Phylogenetic hypotheses have become increasingly important and frequently used tools in studies of macroevolutionary patterns. In particular, phylogenetic trees are commonly used to study variation in rates of diversification through time and among groups. Inferences stemming from reconstruction of diversification-rate variation can inform researchers on the role of geological or climatic events, the role of evolutionary novelty and key innovations, and adaptive and nonadaptive radiations in explaining diversification history and extant species richness (e.g., Harmon 2003; Jiggins et al. 2006; Weir 2006; Phillimore and Price 2008; Rabosky and Lovette 2008; Fordyce 2010a). Various approaches have been developed to identify diversification-rate variation evident in phylogenetic hypotheses. Two distinct kinds of questions are addressed by distinct methods; diversification rate variation through time and differences in diversification between groups (Fig. 1).

Variation through time methods directly examine the accumulation of lineages through time based upon a chronogram (i.e., an ultrametric phylogram where branch lengths are scaled as time). That is, they examine the vector of cladogenic events for a monophyletic group through time. This includes methods that explicitly model the process that determines the shape of the log-lineages through time plot, and estimate the parameters that describe the rate. Generally, a pure-birth (Yule) process is used as a null hypothesis. The pure-birth process predicts a linear increase in log-lineages through time. When there is deviation from this pure-birth process, other models, such as birth–death, density-dependence, etc., are applied to the data to find the best model that describes the accumulation of lineages (Nee et al. 1994a,b; Rabosky 2006; Morlon et al. 2010; Stadler 2011). Other approaches have borrowed from survival analysis where the mean waiting time to cladogensis per lineage is modeled (Paradis 1997). Another commonly used approach, Pybus and Harvey’s (2000) constant-rates test (commonly referred to by its test statistic, ), does not model the rate parameter, but rather examines the shape of the distribution of ordered cladogenic events. The constant-rates test has been used to test for a slowdown in diversification or, conversely, evidence for a burst of diversification early in a group’s history, however this method has limitations that compromise its power to detect rate variation early in a clade’s history (Fordyce 2010b). Other recently developed approaches search for discrete shifts in patterns of diversification through time (McInnes et al. 2011; Stadler 2011). These approaches examine the entire tree (monophyletic group) as it changes through time, and do not explicitly consider rate variation among lineages within a tree. That is, they assume all lineages/subclades within a tree are characterized by the same time-dependent diversification process.

Difference between groups methods have been developed to examine rate variation within a tree and identify subclades in the tree with higher or lower relative rates. The simplest of these methods compare the species richness of two or more clades to evaluate whether differences in observed diversity are consistent with stochastic variance or are better explained by distinct diversification rates. Different rates of diversification and the processes underlying this variation can also be detected by examining tree balance, or the symmetry of a tree (Shao and Sokal 1990; Rohlf et al. 1990; Mooers and Heard 1997; Chan and Moore 2005). Some methods need not require an ultrametric tree, rather they examine the number of nodes along a path of edges in a tree to determine if punctuated evolution has occurred in a tree’s history (Webster et al. 2003; Venditti et al. 2006). The MEDUSA (Modeling Evolutionary Diversification Using Stepwise Akaike Information Criterion [AIC]) approach of Alfaro et al. (2009) uses edge lengths to estimate the parameters of a birth–death process based upon the model described by Rabosky et al. (Rabosky et al. 2007) (but see Rabosky [2010]).

Here, we present a new method aimed at identifying subclades of a tree with relatively higher and lower rates of diversification, the parametric rate comparison test (hereafter, PRC). This approach explicitly examines the distribution of branch lengths, rather than the distribution of cladogenic events across the entire tree (Fig. 1), and does not require that comparisons be made among monophyletic groups. It allows for the detection and comparison of rate variation among both monophyletic and paraphyletic groups. This approach also provides the opportunity to compare diversification rate histories among a priori defined groups. This method is not contingent on a particular evolutionary process; rather, it is phenomenological in nature allowing comparison of various probability distributions. PRC differs from MEDUSA in being a generalized statistical analysis rather than fitting the specific constant birth–death branching model of Kendall (1948) (see also Paradis [2003] and Rabosky [2007]). As such, the PRC method can employ a variety of statistical distributions to characterize the distribution of branch lengths (internodes). This flexibility is the primary advantage of PRC as an addition to the comparative diversification analysis toolbox. We apply the PRC to the well-studied radiation of *Plethodon* salamanders in eastern North America using a few simple distributions as an example of the utility of this method.