plumage coloration between the two sexes might simply be a genetically correlated response in one sex, male or female, to selection in the other sex (Lande 1980, Roulin and Jensen 2015, but see [START_REF] Gluckman | Pathways to elaboration of sexual dimorphism in bird plumage patterns[END_REF]. In such a case, one would expect to observe a negative relationship between fitness and the intensity of plumage coloration in one sex and a positive one in the other one [START_REF] Fitzpatrick | Ornaments or offspring: costs to reproductive success restrict sexual selection processes[END_REF][START_REF] Roulin | Sex-dependent selection on an autosomal melanic female ornament promotes the evolution of sex ratio bias[END_REF], if color entails production or maintenance costs, which may be the case with iridescent colors [START_REF] Dyck | Structure and light reflection of green feathers of fruit doves (Ptilinopus spp.) and an imperial pigeon (Ducula concinna)[END_REF][START_REF] Eliason | Decreased hydrophobicity of iridescent feathers: a potential cost of shiny plumage[END_REF][START_REF] Meadows | Dietary protein level affects iridescent coloration in Anna's hummingbirds, Calypte anna[END_REF]). Although we did not assess the consequences of variation in plumage coloration in terms of survival or reproductive output here, we did not detect sex-related differences in the relationship between plumage coloration and body condition. Genetic theories of sexual selection predict that most ornamental ccepted Ar ticle secondary sexual traits provide reliable indication of the genetic quality of their bearers [START_REF] Brown | A theory of mate choice based on heterozygosity[END_REF][START_REF] Fromhage | Evolution of mate choice for genome-wide heterozygosity[END_REF]. Although direct relationships between coloration and genome-wide heterozygosity or level of inbreeding have been evidenced in birds [START_REF] Ar Ticle García-Navas | Heterozygosity-based assortative mating in blue tits (Cyanistes caeruleus): implications for the evolution of mate choice[END_REF][START_REF] Bolund | Inbreeding depression of sexually selected traits and attractiveness in the zebra finch[END_REF][START_REF] Ferrer | Multiple sexual ornaments signal heterozygosity in male blue tits[END_REF] and neutral locus heterozygosity is known to influence adult survival in our species [START_REF] Cézilly | Adult survival selection in relation to multilocus heterozygosity and body size in a tropical bird species, the Zenaida dove, Zenaida aurita[END_REF], we found only moderate evidence for a relationship between plumage coloration and individual heterozygosity in the Zenaida dove. However, ornaments could be linked to other aspects of genetic quality such as MHC diversity [START_REF] Von Schantz | MHC genotype and male ornamentation: genetic evidence for the Hamilton-Zuk model[END_REF][START_REF] Grahn | MHC genotype and ornamentation[END_REF][START_REF] Dunn | MHC variation is related to a sexually selected ornament, survival and parasite resistance in the common yellowthroat[END_REF][START_REF] Whittingham | Different ornaments signal male health and MHC variation in two populations of a warbler[END_REF]. Another possibility is that sexually selected ornaments are condition-dependent and are thus more informative of the phenotypic quality of individuals than of their genetic one [START_REF] Bonduriansky | The evolution of condition-dependent sexual dimorphism[END_REF]. Alternatively, the signal may include a behavioral component, which we did not assess here, and which may enhance the attractiveness of the ornamental trait [START_REF] Hasson | Amplifiers and the handicap principle in sexual selection -a different emphasis[END_REF][START_REF] Galván | The importance of white on black: unmelanized plumage proportion predicts display complexity in birds[END_REF][START_REF] Byers | Female mate choice based upon male motor performance[END_REF]). This might be the case in Zenaida doves, in which males shake their head while females outstretch their neck during courtship displays [START_REF] Wiley | Ecology and behavior of the Zenaida dove[END_REF].

Observed relationships between some individual characteristics and color parameters are however more suggestive of direct benefits, with coloration acting as an honest signal of phenotypic quality in the Zenaida dove. Iridescent patches of larger individuals of both sexes were brighter, with relatively higher blue and smaller red peaks, and territorial individuals showed brighter iridescent patches when they were in better condition, while the reverse was true for non-territorial individuals. Our results are consistent with a number of studies that iridescent coloration covary with individual condition and size in birds (i.e. [START_REF] Doucet | Structural plumage coloration, male body size, and condition in the Blue-Black Grassquit[END_REF][START_REF] Møller | Condition dependence, multiple sexual signals, and immunocompetence in peacocks[END_REF], Doucet and Montgomerie 2003[START_REF] Costa | Coccidian oocyst parasitism in the blue-black grassquit: influence on secondary sex ornaments and body condition[END_REF][START_REF] Legagneux | Condition dependence of iridescent wing flash-marks in two species of dabbling ducks[END_REF][START_REF] Meadows | Dietary protein level affects iridescent coloration in Anna's hummingbirds, Calypte anna[END_REF], and suggest that iridescent color may have a signaling function. Iridescence may thus be used in mutual mate choice in Zenaida doves, or mediate agonistic intrasexual encounters during territorial defense [START_REF] Doucet | Structural plumage coloration, male body size, and condition in the Blue-Black Grassquit[END_REF]Meadows 2009, Quinard andCézilly 2012).

We also observed an overall difference in color between territorial individuals living in Holetown and non-territorial individuals feeding in flocks at the Roberts site. However, this difference may not necessarily reflect differences in phenotypic quality between the two groups, although such differences exist [START_REF] Monceau | Territoriality versus flocking in the Zenaida dove (Zenaida aurita): resource polymorphism revisited using morphological and genetic analyses[END_REF]. Roberts is an animal food factory, and birds foraging there are exposed to a certain amount of dust. It has been shown that soil principally causes a decrease in plumage UV chroma and brightness [START_REF] Zampiga | Preening, plumage reflectance and female choice in budgerigars[END_REF][START_REF] Surmacki | Soil and preen waxes influence the expression of carotenoidbased plumage coloration[END_REF][START_REF] Ccepted Ar Ticle Doucet | Do museum specimens accurately represent wild birds? A case study of carotenoid, melanin, and structural colours in long-tailed manakins Chiroxiphia linearis[END_REF], Pérez-Rodriguez et al. 2011). Accordingly, we found that territorial individuals from Holetown were relatively brighter in the UV on the breast than individuals from the Roberts factory. In addition, air pollution is known to enhance ccepted Ar ticle melanin-based coloration [START_REF] Mcgraw | An update on the honesty of melanin-based color signals in birds. -Pigm[END_REF], and individuals sampled at Roberts were indeed more reddish on the mantle, and marginally on the crown. Differences between individuals from Holetown and from Roberts were then probably related to the distinct environments of the sampling locations more than to the territorial status of individuals. It is not possible, however, to disentangle the effects of these two factors with our data set. 1. Effects of sex, territorial status, wing chord and the interaction between sex and wing chord on hue parameters of pigment-based colored plumage areas in Zenaida dove. The effects of heterozygosity and body condition, initially included, were not retained in the final model. MANOVA Wilks' lambda and exact F statistics for the hypothesis of no overall effects on hue, and corresponding univariate tests for each body region are presented. The effect of sex estimates the difference between males taken as the reference and females. The effect of territorial status estimates the difference between territorial individuals taken as the reference and non territorial birds. P-values in bold are significant at P < 0.0125 after a BY-FDR correction. Significant relationships are illustrated in Fig. 2a andb. ccepted Ar ticle

Hue

Further

  research is now required to confirm the role of plumage coloration in social signaling, mate choice and individual recognition in Zenaida dove. For instance, paired and unpaired territorial individuals could be compared to investigate mating patterns among natural pairs in the field, or coloration could be manipulated in controlled lab experiment of mate choice. ccepted Ar ticle 'This article is protected by copyright. All rights reserved.'

Figure 1 .

 1 Figure 1. Adult Zenaida dove (a) in Sunset Crest, Holetown, Barbados, (b) focus on the head,

Figure 3 .

 3 Figure 3. Plot of color distances ΔS in units of just noticeable differences (JNDs) between males and females, as viewed by rock dove visual system. Dots and error bars indicate mean ± standard deviation chromatic distances between all pairs of different sexes. The dashed line marks JND = 1 above which the pair of color patches is considered to be discernible by birds.

Table legends Table

 legends

Table 2 .

 2 Effect of body condition and territorial status on brightness parameters of pigment-based colored plumage areas in Zenaida dove. The effects of sex, heterozygosity and body size (wing chord), initially included, were not retained in the final model. MANOVA Wilks' lambda and exact F statistics for the hypothesis of no overall effects on brightness, and corresponding univariate tests for each body region are presented. The effect of territorial status estimates the difference between territorial individuals taken as the reference and non territorial birds. P-values in bold are significant at P < 0.0125 after a BY-FDR correction. The significant relationship between crown brightness and body conditions is illustrated in Fig.2c.

		Sex				Territorial status			Wing chord			Sex x Wing chord
	Wilks'
	lambda	0.6535				0.8707				0.8395				0.8697
		F df	P	Estimate ± s.e. F df	P	Estimate ± s.e. F df	P	Estimate ± s.e. F df	P	Estimate ± s.e.
	MANOVA 4.65 4,114	<0.001			4.25 4,114 0.003			8.88 4,114 <0.001			4.27 4,114	0.002
	Crown	10.95 1,117 0.001 -13.62	4.11	4.97 1,117 0.02	0.33	0.14	24.65 1,117 <0.001 -0.10	0.02	9.95 1,117 0.002	0.08	0.02
	Mantle	0.0004 1,117 0.98	0.09	4.88	12.36 1,117 <0.001 0.62	0.17	0.07 1,117 0.77	-0.007	0.02	0 1,117	0.99	-0.0001 0.03
	Breast	2.56 1,117	<0.001 -7.47	4.66	3.99 1,117 0.04	-0.33	0.16	5.85 1,117 0.01	-0.05	0.02	2.21 1,117	0.13	0.04	0.03
	Belly	1.52 1,117	0.21	6.17	4.99	0.75 1,117 0.38	0.15	0.18	0.15 1,117 0.69	0.009	0.02	1.67 1,117	0.19	-0.04	0.03

'This article is protected by copyright. All rights reserved.' 'This article is protected by copyright. All rights reserved.'

Table 3 .

 3 Effect of territorial status on UV chroma parameters of pigment-based colored plumage areas in Zenaida dove. The effects of sex, heterozygosity, body size (wing chord) and body condition, initially included, were not retained in the final model. MANOVA Wilks' lambda and exact F statistics for the hypothesis of no overall effects on UV chroma, and corresponding univariate tests for each body region are presented. The effect of territorial status estimates the difference between territorial individuals taken as the reference and non territorial birds. P-values in bold are significant at P < 0.0125 after a BY-FDR correction.

	UV chroma	Territorial status
	Wilks' lambda	0.80
		F df	P	Estimate ± s.e.
	MANOVA	7.07 4,117 <0.001
	Crown	1.39 1,120 0.23	0.22	0.18
	Mantle	0.24 1,120 0.63	0.09	0.18
	Breast	14.61 1,120 <0.001 0.66	0.18
	Belly	26.20 1,120 <0.001 0.85	0.16

'This article is protected by copyright. All rights reserved.'

Table 4 .

 4 Effect of sex, heterozygosity, territorial status and the interaction between sex and heterozygosity on yellow-red chroma parameters of pigment-based colored plumage areas in Zenaida dove. The effects of body size (wing chord) and body condition, initially included, were not retained in the final model. MANOVA Wilks' lambda and exact F statistics for the hypothesis of no overall effects on UV chroma, and corresponding univariate tests for each body region are presented. The effect of sex estimates the difference between males taken as the reference, and females. The effect of territorial status estimates the difference between territorial individuals taken as the reference and non territorial birds. P-values in bold are significant at P < 0.0125 after a BY-FDR correction. Significant relationships are illustrated in Fig.2jto m.

	Yellow-red
	chroma	Sex			Heterozygosity		Territorial Status	Sex x Heterozygosity
	Wilk's
	lambda	0.98			0.97			0.79		0.92
		F df	P	Estimate ± s.e. F df	P	Estimate ± s.e. F df	P	Estimate ± s.e. F df	P	Estimate ± s.e.
	MANOVA	0.66 4,113	0.62		0.96 4,113 0.43		7.68 4,113 <0.001	2.55 4,113 0.04
	Crown	1.31 1,116	0.26 -0.42	1.09 1.11 1,116 0.30 0.37	1.00 2.48 1,116 0.12	-0.29	0.19 0.04 1,116 0.84 0.30	1.43
	Mantle	0.05 1,116	0.82 -2.75	1.08 1.11 1,116 0.74 -1.68	0.99 0.77 1,116 0.38	-0.15	0.18 6.87 1,116 0.009 3.74	1.42
	Breast	0.07 1,116	0.80 -1.48	1.04 0.09 1,116 0.76 -1.29	0.96 15.43 1,116 <0.001 -0.70	0.18 1.97 1,116 0.16 1.92	1.37
	Belly	0.69 1,116	0.41 -2.11	0.98 2.54 1,116 0.11 -0.99	0.90 29.18 1,116 <0.001 -0.90	0.17 4.25 1,116 0.04 2.65	1.29

'This article is protected by copyright. All rights reserved.'

Table 5 .

 5 Effect of territorial status, body condition, wing chord and the interaction between territorial status and body condition on parameters of the iridescent plumage patch in Zenaida dove. The effects of sex and heterozygosity, initially included, were not retained in the final model. MANOVA Wilks' lambda and exact F statistics for the hypothesis of no overall effects on the color of the iridescent patch, and corresponding univariate tests for each color parameter are presented. The effect of territorial status estimates the difference between territorial individuals taken as the reference and non territorial birds. P-values in bold are significant at P < 0.0125 after a BY-FDR correction. Significant relationships are illustrated in Fig.2dto i.

	Iridescent
	patch	Territorial status			Body condition			Wing chord			Territorial status x Body condition
	Wilks' lambda 0.94				0.91				0.79				0.82
		F df	P	Estimate ± s.e. F df	P	Estimate ± s.e. F df	P	Estimate ± s.e. F df	P	Estimate ± s.e.
	MANOVA	1.09 7,111	0.37			1.53 7,111 0.16			4.22 7,111 <0.001			3.59 7,111	0.002
	Brightness	2.17 1,117	0.14	-5.79	1.82	2.74 1,117 0.10	-0.72	0.02	12.01 1,117 <0.001 0.24	0.11	14.42 1,117 <0.001 0.09	0.05
	UV chroma	0.21 1,117	0.65	1.79	-0.16 0.49 1,117 0.48	-0.004	0.009 8.43 1,117 0.01	0.06	0.02	5.67 1,117	0.09	0.03	0.01
	UV spectral
	position	0.35 1,117	0.55	-6.83	11.73 0.12 1,117 0.73	-0.04	0.06	1.09 1,117 0.30	0.11	0.10	0.42 1,117	0.52	0.05	0.08
	Blue chroma	1.09 1,117	0.29	-0.11	0.04	1.07 1,117 0.30	-<0.001 <0.001 6.78 1,117 0.01	<0.001	<0.001 3.26 1,117	0.17	<0.001	<0.001
	Blue spectral
	position	0.02 1,117	0.90	9.59	20.30 0.24 1,117 0.63	0.07	0.11	0.25 1,117 0.62	0.09	0.18	0.24 1,117	0.63	-0.07	0.14
	Red chroma	0.49 1,117	0.49	0.07	0.07	0.95 1,117 0.33	<0.001	<0.001 11.17 1,117 0.001 -<0.001 <0.001 4.58 1,117	0.05	-<0.001 <0.001
	Red spectral
	position	0.78 1,117	0.38	-6.49	3.26	0.001 1,117 0.97	-0.03	0.02	3.52 1,117 0.08	0.03	0.03	0.26 1,117	0.64	0.05	0.02

Acknowledgements

We are particularly grateful to Mr. Steve Devonish, Director of Natural Heritage (division of Ministry of Environment and Drainage of Barbados) and Kim Downes Agard for granting us the permission to capture, blood sample, and ring Zenaida doves. We thank the CRBPO, and particularly Olivier Dehorter, for kindly providing us with aluminium rings. We thank Carla Daniel for help in catching birds and Cyril Bhola for hospitality. The study was supported by the Agence Nationale pour la Recherche (programme blanc Monogamix), the Conseil Régional de Bourgogne, the CNRS, and the Institut Universitaire de France. Finally, we would like to thank the Subject Editor, Alexandre Roulin, and two reviewers for their detailed and helpful comments on previous versions of the manuscript.

ccepted Ar ticle


Xavier Buet

Coralie Brun

Jérôme Gâteau

Seyed Bruno Bresson

SEYED Reza Sandoghchi

Eric Numkam Fokoua

Marco Petrovich

Francesco Poletti

David Richardson

Damien Vandembroucq

Gilles Tessier
email: gilles.tessier@parisdescartes.fr

Nondestructive measurement of the roughness of the inner surface of hollow core-photonic bandgap fibers

Hollow core-photonic bandgap fibers (HC-PBGFs) represent a potential candidate for optical communication applications that require ultra-low latency. HC-PBGFs are essentially formed by a periodic cladding made of air holes in a silica glass matrix which confine light in a central air core. Guidance in an air core allows for a much lower nonlinearity and latency compared to classical solidcore fibers [ 1,2]. Furthermore, HC-PBGFs offer reduced losses by Rayleigh scattering, impurities, or multiphonon absorption relative to solid fibers. However, the lowest loss values reported on HC-PBGFs so far are still one order of magnitude higher than those of solid single mode fibers [3]. Losses in HC-PBGFs are fundamentally limited by scattering at the numerous and intrinsically "rough" air/glass interfaces present in these structures [ 3]. Scattering due to the surface roughness component at low spatial frequencies (i.e. below 1µm -1 ) is understood to provide the dominant contribution to the overall loss [ 4]. The study of roughness in this frequency range requires precise surface measurements over distance scales of several hundreds of micrometers, which is not possible with most Atomic Force Microscopes (AFMs).

The structure of glasses is amorphous, mostly owing to their past liquid state: to a first approximation, glass can be viewed as a liquid abruptly frozen at the glass transition temperature TG. Surface capillary waves (SCWs) that are thermally excited in the liquid state are suddenly frozen during the fiber drawing process [ 3,5,6]: the glass surface structure therefore reflects the thermal fluctuations of the liquid surface at TG.. These SCWs result from the interplay of two opposing effect: thermal noise (which tends to destabilize the surface), and interface tension (which tends to dampen the oscillations and flatten the surface). A simple estimate of the variance of the height fluctuations, δh², is given by the ratio between the thermal noise energy at glass transition kBTG, and the interface tension γ. This fundamental thermodynamic process imposes the ultimate limit to roughness in glasses, and thus to the loss of HC-PBGFs. The resulting roughness is extremely low: for standard values of TG and γ of amorphous silica, the RMS roughness amounts to / 0.4

B G k T nm σ γ ≈ ≈
. However, this value provides only a partial measure of the superposition of roughness contributions which extend over a wide range of length scales, ranging from the nanometer to the millimeter regime [ 6], as shown below.

In this work, we demonstrate a method for the selective filling of HC-PBGFs which allows the focusing of an optical profilometer inside the hollow core to measure for the first time the surface roughness at frequencies below 1 µm -1 . The measured roughness levels are compatible with AFM measurements and SCW-based roughness modelling over most of the spectrum but they deviate considerably below a certain cutoff frequency, providing new insight on the loss limits in these complex fiber waveguides. Fig. 1a shows the polarization-modulated differential profilometer which we used to measure the glass roughness on the inner surface of the core of HC-PBGFs (Fig. 1b). The measurements were performed over length scales of hundreds of micrometers with a picometer-range vertical precision. Immersion oil matching the PBGFs' refractive index was used to eliminate unwanted reflections. In this system inspired by Gleyzes and Boccara [ 7], a laser beam polarized at 45° relative to the axes of a Wollaston prism is divided in two beams of identical intensity carrying orthogonal polarizations. The beams corresponding to each arm are focused into two laser spots separated by a distance d ≈ 3 µm on the surface of the sample. After reflection on the surface of interest, these beams are recombined in the Wollaston prism, following precisely their previous path if the prism is in the back focal plane of the objective. The beamsplitter then deflects a portion of the beam to a photoelastic polarization modulator working at 50 kHz. Both polarizations are projected on an analyzer set at 45° relative to both of them to allow interference, and the beam is collected by a photodiode. After lock-in detection, the interference yields a signal proportional to the optical path difference between the two beams, and therefore to the height difference D(x)=h(x+d/2)-h(x-d/2) between them (where x is the horizontal coordinate along the surface and h(x) the height profile). D(x) is measured while continuously moving the sample along the x direction (with a PI M 126.2S1 translation stage), and can be equated in a first approximation to the spatial derivative of the profile.

The ultra-low noise levels obtained with this instrument, around six to ten picometers [ 8], make it especially suited to the characterization of ultrasmooth glass surfaces with typical RMS roughness in the sub-nanometer range. The accuracy of the instrument was validated by cross-comparison with AFM measurements on reference samples [ 8]. Fig. 2: Selective filling process: (a) a portion of HC-PBGF fiber is (b) dipped in a UV-curable polymer (arrow). Due to its viscosity, the polymer penetrates faster in the central hollow core than in the smaller peripheral capillaries. After UV curing, the fiber is cleaved along the red dotted line to obtain (c) a PBGF with a polymer plug obstructing the core. (d) The PBGF is immersed in index-matching oil (yellow), which penetrates the whole structure except the air-filled core (blue) which becomes the only optically visible feature.

However, accessing the inner wall of a micrometer-sized HC-PBGF with an AFM probe is extremely difficult. Several techniques have been developed in order to expose portions of the inner core and allow AFM measurements. Crushing the fiber and identifying a portion of the walls of the central hole among the fragments [ 3] or bending the fiber and polishing until a sufficient portion of the inner core is exposed [ 9] are efficient methods, but contamination of the surface by glass fragments, dust, or the polishing solution are difficult to avoid and are thus are very likely to affect the measurement results. More recently, an efficient method using thermal expansion has been proposed in order to cleave fibers along their axis [10] and analyze tubes with AFM or electron microscopy. We have found that an overestimation of the intrinsic roughness due to surface contamination is highly likely if a complex cleaning procedure is not followed scrupulously. Moreover, access to the surface over millimeter-range distances remains extremely difficult.

As previously demonstrated [ 8], oil immersion eliminates unwanted reflections off the outer surface of glass objects. In this paper, to study the inner hollow core of PBGFs without opening the fiber, we chose to fill the small tubes defining the cladding with oil while leaving the central core filled with air. To achieve this, we developed a technique similar to [11], based on selective filling of the PBGF (Fig. 2). Exploiting capillary action, the core and cladding were partially filled with a viscous photopolymer which propagates faster and (in a given short time) further in the core than in the smaller cladding holes (Fig. 2.b). The traveling front of the infusing polymer was cured and fixed by UV photopolymerization and the fiber was cleaved under a microscope, precisely in the region (typically a few millimeters) where the polymer has only penetrated the core. The fiber portion which had a core obstructed by the polymer on one side (Fig. 2.c) was then immersed in index-matching oil. The obstruction only allowed the oil to penetrate into the cladding holes (Fig. 2.d). Under an oilimmersion objective, and with an oil index that matches that of the glass, the only remaining optically visible feature was therefore the boundary of the central air-filled core. The two beams of the optical profilometer (Fig. 1) were then focused on this surface and the fiber was scanned longitudinally to measure the inner roughness of the core wall. This technique allows scans over several millimeters with picometer vertical precision inside pristine, un-contaminated fibers. Therefore, it is extremely valuable in the accurate characterization of the roughness of HC-PBGFs. In particular, as shown below, this gives access to the roughness at low spatial frequencies, i.e. below 1 µm -1 , which have substantial impact on the losses of these fibers. The recorded data was processed to extract information on the roughness. In Fig. 3 (top), we show a differential profile measured on the inner surface of a PBGF over 200 µm (extracted from a 2 mm long scan). The extremely low height fluctuations (a few hundred pm) are compatible with a frozen capillary waves scenario [3,5,6]. To be more quantitative, we characterize the Fourier spectrum of the height profile, for which a 1/f profile is expected (where f is the spatial frequency) in a frozen capillary wave scenario. Let us call hSCW the height fluctuations induced by surface capillary waves, the Power Spectral Density (PSD) expected over 1D profiles can be expressed as [3,5,6]:

( ) ² 4 B G SCW k T h f f πγ = (1)
with kB the Boltzmann constant, TG the glass transition temperature, γ the surface tension, and a Fourier transform defined as:

( ) 2 ( ) i fx g f g x e dx π +∞ -∞ =   (2)
The most straightforward way to obtain the roughness of the sample would be to integrate the measured differential signal to obtain the profile of the surface, and then compute its Fourier spectrum. However, as discussed in [ 8], the measured profile is not the exact derivative of the height of the surface due to the finite distance d between the probe beams and the size of the spots. For this reason, the PSD of the height signal ( ) ² h f  was obtained by dividing, in the Fourier space, the PSD of the bare differential signal ( ) ² D f  by the experimental response function of the measurement system, ( ) ² R f  . The result can be quantitatively compared with the theoretical expectation

( ) ² SCW h f 
given above in Eq. ( 1) for surface capillary waves. Note here that, because of its differential nature, the experimental set-up is blind to the spatial frequency fd =1/d and its multiples, associated with the distance d separating the two beams. This can be understood easily by considering that the two beams would always be at the same height when scanned on a hypothetical sinusoidal surface with a period d, yielding an artificially null differential signal. This blind frequency translates as a zero in the response function, ( )

0 d R f = 
, and therefore a high noise level at frequencies close to fd. The lowest accessible spatial frequency, currently a few 10 -3 µm -1 , is essentially set by the available measurement length. Currently, the translation stage is limited to ~2 mm due to practical difficulties in maintaining a correct alignment and focusing over longer scanning distances. Nonetheless, this already represents an improvement by 2-3 orders of magnitude in comparison to AFM, and could probably be further improved with better mechanical alignment since the selective filling process is able to produce samples measurable over a few centimeters.

The PBGF on which we measured the roughness was fabricated using the conventional two-step stack and draw process and is shown Fig. 1b). In a first step, meter-long cylindrical fused silica capillaries were stacked in a triangular lattice with 37 capillaries omitted to form the core defect. The assembly was then drawn into meter long canes of a few mm in diameter. In a second step, the cane was inserted into a sleeve jacket and the assembly drawn down to fiber dimensions. The application of positive pressure resulted in a fiber with a large air filling fraction of ~90% and an average cladding pitch Λ=4.8 μm. The fiber core measured on average 36μm in diameter. The fiber loss measured by cutback had a minimum value of 9.3 dB/km at 1.55 μm.

Using the selective filling procedure described above on this fiber, we performed optical measurements on the inner surface of its core. For validation purposes, AFM measurements were also carried out on a portion of the same fiber. Under a microscope, the fiber was mechanically cleaved at low angles with respect to the fiber axis in order to expose portions of the core. Although this procedure is much simpler than the one described in [10], it is relatively inefficient and therefore time-consuming. The measurements were carried out using a Bruker Dimension Icon AFM, and one of the images (10x2.5 µm) is presented in Fig. 3 In Fig. 4, we present power spectral densities (PSDs) obtained through the data processing presented above for optical profilometry, and with a procedure described in [6] for the AFM measurements. The optical profilometry PSD results from the average of 12 PSDs obtained on the same fiber from independent differential profiles acquired over typically 1-2 mm, in order to have enough statistics and to reduce the noise. We note that in the range [5×10 -2 µm -1 -2×10 -1 µm -1 ], the PSDs are reasonably consistent with the 1/f behavior expected from a capillary wave model. This behavior had already been measured in the range [0.3 µm -1 -30 µm -1 ] by AFM measurements [3] but, to the best of our knowledge, the lower frequency regime presented here, which has the highest impact on PBGF losses, had not yet been measured. The values of TG/γ which best describe these PSDs is of the order of 2500, and is lower than the classical TG/γ value of 5000 given for amorphous silica. This effect, which could be attributed to the strain applied to the fibers during the drawing process, remains to be investigated in more detail.

As discussed above, the optical profilometry PSD near 0.3 µm -1 is affected by the proximity of the blind frequency fd and was discarded. While a spatial frequency down to 10 -3 µm -1 would in principle be accessible with 2 mm long scans, we chose to truncate the data below 6.10 -3 due to its limited statistical significance and to the fact that low frequencies are affected by the limited length of the scan and possibly by mechanical noise in the motorized translation stage. Interestingly, in the measurement presented here and in others we have conducted on similar samples, we consistently observe an increase in the slope of the PSD function for frequencies below 5.10 -2 µm -1 . A similar change had been predicted (but never observed before) due to the "cylindrical" nature of the core which quantifies the azimuthal component of the roughness spatial frequency, resulting in a PSD of the form [3]:

( ) ( ) 2 coth 4 B G SCW k T h f Wf f π πγ = ( 3
)
where W is the perimeter of the core boundary. This curve is also shown in Fig. 4. Note that the 1/f scaling of the one-dimensional PSD along the fibre axis results from a re-summation over the azimuthal modes along the perimeter. The lack of such modes at low spatial frequency due to the periodic boundary condition associated with the cylindrical geometry induces a crossover toward the 1/f² scaling of the longitudinal modes. While this theory predicts quite accurately the inflection frequency at which the slope changes, 2π/W (W=110μm), the measured slope is actually much steeper than the expected asymptotical 1/f 2 behavior of the coth function. As shown in the figure a better fit is achieved assuming a 1/f 3 dependency. Based on our current understanding, this appears to be a true feature of the surface, since measurements on larger tubes did not deviate from a classical 1/f behavior [8].While the origin of this behavior remains unclear, it suggests that, while the roughness at high frequencies can be well explained by a SCW model for planar structures, more work is required to fully interpret the deviations observed at lower frequencies.

To summarize, we have described a method for the selective filling of the cladding of HC-PBGFs which enables the direct optical interferometric characterization of their inner core roughness with picometer-scale sensitivity without the need to physically open (i.e. crush) the fibers. This measurement technique is therefore remarkably immune to sample contamination issues, noises, and vibrations. Besides, it allows reaching a previously inaccessible range of spatial frequencies, [6.10 -3 , 2.10 -1 ] µm -1 . Using this method we have characterized the inner core surface of a 37cell PBGF. Over a wide spectral range the results have shown good agreement with separate AFM measurements obtained, in contrast, by crushing the fiber microstructure. However, an inflection point in the PSD at short frequencies has been directly observed for the first time. Whilst more work is required to lower the minimum frequency range measurable with confidence with this method, we believe that the ability to characterize nondestructively the roughness of fabricated HC-PBGFs over relevant spatial scales shown here will prove most valuable in attempts to optimize their loss.

Fig. 1 :

 1 Fig. 1: a) Polarization-modulated differential scanning interferometer. b) Scanning Electronic Microscopy image of a section of the HC-PBGF showing its inner structure.

Fig. 3 :

 3 Fig. 3 : (Top) Differential profile of the hollow core wall of a selectively filled PBGF measured by optical profilometry over 200 µm. (Bottom) 10 x 2.5 µm AFM image (scale bar : 1 µm) of the inner surface of the same fiber. In both cases, the height fluctuations are of the order of a few hundreds of pm.

Fig. 4 :

 4 Fig. 4: Roughness measurements of the inner wall of a PBGF by AFM (red curve) and optical profilometry (blue). The optical profilometry PSD is calculated by averaging 12 independent measurements, and is valid up to an instrumental cutoff frequency of 2.10 -1 µm -1 . The continuous black line corresponds to the capillary waves model described by equation (1), plotted for TG/γ=2500. The dashed lines correspond to Equ. (3) and 1/f 3 . The vertical line indicates the spatial frequency 2π/W of the inflection point of Equ. (3)

Funding sources .

 sources This work was supported by the EU 7th Framework Programme under grant agreement 228033 (MODE-GAP). X.B. acknowledges the support of Programme DIM OxyMORE, Ile de France.