How robust are the results?
A major criticism from Sánchez-Tójar et al. is that Yin et al. did not fully account for non-independence in the data. As only accounting for phylogenetic non-independence changes the results (Supplementary information 5 in Sánchez-Tójar et al. and Fig. S1), the discussion will focus on this point. First, as we have briefly addressed in Yin et al., ignoring phylogenetic structure is not because it is unimportant or non-exiting, but because such non-independence due to a shared common ancestor probably very weak and extremely difficult, if not impossible, to estimate with our data. The data include both plants and animals that are so remotely related, that too many events such as independent selection get involved in the evolution of these organisms, thus substantially weakening the constraints imposed by the common ancestor. Furthermore, our data include various nonhomologous traits measured for different species. The common ancestor of these traits, if any, is difficult to be approximated with the phylogenetic relatedness of species.
Even if such approximation was properly, the approach of the comment still has issues. First, the authors employ the Brownian motion model (Felsenstein 1985) to estimate the variance-covariance matrix (Fig. 1), which assumes evolutionary change to be gradual with time and the absence of selection that could change the rate of evolution. While such a neutral assumption may hold for short evolutionary time or small phylogenies, it is hardly applicable to our data including plants and animals. Second, the Brownian motion model requires using coalescence time to estimate branch lengths, but the authors use the number of leaves of subtrees (Grafen 1989) instead. Such estimation is biased by the sample size along each branch; e.g., underestimation of the branch length of gymnosperm (Supplementary information 3.1 in Sánchez-Tójar et al. and Fig. S2). Ignoring these assumptions and blindly employing phylogenetic structure can dramatically reduce statistical power, leading to overly conservative results. This approach appears to reduce the independent sample size to three referring to three major clades of plants, invertebrates and vertebrates, with high variance-covariance coefficients (>0.6) within each clade (Fig. 2). Although alternative evolutionary models can generate significant results (Fig. S1), I do not consider these models to be reasonable, as critical assumptions have been violated before adopting them.