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Understanding which traits drive species diversification is essential for macroevolutionary studies and to understand patterns of species richness among clades. An important tool for testing if traits influence diversification is to estimate rates of net diversification for each clade, and then test for a relationship between traits and diversification rates among clades. However, this general approach has become very controversial. Numerous papers have now stated that it is inappropriate to analyze net diversification rates in groups in which clade richness is not positively correlated with clade age. Similarly, some have stated that variation in net diversification rates does not explain variation in species richness patterns among clades across the Tree of Life. Some authors have also suggested that strong correlations between richness and diversification rates are a statistical artifact and effectively inevitable. If this latter point is true, then correlations between richness and diversification rates would be uninformative (or even misleading) for identifying how much variation in species richness among clades is explained by variation in net diversification rates. Here, we use simulations (based on empirical data for plethodontid salamanders) to address three main questions. First, how is variation in net diversification rates among clades related to the relationship between clade age and species richness? Second, how accurate are these net diversification rate estimators, and does the age-richness relationship have any relevance to their accuracy? Third, is a relationship between species richness and diversification rates an inevitable, statistical artifact? Our simulations show that strong, positive age-richness relationships arise when diversification rates are invariant among clades, whereas realistic variation in diversification rates among clades frequently disrupts this relationship. Thus, a significant age-richness relationship should not be a requirement for utilizing net diversification rates in macroevolutionary studies. Moreover, we find no difference in the accuracy of net diversification rate estimators between conditions in which there are strong, positive relationships between clade age and richness and conditions in which these strong relationships are absent. We find that net diversification rate estimators are reasonably accurate under many conditions (true and estimated rates are strongly corrrelated, and typically differ by ∼10-20%), but become more accurate when clades are older and less accurate when using incorrect assumptions about extinction. We also find that significant relationships between richness and diversification rates fail to arise under many conditions, especially when there are faster rates in younger clades. Therefore, a significant relationship between richness and diversification rates is not inevitable. Given this latter result, we suggest that relationships between richness and diversification should be tested for when attempting to explain the causes of richness patterns, to avoid potential misinterpretations (e.g., high diversification rates associated with low-richness clades). Similarly, our results also provide some support for previous studies suggesting that variation in diversification rates might explain much of the variation in species richness among major clades, based on strong relationships between clade richness and diversification rates.

Testing the Relationships between Diversification, Species Richness, and Trait Evolution