Carotenoid-based breast plumage colour, body condition and clutch size in red fodies (Foudia madagascariensis)

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1 Ostrich 2006, 77(3&4): Printed in South Africa All rights reserved Copyright NISC Pty Ltd OSTRICH EISSN X Carotenoid-based breast plumage colour, body condition and clutch size in red fodies (Foudia madagascariensis) Laura K Estep 1 *, Matthew D Shawkey 2 and Geoffrey E Hill Department of Biological Sciences, 331 Funchess Hall, Auburn University, Alabama 36849, USA 1 Current address: Department of Epidemiology and Public Health, Yale School of Medicine, 60 College Street, PO Box , New Haven, CT , Connecticut, USA 2 Current address: Department of Environmental Science, Policy and Management, 137 Mulford Hall #3114, University of California, Berkeley, CA , USA * Corresponding author, laura.estep@yale.edu Carotenoid-based feather colouration is a classic example of a condition-dependent ornamental trait. In some species of birds, red, orange and yellow feather colouration reflects male quality and advertises the carotenoid concentration of feathers. Such colouration is an important aspect of mate selection by females. The red fody (Foudia madagascariensis) is a highly sexually dimorphic species of the family Ploceidae, in which males exhibit extensive carotenoid-based plumage. We investigated associations between body condition, clutch size, first egg date and carotenoid-based red plumage colour of male red fodies. Breast plumage brightness was positively associated with male body condition, suggesting that this component of colour is condition-dependent. Brighter-red males did not breed earlier but were mated to females that laid larger clutches compared to females mated to duller-coloured males. These data suggest that red colour in red fodies has the potential to function as an honest signal of male quality. Introduction One explanation for the existence of ornamental traits in animals is that such traits evolved as reliable signals of individual quality (Zahavi 1975, Kodric-Brown and Brown 1984, Grafen 1990). Carotenoid-based colour displays in the skins of fish and the feathers of birds have played a central role in testing honest-signalling theory (Andersson 1994, Hill 2002). This theory relies upon the precept that ornaments used in honest signalling must be costly to produce or maintain (Andersson 1994). Carotenoid-based ornaments are likely to be honest signals of quality, because of the cost associated with the acquisition and utilisation of the pigments needed for maximum colour display (reviewed in Hill 2002, 2006a). Numerous studies on fish and birds have shown that carotenoid-based colouration can serve as an honest signal of quality (reviewed in Houde 1997, Hill 2002). In general, these studies have shown that males with access to more pigment resources, who are in better nutritional condition, or who have lower parasite loads during moult, grow feathers or scales with more saturated or longer-wavelength colouration. Furthermore, many studies have shown that females prefer to mate with males who have more saturated or redder ornaments (Houde 1997, Hill 2006b) and a few studies have shown that females mated to redder males experience material benefits in the form of greater paternal provisioning and higher reproductive success (Hill 1991, McGraw et al. 2001). Within birds, the vast majority of studies of carotenoid colouration have been conducted on Cardueline finches (family Fringillidae, sub-family Carduelinae) and tits (family Paridae). It is primarily from these studies that the above generalities are drawn (e.g. Hill and Montgomerie 1994, Thompson et al. 1997, Lindström and Lundström 2000, Hõrak et al. 2001, Tschirren et al. 2003). Studies of carotenoid-based plumage colour in weaver finches (family Ploceidae) show that carotenoid colouration can also serve functions other than mate attraction. The carotenoid-based plumage ornaments of both Red-collared (Euplectes ardens) and Red-shouldered Widowbirds (Euplectes axillaries) are important for signalling status and resource-holding potential. In Cardueline finches, the quality of colour display is condition-dependent and the object of sexual selection, but in weaver finches, it is generally the size of the ornament rather than colour quality that is condition-dependent and functions in sexual signalling (Pryke et al. 2001, Pryke and Andersson 2003a, 2003b). In the Red-billed Quelea (Quelea quelea), another weaver finch, carotenoid-based plumage ornamentation is not condition-dependent and does not function in sexual signalling (Dale 2000), but rather appears to be important in individual recognition (Dale et al. 2001). In a model, Dale et al. (2001) proposed a number of features that distinguish plumage colour that functions in individual recognition from plumage colour that functions in sexual signalling (Dale 2006). For example, a bimodal distribution of colour suggests that it functions in individual recognition, while a unimodal distribution suggests that it functions in sexual signalling. In contrast to the continuous distribution of colour in Cardueline finches, colour patches in queleas are distributed bimodally as discrete red and

2 Ostrich 2006, 77(3&4): orange morphs, suggesting that they function in individual recognition. By identifying the features of plumage colour in a species and interpreting them in terms of this model, we may thereby gain some understanding of its function. We applied the concepts of Dale et al. s (2001) model to the plumage colour of red fodies (Foudia madagascariensis), a little-studied weaver finch. Red fodies are highly sexually dichromatic during breeding; females are olive and drab brown, while males vary continuously from bright red to drab yellow over their entire bodies, excluding the tail and wings (Langrand 1990). This sexual dichromatism suggests that bright plumage colours in this species may have evolved through sexual selection (reviewed in Badyaev and Hill 2003). Furthermore, the low variation in patch size (Langrand 1990 in contrast to that of widowbirds) and continuous unimodal distribution of colour (this study, in contrast to that of queleas) suggests that the colour could function as an honest signal of quality. The signal content of colour in this species is, to our knowledge, entirely unstudied. By examining associations between plumage colour and measures of male body condition and reproductive success, we tested the hypothesis that the red colouration in this species could serve as a signal of individual quality. Procedures Data collection We studied red fodies from January April 2004 on their breeding and foraging ground in Ranomafana National Park, along the eastern escarpment of Madagascar. We centred our study site on the rice paddy that is directly adjacent to the village of Vohiparara, which is used by flocks of red fodies for foraging (21 14 S, E). We captured males in mist-nets set up along the perimeters of rice paddies from 07:00 to 11:00 and from 14:00 to 18:00. Upon capture, we banded males with unique combinations of one numbered aluminum band (Band and Tag Corporation) and three coloured plastic leg bands. We recorded standard morphological measurements (wing chord, tail length, tarsus length, bill length and mass) for all individuals. We pulled breast feathers from approximately the same area on each male and stored them in envelopes for future colour analyses. We did not measure breast patch size because the red colouration of all males used in this study extended from under the bill to the tip of the undertail coverts (Langrand 1990). Data concerning the dates of the onset of breeding for this species in the Ranomafana region were not available prior to our study, and full details of our data on the basic breeding biology of this species will be published separately elsewhere. Briefly, we intensively searched for nests in the area surrounding the central rice paddy complex and checked nests every three days. We began our surveys for nests in mid-december, but did not discover nests until mid-january, suggesting that this was the beginning of the breeding season. Mated pairs were never observed utilising the same nest for multiple clutches, suggesting that fodies change location with each new breeding attempt. Thus, we took the date at which a male was first associated with a nest to be the date of his first breeding attempt of the season. We recorded the number of eggs or nestlings at each visit. On some breeding territories, we captured the male of the pair with mist-nets set up in the breeding territory at least m from the nest location. Males were highly territorial, chasing other males and singing from regularly-used perches (LK Estep, pers. obs.); thus, we were certain that the captured male was the social mate. Males captured on the territories were processed following the same procedure used for males captured on the rice paddy. Because of high depredation rates and flooding of nests containing nestlings (57.1%), we used final clutch size as our measure of reproductive success (Badyaev et al. 2000, Doucet et al. 2004). Colour analyses We stacked and taped five feathers from each male to gloss-free black construction paper and recorded spectral data from them using an Ocean Optics S2000 Spectrometer (range of nm, Dunedin, FL, USA) and a UV (deuterium bulb) and visible (tungsten-halogen bulb) light source. We used a bifurcated fibre-optic measuring probe (Ocean Optics, Dunedin, FL, USA), which provided illumination from the lamp and transferred light reflected from the feather sample back to the spectrometer. This probe was held at a 90 angle to the feather surface. Ambient light was excluded with a block sheath that held the tip at a fixed distance of 5mm from the feather surface, providing a reading area of 2mm. All reflectance data were generated relative to a white standard (WS-1, Ocean Optics, Dunedin, FL, USA). The probe was lifted and replaced, and a new measurement taken, five times on each feather sample. Each of these five measurements was an average of 20 sequential spectra generated by 00Ibase software, a spectra acquisition software package (Ocean Optics, Dunedin, FL). We then averaged these five measurements for each feather sample. We calculated standard indices for three different elements of colour from these reflectance spectra (Hailman 1977, Norris et al. 2004). These indices were restricted to wavelengths between 300nm and 700nm, as evidence suggests that this is the range of sensitivity for the avian visual system (Jacobs 1981, Cuthill et al. 2000). Red chroma, or spectral purity in the red region, is the proportion of light reflected in the range from nm, and UV chroma is the proportion of light reflected in the range from nm (Norris et al. 2004). Brightness is the summed reflectance from nm (Endler 1990). Repeatability of measurements from the same individual male was 0.67 for brightness (F = 11.33, df = 81,328, p <.0001), 0.73 for UV chroma (F = 14.95, df = 81,328, p <.0001) and 0.75 for red chroma (F = 15.95, df = 81,328, p <.0001) (Lessells and Boag 1987). We chose these variables based on the shape of the reflectance curve (see Figure 1), which exhibited a peak in the UV and a long plateau at longer wavelengths. Furthermore, red chroma has been found to accurately indicate the amount of carotenoids present in feathers (Inouye et al. 2001, Saks et al. 2003a). To determine whether colour variables were unimodally or bimodally distributed, we visually examined histograms of UV chroma, red chroma and brightness for modality patterns.

3 166 Estep, Shawkey and Hill PERCENT REFLECTANCE (%) WAVELENGTH (nm) FREQUENCY BRIGHTNESS (%) Figure 1: Representative spectrometric curve of red breast feathers of a male Madagascar red fody Verification of the presence of carotenoids We used an acidified pyridine extraction method (McGraw et al. 2005) to verify the presence of carotenoids in feathers. The acidified pyridine was coloured bright red following incubation, and the feathers from which pigments were extracted were white. These results suggest that carotenoids are primarily responsible for the red colour of this plumage (McGraw et al. 2005). Statistical analyses We used linear regression to compare first egg date and male body condition to the three measured colour variables. We used the residuals of mass on tarsus length as our measure of body condition, as is common for studies of live birds (for review, see Blem 1990, Brown 1996). Although this approach to measuring body condition has attracted some criticism (Green 2001), recent research suggests that such criticism may be unwarranted (Schulte-Hostedde et al. 2005). Both response variables of first egg data and male body condition were normally distributed (n = 12, D = 0.224, p = and n = 13, D = 0.068, p > 0.150, respectively, Kolmogorov-Smirnov test). We used backwards elimination to remove variables, until arriving at a final model (alpha-todrop = 0.05). Because the response variable of final clutch size was not normally distributed (n = 13, D = 0.394, p <.0, Kolmogorov-Smirnov test), we used non-parametric correlations with a Bonferroni correction to compare the number of eggs to the three colour variables. Results We captured and processed 82 males in and around the rice paddy. The reflectance spectra of the red feathers was similar to that of the feathers of other bird species with carotenoid-based red colouration (Eaton and Lanyon 2003), with a small peak in the UV wavelengths and a long plateau in the red wavelengths (Figure 1). Histograms indicated that all three colour variables were unimodally distributed (Figure 2). Bins for the histograms were evenly distributed across the range of values for each variable (Figure 2). To test the hypothesis that plumage colouration is related to body condition, we compared saturation and brightness FREQUENCY FREQUENCY < RED CHROMA (%) UV CHROMA (%) Figure 2: Histograms for the colour variables UV chroma, red chroma and overall brightness for the red breast feathers of Madagascar red fodies (n = 82) to body condition. The final linear regression model arrived at for male body condition included only feather brightness (Figure 3, linear regression, n = 82, r 2 =.084, β = 0.290, F = 7.371, p = 0.008). UV chroma dropped out of the model at the first step in the selection process (β = 6.19, t = 1.12, p = 0.266), and red chroma dropped out in the second step (β = 2.57, t = 1.29, p = 0.201). As an indirect test of female mate preference and male plumage colouration, we compared nest initiation date to male colouration. We monitored the nests of 13 males for which we had plumage colour data. Data for exact nest initiation date were unavailable for one nest. Neither red nor UV chroma nor brightness of breast feather colouration predicted nest initiation date. Feather brightness was dropped from the model first (β = 3.53, t = 0.54, p = 0.602), followed by UV

4 Ostrich 2006, 77(3&4): RESIDUALS OF MASS/TARSUS Linear regression n = 82, r 2 = 0.84 ß = F = 7.371, p = MALE BREAST BRIGHTNESS (%) Figure 3: Scatterplot of male body condition (residuals of mass/tarsus) and male breast brightness for male red fodies captured on the rice paddy and on breeding territories FINAL CLUTCH SIZE Spearman Rank Correlation N = 13 r s = p = MALE BREAST BRIGHTNESS (%) Figure 4: Scatterplot of number of eggs for the first nest of the breeding season and the brightness of male breast colouration chroma (β = , t = 1.61, p = 0.141), then red chroma (β = 35.72, t = 0.39, p = ). However, there was a significant positive relationship between male colouration and final clutch size (Figure 4, Spearman rank correlation, N = 13, r s = 0.797, p = 0.001) and this pattern remained significant after Bonferroni correction (adjusted alpha = 0.017). Clutch size was not correlated with UV chroma or red chroma (Spearman Rank Correlation, N = 13, r s = 0.491, p = 0.089; N = 13, r s = 0.343, p = 0.251, respectively). Discussion Brightness of breast plumage colour was positively associated with male body condition and clutch size, but not first egg date for male fodies. Only one other study (Saks et al. 2003b) has shown a significant correlation between overall brightness of carotenoid-based ornamental colouration and male quality. These first two patterns are thus not consistent with most studies of plumage colouration in Cardueline finches and members of the family Paridae, in which hue and saturation tend to be correlated with male quality (reviewed in Hill 2002). Hue and saturation reflect the composition and concentration of carotenoid pigments, respectively (Inouye et al. 2001, Saks et al. 2003a), while brightness has no clear relationship to the carotenoid content of feathers (Saks et al. 2003b). Of the three colour variables, brightness is most likely to be affected by the underlying white structural colour as well as carotenoid content (Shawkey and Hill 2005). In both experimental and field correlational studies, carotenoid pigmentation of feathers has been clearly shown to be condition-dependent (reviewed in Hill 2002, 2006a). The hypothesis that structural colouration is condition-dependent is not as strongly supported (Prum 2006), but some studies have shown a relationship between structural colour variables and condition (Doucet 2002, Doucet and Montgomerie 2003, Hill et al. 2005). Thus, both deposition of carotenoids and formation of the underlying white structural tissue may be condition-dependent in fodies. Experimental tests of the effects of condition on these two processes will be needed to test this hypothesis. However, a recent experimental study demonstrated that carotenoid deposition, but not white structural colour, was dependent on condition during molt in American Goldfinches Carduelis tristis (Shawkey et al., in press). Our examination of male plumage colouration in relation to fitness measures produced mixed results. Brighter males did not breed earlier than duller males, but females mated to males with brighter plumage colouration laid more eggs. Breeding early may not confer the same advantages to tropical species such as fodies as it does to temperate species (Stutchbury and Morton 2001), so nest initiation date may not be a relevant gauge of male success in tropical environments. The larger clutch size in the nests of brighter males suggests that females may produce larger clutches when mated to brighter males or that brighter males may be mated to higher-quality females, suggesting that colour may function as a sexual signal in fodies in the same manner as in Cardueline finches (Hill 2002). Alternatively, brighter males may acquire higher-quality territories, and it is the resources held by a male rather than his colouration per se that determines the number of eggs a female lays. It should be noted that this specific result applies to the entire male fody population we studied, contingent upon the assumption that events such as flooding and depredation that resulted in clutch loss were stochastic, with respect to male quality. Otherwise, our results apply specifically to the subset of the males who were less likely to lose clutches during such events. The nature of fody plumage colour suggests that it serves as an indicator of individual quality. Dale et al. (2001) propose that such indicators should be relatively less variable, condition-dependent, unimodally distributed, positively correlated with fitness measures, and have positively correlated component characters. While we cannot address the final condition of the model, the remainder of the conditions fit the case of the fody well. Carotenoid colouration in fodies is largely restricted to a UV-red colour, appears to be condition-dependent, is unimodally distrib-

5 168 Estep, Shawkey and Hill uted and is positively correlated with some, but not all, fitness measures. By contrast, the colour of the quelea, which has been argued to function in individual recognition, is highly variable and bimodally distributed into two discrete colour morphs, and is not correlated with fitness measures. Thus, by the terms of this model, the red colour of the fody likely functions as an indicator of individual quality. Why the colour of the widowbirds does not clearly fit either set of conditions is not clear, although it appears that the size, rather than the colour, of the ornament may function as an indicator of quality (Pryke and Andersson 2003a, 2003b). Conclusions We showed that red colour in fodies reflects body condition and a measure of reproductive success and thus could potentially be used as a sexual signal. Whether red colour functions in female choice or male-male competition could not be determined in this study; however, the fit of this species plumage characteristics to the model in Dale et al. (2001) suggests that carotenoid colouration in fodies could function as an indicator of individual quality. Future studies should explicitly examine whether females assess this colour when making mate-choice decisions, or if males use it in competition with one another. Acknowledgements We are grateful to Solohery Rasamison for field assistance and to MICET/ICTE Madagascar and Aristide Andrianarimisa at the Peregrine Fund Madagascar for assistance in Madagascar. We thank ANGAP, the Ranomafana National Park Service, the Centre Valbio, and local officials in the village of Vohiparara for helping us with the logistics of establishing our field site. Herman L Mays Jr and Lynn Siefferman provided helpful comments and insight during revision of this manuscript. This study was done under the Auburn University IACUC (Permit # PRN ) and was financially supported by an Alabama Space Grant Consortium Fellowship to LKE and National Science Foundation grants (IBN and DEB ) to GEH. References Andersson M Sexual Selection. Princeton University Press, Princeton, New Jersey, USA Badyaev AEV and Hill GE Avian sexual dichromatism in relation to phylogeny and ecology. Annual Review of Ecology, Evolution and Systematics 34: Badyaev AEV, Hill GE, Stoehr AM, Nolan PM and McGraw KJ The evolution of sexual dimorphism in the house finch: II. Population divergence in relation to local selection. Evolution 54: Blem CR Avian energy storage. In: Power DM (ed) Current Ornithology. pp Plenum Press, New York Brown ME Assessing body condition in birds. In: Nolan V and Ketterson ED (eds) Current Ornithology. pp Plenum Press, New York Cuthill IC, Bennett ATD, Church SC, Hart NS and Hunt S Ultraviolet vision in birds. In: Slater PJB, Rosenblatt JS, Snowdon CT and Roper TJ (eds) Advances in the Study of Behavior, Vol. 29. pp Academic Press, San Diego Dale J Ornamental plumage does not signal male quality in Red-billed Queleas. Proceedings of the Royal Society of London Series B: Biological Sciences 267: Dale J Intraspecific variation in bird colors. In: Hill GE and McGraw KJ (eds) Bird Coloration, Vol. 2: Function and Evolution. pp Harvard University Press, Cambridge Dale J, Lank DB and Reeve HK Signaling individual identity versus quality: a model and case studies with ruffs, queleas, and house finches. American Naturalist 158: Doucet SM Structural plumage coloration, male body size, and condition in the Blue-black Grassquit. Condor 4: Doucet SM and Montgomerie R Multiple sexual ornaments in Satin Bowerbirds: ultraviolet plumage and bowers signal different aspects of male quality. Behavioral Ecology 14: Doucet SM, Mennill DJ, Montgomerie R, Boag PT and Ratcliffe LM Achromatic plumage reflectance predicts reproductive success in male Black-capped Chickadees. Behavioral Ecology 16: Eaton MD and Lanyon SM The ubiquity of avian ultraviolet plumage reflectance. Proceedings of the Royal Society of London Series B: Biological Sciences 270: Endler JA On the measurement and classification of color in studies of animal color patterns. Biological Journal of the Linnean Society 41: Grafen A Biological signals as handicaps. Journal of Theoretical Biology 144: Green AJ Mass/length residuals: measures of body condition or generators of spurious results? Ecology 82: Hailman JP Optical Signals: Animal Communication and Light. Indiana University Press, Bloomington, USA Hill GE Plumage coloration is a sexually-selected indicator of male quality. Nature 350: Hill GE A Red Bird in a Brown Bag: the Function and Evolution of Ornamental Plumage Coloration in the House Finch. Oxford University Press, New York Hill GE 2006a. Environmental regulation of ornamental coloration. In: Hill GE and McGraw KJ (eds) Bird Coloration, Vol. 1: Mechanisms and Measurements. pp Harvard University Press, Cambridge Hill GE 2006b. Female mate choice for ornamental coloration in birds. In: Hill GE and McGraw KJ (eds) Bird Coloration, Vol. 2: Function and Evolution. pp Harvard University Press, Cambridge Hill GE and Montgomerie R Plumage colour signals nutritional condition in the House Finch. Proceedings of the Royal Society of London Series B: Biological Sciences 258: Hill GE, Doucet SM and Buchholz R The effect of coccidial infection on iridescent plumage coloration in wild turkeys. Animal Behaviour 69: Hõrak P, Ots I, Vellau H, Spottiswoode C and Møller AP Carotenoid-based plumage coloration reflects hemoparasite infection and local survival in breeding Great Tits. Oecologia 126: Houde AE Sex, Color, and Mate Choice in Guppies. Princeton University Press, Princeton Inouye CY, Hill GE, Stradi RD and Montgomerie R Carotenoid pigments in male House Finch plumage in relation to age, subspecies, and ornamental coloration. Auk 118: Jacobs GH Comparative Color Vision. Academic Press, New York Kodric-Brown A and Brown JH Truth in advertising: the kinds of traits favored by sexual selection. American Naturalist 124: Langrand O Guide to the Birds of Madagascar. Yale University Press, New Haven Lessells CM and Boag PT Unrepeatable repeatabilities: a common mistake. Auk 4: Lindström K and Lundström J Male green finches

6 Ostrich 2006, 77(3&4): (Carduelis chloris) with brighter ornaments have higher virus infection clearance rate. Behavioral Ecology and Sociobiology 48: McGraw KJ, Hudon J, Hill GE and Parker RS A simple and inexpensive chemical test for behavioral ecologists to determine the presence of carotenoid pigments in animal tissues. Behavioral Ecology and Sociobiology 57: McGraw KJ, Stoehr AM, Nolan PM and Hill GE Plumage redness predicts breeding onset and reproductive success in the House Finch: a validation of Darwin s theory. Journal of Avian Biology 32: Norris DR, Marra PP, Montgomerie R, Kyser TK and Ratcliffe L Reproductive effort, molting latitude, and feather color in a migratory songbird. Science 306: Prum RO Anatomy, physics, and evolution of avian structural color. In: Hill GE and McGraw KJ (eds) Bird Coloration, Vol. 1: Mechanisms and Measurements. Harvard University Press, Cambridge Pryke SR and Andersson S 2003a. Carotenoid-based epaulettes reveal male competitive ability: experiments with resident and floater Red-shouldered Widowbirds. Animal Behaviour 66: Pryke SR and Andersson S 2003b. Carotenoid-based status signalling in Red-shouldered Widowbirds (Euplectes axillaris): epaulet size and redness affect captive and territorial competition. Behavioral Ecology and Sociobiology 53: Pryke SR, Lawes MJ and Andersson S Agonistic carotenoid signalling in male Red-collared Widowbirds: aggression related to the colour signal of both the territory owner and model intruder. Animal Behaviour 62: Saks L, McGraw K and Horak P 2003a. How feather colour reflects its carotenoid content. Functional Ecology 17: Saks L, Ots I and Horak P 2003b. Carotenoid-based plumage coloration of male green finches reflects health and immunocompetence. Oecologia 134: Schulte-Hostedde AI, Zinner B, Millar JS and Hickling GJ Validating body condition indices. Ecology 86: Shawkey MD and Hill GE Carotenoids need structural colours to shine. Biology Letters 1: Shawkey MD, Hill GE, McGraw KJ, Hood WR and Huggins KL in press. An experimental test of the relative contribution and condition-dependence of microstructure and carotenoids in yellow plumage coloration. Proceedings of the Royal Society of London B Stutchbury BJ and Morton ES Behavioral Ecology of Tropical Birds. Academic Press, San Diego Thompson CW, Hillgarth N, Leu M and McClure HE High parasite load in House Finches (Carpodacus americanus) is correlated with reduced expression of a sexually-selected trait. American Naturalist 149: Tschirren B, Fitze PS and Richner H Proximate mechanisms of variation in the carotenoid-based plumage coloration of nestling Great Tits (Parus major L.). Journal of Evolutionary Biology 16: 91 0 Zahavi A Mate selection a selection for a handicap. Journal of Theoretical Biology 53: Received January 2006, accepted June 2006 Editor: WRJ Dean

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