Responses to increased costs of activity during incubation in a songbird with female-only incubation: does feather colour signal coping ability?

Keywords: Feather colouration, female ornaments, Great Tit, handicapping, incubation behaviour, nest attentiveness Zusammenfassung Reaktionen auf erhöhte Kosten bei der Bebrütung von Singvögeln mit Inkubation ausschließlich durch das Weibchen: Ist die Gefiederfarbe ein Anzeichen für bessere Stressbewältigung? während der Brutpflege umzugehen und sie zeigen dies anhand ihrer Gefiederfarbe. Wir untersuchten die Auswirkung einer zusätzlichen Belastung, mit der energetisch kostspieligen Einschränkung der Flugfähigkeiten umzugehen. Sollte dies der Fall sein, sollten intensiver gefärbte Weibchen besser mit der zusätzlichen Belastung umgehen können, als weniger stark gefärbte Weibchen. Dementsprechend sollten der Masseverlust und die Nestattraktivität negativ mit der Gefiederfärbung korreliert sein. Weibchen mit gestutzten Federn nahmen stärker ab als die Weibchen der Kontrollgruppe, hatten aber nicht deutlich unattraktivere Nester, was darauf hindeutet, dass beeinträchtigte Weibchen die Mehrkosten durch die zusätzliche Belastung auf sich nehmen. Bereits schwache Weibchen wurden durch die zusätzliche Belastung stärker die Färbung des Brustgefieders nicht auf die Fähigkeit der Stressbewältigung eines Weibchens während der Inkubation schließen lässt

Individuals differ in their ability to cope with energetically demanding situations while caring for the current brood and they can signal this ability by their colouration. We examined the impact of handicapping (clipping of wing and tail feathers) on an energetically demanding care behaviour (incubation) in the Great Tit (Parus major) females. We hypothesised that the intensity of carotenoid-based breast feather colouration signals the ability to cope with impaired flight ability and consequent increased energetic demands. If this is the case, females with more intensely coloured feathers should cope better with the handicap compared with less intensely coloured females, i.e. the impact of handicapping on mass loss and nest attentiveness should be negatively correlated with colouration. Handicapped females lost more weight than control females but did not decrease nest attentiveness to a greater extent, suggesting that females take the costs of handicapping on themselves. Females in poor condition were more severely influenced by handicapping.

Intensity of breast feather colouration therefore does not appear to signal female ability to cope with this energetically demanding situation during incubation.

Introduction

One of the basic tenets of evolutionary biology is that individuals differ in their ability to survive and cope with challenging environmental conditions. This ability can be influenced by the quality, age and condition of the individual (Fox et al. 2001). Individual quality and condition can be signalled to potential mates or rivals by various types of ornaments including those based on carotenoids [START_REF] Searcy | The evolution of animal communication[END_REF]. Carotenoid-based colouration is widespread in animals, including feathers and bare parts in birds [START_REF] Olson | Interspecific variation in the use of carotenoid-based coloration in birds: diet, life history and phylogeny[END_REF].

Carotenoids cannot be synthesised by animals, must be obtained from food, and thus are potentially in short supply [START_REF] Olson | Costly sexual signals: are carotenoids rare, risky or required?[END_REF]. Full expression of carotenoid-based colouration is costly and carotenoids are involved in a number of trade offs with important physiological functions, including immune function and the level of oxidative stress [START_REF] Von Schantz | Good genes, oxidative stress and condition-dependent sexual signals[END_REF][START_REF] Mcgraw | Mechanics of carotenoid-based coloration[END_REF]. Consequently, intensity of carotenoid-based colouration is expected to indicate individual quality, condition, and/or capability of parental effort [START_REF] Møller | Carotenoiddependent signals: Indicators of foraging efficiency, immunocompetence or detoxification ability?[END_REF]Griffith et al. 2006).

The role of feather ornaments as indicators of quality, condition, and parental effort has been traditionally studied in males (reviewed in [START_REF] Griffith | Benefits to female birds of assessing color displays[END_REF]. However, there has been a recent surge of interest in the function and evolution of female ornaments (reviewed in Amundsen 2000; [START_REF] Amundsen | Female coloration: review of functional and nonfunctional hypotheses[END_REF]Kraaijeveld et al. 2007;[START_REF] Clutton-Brock | Sexual selection in females[END_REF].

Recent studies have demonstrated that female ornaments might work as badges of status enabling better access to resources [START_REF] Murphy | Female American goldfinches use carotenoid-based bill coloration to signal status[END_REF][START_REF] Griggio | Female ornamentation, parental quality and competitive ability in the rock sparrow[END_REF] or as signals of good parenting abilities [START_REF] Linville | Plumage brightness as an indicator of parental care in northern cardinals[END_REF][START_REF] Siefferman | Evidence for sexual selection on structural plumage coloration in female eastern bluebirds (Sialia sialis)[END_REF]; but see [START_REF] Smiseth | Does female plumage coloration signal parental quality? A male removal experiment with the bluethroat (Luscinia s. svecica)[END_REF][START_REF] Griggio | Female ornamentation, parental quality and competitive ability in the rock sparrow[END_REF]. It has been even demonstrated that breeding success might be correlated with female ornament expression [START_REF] Morales | Female ornaments in the Pied Flycatcher Ficedula hypoleuca: associations with age, health and reproductive success[END_REF][START_REF] Bitton | Plumage characteristics, reproductive investment and assortative mating in Tree Swallows Tachycineta bicolor[END_REF] and males might base their mate choice at least partly on the degree of female ornamentation [START_REF] Griggio | Female ornamentation and directional male mate preference in the rock sparrow[END_REF]; but see [START_REF] Murphy | Female American goldfinches use carotenoid-based bill coloration to signal status[END_REF]). However, studies examining female ornaments during reproduction in birds have been carried out during the nestling period while incubation was almost completely neglected [START_REF] Amundsen | Why are female birds ornamented?[END_REF][START_REF] Amundsen | Female coloration: review of functional and nonfunctional hypotheses[END_REF]but see [START_REF] Hanssen | White plumage reflects individual quality in female eiders[END_REF].

Incubation is a very important part of the breeding cycle in birds and parental effort during incubation can have strong consequences for the reproductive success of the pair [START_REF] Deeming | Avian Incubation: Behaviour, Environment and Evolution[END_REF]. Normal embryo development requires eggs to be kept within a narrow range of temperatures [START_REF] Webb | Thermal tolerance of avian embryos: a review[END_REF]. Non-optimal temperatures can lead to reduced hatchability and longer incubation periods [START_REF] Lyon | Incubation feeding in snow buntings: female manipulation or indirect male parental care?[END_REF][START_REF] Webb | Thermal tolerance of avian embryos: a review[END_REF][START_REF] Martin | Egg size variation among tropical and temperate songbirds: An embryonic temperature hypothesis[END_REF]. At the same time, incubation is energetically demanding for the incubating individual (Willams 1996;Thomson et al. 1998;[START_REF] Tinbergen | Energetics of incubation[END_REF], who has to split its time between warming the eggs and foraging for itself. Hence, the ability to cope with energetically challenging situations during incubation can be very important for the reproductive success of the pair. In species with female-only incubation females can signal this ability by their carotenoid-based feather colouration and males might accordingly base their mate choice on the intensity of female's colouration [START_REF] Amundsen | Female coloration: review of functional and nonfunctional hypotheses[END_REF]Kraaijeveld et al. 2007).

Handicapping is a useful and widely employed method to study the effects of energetically challenging situations on bird behaviour [START_REF] Harrap | How is sexual conflict over parental care resolved? A meta-analysis[END_REF]. Birds can be handicapped by adding weights [START_REF] Wright | Manipulation of sex differences in parental care[END_REF][START_REF] Griggio | Should I stay or should I go? Female brood desertion and male counterstrategy in rock sparrows[END_REF], taping their feathers (Senar et al. 2002a) or feather clipping [START_REF] Slagsvold | Ultimate adjustment of clutch size to parental feeding capacity in a passerine bird[END_REF][START_REF] Sanz | Differential response by males and females to manipulation of partner contribution in the great tit (Parus major)[END_REF]. The last method is particularly suitable because it simulates events that can happen in the wild due to attacks by predators, and hence represents a risk to which birds might have become adapted [START_REF] Slagsvold | Influence of male and female quality on clutch size in tits (Parus spp.)[END_REF]. Broken or missing feathers are among the most often encountered natural handicaps in free ranging birds [START_REF] Dawson | Sex-dependent frequency and consequences of natural handicaps in American Kestrels[END_REF]. The ability to cope with such a handicap might therefore reveal an important component of individual quality [START_REF] Harding | Flexibility in the parental effort of an Arctic-breeding seabird[END_REF]).

In our study, we examined effects of handicapping (feather clipping) on incubation behaviour in the Great Tit (Parus major), a small, short-lived songbird with female-only incubation. In particular, we determined whether females differed in their responses to this energetic constraint in relation to the intensity of their yellow, carotenoid-based feather colouration. We predicted that impaired flight ability caused by handicapping would 1) extend the time females spent foraging off the nest and hence decrease time they spent on the nest, and/or 2) lead to higher body mass loss during incubation compared with controls. Moreover, if carotenoidbased feather colouration of the Great Tit females indicates ability to cope with such energetic constraint, females with more intense feather colour can be expected to be less affected by the challenge [START_REF] Smiseth | Does female plumage coloration signal parental quality? A male removal experiment with the bluethroat (Luscinia s. svecica)[END_REF][START_REF] Doutrelant | Female coloration indicates female reproductive capacity in blue tits[END_REF].

Methods

General field work

This work was conducted on three adjacent nest-box plots which are ca. 1 km apart in a broadleaved forest dominated by oak (Quercus petraea) on Velký Kosíř in the east of the Czech Republic (49°32′N, 17°04′E). There are 300 nest-boxes in total placed about 1.5 m above ground and besides Great Tits they are inhabited by Collared Flycatchers (Ficedula albicollis), Blue Tits (Cyanistes caeruleus), Nuthatches (Sitta europea) and Coal Tits (Periparus ater).

Fieldwork was carried out in 2008 from early April until May. We checked nest-boxes daily to record laying of the first egg and final clutch size. Day 0 was the day when the last egg was laid. Eggs in our population usually start to hatch on days 11-13 and hatching lasts for 2-3 days.

Cross-fostering

We wanted to isolate the direct effects of female incubation behaviour (i.e. egg warming) on hatching success and incubation period length, excluding any genetic or maternal effects.

Therefore, we matched pairs of nests by their age and clutch size and exchanged clutches between pairs of nests. Clutches were exchanged as soon as, or immediately after, egg laying ended. We took the whole clutch from a nest, weighed it on a digital balance to the nearest 0.01 g and swapped it within the dyad (in 67 out of 82 nests on day 1, range 0-3). Nests were always exactly matched by the date when the last egg was laid. There was no difference in clutch size in 52 nests, a difference of one egg in 28 nests and of two eggs in two nests. The transfer of eggs took on average 8 min (range = 3-14 min).

Nest attentiveness

During incubation, we monitored the percentage of time incubating females spent on eggs, i.e. nest attentiveness. We deployed temperature data loggers by inserting a probe through the nest wall into the bottom of the nest cup. A second probe was mounted under the nest-box. We measured inner and outer temperature from 5 a.m. until 10:40 p.m. in 16-s intervals. On the nest temperature recordings, time when the incubating female is away from the nest is recognizable by downward spikes. Temperature drops quickly when the female leaves the clutch (off-bout) and then starts to increase sharply when she returns (on-bout; Fig. 1).

Consequently, it is easy to make the difference between an attended and an empty nest (e.g. [START_REF] Zimmerling | Variation in incubation patterns of red-winged blackbirds nesting at lagoons and ponds in eastern Ontario[END_REF]. From the pattern of nest temperatures, we calculated nest attentiveness throughout the day. To get ambient temperature for every nest, we took outer temperature for the start of each on-and off-bout and averaged it across the day. The data loggers were deployed on day 3 or 4 of incubation and the nest attentiveness was measured on the subsequent day (i.e., on days 4-5). Four days after experimental treatment (see below), we measured nest attentiveness again in the same way (i.e., on days 9-10).

Experimental treatment

The day after nest attentiveness was measured for the first time we captured females in the nestbox (i.e., on days 5-6) and weighed them on a spring Pesola balance (to the nearest 0.25 g). We handicapped every first and second female and left every third female as a control. In experimental females, we clipped primaries number 5, 6 and 8 (out of the total of 10 primaries, counted from the outside) on both wings, together with the four central tail feathers (out of the total of 12 tail feathers). We clipped the feathers as close to their bases as possible. This methodology was modified from Slagsvold and Lifjeld (1990). We handled control females in the same way as experimental females except that we did not clip the feathers. We returned all the females back to the nest-box through the entrance. Then we covered the entrance and waited for about one minute before leaving. The effect of handicapping was temporary and lasted until the post-breeding moult. Experimental and control females did not differ significantly in their initial body weight (F 1,75 = 1.2, P = 0.283).

Females and clutches

The day after nest attentiveness was measured for the second time we captured females in the nest-box again (i.e., on days 10-11). We aged them (one year old or older, Svensson 1992), weighed them on a spring Pesola balance (nearest 0.25 g), and measured their tarsus by a digital calliper (nearest 0.01 mm). We took 10 to 15 yellow feathers from the upper right part of breast for later spectrophotometric analysis. Experimental and control females did not differ significantly in their tarsus length (F 1,54 = 0.14, P = 0.706). After this day we checked nestboxes daily to determine hatching success. We removed eggs that did not hatch and dissected them to determine the cause of hatching failure, i.e. eggs with no sign of embryo development or apparent dead embryo. We defined hatching success as percentage of fertilised eggs that hatched. Since we were interested in the effects of incubation behaviour on hatching success, we excluded eggs with no sign of embryo development from the analyses. Some unhatched eggs disappeared from the nest before we were able to dissect them. We removed these nests from the analyses of hatching success and thus the sample size was reduced. We calculated incubation period as the time from laying of the last egg to hatching of the first egg [START_REF] Lyon | Incubation feeding in snow buntings: female manipulation or indirect male parental care?[END_REF].

Laboratory analyses

We quantified reflectance spectra of yellow feathers sampled from the breast using standard procedures [START_REF] Andersson | Quantifying colors[END_REF]. We used 10-15 feathers from each bird, which is sufficient to obtain reliable values from our species [START_REF] Quesada | Comparing plumage colour measurements obtained directly from live birds and from collected feathers: the case of the great tit Parus major[END_REF]. We used an Avantes AvaSpec-2048 fibre optic spectrometer together with an AvaLight-XE xenon pulsed light source and a WS-2 white reference tile. The probe was used both to provide light and to sample the reflected light and was held perpendicular to the feather surface. We took five readings, each from a different part of each set of feathers. Feathers were arranged on black, nonreflective surface so that they overlapped extensively.

We obtained reflectance (%) from the wavelength of 320 to 700 nm in 1-nm increments (Fig. 2). We calculated so called carotenoid chroma, because it has been demonstrated that it correlated positively with the amount of carotenoids deposited in feathers in the Great Tit (Isaksson et al. 2008, Isaksson andAndersson 2008, see also [START_REF] Andersson | Quantifying colors[END_REF].

Carotenoid chroma is a preferable index of the concentration of carotenoids in feathers in unsaturated carotenoid-based colours [START_REF] Andersson | Quantifying colors[END_REF]. Carotenoids present in Great Tit breast feathers (lutein, zeaxanthin) absorb maximally at around 450 nm [START_REF] Andersson | Quantifying colors[END_REF] and the colour of our Great Tits was unsaturated, because we still had reasonable reflectance around 450 nm (see Fig. 2). We calculated carotenoid chroma as (R 700 minus R 450 ) divided by R 700 , where R 700 is reflectance at 700 nm and R 450 reflectance at 450 nm. In statistical analyses, we used the average carotenoid chroma calculated from the five readings from each set of feathers. To assess repeatability of our measurements, in a subsample of feathers, we arranged feathers anew and took other five readings and again averaged the carotenoid chroma calculated from them. We calculated repeatability of these two average carotenoid chroma estimates using the intraclass correlation coefficient [START_REF] Lessels | Unrepeatable repeat abilities: a common mistake[END_REF], which was high (r i = 0.85, P < 0.001, n = 55). As previous studies used also other characteristics derived from reflectance spectra, we also calculated brightness (R avg ), hue (λ R50 ), and UV-chroma (see [START_REF] Montgomerie | Analyzing colors[END_REF]. We calculated brightness (R avg ) and hue (λ R50 ) according to Andersson and Prager (2006, p. 78). R avg is reflectance averaged over the interval from 320 to 700 nm. λ R50 is wavelength halfway between R max and R min , where R max is maximum reflectance and R min is minimum reflectance between 320 and 700 nm. We also calculated UV-chroma as reflectance between 320 and 400 nm divided by reflectance between 320 and 700 nm. Experimental and control females did not differ significantly in either of the four colour characteristics: carotenoid chroma (F 1,54 = 0.02, P = 0.883), brightness (F 1,54 = 0.78, P = 0.381), hue (F 1,54 = 1.49, P = 0.227), and UV-chroma (F 1,54 = 1.43, P = 0.237).

Statistical analyses

We analysed the effects of experimental treatment on desertion rate (Likelihood-ratio test), change in nest attentiveness and female mass, incubation period length (general linear models), and hatching success (generalised linear models with binomial error distribution and logit link).

We analysed all data using JMP software, with the exception of hatching success where we used SAS. Binomial models were fitted as the number of eggs that hatched / clutch size. We confirmed that the data met the assumptions of general linear models where these were used [START_REF] Grafen | Modern statistics for the life sciences[END_REF]. We also checked that data in the binomial model were not overdispersed (deviance / df = 1.30).

Initial models included treatment and relevant other factors as predictors, which are apparent from Tables 1 and2. In the analyses of the change in nest attentiveness (attentiveness before treatment minus after treatment) and body mass (mass after treatment minus before treatment), we fitted also interactions of treatment with female initial condition and breast carotenoid chroma (see Table 1). We did this because we wanted to know whether females differed in their response to handicapping based on their initial condition and yellow colouration. In the analyses of incubation period length and hatching success, we fitted only the interaction of treatment with female breast carotenoid chroma (see Table 2). We also re-ran all the models with other colour characteristics (hue, brightness, UV-chroma) instead of carotenoid chroma (see Table 3). Date of experiment was set so that the day of first experiment = 1. Body condition for each female was calculated as the residual from the linear regression of initial body mass on tarsus length. We always retained treatment in the final model as our main factor of interest whatever its statistical significance (see [START_REF] Grafen | Modern statistics for the life sciences[END_REF]. Other predictors were removed from the models starting with interactions. We removed non-significant predictors until we ended only with factors significant at α = 0.05. In tables, we give F, DF, and P values of nonsignificant predictors immediately before they were removed from the model. Data are presented as mean ± SD.

Nest attentiveness is strongly affected by ambient temperature in the Great Tit [START_REF] Kluijver | Daily routines of the Great Tit, Parus m. major[END_REF]. Thus, when using attentiveness as a predictor in the analyses of incubation period length and hatching success, we adjusted for variation in ambient temperature among nests during sampling as follows. We fitted a regression of nest attentiveness on ambient temperature separately for both measurements (i.e., before and after treatment). In both cases there was a significant negative relationship (linear regression: before treatment F 1,75 = 13.3, P = 0.001, R 2 = 0.15; after treatment F 1,50 = 18.6, P < 0.001, R 2 = 0.27). We calculated the residual nest attentiveness and averaged the residuals from these two regressions. In this way, we obtained temperature-independent attentiveness for each female as a predictor variable.

When analysing observational data on mass decrease, it is necessary to take into account the problem of the regression toward the mean. Regression toward the mean occurs in repeatedmeasures analyses where subsets of population are compared based on their initial measurements. Thus, for instance it follows from this effect that initially heavy individuals will loose more mass than initially light individuals. However, since regression to the mean will affect both experimental and control groups, experimental studies are not subject to this problem [START_REF] Kelly | Correcting for Regression to the Mean in Behavior and Ecology[END_REF]. Accordingly, in our study we interpret only the difference in mass loss between handicapped and control females, not the pattern in control females itself, which might be subject to the problem of the regression to the mean. However, this does not seem to be the case, because our results are the same even when the data is mathematically adjusted according to Kelly and Price (2005: Equation 6; results not shown).

Results

Altogether we performed cross-fostering on 82 nests. Five females deserted their nests after cross-fostering, leaving 77 females for our experiment (54 experimental and 23 control). There was a strong tendency for experimental females to desert their nests more often after treatment compared to control females (18 experimental and three control, χ 2 = 3.68, P = 0.055, n = 77). Clutch size in our population was 10.4 ± 1.20 eggs (n = 82). Carotenoid chroma of yellow breast feathers was 0.64 ± 0.06 (range: 0.44 -0.75), brightness was 0.24 ± 0.038 (0.17 -0.33), hue was 501.3 ± 3.95 (495.0 -505.6), and UV-chroma was 0.14 ± 0.008 (0.12 -0.16, n = 56 in all four cases).

Nest attentiveness

Nest attentiveness before the treatment was 76.6 ± 4.77% (n = 77) and did not differ between experimental and control females (F 1,75 < 0.1, P = 0.875). On average, nest attentiveness decreased between the first and second measurement by 1.4 ± 5.52% (n = 52). Treatment had no influence on the amount of change in nest attentiveness. However, although our nests were highly synchronised and differed by less than 14 days, there was a significant effect of date. In the first nests of the breeding season, nest attentiveness increased by about 5%, whereas in the last nests, it on the contrary decreased by about 5% (Table 1). No other factor had any influence on the change in nest attentiveness (Table 1,Fig 3a).

Body mass loss

Female body mass before the experiment was 20.37 ± 0.88 g (n = 77). Body mass loss between the first and the second weighing was 0.66 ± 0.58 g (n = 56). Mass loss was significantly higher in experimental females (0.81 ± 0.52 g, n = 36) than in control females (0.38 ± 0.59 g, n = 20; simple effect of treatment: F 1,54 = 8.0, P = 0.007, Fig 3b). Mass loss was, however, also related to the initial condition of the female and the relationship differed between experimental and control females, as evidenced by the significant interaction between treatment and initial female condition (Table 1,Fig 4). No other factors were significant (Table 1).

Incubation period

Length of the incubation period was 11.8 ± 0.97 days (n = 48). Treatment had no effect on the length of the incubation period. It was negatively related to season and temperatureindependent nest attentiveness; other factors were not significant (Table 2).

Hatching success

Overall hatching success was 91.1 ± 11.52% (n = 51). There was no effect of treatment on hatching success; similarly, no other factor was significant (Table 2).

It follows from the above results that female carotenoid-based feather colouration expressed as carotenoid-chroma was not correlated with her ability to cope with energetic handicap during incubation (see also Table 1). Similarly, no other colour characteristic (hue, brightness, and UV-chroma) was correlated with female coping ability, incubation period length or hatching success (Table 3).

Discussion

Handicapping had no influence on female incubation behaviour, the length of incubation period or hatching success. However, during incubation handicapped females lost overall more body weight than control females. Females in poor condition were more severely influenced by handicapping. Intensity of female breast feather colouration did not correlate with either female incubation behaviour, body mass loss during incubation, incubation period length or hatching success.

It seems that most of the costs of handicapping were channelled to female mass loss. This agrees with a previous study of the Great Tit, where handicapped females kept feeding rates to the nestlings unchanged at the cost of deteriorating own body condition [START_REF] Sanz | Differential response by males and females to manipulation of partner contribution in the great tit (Parus major)[END_REF].

Similar results were obtained in a study of the Tree Swallow Tachycineta bicolor where the costs of handicapping were paid through the loss of female body mass while nestling condition was unaffected [START_REF] Winkler | Effects of handicapping on female condition and reproduction in tree swallows (Tachycineta bicolor)[END_REF]. However, in incubating Tree Swallows, handicapped females both lost more mass than control females and also slightly decreased nest attentiveness [START_REF] Ardia | Individual quality and age affect responses to an energetic constraint in a cavity-nesting bird[END_REF]. In some other species handicapping did not influence female body mass or body condition but it did influence feeding rate and consequently nestling condition and growth, e.g. in Antarctic Petrels Thalassoica antarctica, Leach's Storm-petrels Oceanodroma leucorhoa, Cory's Shearwaters Calonectris diomedea, and tropical House Wrens Troglodytes aedon [START_REF] Saether | Regulation of parental effort in a long-lived seabird: an experimental manipulation of the cost of reproduction in the antarctic petrel, Thalassoica antarctica[END_REF][START_REF] Mauck | Petrel parents shunt all experimentally increased reproductive costs to their offspring[END_REF][START_REF] Navarro | Experimental increase of flying costs in a pelagic seabird on foraging strategies, nutritional state and chick condition[END_REF][START_REF] Tieleman | Effects of experimentally increased costs of activity during reproduction on parental investment and self-maintenance in tropical house wrens[END_REF]. The two species where females invested into current brood at the expense of their own condition (Great Tits and Tree Swallows) are both short-lived with low probabilities of future reproduction, which selects for increased investment into current breeding attempt. On the contrary, long-lived species with a high probability of future reproduction, including Antarctic Petrels, Leach's Storm-petrels, Cory's Shearwaters, and tropical House Wrens, are expected to reduce any increases of investment into current brood to maximise their own survival [START_REF] Roff | The Evolution of Life Histories: Theory and Analysis[END_REF][START_REF] Ghalambor | Fecundity-survival trade-offs and parental risk-taking in birds[END_REF].

Our experimental treatment affected females that were in poor condition disproportionately more than those in good condition (see Fig. 4). The importance of good overall state of females for successful incubation in the Great Tit is further supported by our finding that handicapped females deserted their clutches more often than control females. Similar relationships between female condition and nest desertion have been also found in other species [START_REF] Wiggins | Correlates of clutch desertion by female Collared Flycatchers Ficedula albicollis[END_REF]Yorio and Dee Boersma 1994;[START_REF] Merilä | Mass loss in breeding blue tits: the role of energetic stress[END_REF]; but see [START_REF] Bleeker | Body condition and clutch desertion in penduline tit Remiz pendulinus[END_REF]). An obvious explanation for this pattern is that incubation is energetically demanding and females in poor condition, caused by low body mass or impaired flight abilities, are not able to withstand the energetic stress (Willams 1996;Thomson et al. 1998;[START_REF] Tinbergen | Energetics of incubation[END_REF].

Intensity of yellow breast feather colouration was not related to the ability of females to cope with the handicap. One might ask how female colouration could help prevent a change in body mass. Handicapping is a standard way of testing whether an individual is of higher quality, i.e., is better able to cope with a challenging situation. Our experimental approach was motivated by a widespread finding that individual quality often shows up only under unfavourable conditions (e.g. brood size manipulations, various forms of handicapping, food restrictions; e.g. [START_REF] Ardia | Individual quality and age affect responses to an energetic constraint in a cavity-nesting bird[END_REF][START_REF] Doutrelant | Female coloration indicates female reproductive capacity in blue tits[END_REF]. We conjecture that handicapped females could overcome the handicap by working harder. On a mechanistic basis, it means to put more energy into flight to get resources (self-maintenance) and simultaneously care for the clutch (incubate), without these functions being compromised. Of course, this higher effort is expected to bear costs, e.g. higher metabolic rate and higher oxidative stress generated by heavy work. This can be presumably achieved only by higher-quality individuals. There certainly was a variation among females in the degree of their body mass loss (see Figs 3 and4), i.e., in their ability to cope. We were interested whether this variation could be ascribed to female colouration and found out that this was not the case.

We would like to mention three potential problems when generalizing our results. First, costs of the manipulation could have also been observed after hatching. This might have been particularly true during nestling feeding, when females have to fly more. Previously, all studies examining female feather colouration during reproduction in birds have been carried out during the nestling period [START_REF] Amundsen | Female coloration: review of functional and nonfunctional hypotheses[END_REF]; but see [START_REF] Hanssen | White plumage reflects individual quality in female eiders[END_REF]. Several of them investigated the function of yellow breast feather colouration in Great and Blue Tits but generated mixed results. Some found a positive relationship between the intensity of female yellow colouration and breeding success, whereas others found no or even a negative relationship (correlative studies: Senar et al. 2002b;[START_REF] Mänd | Negative relationship between plumage colour and breeding output in female great tits, Parus major[END_REF][START_REF] Hidalgo-Garcia | The carotenoid-based plumage coloration of adult Blue Tits Cyanistes caeruleus correlates with the health status of their brood[END_REF]experiment: Doutrelant et al. 2008). Hence, information content of female yellow colouration might differ between parts of the breeding cycle, i.e., incubation vs. feeding of young. Second, the coloration of the females that deserted just after the manipulation is missing. It is possible that these deserting females had low carotenoid chroma values and were of inferior quality.

Consequently, if we were left with only higher-quality individuals, our test of the indicator potential of the carotenoid-based coloration in females would have been weakened. Third, males feed females during incubation in the Great Tit. If we found better coping ability in more colourful females, we would not be sure whether they cope better because they are able to work harder, or because they are more helped by their males. However, male incubation feeding is not a source of potential bias in our study, because we found no effect of female colour on the ability to cope with energetic stress. Moreover, we have studied this problem during three years in a nearby population and there was no effect of female colour on male incubation feeding [START_REF] Matysioková | Incubation feeding and nest attentiveness in a socially monogamous songbird: role of feather colouration, territory quality and ambient environment[END_REF].

While bearing the above-mentioned reservations in mind, our results are not consistent with a role for feather carotenoids as indicators of female quality or capacity for extra parental effort, as has been demonstrated by several other studies (see above). Differences in the results of multiple studies investigating feather ornaments in the same species are known to occur due to population differences in the information content of the ornamental traits [START_REF] Dunn | Geographic variation in the function of ornaments in the common yellowthroat Geothlypis trichas[END_REF][START_REF] Galván | Variation in effects of male plumage ornaments: the case of Iberian Pied Flycatchers[END_REF] and different expression of ornaments in different populations and subspecies [START_REF] Hill | A red bird in a brown bag[END_REF]. Great Tit subspecies differ strongly in the intensity of yellow breast colouration [START_REF] Harrap | How is sexual conflict over parental care resolved? A meta-analysis[END_REF]. However, there is no work quantifying differences in yellow colouration and in the functional ecology of feather ornaments among populations of the Great Tit. Nevertheless, it is at least possible that different populations are subject to different constraints on the expression of yellow colouration and that the information content of feather ornaments varies in space. Only rigorous studies conducted in an explicitly comparative framework might provide answers to the heterogeneity of studies conducted so far (Senar et al. 2002b;[START_REF] Mänd | Negative relationship between plumage colour and breeding output in female great tits, Parus major[END_REF][START_REF] Hidalgo-Garcia | The carotenoid-based plumage coloration of adult Blue Tits Cyanistes caeruleus correlates with the health status of their brood[END_REF][START_REF] Doutrelant | Female coloration indicates female reproductive capacity in blue tits[END_REF]this study). Final models: a F 2,49 = 3.7, P = 0.031, R 2 = 0.13, n = 52; b F 3,52 = 5.9, P = 0.002, R 2 = 0.25, n = 56.

Figure captions

c P-values of the final models are in bold.

d Sign (+ or -) or text in Estimate show the direction of the nonsignificant effects; exact parameter estimates are listed only for variables retained in final models, including treatment whatever its significance. Final models: a F 3,44 = 10.3, P < 0.001, R 2 = 0.41, n = 48; b n = 41.

c P-values of the final models are in bold.

d Sign (+ or -) in Estimate shows the direction of nonsignificant effects; exact parameter estimates are listed only for variables retained in final models, including treatment whatever its significance.

Table 3 Tests of the effects of brightness (R avg ), hue (λ R50 ), and UV-chroma, together with their interaction with handicapping, on the change in nest attentiveness and body mass, incubation period length, and hatching success. Colour characteristics were tested while added in turn to full models presented in Tables 1 and2 (without carotenoid chroma).

Fig. 1

 1 Fig. 1 Graph of a typical incubation profile of the Great Tit.

Fig. 2

 2 Fig. 2 Average (± SD) reflectance spectrum of yellow breast feathers of female Great Tits in 1-

Fig. 3 Fig. 4

 34 Fig. 3 Nest attentiveness (a; mean ± SE) and body mass of incubating females (b) in control

  Fig 3

Table 1

 1 Models explaining the change in nest attentiveness and in female body mass during

	incubation
		Change in nest attentiveness (%) a		Change in body mass (g) b
	Factor	F	DF	P c	Estimate (SE) d	F	DF	P c	Estimate (SE) d
	Intercept				-4.71 (2.370)				-0.36 (0.116)
	Treatment	0.1	1,49 0.818	0.35 (1.531)	10.0	1,52 0.003	-0.46 (0.144)
					(handic.)				(handic.)
	Date of experiment	7.4	1,49 0.009	0.84 (0.308)	0.3	1,49 0.601	+
	Female carotenoid	<0.1 1,46 0.952	+	1.6	1,50 0.213	-
	chroma
	Female age	3.6	1,48 0.064	older>1y old	3.1	1,51 0.086	older>1y old
	Female condition	2.2	1,47 0.144	+	5.8	1,52 0.020	-0.41 (0.140)
	Female condition x	0.1	1,44 0.719		5.2	1,52 0.026	0.40 (0.175)
	Treatment								(handic.)
	Female carotenoid	0.6	1,45 0.461		0.6	1,48 0.425
	chroma x Treatment

Table 2

 2 Models explaining incubation period length and hatching success

			Incubation period (day) a		Hatching success (logit scale) b
	Factor	F	DF	P c	Estimate (SE) d	χ 2	DF	P c	Estimate (SE) d
	Intercept				13.43 (0.358)				3.74 (0.584)
	Treatment	0.8	1,44	0.372	0.21 (0.236)	0.3 1,39 0.570	0.44 (0.771)
					(handic.)				(handic.)
	Date of experiment	24.1	1,44 <0.001	-0.23 (0.047)	0.1 1,35 0.925	-
	Temperature-indep.	4.6	1,44	0.037	-7.14 (3.325)	0.4 1,37 0.515	+
	nest attentiveness
	Clutch size	1.47	1,43	0.232	+	1.8 1,38 0.186	+
	Female carotenoid	0.333 1,42	0.567	+	0.3 1,36 0.592	-
	chroma
	Female carotenoid	0.12	1,41	0.730		3.5 1,34 0.063
	chroma x
	Treatment

Acknowledgements

We are grateful to Freya Harrison and Miloš Krist for helpful comments on the manuscript.

This study was supported by the Czech Ministry of Education (MSM6198959212). It complies with the current law of the Czech Republic.