Supplementary data are available at Bioinformatics online.

Time-calibrated molecular phylogenies of extant species ("extant timetrees") are widely used for estimating the dynamics of diversification rates (1-6) and testing for associations between these rates and environmental factors (5, 7) or species traits (8). However, there has been considerable debate surrounding the reliability of these inferences in the absence of fossil data (9-13), and to date this critical question remains unresolved. Here we mathematically clarify the precise information that can be extracted from extant timetrees under the generalized birth-death model, which underlies the majority of existing estimation methods. We prove that for a given extant timetree and a candidate diversification scenario, there exists an infinite number of alternative diversification scenarios that are equally likely to have generated a given tree. These "congruent" scenarios cannot possibly be distinguished using extant timetrees alone, even in the presence of infinite data. Importantly, congruent diversification scenarios can exhibit markedly di erent and yet plausible diversification dynamics, suggesting that many previous studies may have over-interpreted phylogenetic evidence. We show that sets of congruent models can be uniquely described using composite variables, which contain all available information about past dynamics of diversification (14); this suggests an alternative paradigm for learning about the past from extant timetrees.

SummaryOur growing understanding of the plant tree of life provides a novel opportunity to uncover the major drivers of angiosperm diversity.Using a time-calibrated phylogeny, we characterized hot and cold spots of lineage diversification across the angiosperm tree of life by modeling evolutionary diversification using stepwise AIC (MEDUSA). We also tested the whole-genome duplication (WGD) radiation lag-time model, which postulates that increases in diversification tend to lag behind established WGD events.Diversification rates have been incredibly heterogeneous throughout the evolutionary history of angiosperms and reveal a pattern of 'nested radiations' -increases in net diversification nested within other radiations. This pattern in turn generates a negative relationship between clade age and diversity across both families and orders. We suggest that stochastically changing diversification rates across the phylogeny explain these patterns. Finally, we demonstrate significant statistical support for the WGD radiation lag-time model.Across angiosperms, nested shifts in diversification led to an overall increasing rate of net diversification and declining relative extinction rates through time. These diversification shifts are only rarely perfectly associated with WGD events, but commonly follow them after a lag period.

Global patterns of biodiversity are influenced by spatial and environmental variations in the rate at which new species form. We relate variations in speciation rates to six key patterns of biodiversity worldwide, including the species-area relationship, latitudinal gradients in species and genetic diversity, and between-habitat differences in species richness. Although they sometimes mirror biodiversity patterns, recent rates of speciation, at the tip of the tree of life, are often highest where species richness is low. Speciation gradients therefore shape, but are also shaped by, biodiversity gradients and are often more useful for predicting future patterns of biodiversity than for interpreting the past.

Most existing methods for modeling trait evolution are univariate, although researchers are often interested in investigating evolutionary patterns and processes across multiple traits. Principal components analysis (PCA) is commonly used to reduce the dimensionality of multivariate data so that univariate trait models can be fit to individual principal components. The problem with using standard PCA on phylogenetically structured data has been previously pointed out yet it continues to be widely used in the literature. Here we demonstrate precisely how using standard PCA can mislead inferences: The first few principal components of traits evolved under constant-rate multivariate Brownian motion will appear to have evolved via an "early burst" process. A phylogenetic PCA (pPCA) has been proprosed to alleviate these issues. However, when the true model of trait evolution deviates from the model assumed in the calculation of the pPCA axes, we find that the use of pPCA suffers from similar artifacts as standard PCA. We show that data sets with high effective dimensionality are particularly likely to lead to erroneous inferences. Ultimately, all of the problems we report stem from the same underlying issue--by considering only the first few principal components as univariate traits, we are effectively examining a biased sample of a multivariate pattern. These results highlight the need for truly multivariate phylogenetic comparative methods. As these methods are still being developed, we discuss potential alternative strategies for using and interpreting models fit to univariate axes of multivariate data.

Understanding the rate at which new species form is a key question in studying the evolution of life on earth. Here we review our current understanding of speciation rates, focusing on studies based on the fossil record, phylogenies, and mathematical models. We find that speciation rates estimated from these different studies can be dramatically different: some studies find that new species form quickly and often, while others find that new species form much less frequently. We suggest that instead of being contradictory, differences in speciation rates across different scales can be reconciled by a common model. Under the “ephemeral speciation model”, speciation is very common and very rapid but the new species produced almost never persist. Evolutionary studies should therefore focus on not only the formation but also the persistence of new species.

As a result of the process of descent with modification, closely related species tend to be similar to one another in a myriad different ways. In statistical terms, this means that traits measured on one species will not be independent of traits measured on others. Since their introduction in the 1980s, phylogenetic comparative methods (PCMs) have been framed as a solution to this problem. In this article, we argue that this way of thinking about PCMs is deeply misleading. Not only has this sowed widespread confusion in the literature about what PCMs are doing but has led us to develop methods that are susceptible to the very thing we sought to build defenses against-unreplicated evolutionary events. Through three Case Studies, we demonstrate that the susceptibility to singular events is indeed a recurring problem in comparative biology that links several seemingly unrelated controversies. In each Case Study, we propose a potential solution to the problem. While the details of our proposed solutions differ, they share a common theme: unifying hypothesis testing with data-driven approaches (which we term "phylogenetic natural history") to disentangle the impact of singular evolutionary events from that of the factors we are investigating. More broadly, we argue that our field has, at times, been sloppy when weighing evidence in support of causal hypotheses. We suggest that one way to refine our inferences is to re-imagine phylogenies as probabilistic graphical models; adopting this way of thinking will help clarify precisely what we are testing and what evidence supports our claims.

In the face of the biodiversity crisis, it is argued that we should prioritize species in order to capture high functional diversity (FD). Because species traits often reflect shared evolutionary history, many researchers have assumed that maximizing phylogenetic diversity (PD) should indirectly capture FD, a hypothesis that we name the “phylogenetic gambit”. Here, we empirically test this gambit using data on ecologically relevant traits from >15,000 vertebrate species. Specifically, we estimate a measure of surrogacy of PD for FD. We find that maximizing PD results in an average gain of 18% of FD relative to random choice. However, this average gain obscures the fact that in over one-third of the comparisons, maximum PD sets contain less FD than randomly chosen sets of species. These results suggest that, while maximizing PD protection can help to protect FD, it represents a risky conservation strategy.