Facultative adjustment of the offspring sex ratio and male attractiveness: a systematic review and meta-analysis : Sex ratio adjustment and male attractiveness
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Abstract
Females can benefit from mate choice for male traits (e.g. sexual ornaments or body
condition) that reliably signal the effect that mating will have on mean offspring
fitness. These male-derived benefits can be due to material and/or genetic effects.
The latter include an increase in the attractiveness, hence likely mating success,
of sons. Females can potentially enhance any sex-biased benefits of mating with certain
males by adjusting the offspring sex ratio depending on their mate's phenotype. One
hypothesis is that females should produce mainly sons when mating with more attractive
or higher quality males. Here we perform a meta-analysis of the empirical literature
that has accumulated to test this hypothesis. The mean effect size was small (r =
0.064-0.095; i.e. explaining <1% of variation in offspring sex ratios) but statistically
significant in the predicted direction. It was, however, not robust to correction
for an apparent publication bias towards significantly positive results. We also examined
the strength of the relationship using different indices of male attractiveness/quality
that have been invoked by researchers (ornaments, behavioural displays, female preference
scores, body condition, male age, body size, and whether a male is a within-pair or
extra-pair mate). Only ornamentation and body size significantly predicted the proportion
of sons produced. We obtained similar results regardless of whether we ran a standard
random-effects meta-analysis, or a multi-level, Bayesian model that included a correction
for phylogenetic non-independence. A moderate proportion of the variance in effect
sizes (51.6-56.2%) was due to variation that was not attributable to sampling error
(i.e. sample size). Much of this non-sampling error variance was not attributable
to phylogenetic effects or high repeatability of effect sizes among species. It was
approximately equally attributable to differences (occurring for unknown reasons)
in effect sizes among and within studies (25.3, 22.9% of the total variance). There
were no significant effects of year of publication or two aspects of study design
(experimental/observational or field/laboratory) on reported effect sizes. We discuss
various practical reasons and theoretical arguments as to why small effect sizes should
be expected, and why there might be relatively high variation among studies. Currently,
there are no species where replicated, experimental studies show that mothers adjust
the offspring sex ratio in response to a generally preferred male phenotype. Ultimately,
we need more experimental studies that test directly whether females produce more
sons when mated to relatively more attractive males, and that provide the requisite
evidence that their sons have higher mean fitness than their daughters.
Null hypothesis significance testing (NHST) is the dominant statistical approach in biology, although it has many, frequently unappreciated, problems. Most importantly, NHST does not provide us with two crucial pieces of information: (1) the magnitude of an effect of interest, and (2) the precision of the estimate of the magnitude of that effect. All biologists should be ultimately interested in biological importance, which may be assessed using the magnitude of an effect, but not its statistical significance. Therefore, we advocate presentation of measures of the magnitude of effects (i.e. effect size statistics) and their confidence intervals (CIs) in all biological journals. Combined use of an effect size and its CIs enables one to assess the relationships within data more effectively than the use of p values, regardless of statistical significance. In addition, routine presentation of effect sizes will encourage researchers to view their results in the context of previous research and facilitate the incorporation of results into future meta-analysis, which has been increasingly used as the standard method of quantitative review in biology. In this article, we extensively discuss two dimensionless (and thus standardised) classes of effect size statistics: d statistics (standardised mean difference) and r statistics (correlation coefficient), because these can be calculated from almost all study designs and also because their calculations are essential for meta-analysis. However, our focus on these standardised effect size statistics does not mean unstandardised effect size statistics (e.g. mean difference and regression coefficient) are less important. We provide potential solutions for four main technical problems researchers may encounter when calculating effect size and CIs: (1) when covariates exist, (2) when bias in estimating effect size is possible, (3) when data have non-normal error structure and/or variances, and (4) when data are non-independent. Although interpretations of effect sizes are often difficult, we provide some pointers to help researchers. This paper serves both as a beginner's instruction manual and a stimulus for changing statistical practice for the better in the biological sciences.
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