Testes size in birds: quality versus quantity—assumptions, errors, and estimates

Across a wide range of both invertebrate and vertebrate taxa, relative larger testes are associated with female and/or male promiscuity (e.g., mammals: Short 1979; Harcourt et al. 1981; Harvey and Harcourt 1984; Kenagy and Trombulak 1986; Hosken 1997, 1998; but see Heske and Ostfield 1990; birds: Cartar 1985; Møller 1991; Birkhead and Møller 1992; Møller and Briskie 1995; reptiles: Olsson and Madsen 1998; amphibians: Jennions and Passmore 1993; Byrne et al. 2002; fish: Stockley et al. 1997; Balshine et al. 2001; butterflies: Gage 1994; Drosophila flies: Pitnick 1996; acanthocephalan worms: Poulin and Morand 2000). Two general hypotheses have been proposed to explain interspecific variation in testes size: 1) sperm competition (Parker 1970) and 2) sperm depletion (Short 1981). Available data suggest that sperm competition may be a more important selective force than sperm depletion in the evolution of avian testes size (e.g., in birds: Møller 1991; Birkhead and Møller 1992). As a result, species-specific testes size data have been used as convenient and assumedly reliable index of sperm competition levels in comparative studies, particularly of birds (see, e.g., Møller 1991; Briskie and Montgomerie 1992; Møller and Briskie 1995; Stutchbury and Morton 1995; Dunn et al. 2001; Morrow et al. 2003; Garamszegi et al. 2005; Pitcher et al. 2005). Estimating testes size is particularly difficult in taxa where the gonads are located internally and show enormous seasonal changes in size as in birds (Lofts and Murton 1973) and reptiles (James and Shine 1985). One of the main difficulties is that to gain access to the gonads, one must use invasive approaches, such as dissection or laparotomy (e.g., Wingfield and Farner 1976), although as technology improves it may be possible to use noninvasive magnetic resonance imaging techniques (Czisch et al. 2001). Data on testes size are available from a variety of sources, from detailed field studies of particular species to museum skins. Comparative studies of avian testes size have used different estimation methods, several sources of data, and hitherto unchecked methodological assumptions to compile species-specific testes size estimates. Our aim is not to criticize previous work, which has been pioneering in its attempts to obtain these estimates for a wide range of avian taxa, but rather to 1) demonstrate how and why the reliability and accuracy of those estimates differ both across and within studies and 2) point out how the quality of avian testes size data might affect the results obtained when larger, low-quality data sets are used in comparative analyses. All the statistical and simulation analyses were conducted using R v.2.0.1 (R Development Core Team 2004) and (S)MATR (Falster et al. 2003) computer software packages. Results are presented as means with standard errors, unless specified otherwise. In a careful revision of the quality of the available estimates of mass of both testes (combined testes mass, hereafter referred to as CTM) from all currently available data sets (Cartar 1985; Møller 1991; Møller and Briskie 1995; Stutchbury and Morton 1995; Dunn et al. 2001; Garamszegi et al. 2005; Pitcher et al. 2005), we found two recurrent issues: 1) CTM estimates that differed markedly across studies and 2) the use of erroneous estimates. Examples of the latter include CTM estimates for the chaffinch (Fringilla coelebs), which vary twofold across studies, and the CTM estimate for the rook (Corvus frugilegus), which despite being wildly incorrect in the first study has been used in every subsequent one (see supplementary material for more details). Because detailed studies of natural testes size cycles in wild birds are relatively rare, most currently available data have been compiled from museum collections (e.g., 75% of the Dunn et al. [2001] data set). Museum data generally consist of linear dimensions (length and/or width) of at least one testis (often only the larger of the pair) of males caught from diverse geographic locations and throughout the year. The use of these sources must therefore be made with caution because CTM estimates are obtained through indirect calculation from linear dimensions and assuming the use of a representative sample of males. Previous authors assumed such data to be reliable on the basis of several untested assumptions (Table 1). We checked these assumptions using a data set of 45 species for which we had detailed testicular dimensions (linear and wet mass) and examples from the literature (see supplementary material). It is difficult to assess quantitatively the magnitude of the errors associated with the failure to meet each assumption (see Table 1), but it is clear that ignoring them will clearly lead to erroneous CTM estimates. Testing the influence of the methodological assumptions in obtaining testes size estimates df, degrees of freedom. Testing the influence of the methodological assumptions in obtaining testes size estimates df, degrees of freedom. The seasonal change in CTM generally takes the form of either an inverted U-shaped curve in seasonal breeders or a series of discrete multiple peaks in nonseasonal breeders (Murton and Westwood 1977). The rates of seasonal testes size change and the duration of the period when testes size is maximal (or peak window) differ across species and even within families (e.g., Frith et al. 1976). Identifying the peak window is crucial for obtaining a meaningful species-specific peak CTM. Two approaches have been used to estimate it, referred to here as the 1) “Means” and 2) “Polynomial” methods. The Means method, used by Møller (1991), Stutchbury and Morton (1995), and Dunn et al. (2001), estimates peak CTM by averaging CTM across individuals sampled within a predefined “breeding season.” Intermale differences in breeding cycle will result in an underestimation of that species' CTM, through the inclusion of individuals sampled during the growth and regression phases of their testicular cycle, despite all being within the predefined calendar date limits of the species' breeding season. Møller (1991) defined breeding season as the period from 2 weeks preceding the start of egg laying until the last egg of the last clutch is laid. This definition is probably reasonable for taxa breeding in temperate regions, which tend to be more synchronous than those breeding at lower latitudes (e.g., Stutchbury and Morton 1995). However, tropical species may lack a clear breeding season (e.g., Ward 1969) or may show marked geographic asynchrony in breeding (Stutchbury and Morton 2001; Moore et al. 2005). As a result, males of the same species are likely to be at different stages of their seasonal testis cycle at any time. The Polynomial method, first used by Møller and Briskie (1995), involves fitting second-order polynomial curves to plots of testis size against calendar date within the breeding season (sensu Møller 1991). The maxima of the fitted curve are then considered that species' peak testis size. Møller and Briskie (1995) used this approach to determine testis peak length and peak width separately, which were then converted into CTM using Møller's (1991) formula. However, it is more logical that the Polynomial method be used on the data for wet (or indirectly calculated) mass rather than on the 2 linear measures independently. The Polynomial method better allows for exclusion of males sampled outside their peak in testicular cycle than the Means method. We compared the 2 CTM estimation approaches in terms of their accuracy and reliability and also investigated the effect of using these 2 methods on 2 types of data sources: literature on natural testis cycles and museum collections, referred to here as “study” and “museum” sources, respectively. Two different data sets for dark-eyed juncos (Junco hyemalis) were used: the study raw data were kindly provided by Deviche et al. (2000) and the museum data set for the same species was compiled from museum Web pages (see supplementary material for more details). To investigate the reliability of the 2 CTM estimation techniques with different sample sizes, we conducted resampling simulations where either an average value (Means method) or the maxima of a polynomial curve fit (Polynomial method) were obtained at increasing sample sizes (minimum n = 5 and n = 10 for each method, respectively; 1000 repeats; nonreplacement method). The resulting bootstrapped estimate and the variance between estimates were computed at every n. The variance in CTM across repeated estimates decreases exponentially with increasing sample size, for both methods and data sources, but these simulations also revealed that sample sizes below 20 or 30 individuals clearly provide inconsistent (i.e., more variable) CTM estimates for both methods. Also, for both Means and Polynomial, the museum data set always provided more variable CTM estimates than the study data set at every n. For both study and museum data sets, we also tested if restricting the data set in the direction of a presumed peak window affects the accuracy of the Means approach, by sequentially trimming the values on either side of the plot of testes mass against date until a sample of about 20 individuals remained. We averaged CTM across these increasingly small subsets and compared it with a benchmark estimate for the dark-eyed junco (CTM = 0.386 g; this estimate was obtained by applying the Polynomial method to the study data set). The results suggest that the accuracy of the Means method is very dependent on the correct identification of the peak window in testes size: the more restricted the sampling period used is toward this peak, the more similar the estimate obtained from the Means method is to the benchmark CTM. Interestingly, CTM values obtained from the museum data set show the same rate of increasing accuracy with restriction of data set as estimates obtained from the study data set (the slopes of CTM against sample size do not differ significantly: t = 0.02, P = 0.987); however, museum estimates consistently show larger deviances from the benchmark estimate than the study data (different intercepts: t = 20.47, P < 0.001). Using data for dark-eyed juncos and 7 other passerine species for which both a study and a museum CTM data were available (see supplementary material), we found that the Polynomial approach when applied to museum data sets did not result in significantly different CTM estimates from those obtained from study data sets (Wilcoxon signed-rank test: Z = 0.14, P = 0.889, n = 8). In contrast, the Means method applied to museum data significantly underestimated CTM (Z = 2.52, P = 0.012, n = 8) and unpredictably so (range = −5% to −52% of the correct estimate). In summary, the Means approach is accurate only if one can be sure the males sampled are at their peak: for most museum sources, this is unfeasible. In contrast, the Polynomial method provides more accurate estimates, without the need for such detailed information on the stage of the reproductive cycle of the males used in the sample, although sampling throughout the breeding season is necessary. In short, the Polynomial method is the most reliable approach, particularly when estimating CTM from museum sources. If we are to robustly test hypotheses relating to relative testes size in birds, it is essential that we obtain reliable and sufficiently large data sets of CTM for use in comparative studies. However, the large data sets available (e.g., n > 1000 in Dunn et al. 2001) are, as shown above, very prone to errors. We investigated whether the outcome of existing comparative analyses have been affected by the quality of the data sets used, by repeating some of these analyses, using a smaller, more reliable CTM data set (n = 113; see supplementary material for details). We repeated only those analyses for which species-level univariate test results had been presented. In this way, direct comparisons between data set size and quality could be made. Analyses that control for phylogeny, although essential (e.g., Felsenstein 1985), will ultimately depend on the level of resolution in the phylogeny used and are therefore harder to standardize between the current and previous analyses. Whenever previous results and ours did not match, the effect size (EF) for each test was calculated from the analyses conducted on our data set (EF = Cohen's d, Cohen 1988). The minimum sample size required (“needed” n) for each EF to be statistically significant was computed using G*Power (Faul and Erdfelder 1992). A conservative, qualitative assessment of the validity of the previous results was then made: previous findings describe true patterns when either 1) they are matched by the reanalyses conducted on our smaller data set or 2) previous data sets were larger than the needed n. Otherwise, we cannot be confident that the previously reported results were not artifacts of the errors in the (relative) testes size estimates used. Our conclusions can be considered as an illustrative example of how the accuracy in estimating testes size is essential for relative testes size to be a meaningful index of sexual selection. Our results show that in 6 out of 10 analyses, the smaller data set yield results that differ significantly from those previously found using a larger, potentially biased data set (Table 2). In one-third of these (2 out of 6), the sample size of the larger data set was sufficient to significantly detect the corresponding EF. We can therefore be confident that these previously reported patterns are not an artifact of errors in testes size estimates. We cannot, however, be equally confident of the validity of the reported associations between relative testes size and the remaining 4 traits: breeding density, clutch size, extrapair paternity, and migratory behavior. Quality versus quantity: comparison of previous results using larger, less reliable data sets and those obtained from our smaller, more accurate data set of testes mass estimates See text for details of validity assessment. EPP, extrapair paternity. Comparison done using species values results only. EF was calculated from the smaller data set; it refers to Cohen's d (Cohen 1988). n required for the given EF to be statistically significant, with statistical power set to 0.8 and alpha to 0.05. Quality versus quantity: comparison of previous results using larger, less reliable data sets and those obtained from our smaller, more accurate data set of testes mass estimates See text for details of validity assessment. EPP, extrapair paternity. Comparison done using species values results only. EF was calculated from the smaller data set; it refers to Cohen's d (Cohen 1988). n required for the given EF to be statistically significant, with statistical power set to 0.8 and alpha to 0.05. The allometric relationship between testes mass and body mass, obtained from the data sets used in comparative studies, provides the necessary value of residual testes mass in order to decide whether a particular (novel) species has relatively large or relatively small testes (e.g., Sheldon and Birkhead 1994; Pitcher et al. 2005). Møller (1991) concluded that there was no difference in the allometric relationship between passerine and nonpasserine orders, despite the several differences in reproductive biology between these 2 groups (e.g., Wolfson 1954; McFarlane 1963). Because the data in Møller's (1991) study came from a variety of sources, we rechecked this premise using our restricted and more reliable data set. Not only did our results confirm Møller's (1991) conclusion that a common testes size allometric slope is justified but also we found that a common intercept is also valid for Aves (see supplementary material; “reliable” data set, species values, model I regression, slope: t = 0.62, P = 0.540; intercept: t = 0.26, P = 0.800). There were also no significant differences in the allometric relationship between data sets differing in size and quality (see supplementary material). However, the smaller data set provides the most conservative avian testes size allometric relationship, because these estimates are more accurate, and the body size range is virtually the same as in the larger data set. Moreover, we suggest that confidence intervals (CIs) of the slope should also be considered. For instance, a conservative approach for deciding whether a particular species has a relatively large or small testes size would be to consider those species within the area within CIs to have residual testes size of zero; above this area, positive residuals; and below this area, negative residuals. Supplementary material lists the allometric relationships (regression models I and II, with 90%, 95%, and 99% CI) obtained from different data sets of varying quality. We pragmatically suggest that in order to qualitatively assess a particular (novel) species' relative testes size, the model II common allometric slope and its 95% CI obtained from the good-quality data set be used: log CTM (g) = −1.81 + 0.85 (0.78–0.93) × log body mass (g) (R2 = 0.76, P < 0.0001). Researchers often face trade-offs between the quality and quantity of data they use—a problem exemplified in the study of the evolution of testes size in birds. Avian testes size is difficult to measure, and previous studies have relied on several assumptions and applied different techniques to obtain estimates of avian testes size. We demonstrate how accuracy and reliability of testes mass estimates are influenced by 1) previously unchecked methodological assumptions, 2) the estimation approach used, and 3) the quality of the source of testes size data. A review of the currently available avian testes mass estimates showed that reliable values are scarce (11% of the 1044 species) because the majority of estimates have been obtained indirectly (from linear dimensions) from the more convenient and widely available museum skin tags, using a method that averages across individuals (Means). Museum collections have allowed researchers to obtain testes size data for about 10% of all avian taxa. However, these large data sets do not compensate for the poor quality of data that museum specimens generate if used uncritically. We recommend the use of more stringent methodological criteria for estimating meaningful species-specific testes sizes. Estimates should be obtained directly as wet mass of both testes, from a sample of at least 30 adult males from a breeding population from a specific geographic location. This sample must exclude juveniles, nonbreeders, and first-year breeding males, and body mass data should originate from the same source. In order to obtain reliable estimates of a species' peak testes size, the Polynomial approach should always be used whenever 1) sampling spans the breeding season, 2) sample sizes are sufficient (n ≥ 30), but 3) details of the birds' breeding stage is unknown. We recommend that the Means method not be used on museum sources because it is particularly prone to errors. Testing evolutionary hypotheses relating to sexual selection relies heavily on accurate measures of reproductive investment and/or levels of sperm competition, such as relative testes size. Until now, our understanding of these patterns across avian taxa has been based on the results of comparative studies that have employed large data sets. The fact that we have identified serious errors and biases in these data sets means, first, that the results from these studies should be treated with caution and, second, there is no longer any excuse for their uncritical use. Large samples have greater statistical power, but unless the data are of high quality, they merely create an illusion of greater precision. For this particular trade-off, more is certainly not better. Supplementary material can be found at http://www.beheco.oxfordjournals.org/. We thank S. Nakagawa and J. Hadfield for statistical advice; I.P.F. Owens, T.E. Pitcher, P.O. Dunn, B.J.M. Stutchbury, A.P. Møller, J.M. Briskie, R. Montgomerie, and S. Nakagawa for valuable comments on the manuscript; and P. Deviche, T.E. Pitcher, and P.O. Dunn for the use of their unpublished data. S.C. was supported by a doctorate research grant from the Portuguese Science and Technology Foundation (FCT, Portugal, SFRH/BD/10040/2003).