Behavioral Ecology Vol. 10 No. 5: 476-486
© 1999 International Society for Behavioral Ecology
The strength of sexual selection: a meta-analysis of bird studies
Laboratoire d'Ecologie, CNRS URA 258, Université Pierre et Marie Curie, Bât. A, 7ème étage, 7 quai St. Bernard, Case 237, F-75252 Paris Cedex 5, France
Address correspondence to A. P. Møller. E-mail: amoller{at}hall.snv.jussieu.fr .
Received 18 May 1998; revised 5 January 1999; accepted 31 January 1999.
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ABSTRACT |
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Sexual selection has been demonstrated to sometimes be strongly related to the expression of secondary sexual characters, as shown by a number of classical textbook examples, thereby providing evidence for the importance of sexual selection in the maintenance of secondary sexual characters, but equally many studies with no or only weak effects also exist. Because there is no general estimate of the magnitude of the relationship between intensity of sexual selection and expression of secondary sexual characters, we do not know to which extent extreme effects are typical, and whether there is an overall effect across studies. We made a meta-analysis of visual sexual signals in birds to test whether there is a general, significant relationship between the strength of sexual selection and the expression of secondary sexual characters and determined factors that accounted for some of the heterogeneity in effects among studies. The average effect size, measured as the Pearson product-moment correlation coefficient, was 0.30 for studies and 0.31 for species as units of analysis, which implies that 9-10% of the variance in male mating success is accounted for by intraspecific variation in the expression of secondary sexual characters. This finding is extremely robust given the high fail-safe number. We found some evidence consistent with publication bias, such as a decreasing effect with increasing sample size, whereas a decreasing variance in effect size with increasing sample size and the most common effect size being close to the average effect size did not suggest publication bias. Effect size was significantly negatively related to year of publication, suggesting that more representative studies have been published in recent years. Experimental studies demonstrated stronger effects than observational studies (weighted Pearson's r for experimental studies was 0.35), apparently because experimental studies increase the range of phenotypes and control for potentially confounding factors. Color signals did not differ in effect size from morphological structures. Monogamous and lekking species tended to show stronger effects than polygynous species (mean Pearson's r were 0.29, 0.48 and 0.23, respectively). Mean weighted effect size was larger for studies based on mating success than for studies based on mate preferences or reproductive success (mean Pearson's r were 0.35, 0.30, 0.28, respectively). A multiple regression analysis taking sample size into account demonstrated a significant effect of experiment and year of publication on effect size. Sexual selection on visual secondary sexual characters can thus be considered to have an intermediate effect on their maintenance.
Key words: birds, mating system, meta-analysis, publication bias, secondary sexual characters.
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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The extravagant secondary sexual characters of many animals have attracted considerable attention since Darwin's (1871
) treatise more than 100
years ago. Currently, several textbook examples of intense sexual selection
have reached a wide audience (Andersson,
1982; Partridge,
1980; Møller,
1988b), and such examples may give scientists the impression that
strong effects are commonplace or even typical in studies of sexual selection.
Clear textbook examples of sexual selection may thus lead to the appreciation
that sexual selection is an important evolutionary force. Is it the case that
strong effects of sexual selection are generally very common?
Sexual selection has recently been extensively reviewed
(Andersson, 1994;
Møller, 1994b). The
first of these reviews presents an extensive list of studies providing
evidence in support of sexual selection, and in particular female choice,
playing an important role in the maintenance of secondary sexual characters.
However, it is less frequently appreciated that contradictory evidence is
widespread in the literature. For example, Andersson
(1982) did not find any
evidence that male mating success is related to natural variation in male
phenotype (reported as unpublished information in
Andersson, 1982). Similar
absence of significant selection on secondary sexual characters has also been
reported for several characters in many other studies
(Gibson and Bradbury, 1987;
Mc-Donald, 1989;
Pruett-Jones and Pruett-Jones,
1990; Wittzell,
1991; Zuk et al.,
1990d). A better understanding of the importance of sexual
selection can only be achieved by considering supportive and contradictory
evidence, and thus summarizing the entire body of evidence while considering
the power of the statistical tests.
Weak effects of sexual selection may arise for a number of different
reasons. Many studies in field biology, particularly experimental studies, are
limited by relatively small sample sizes. Hence, the power of the statistical
tests used to evaluate the findings is often low, and this gives rise to only
large effects being considered significant. A nonsignificant result does not
imply that the null hypothesis necessarily can be accepted. Small effects may
be considered to represent no effects, although the real conclusion should be
that the null hypothesis has not been rejected. Furthermore, studies with
small effects may not be submitted, or if submitted not accepted for
publication. The second kind of weak effect arises for biological reasons. For
example, it has been argued that persistent directional sexual selection will
tend to deplete any genetic variation that is the ultimate function of the
mate preference; hence the lek paradox
(Taylor and Williams, 1982).
Assessment of a body of scientific literature for overall effects (weak and
strong), as well as determination of factors that contribute to variation in
effects among studies, is most readily done using a meta-analytic approach
(Hedges and Olkin, 1985;
Hunter and Schmidt, 1990;
Rosenthal, 1991,
1994). While narrative
summaries of a body of literature do not consider the power of statistical
tests, meta-analysis takes sample size and hence the power of tests into
consideration.
In this paper we present a meta-analysis of the literature on visual sexual
signals in birds in order to assess the magnitude of the effect of sexual
selection on secondary sexual characters. We found it unfeasible to perform a
complete quantitative assessment of the entire literature on all organisms.
Because birds have played an important role in the conceptualization of sexual
selection ever since Darwin wrote his book on the subject
(Andersson, 1982,
1994;
Darwin, 1871;
Møller, 1988b,
1994b), we chose to use this
group of species as a model system for the meta-analysis. Previous studies
have demonstrated that a large number of bird species does not demonstrate
clear evidence of sexual selection, while others do (review in
Møller, 1993). This
pattern may suggest that the two groups of birds differ with respect to the
kinds of quality properties being signaled by the secondary sexual characters.
Alternatively, different processes of sexual selection may operate in
different taxa. This interpretation is supported by a direct relationship
between evidence of strong current sexual selection and social mating system
(Møller, 1993) and
between the presence of multiple sexual signals and social mating system
(Møller and Pomiankowski,
1993).
A large number of studies of visual signals in birds allows an analysis of potential factors influencing current sexual selection. These include (1) whether the study in question is observational or experimental (the latter might more readily reveal evidence of sexual selection because confounding variables are controlled); (2) whether the character investigated is a color signal or the size of a feather (the latter is affected by an aerodynamic cost that does not influence the former category of characters); (3) whether the social mating system is monogamous, polygynous, or lekking (the intensity of sexual selection is generally presumed to increase with increasing skew in male mating success as found in highly polygynous and lekking species); and (4) whether the currency of mating success is a mate preference, mating success, reproductive success, or paternity.
The aims of the present study were to determine whether (1) there is an overall significant effect of sexual selection on secondary sexual characters, using Pearson's product-moment correlation coefficient as a measure of effect size; (2) publication bias may have influenced studies in the literature by estimating the fail-safe number (see Methods) and the distribution of effect sizes in relation to sampling effort and year of publication; (3) experiments provide stronger effects than observational studies; (4) morphological traits demonstrate effects that differ from those of colors; (5) effect size differs among social mating systems; and (6) effect size differs among different currencies of mating success.
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MATERIALS AND METHODS |
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Data set and classification of variables
We obtained our data set from an extensive search of the literature and included all studies published before 1 January 1998. We made a complete search of the following journals for the years 1980-1997: American Naturalist, American Zoologist, Animal Behaviour, Auk, Behaviour, Behavioral Ecology, Behavioral Ecology and Sociobiology, Biological Journal of the Linnean Society, Condor, Ecology, Ethology, Evolution, Heredity, Ibis, Journal für Ornithologie, Journal of Avian Biology, Journal of Evolutionary Biology, Nature, Ornis Scandinavica, Ostrich, Proceedings of the National Academy of Sciences of the USA, Proceedings of the Royal Society of London B, Science, and Zeitschrift für Tierpsychologie. These sources of information should provide complete coverage of the published data on the subject. A few articles found in other journals were also included in the study.
Meta-analyses often become problematic if null results tend not to be
published (Hunter and Schmidt,
1990). Obviously, we can never know how many unpublished studies
of negative results are available, but one way of addressing this problem is
by calculating the fail-safe number of publications, which is the number of
null results needed to nullify an overall effect
(Rosenthal, 1991).
We used Pearson's product-moment correlation coefficient as a measure of effect size in the present study, which has the intuitive appeal that its value squared represents the amount of variance accounted for by a particular relationship. We searched the literature for correlation coefficients, or other statistics that could be converted into correlation coefficients, based on the relationship between sexual selection and the expression of secondary sexual characters.
If there is statistically significant heterogeneity in effects among
studies, this implies that one or more moderator variables may influence the
relationship between secondary sexual characters and mating success. The
absence of significant heterogeneity does not imply that effect sizes are not
influenced by one or more variables. However, it implies that we have no
formal statistical justification for expecting such an effect in the data
available. Given statistically significant heterogeneity among effect sizes in
the meta-analysis, we tested for the influence of four moderator variables
that we believe could potentially explain some or all of this heterogeneity in
the different tests. Data on these variables were based on information in the
original sources. First, we considered whether the study was experimental or
observational, with the prediction that relationships based on experimental
studies will be stronger because confounding variables are controlled. Studies
were considered to be experimental if the secondary sexual character in
question was experimentally manipulated. Obviously, observational studies are
heterogeneous because some studies are based on simple correlations, whereas
others have carefully attempted to control for potentially confounding
variables. Second, we considered whether the secondary sexual character is a
structural, morphological trait or a color trait. The assumption is that
morphological traits have an additional cost imposed by aerodynamics. Third,
we considered whether effect size differed among species with different social
mating systems. Because the intensity of sexual selection is presumed to be
more intense in highly polygynous and lekking species
(Andersson, 1994;
Payne, 1984), we expected that
effect sizes might increase with increasing skew in male mating success.
Fourth, we considered whether effect size differed in relation to the currency
used to estimate success. These were classified as mate preference, mating
success, breeding success, or paternity. The assumption was that mating
success is more closely related to fitness than a mate preference, and
similarly paternity is more closely related to fitness than simple
reproductive success without considering paternity.
Meta-analysis
The measure of effect size used was Pearson's correlation coefficient. If
the original sources did not provide a correlation coefficient, we transformed
the statistics into a correlation coefficient using the formulae for
transformation given by Rosenthal
(1994: Table 16.1). In cases
where only probabilities were reported, these were transformed into Pearson
correlation coefficients using the standard transformation
(Sokal and Rohlf, 1995).
Pearson correlation coefficients were subsequently transformed by means of
Fisher's transformation to z values on which all subsequent analyses
were performed. Analyses at the level of species were based on mean effect
sizes for the different studies with total sample size being the sum of the
sample sizes for all studies. The measure of effect size was adjusted for
sample size using N - 3 as an adjustment factor
(Rosenthal, 1991), based on
the assumption that a larger sample size should provide a more reliable
estimate of a true relationship.
We tested whether there was an overall effect using Pearson's correlation
coefficients after z transformation and adjusted for sample size as
described above. This was done by testing whether the mean effect size
differed significantly from zero
(Rosenthal, 1991) using the
equation:
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An estimate of heterogeneity in effect sizes among samples was subsequently
calculated using the formula provided by Rosenthal
(1991: 73-74):
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Provided that there was statistically significant heterogeneity among
effect sizes of studies, we proceeded by testing for the effects of potential
explanatory variables by calculating a standard normal deviate, as suggested
by Rosenthal (1991):
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j is the contrast weight determined by a hypothesis
of the analysis unit (samples, species), chosen so that the sum of the values
of j equals zero. 1/Nj is the weighting factor,
where Nj is the number of samples in each of the
j categories, and wj is the inverse of the
variance of the effect size for the analysis unit. The 95% confidence
intervals were calculated according to Hedges and Olkin
(1985).
The fail-safe number of studies, X, needed to nullify an effect
was calculated, following Rosenthal
(1991) as:
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,
and K is the number of analysis units.
We investigated whether the data sets demonstrated any indication of
publication bias by testing for three predictions of unbiased samples (e.g.,
Begg, 1994;
Light and Pillemer, 1984): (1)
that the variance in effect size decreases with increasing sample size; (2)
that the most common observation is close to the true effect size; and (3)
that the distribution of effect sizes around the true value is symmetrical
(i.e., has a normal distribution with zero skewness and kurtosis).
We used two-tailed tests with a significance level of 5%.
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RESULTS |
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The average effect size for studies of sexual selection in relation to the expression of secondary sexual characters was zr = 0.3095, which equals a Pearson r =.3000, differing significantly from a value of zero (p <.001). The fail-safe number for this average effect size of studies was 47,194 studies. This number is an estimate of the number of studies unknown to us because journals reject papers with null results, and/or because authors do not submit papers with null results as often.
It is also an estimate of the number of future studies needed to change the
significant effect size into a nonsignificant one. When this analysis was
repeated for species, we found an average effect size of
zr = 0.3136 (Pearson r =.3037), differing
significantly from a value of zero (p <.001). The fail-safe number
for this average effect size of species was 21,706 studies. Hence, both
analyses revealed intermediate effects [i.e., effects that account for around
10% of the variance as arbitrarily suggested by Cohen
(1988)], with an overall
robust conclusion.
The frequency distribution of effect sizes was not normal, although the most common effect size was very close to the average value (Figure 1). For studies as units of analysis, skewness was 2.326 and kurtosis 7.812, with both values differing significantly (p <.001) from zero. For species as units of analysis, skewness was 2.387 and kurtosis was 7.236; again differing significantly (p <.001) from zero. These values were due to more large effect sizes than expected by chance. The distribution of effect sizes demonstrated larger variances for small sample sizes for species, but not for studies as units of analysis (Figure 2). F tests for effect sizes above and below the median sample size demonstrated a significantly larger variance for the group of small sample sizes for species (variance for studies below the median 0.379, variance for studies equal to or above the median 0.108, F = 3.51, df = 39,39, p <.001), but not for studies as units of analysis (variance for studies below the median 0.324, variance for studies equal to or above the median 0.311, F = 1.04, df = 68,68, ns).
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Sampling effort explained a significant amount of variation in effect size because we found a negative relationship between effect size and sample size when based on studies and species as units of analysis, respectively [linear regression using log-transformed sample size, studies: F = 7.14, df = 1,136, r2 =.050, p =.0085, ß (SE) = -0.293 (0.110); species: F = 10.718, df = 1,77, r2 =.122, p =.0016, ß (SE) = -0.332 (0.101)].
The year of publication was investigated as an explanatory variable because we hypothesized that initially strong effects would be followed by weaker effects. We found a significant negative relationship between effect size and year both for studies and species as units of analysis (linear regression: studies: F = 5.14, df = 1,136, r2 =.036, p =.025, ß (SE) = -0.028 (0.012); species: F = 6.49, df = 1,77, r2 =.078, p =.013, ß (SE) = -0.035 (0.014)).
Tests for heterogeneity among effect sizes revealed highly significant
results both when the analyses were based on studies (
2 =
1933.60, df = 137, p <.0001) and species as units of analysis
(2 = 872.26, df = 79, p <.0001). Therefore, we
proceeded by determining the effects of potential moderator variables.
Experimental studies differed significantly from observational ones in terms of average effect size (Tables 1 and 2). Both studies and experiments revealed significantly larger average effects among experimental as compared to observational studies. When this comparison was restricted to species with both observations and experiments, we found a nonsignificant difference between observations and experiments [mean effect size corrected for sample size (SE): observations: 0.315 (0.051), experiments: 0.419 (0.071), paired t-test, t = 1.17, df = 21, p =.26]. The amount of variance explained in the latter comparison increased from 9.9% to 17.6% by adopting an experimental approach.
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Color signals and morphological structures did not differ significantly with respect to average effect size (Table 1 and 2).
Mating systems differed significantly in average effect size both for studies and species as units of analysis (Tables 1 and 2). For studies we found a weaker effect for polygynous than monogamous and lekking species (Table 1). For species as units of analysis we found a similar pattern (Table 2).
The currency of mating success differed significantly in average effect size both for studies and species as units of analysis (Table 1 and 2). For studies as units of analysis, we found weaker effect for studies based on reproductive success as compared to studies based on choice and in particular mating success (Table 1). For species as units of analysis, we found a similar pattern (Table 2).
Because the different explanatory variables may be correlated with each other, we made a multiple regression with effect size as the dependent variable and type of study, character, and mating system as independent variables. None of the two- or three-way interactions approached significance (p >.30), and they were thus excluded from the analyses. The best-fit models that included independent variables with p values <.10 only included experiment, sample size, and year of publication as significant variables (Table 3).
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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Our meta-analysis of sexual selection on visual signals in birds revealed a moderate effect size with a mean r =.30 for studies and 0.31 for species as units of analysis. These mean effect sizes can be compared to a much larger value of 0.68 for euplectes progne (Andersson, 1982
) and a value
of 0.78 for Hirundo rustica
(Møller, 1988b) from
two of the often-cited studies of sexual selection in birds. Such high values
from single studies imply that the effects of sexual selection can be
important in particular circumstances, but that typical values generally are
much smaller. The meta-analysis may have been biased to some extent because
probabilities were sometimes converted into effect sizes based on
inequalities. Similarly, estimates of effect size based on studies without
tests for paternity may provide evidence of weaker effects than is actually
the case, as observed for birds in general
(Møller and Ninni,
1997). We consistently analyzed effects using both studies and
species as independent observations because multiple studies of the same
species potentially may bias overall conclusions. However, we found little
effect of the level of analysis on the results. The average effect sizes imply
that 9-10% of the variance in male mating success (or female mate preferences)
is caused by variation in the expression of the secondary sexual character.
Hence, the large effect sizes reported in some textbook examples of sexual
selection appear to be the exception rather than the rule. The results
demonstrate that the average effect size, which measures the standardized
magnitude of sexual selection, is similar to the effect size involved in
sexual selection on fluctuating asymmetry (r = -.31 when the analysis
is based on species as units of analysis;
Møller and Thornhill,
1998). A meta-analysis of the relative importance of size and
asymmetry in species where the importance of both variables were estimated in
the same studies demonstrated a significantly larger mean effect size for
asymmetry (Thornhill and Møller,
1998).
Publication bias may provide serious problems for meta-analyses if the
studies included are biased with respect to effect size—for example due
to null results tending not to be published
(Hunter and Schmidt, 1990). We
assessed this problem in two different ways. First, we determined the
fail-safe number, which represents a measure of the number of results with an
average effect size of zr = 0.00 needed to nullify the
recorded effect. We found a very large fail-safe number of 47,194 for studies
and 21,706 for species as units of analysis, which implies that the conclusion
that the expression of secondary sexual characters affects sexual selection is
a very robust finding. Second, we determined the distribution of effect sizes.
The variance in effect sizes was clearly negatively related to sample size
(Figure 2). An F test
revealed a significantly larger effect size in the sample below as compared to
above the median sample size for species as units of analysis, but not for
studies, implying that the sampling variance was generally larger for studies
with small samples, as expected for an unbiased sample of studies. The
frequency distribution of effect sizes peaked around the average effect size
recorded in our study (Figure
2). This suggests that more observations were located around the
presumed true effect size, as expected for unbiased samples of studies.
Furthermore, we found that average effect size was negatively related to
sample size, which is contrary to expectation for unbiased samples of studies.
Finally, effect size was significantly related to year of publication, which
is what one might expect because novel results usually tend to be strong,
whereas more negative or weaker results tend to accumulate with time as a
discipline matures. This negative relationship differs from the positive
relationship found when a certain type of results become acceptable due to
paradigm shifts (Alatalo et al.,
1997).
Obviously, we have to look for alternative explanations for the patterns
described here, and not all of these may be consistent with evidence of
publication bias (Thornhill et al.,
1999). First, experimental studies tend to manipulate variables to
increase the variance, thereby producing greater effect sizes than
observational studies, and experiments also often have smaller sample sizes
than observational studies when the scientist realizes the greater power of
well-planned design. Second, when a small effect has been published for a
particular organism, investigators may subsequently increase sample size,
thereby giving rise to a negative relationship between effect size and sample
size. Third, when a scientist knows a particular system and the effects from
previous experiments, this will invariably lead to careful planning of future
experiments with well-planned sample sizes. Hence, power analysis leads to
large sample sizes if effects are small, and vice versa for large effects. On
a cautionary note, the line of reasoning adopted here may not be the best way
of addressing potential problems of publication bias because effect sizes were
unweighted by sampling effort. Development of methods of analysis may
alleviate this problem. Furthermore, any effects of publication bias will only
appear for units of research that are considered for publication. Hence,
analysis at the level of studies with multiple traits being included for some
studies may provide biased estimates, while analysis at the level of species
with multiple traits being included for some species may provide more rigorous
estimates.
The second finding was statistically significant heterogeneity in effect size among studies and species. Hence some species show clear evidence of strong current sexual selection, but a substantial number of studies do not demonstrate such an effect. The most obvious variable to investigate with respect to heterogeneity among effect sizes is whether the study is based on observations or experiments. Experiments are made to control for potentially confounding variables and thereby assess whether a causal relationship exists between two or more variables. Experiments also increase the variance in the size of secondary sexual characters (although usually within the natural range observed) and thereby maximize the probability of detecting any relationship with mating success. We found a highly significant difference in effect size between the two categories of studies. However, experiments only increased average effect size slightly compared to observational studies. For example, we found that observations accounted for 8.3% of the variance in success based on studies as units of analysis, whereas experiments accounted for 10.4% (Table 1). Similarly, when the analyses were based on species as units of analysis, we found a coefficient of determination of 6.5%, whereas this amounted to 13.4% for experiments (Table 2). Hence, experiments increased the average relationships by 25% and 106%, respectively, for the two types of analyses. If scientists tended to pick species that were amenable to experimentation, the difference in effect size between observational and experimental studies may have been biased. We investigated this potential bias by making a paired comparison of the two types of studies performed on the same species. However, the difference in effect size remained large even in this situation, although not significantly so. This confirms that an experimental approach is crucial for eliminating noise arising from potentially confounding variables.
The second moderator variable that we investigated was whether the
secondary sexual character was a color signal or a morphological character.
Secondary sexual characters are usually supposed to be costly to develop
and/or maintain (Andersson,
1994), and natural and sexual selection thus tend to be opposing
forces. The maintenance costs of secondary sexual characters range from
aerodynamic and locomotory costs of heavy and unwieldy characters to costs of
parasitism and predation (review in
Andersson, 1994). Structural
characters differ from colors in that the former have a direct effect on
locomotion. If there is a balance between costs and benefits of secondary
sexual characters, we should expect effect sizes to be similar for the two
categories of characters. If the addition of a cost for morphological traits
affected sexual selection, we should expect a weaker effect for these traits
compared to colors. However, we found no significant difference in average
effect size between the two categories of sexual signals (Tables
1 and
2).
The social mating system has been supposed to reflect the intensity of
sexual selection, with the skew in male mating success being more extreme in
highly polygynous as opposed to less polygynous or monogamous species
(Andersson, 1994;
Payne, 1984). If the intensity
of sexual selection has any impact on the magnitude of direct or indirect
genetic benefits for choosy females, because directional selection tends to
result in alleles going to fixation
(Falconer and Mackay, 1996),
we might expect to see a reduction in the average effect size in highly
polygynous species as compared to monogamous ones. We found significant
heterogeneity among mating systems, with monogamous species having average
effect sizes stronger than polygynous species (Tables
1 and
2). Hence, the empirical
findings are consistent with the expectation that current sexual selection is
more closely related to the expression of secondary sexual characters in
socially monogamous as compared with polygynous species. These results have to
be viewed in the light of different currencies being used to measure sexual
selection in different studies. Mean effect sizes were generally smaller for
studies based on measures of reproductive success than studies based on mate
preferences and, in particular, mating success
(Table 2).
Given that the planned contrast analyses may have been confounded because the moderator variables themselves are intercorrelated, we conducted a multiple regression analysis to determine the independent effect of the three moderator variables. This analysis revealed that except for sampling effort, year of publication, and experiment, none of the other variables approached statistical significance (Table 3). Hence, we can conclude that only sampling effort, year, and experiment had any clear relationship with effect size.
Why was the effect of sexual selection on visual signals in birds not
stronger than indicated in the present analysis? One possibility is that most
signaling systems consist of multiple signals that may be redundant to some
extent (Møller and Pomiankowski,
1993). For example, certain signals may only be important in
certain contexts. Alternatively, different signals may interact in an additive
or multiplicative fashion and thereby account for a large proportion of the
variance in male mating success (e.g.,
Møller et al., 1998).
The final possibility is that the magnitude of the effect of sexual selection
is no stronger than indicated in the present study, with around 17-18% of the
variance in male mating success being determined by variation in the
expression of their secondary sexual characters.
In conclusion, we found a highly robust, but intermediate effect (i.e.,
explaining around 10% of the variance) for the relationship between various
measures of sexual selection and the expression of visual secondary sexual
characters in birds. There was considerable variation among studies caused by
sample size, year of publication, and experimental approach. The usefulness of
studies of publication bias lies in the realization that reported results of
scientific inquiry may deviate considerably from the underlying distributions.
It is by means of such assessment that we will be able to approach unbiased
estimates of underlying relationships in
nature.
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ACKNOWLEDGEMENTS |
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This research was supported by a grant from the Danish Natural Science Research Council and an ATIPE BLANCHE from CNRS.
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