Estimates of the average strength of natural selection are not inflated by sampling error or publication bias

Kingsolver et al.'s review of phenotypic selection gradients from natural populations provided a glimpse of the form and strength of selection in nature and how selection on different organisms and traits varies. Because this review's underlying database could be a key tool for answering fundamental questions concerning natural selection, it has spawned discussion of potential biases inherent in the review process. Here, we explicitly test for two commonly discussed sources of bias: sampling error and publication bias. We model the relationship between variance among selection gradients and sample size that sampling error produces by subsampling large empirical data sets containing measurements of traits and fitness. We find that this relationship was not mimicked by the review data set and therefore conclude that sampling error does not bias estimations of the average strength of selection. Using graphical tests, we find evidence for bias against publishing weak estimates of selection only among very small studies (N < 38). However, this evidence is counteracted by excess weak estimates in larger studies. Thus, estimates of average strength of selection from the review are less biased than is often assumed. Devising and conducting straightforward tests for different biases allows concern to be focused on the most troublesome factors.