Abstract
Over the past decade or so it has become increasingly popular to use reconstructed evolutionary trees to investigate questions about the rates of speciation and extinction. Although the methodology of this field has grown substantially in its sophistication in recent years, here I will take a step back to present a very simple model that is designed to investigate the relatively straightforward question of whether the tempo of diversification (speciation and extinction) differs between two or more phylogenetic trees, without attempting to attribute a causal basis to this difference. It is a likelihood method, and I demonstrate that it generally shows type I error that is close to the nominal level. I also demonstrate that parameter estimates obtained with this approach are largely unbiased. As this method can be used to compare trees of unknown relationship, it will be particularly well‐suited to problems in which a difference in diversification rate between clades is suspected, but in which these clades are not particularly closely related. As diversification methods can easily take into account an incomplete sampling fraction, but missing lineages are assumed to be missing at random, this method is also appropriate for cases in which we have hypothesized a difference in the process of diversification between two or more focal clades, but in which many unsampled groups separate the few of interest. The method of this study is by no means an attempt to replace more sophisticated models in which, for instance, diversification depends on the state of an observed or unobserved discrete or continuous trait. Rather, my intention is to provide a complementary approach for circumstances in which a simpler hypothesis is warranted and of biological interest.
Highlights
Over the past several decades, the field of phylogenetic comparative biology has emerged to assume a leading role in the study of evolutionary change through time (Felsenstein, 1985; Harvey & Pagel, 1991; O’Meara, 2012)
The first explicitly statistical method designed to estimate speciation and extinction rates from a reconstructed phylogenetic tree was proposed by Sean Nee and colleagues in the first half of the 1990s (Nee et al, 1994; prior methods based on sister-group comparisons existed at this time, e.g., Slowinski & Guyer, 1993)
I have proposed a simpler approach for modeling heterogeneity in the rates of speciation and/ or extinction among phylogenetic trees, without purporting to attribute a causal basis to this rate heterogeneity
Summary
Over the past several decades, the field of phylogenetic comparative biology has emerged to assume a leading role in the study of evolutionary change through time (Felsenstein, 1985; Harvey & Pagel, 1991; O’Meara, 2012). The highest observed level of type I error was 0.075 (Table 2) In addition to this analysis of type I error, I examined power and parameter estimation of the method when the null hypothesis of equal speciation and extinction among trees was false. For each pair of simulated trees, I fit a variable speciation model (the known generating model) and recorded the parameter estimates and p-value of the null hypothesis test against a model of equal speciation and extinction rates among trees. Each of 500 replicated analyses consisted in generating two phylogenies with equal speciation and extinction rates, but differing in total depth such that the expected number of lineages in each tree were E(N1) = 100 and E(N2) = 500, respectively, fitting each of the three aforementioned models (plus the equal rates null model) to each pair of trees.
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