Behavioral Ecology Advance Access originally published online on July 9, 2007
Behavioral Ecology 2007 18(5):831-840; doi:10.1093/beheco/arm050
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Assessing the function of house sparrows' bib size using a flexible meta-analysis method
Department of Animal and Plant Sciences, University of Sheffield, Sheffield S10 2TN, UK
Address correspondence to S. Nakagawa. E-mail: itchyshin{at}yahoo.co.nz.
Received 16 October 2006; revised 23 April 2007; accepted 25 April 2007.
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ABSTRACT |
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The black throat patch or bib of male house sparrows, Passer domesticus, is often referred to as a "badge of status" or a "badge" because previous studies have shown bib size to be correlated with the social status of males. Yet, little is known about how strong and robust this relationship is and how the strength of this relationship compares with that of other associations. We conducted a meta-analysis for 6 well-studied correlates of bib size: fighting ability, parental ability (egg incubation and food provisioning), age, body condition, cuckoldry, and reproductive success. We introduce a flexible meta-analysis method in this study that is better suited in the biological sciences than the methods usually employed in popular meta-analysis software because our method accounts for a common form of nonindependence of the data. The relationship between fighting ability and bib size was found to be strong and robust, and the relationship between age and bib size was moderate and robust. Also, body condition was weakly but significantly correlated with badge size. The other parameters showed nonsignificant small effects and/or large confidence intervals. Therefore, we conclude that bib size signals dominance and to a lesser extent age and possibly reflects body condition in house sparrows. There was weak evidence that bib size is currently under sexual selection because there was little association between reproductive success and bib size. This is surprising as the bib size probably affects the outcome of male–male competition. Empirical data on sparrow bib size could not be reconciled with sexual selection theory, although there is ample evidence that it is a condition-dependent trait.
Key words: age, badge of status, condition-dependent trait, house sparrow, meta-analysis, sexual selection.
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INTRODUCTION |
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Understanding phenotypic variation in traits has been a focus of evolutionary biology because phenotypic variation, which is the product of complex interactions between genetic and environmental variation, provides substrates on which natural and sexual selection can act (Roff 1997
; Fox and Wolf 2006). Among the countless phenotypic variations investigated, avian plumage variation both within and between species appears to have attracted a disproportionate amount of research (Hill 2002; Owens 2006). Numerous studies have demonstrated that avian plumage, such as elongated tail feathers and colorful patches, play an important role both in aggressive interactions and in mate choice (reviewed in Andersson 1994; Andersson and Simmons 2006).
Although the plumage of male house sparrows (Passer domesticus) is far from extravagant, the house sparrow is one of the most intensively studied species in relation to plumage variation (reviewed in Jawor and Breitwisch 2003; Anderson 2006; Griffith et al. 2006). House sparrows have been a model organism in studies of sexual selection, in which correlations have been investigated between numerous life-history traits and the size of the black bib (a secondary sexual trait, e.g., Griffith et al. 1999a; reviewed in Anderson 2006). The best-documented association is that between dominance hierarchy and bib size (e.g., Møller 1987a, 1987b; Liker and Barta 2001; Gonzalez et al. 2002; see Table 1). Therefore, the bib is often referred to as a "badge of status" or just a "badge" (Dawkins and Krebs 1978).
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Rohwer (1975)
first suggested that conspicuous size variation in plumage patches within species evolved to signal differences in fighting ability to avoid wasteful fights. However, we have little idea about how strong and robust the association between status and bib size actually is and how the strength of this association compares with that of other associations (e.g., between age and bib size or between parental care and bib size). For such estimations and comparisons, we require a meta-analytical approach, that is, effect-size–based reviews of research (Hunt 1997; see also Nakagawa 2004; Nakagawa and Cuthill 2007). With house sparrows being a model species of sexual selection, we now have an opportunity to conduct meta-analyses using this species alone. However, a prevalent problem of meta-analyses, especially in evolutionary biology and behavioral ecology, is that the statistical assumption of independence of the data is violated when effect sizes from studies by the same research groups or of the same populations or species are used as independent data points (e.g., Møller and Ninni 1998; Dubois and Cézilly 2002; see also Palmer 2000). Meta-analysis software that routinely deals with this nonindependence does not seem to be available (see Methods for more details). In this paper, we used a "flexible" meta-analysis method that dealt with this problem. We examine 6 well-studied associations between male bib size and life-history traits, including fighting ability, parental ability (nestling provisioning and incubation), age, body condition, cuckoldry (loss of paternity to extrapair males), and reproductive success. This paper's aims are 3-fold: 1) to investigate the generality of the alleged associations regarding bib size, 2) to outline and use a method of meta-analysis more suited for the biological sciences, and 3) to explore the current understanding of the bib size of house sparrows as both a sexually selected and a condition-dependent trait, based on previous findings and on theoretical models.
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METHODS |
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Collecting studies and extracting effect sizes
We conducted an extensive search of the literature on the relationship between life-history traits and bib size in house sparrows. We also contacted researchers who have published studies on relevant topics to obtain unpublished information. We considered that, for a meta-analysis, at least 8 studies investigating the same traits in relation to bib size were necessary and that these studies required the inclusion of quantitative information that could be translated into effect size statistics. Our criteria resulted in 6 life-history traits that could be investigated: fighting ability, parental ability, age, body condition (i.e., standardized weight), cuckoldry (the rate or absence/presence of lost paternity due to extrapair paternity [EPP]), and reproductive success (details of studies used in the meta-analysis are summarized in Table 1). In the analysis of parental behavior, we used studies investigating both incubation and feeding behavior. A recent study by Kopisch et al. (2005)
showed incubation time to be a significant predictor of subsequent nestling provisioning in a population, so that treating incubation and provisioning together may be justifiable. Also, this type of integration or grouping is a common practice in meta-analysis. However, we carried out separate meta-analyses on incubation and feeding to further justify our procedure, although, by doing so, we violated our criteria (as there were only 6 studies of feeding and 3 studies of incubation).
Effect size values from different populations were treated as independent data points; also, within the same population, effect size estimates from replicated studies were used for meta-analysis without merging them (see below for how we dealt with pseudoreplication). We employed correlation coefficients, which were subsequently converted into Fisher's Z (Zr) for meta-analysis, as a standardized effect size statistic. The correlation coefficient (r including Pearson's r, Spearman's r, Kendall's 
, point-biserial r, and phi) was extracted from each study. In the cases where studies did not include correlation coefficients, the reported statistics (t, F, 
2, z, and means and standard deviations) were used to estimate r following Rosenthal (1994) and Lipsey and Wilson (2001). When R2 was the only source for estimating effect size, we used the formula
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). When related statistics were not immediately appropriate for estimating the correlation coefficient (e.g., F with a numerator degrees of freedom of more than 2), we used an approximation, which is indicated as ca. in Table 1. If a study included more than one effect size for the same or related traits, we chose values that made more biological sense (e.g., Solberg and Ringsby 1997; Jensen et al. 2006; see Table 1); if this criterion did not decide which effect size to use, we used the one with the largest absolute value (e.g., Hein et al. 2003; note that we also conducted meta-analyses using the alternative effect sizes reported in our collection of studies but none of these changed our main conclusions).
Flexible meta-analytic procedures
All statistical analyses were conducted in the R environment (version 2.4.1; R Development Core Team 2006; the R script and data sets used in this study are available from the corresponding author by request). As far as we are aware, there is no popular meta-analysis software that incorporates a grouping random factor when one or more groups include only a single data point. Incorporation of a grouping factor allows us to use nonindependent effect sizes without merging them prior to a meta-analysis (combining effect size estimates reduces statistical power and loses information). To deal with this, we used a linear mixed-effects model (LMM) approach with the restricted maximum likelihood method (REML, nlme package in R; Pinheiro and Bates 2000). The R function lme in the nlme package enabled us to use a grouping random factor even when each group had only a single data point (one effect size value). Meta-analysis is basically a weighted linear regression analysis with the response (dependent) variable consisting of effect size values and with the weighting being the inverse variance of the corresponding effect size statistic; this type of meta-analysis is usually referred to as a fixed-effects model (Lipsey and Wilson 2001). The weight used for a fixed-effects model with Zr is written as
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2 is the between-study variance (in our case, between-population variance; Raudenbush 1994). A random-effects model (sometimes referred to as a mixed-effects model) in meta-analysis is usually a 3-step process (Rosenberg et al. 2000): in the case of Zr, 1) running a fixed-effects model using weights from Equation 2 to obtain the summary statistics, 2) using these statistics to find 2, and then 3) running a random-effects model using weights from Equation 3 (for more details, see Rosenberg et al. 2000; Lipsey and Wilson 2001). The use of the R function lme with REML achieves an equivalent of this process simultaneously, providing a mean effect size estimate as the intercept of an LMM (see Pinheiro and Bates 2000).
In meta-analysis, the total heterogeneity of a sample, QT, is usually calculated to determine whether a set of effect sizes is homogeneous (Hedges and Olkin 1985). QT is found from Zr by
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is the weighted mean of Zr effect sizes, which is given by
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The heterogeneity QT is tested against a 2-distribution with k – 1 degrees of freedom. When QT is significant (in a fixed-effects model), the variance among effect sizes is greater than expected from sampling error, indicating that some explanatory variables that contribute to significant heterogeneity may exist (Rosenberg et al. 2000). In meta-analysis, explanatory (independent or predictor) variables are often referred to as moderators or moderator variables. For our meta-analyses, we calculated QT using Equations 4 and 5. However, QT may not portray heterogeneity in LMMs well because Equations 4 and 5 treat each effect size as independent, and QT does not take account of a random component of variation between effect sizes. The heterogeneity QT in weighted linear regression analysis equates to a "weighted" residual sum-of-squares of an LMM (calculated as in Equation 4) when the model does not have any fixed factors (fixed moderators) or only has an intercept (see Hedges and Olkin 1985; Lipsey and Wilson 2001). Therefore, we used these residual sum-of-squares as our main measure of heterogeneity (QREML; more precisely, it is an equivalent of residual heterogeneity in random-effects models) and tested QREML against a 2-distribution with k – 1 degrees of freedom (Table 2). For each meta-analysis, we provide a t value to test if the intercept in the respective LMM (i.e., mean effect size estimates; Raudenbush 1994) was significantly greater than zero using the corresponding degrees of freedom from the LMM: k – 1 when no group (i.e., population) had more than one effect size and the number of populations (m) when one or more populations had more than one effect size. Even when the heterogeneity was significant, we did not try to fit any possible moderator variables; for all the traits used in the meta-analysis, the sample size of the effect sizes was small (k = 3–20), so that adding moderators (fixed factors) into our meta-analyses would not have led to any meaningful and/or interpretable results.
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Meta-analysis is often accompanied by one or more types of estimator of publication bias (reviewed in Møller and Jennions 2001
). Popular estimators include fail-safe numbers and rank correlation tests. Due to our small sample size (the number of studies, k in Table 2), both of these publication bias estimators were of little use here. Instead, we used funnel plots (i.e., plots of effect size against the sample size on which each effect size was based) to enable a visual inspection for bias (see Palmer 2000; Cassey et al. 2004). |
RESULTS |
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The results of our 8 meta-analyses are summarized in Table 2, and Figure 1 presents a visual comparison of effect size estimates and their 95% confidence intervals (CIs). Bib size showed a strong positive association with status or fighting ability, a moderate association with age, and a weak association with body condition (all associations were statistically significant; sensu Cohen 1988
; r = 0.1, 0.3, and 0.5 for "small," "moderate," and "large" effects). Parental ability (both provisioning and incubation), cuckoldry, and reproductive success all showed nonsignificant small effects and/or large CIs. Funnel plots for each variable are shown (Figure 2). The degree of asymmetry about the mean effect size in Figure 2 is reflected in the extent of the respective CI (Figure 1), which in turn seems to be influenced by the effect size sample size (k). As far as we can see, there is little indication of publication bias for fighting ability (status), age, and body condition, each of which showed a significant relationship with bib size. The heterogeneity QREML, which incorporated a random component of variation, was significant for body condition and reproductive success (Table 2; note that QT values are shown for comparison; these values were not interpreted as they do not account for random variation between populations). These significant heterogeneities indicated the possible presence of moderator variables for body condition and reproductive success, and, therefore, the estimated effect size values for each factor should be interpreted with care.
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DISCUSSION |
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What is the function of the bib size?
Our meta-analysis revealed that the relationship between fighting ability and bib size is robust and strong in house sparrows (r = 0.464), confirming that the black throat patch indeed acts as a badge of status. Also, the relationship between bib size and age is robust and moderate (r = 0.346), suggesting that bib size also acts as an age indicator, at least to some extent (see Brooks and Kemp 2001
). Anderson (2006) concluded in his monograph on house sparrows that the only consistent finding concerning bib size was the association with age and that other associations, including fighting ability, were equivocal and unconvincing. However, his conclusion was based on a vote-counting–type review, where the overall conclusion was based on the number of papers with significant and nonsignificant results, regardless of sample size (Cooper and Hedges 1994; Hunt 1997). Anderson (2006) is probably correct that age accounts for some component of the badge of status in house sparrows. In many badge-of-status systems, the extent or even existence of badges is sex and/or age specific (Searcy and Nowicki 2005). Our meta-analytic results indicate that the effects of fighting ability and age may be largely dependent on each other because the CIs around the effect sizes of these 2 factors overlap to a large extent (Figure 1). Two experimental studies provide further support for our finding of a strong effect on fighting ability. Gonzalez et al. (2002) showed that males increased the proportion of agonistic interactions won after their bib sizes were experimentally enlarged. Veiga (1993) also reported that males with enlarged bibs acquired more nest sites than did control males or males with reduced bibs. Although the exact proximate mechanisms determining bib expression are still not clear, several studies support the idea that a melanin-based badge of status in house sparrows is a condition-dependent trait (Jawor and Breitwisch 2003; Griffith et al. 2006; see below for more discussion).
Body condition (mass-related condition indices) showed weak but statistical significant association with bib size (r = 0.093, Table 2, Figure 1). Green (2001) emphasized the potential inappropriateness of mass-related body condition indices as they may not capture the size of a bird's real energy store. It is possible, however, that mass-related body condition indices may reflect some component of condition that, in turn, correlates with bib size, supporting the idea that bib size is a condition-dependent trait (see Is the bib size sexually selected?). However, it should be noted that "body condition" here is, at best, a weak correlate of bib size. Furthermore, the significant heterogeneity suggests that a covariate may exist, which may have influenced the estimate of effect size.
The meta-analytical results of the other associations (parental ability, cuckoldry, and reproductive success) revealed nonsignificant small effects and/or large CIs, thus providing little evidence that any of these factors is directly or indirectly related to bib size (see Is the bib size sexually selected? for more on cuckoldry and reproductive success). There is little evidence of an association between parental care (either nestling provisioning or incubation) and bib size. Theoretical models predict the evolution of traits that indicate parental quality in males of species with biparental care (Wolf et al. 1997; Kokko 1998). At the same time, theory also predicts that if the costs of advertising a direct benefit outweigh the benefits, then the signal of parental care will not evolve (Kokko 1998). It seems that, on current evidence, bib size does not signal parental care in house sparrows.
Taken together, we conclude that the function of bib size variation is to signal the fighting ability and also, to lesser extent, the age of individuals. It may also reflect some aspect of the condition of males, but any such effect is weak.
Is the bib size sexually selected?
Sexual selection can act on a trait when there is variation in reproductive success in relation to that trait (Andersson 1994). Our meta-analytical review provided little evidence for sexual selection acting on bib size primarily because the relationship between reproductive success and bib size was not significantly different from zero (note, however, that one or more unidentified moderator variables may have influenced this estimate). This is surprising given the evidence that the male's bib size is used to establish a social hierarchy and, therefore, is likely to be important in male–male competition. However, it does not seem that this effect of bib size is translated into variability in reproductive success. This finding parallels what has been found in studies of the size of the red-and-yellow epaulet in red-winged blackbirds Agelaius phoeniceus, another model species of sexual selection (Searcy and Yasukawa 1995). There is evidence that epaulet size affects the outcome of male–male competition over territories, whereas there is little evidence that variation in reproductive success occurs in relation to epaulet size (reviewed in Searcy and Yasukawa 1995; see also Westneat 2006). There may be substantial costs that cancel out the advantages of large bib size in male–male competition, which we have yet to identify.
Evidence for the other component of sexual selection, female choice, in house sparrows is mixed, and most studies have been observational or correlational (Møller 1988, 1989; Veiga 1993; Kimball 1996; Griffith et al. 1999b; Ockendon 2003). Furthermore, a pair of house sparrows usually stays together in subsequent breeding seasons if both of them are still alive (Anderson 2006; Nakagawa S, personal observation), even though male bib size changes every year, sometimes to a great extent (Griffith 2000). Therefore, female choice in relation to bib size in this species may be a weak selective force.
Another aspect of sexual selection, which is not explored properly in our analysis, is "hidden" sexual selection through EPP. Very few studies have investigated the relationship between gaining EPP and bib size; the information on paternity gain is as important as paternity loss (cuckoldry) to reveal the direction of sexual selection on bib size through EPP (see Griffith et al. 2002). We would predict a positive relationship between gaining EPP gain and bib size, based on two findings: 1) older males gain more EPP (Wetton et al. 1995; Ockendon 2003) and 2) older males tend to have larger bibs. However, Ockendon (2003) did not find significant differences in bib size between males that gained EPP and those that did not. It may be that the effect size of EPP gain in relation to bib size is small (the results were replicated, Nakagawa S, unpublished data). Therefore, there is currently little evidence for hidden sexual selection through EPP, as is also the case for apparent sexual selection through fledging success or recruits.
A real problem in determining the role of the bib size in sexual selection is that its size may have very low or no heritability, meaning that the additive genetic variance underpinning bib size is zero or close to zero (Griffith et al. 1999a; Ockendon 2003; cf. Møller 1989). The variation we observe in the bib size of house sparrows may be largely due to environmental factors during and prior to a molt, such as nutritional conditions (Veiga and Puerta 1996; Poston et al. 2005), rearing conditions (Griffith et al. 1999a), social conditions (McGraw et al. 2003; Jensen et al. 2006), climatic conditions (Jensen et al. 2006), and preceding parental effort (Griffith 2000). Therefore, there is ample evidence that the bib size is a condition-dependent trait, a feature in common with most sexually selected traits (reviewed in Andersson 1994; Jennions et al. 2001).
According to the model by Rowe and Houle (1996), condition-dependent sexually selected traits harbor large amounts of additive genetic variance. In their model, condition is equated to the total pool of resources acquired by an individual, so that condition reflects an internal property that contributes to individual fitness. If the condition revealed by a secondary sexual trait is determined purely by environmental factors, as in the model by Price et al. (1993), the secondary sexual trait is expected to indicate direct benefits. However, the house sparrow's bib does not seem to fit either of these models because 1) in the former model, we still expect heritability in bib size and 2) in the latter model, bib size has to be an indicator of parental quality. There may be heritable indirect genetic effects that influence the expression of the bib (sensu Wolf et al. 1997, reviewed in Qvarnström and Price 2001), but this is unlikely because indirect genetic effects should act on offspring traits that indicate the extent of indirect genetic effects (i.e., the bib size has to be an indicator of parental quality for this model to work). It may be that wearing an honest signal (an appropriate bib size for an individual's condition) is optimal and that males with different bib sizes, which are subject to change every year, achieve similar fitness over their lifetime.
Finally, our meta-analysis on the available data and our examination of current theory suggest that the bib size of male house sparrows is currently under little or, at most, weak sexual selection, although bib size in male house sparrows has been the focus of investigations in sexual selection for many years (Anderson 2006). It is noteworthy that a comparable conclusion concerning the relationship between sexually dimorphic traits and sexual selection theory has been reached in another model bird species, the red-winged blackbird (Searcy and Yasukawa 1995; Westneat 2006).
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FUNDING |
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Top Achiever Doctoral Scholarship from New Zealand Tertiary Education Commission to S.N.
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ACKNOWLEDGEMENTS |
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Our special thanks go to Jarrod Hadfield who suggested the method of meta-analysis used in the paper. We are grateful to Tim Birkhead, Michael Griesser, Mark Hauber, Stefan Lüpold, Ben Sheldon, and 2 anonymous reviewers for comments on earlier versions of the manuscript.
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