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.