BackgroundCombining multiple independent tests, when all test the same hypothesis and in the same direction, has been the subject of several approaches. Besides the inappropriate (in this case) Bonferroni procedure, the Fisher's method has been widely used, in particular in population genetics. This last method has nevertheless been challenged by the SGM (symmetry around the geometric mean) and Stouffer's Z-transformed methods that are less sensitive to asymmetry and deviations from uniformity of the distribution of the partial P-values. Performances of these different procedures were never compared on proportional data such as those currently used in population genetics.ResultsWe present new software that implements a more recent method, the generalised binomial procedure, which tests for the deviation of the observed proportion of P-values lying under a chosen threshold from the expected proportion of such P-values under the null hypothesis. The respective performances of all available procedures were evaluated using simulated data under the null hypothesis with standard P-values distribution (differentiation tests). All procedures more or less behaved consistently with ~5% significant tests at α = 0.05. Then, linkage disequilibrium tests with increasing signal strength (rate of clonal reproduction), known to generate highly non-standard P-value distributions are undertaken and finally real population genetics data are analysed. In these cases, all procedures appear, more or less equally, very conservative, though SGM seems slightly more conservative.ConclusionBased on our results and those discussed in the literature we conclude that the generalised binomial and Stouffer's Z procedures should be preferred and Z when the number of tests is very small. The more conservative SGM might still be appropriate for meta-analyses when a strong publication bias in favour of significant results is expected to inflate type 2 error.

In several animal sp ecies, change in sexual size dimorphism is a correlated response to selection on fecundity. In humans, di¡erent hypotheses have been proposed to explain the variation of sexual dimorphism in stature, but no consensus has yet emerged. In this paper, we evaluate from a theoretical and an empirical point of view the hypothesis that the extent of sexual dimorphism in human p opulations results from the interaction between fertility and size-related obstetric complications. We ¢rst developed an optimal evolutionary model based on extensive simulations and then we performed a comparative analysis for a total set of 38 countries worldwide. Our optimization modelling shows that size-related mortality factors do indeed have the potential to a¡ect the extent of sexual stature dimorphism. Comparative analysis using generalized linear modelling supports the idea that maternal death caused by deliveries and complications of pregnancy (a variable known to be size related) could be a key determinant explaining variation in sexual stature dimorphism across populations. We discuss our results in relation to other hypotheses on the evolution of sexual stature dimorphism in humans.