Inferring the Dynamics of Diversification: A Coalescent Approach Helene �� ` Morlon1*, Matthew D. Potts2, Joshua B. Plotkin1* 1 Department of Biology, University of Pennsylvania, Philadelphia, Pennsylvania, United States of America, 2 Department of Environmental Science, Policy, and Management, University of California Berkeley, Berkeley, California, United States of America Abstract Recent analyses of the fossil record and molecular phylogenies suggest that there are fundamental limits to biodiversity, possibly arising from constraints in the availability of space, resources, or ecological niches. Under this hypothesis, speciation rates decay over time and biodiversity eventually saturates, with new species emerging only when others are driven to extinction. This view of macro-evolution contradicts an alternative hypothesis that biodiversity is unbounded, with species ever accumulating as they find new niches to occupy. These contrasting theories of biodiversity dynamics yield fundamentally different explanations for the disparity in species richness across taxa and regions. Here, we test whether speciation rates have decayed or remained constant over time, and whether biodiversity is saturated or still expanding. We first derive a general likelihood expression for internode distances in a phylogeny, based on the well-known coalescent process from population genetics. This expression accounts for either time-constant or time-variable rates, time-constant or time-variable diversity, and completely or incompletely sampled phylogenies. We then compare the performance of different diversification scenarios in explaining a set of 289 phylogenies representing amphibians, arthropods, birds, mammals, mollusks, and flowering plants. Our results indicate that speciation rates typically decay over time, but that diversity is still expanding at present. The evidence for expanding-diversity models suggests that an upper limit to biodiversity has not yet been reached, or that no such limit exists. Citation: Morlon H, Potts MD, Plotkin JB (2010) Inferring the Dynamics of Diversification: A Coalescent Approach. PLoS Biol 8(9): e1000493. doi:10.1371/ journal.pbio.1000493 Academic Editor: Paul H. Harvey, University of Oxford, United Kingdom Received April 28, 2010 Accepted August 16, 2010 Published September 28, 2010 Copyright: �� 2010 Morlon et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: JBP acknowledges funding from the Burroughs Wellcome Fund, the David and Lucile Packard Foundation, the James S. McDonnell Foundation, and the Alfred P. Sloan Foundation. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. Abbreviations: AICc, second-order Akaike���s Information Criterion * E-mail: morlon.helene@gmail.com (HM) jplotkin@sas.upenn.edu (JBP) Introduction Two hypotheses about the dynamics of species diversity prevail in the literature [1���3]. According to the first hypothesis, diversity expands without limit. Under this view, the present-day richness of a clade results from a combination of the age of the clade and the speed at which species were generated (i.e., the net diversification rate: speciation rate minus extinction rate) [4]. According to the second hypothesis, evolutionary radiations occur when new ecospaces or resources become available between such radiations, speciation rates decay and biodiversity saturates [5���7]. Under this hypothesis, the variation in standing diversity across clades results from ecological factors such as the amount of space available to species [8,9], the number of niches they can occupy [10], or the quantity of resources [11,12] or individuals [13] they partition. Long-term diversity dynamics have been the subject of long- standing debate. Early work expounded the view that diversity accumulates without limit [14]. Subsequently, Raup [15] and Sepkoski [16] suggested that fossil data are consistent with a logistic model in which diversity is bounded. This debate has continued, mostly nourished by analyses of the fossil record [2,17,18]. More recently, molecular phylogenies have provided an alternative source of data, fostering the development of birth��� death models of cladogenesis [19,20]. Hey [21] first compared the performance of models with constant and expanding diversity to reproduce empirical phylogenies, finding more support for the expanding-diversity model. His analyses, however, did not allow rates to vary over time. Further explorations of Hey���s constant- diversity model have been surprisingly scarce (but see [22]). Instead, phylogenies have primarily been analyzed in a framework in which diversity increases from a single species at the time of the most recent common ancestor (an assumption made, e.g., by the Yule process). This approach ignores the fact that the ancestor was likely interacting with other species (with no descendants at present), and that diversity might have even remained constant through time ([1], but see [23,24]). As a consequence, the hypothesis that diversity is constant versus expanding has seldom been tested using molecular phylogenies. Many studies have examined the hypothesis that rates vary over time, and more particularly that speciation rates decay over time, using at least three different approaches. One approach is based on a summary statistic, gamma, that quantifies the position of nodes in a phylogeny compared to the pure-birth Yule model [25]. Phylogenies with negative gamma values indicate nodes situated towards the root of phylogenies, and have been interpreted as a signature of a slowdown in speciation rates. Although such phylogenies are abundant in nature [5,6,25,26], the interpretation of negative gamma values is controversial [26]. Moreover, the PLoS Biology | www.plosbiology.org 1 September 2010 | Volume 8 | Issue 9 | e1000493

gamma statistic fails to detect slowdowns in speciation rates in the presence of extinction [27], and it is not well suited for comparing the performance of various models or for estimating rates (but see [22]). A second approach compares the likelihood of internode distances under various models of cladogenesis [20,21,27���30]. This approach offers two advantages: it allows for comparison between different models and for estimation of rates. Applied to empirical phylogenies, such analyses have suggested a decay in the speciation rate over time [27,30]. However, the levels of extinction estimated by this method are too low to be realistic, suggesting that a major component of diversification is still missing from the modeling [22,26]. Finally, Venditti et al. [31] recently proposed a third approach, based on the distribution of phylogenetic branch- lengths (distances between ancestor and descendant nodes) rather than the likelihood of internode distances (waiting times between successive nodes). Applying their approach to a large set of molecular phylogenies, the authors concluded that speciation occurs at a constant rate in most taxa. To summarize the literature discussed above, despite decades of research aimed at investigating the tempo of evolution from molecular phylogenies, three main questions remain unresolved [2,3,32]: Is diversity presently saturated, or is it still expanding? Have rates of diversification slowed down over time? Do extinctions leave a detectable signal in empirical phylogenies? Here, we tackle these questions using a novel approach, inspired by the well-known coalescent process of population genetics [33]. The coalescent process describes the genealogy of individuals sampled from a population ������backwards in time,������ i.e., from the present to the past. Even though it was originally developed to describe genealogies over short time scales, the coalescent process can also be used to model species��� phylogenies���starting from extant species and going backwards in time, back to the time of the most recent common ancestor. The first advantage of this approach to studying cladogenesis is that diversity is not assumed to consist of a single species at the time of the common ancestor. Rather, diversity can take any value at any point in time, including constant diversity through time. The second advantage of the approach is that it easily accommodates incompletely sampled phylogenies, since coalescent theory is by nature a theory of samples. This advantage is of great practical utility, because many phylogenies omit a large proportion of extant species, particularly in species-rich taxa. Finally, the approach also allows comparison of models in which extinction is a free parameter (e.g., the constant-rate birth���death model) to models in which extinction is assumed to be prevalent (e.g., the Hey model see also [22]) such a comparison allows us to query whether extinction can be detected from molecular phylogenies. Adapting known results for coalescent times in a population with deterministically varying size [34,35], we derived a general expression for the likelihood of internode distances in the phylogeny of species sampled at present. We used this expression to approximate likelihoods of internode distances under a variety of birth���death models with time-constant or time-varying diversity, time-constant or time-varying rates, and present or absent extinction. Armed with this theoretical framework, we analyzed empirical phylogenies to investigate whether diversity is expanding or constant, whether rates are time-constant or time- variable, and whether extinctions can be detected in molecular phylogenies. We used two sets of empirical phylogenies: a relatively homogeneous set of phylogenies of birds, with high confidence in branch-length estimates, assembled by Phillimore and Price [6] and McPeek���s broad compilation of phylogenies, which includes chordates, arthropods, mollusks, and magnolio- phytes [26]. We analyzed a total of 289 phylogenies. Nine Diversification Scenarios We considered nine diversification scenarios, illustrated in Figure 1 (see also Table 1). In each of these scenarios, every lineage is equally likely to diversify or go extinct. Two of the scenarios (Models 1 and 2) correspond to the hypothesis that diversity is saturated. Species go extinct stochasti- cally and each extinction event is immediately followed by a speciation event, so that diversity remains constant through time. The particular case when the turnover rate (i.e., the rate of events in which an emerging species replaces a species going extinct) is constant through time (Model 1) is identical to Hey���s model [21]. Hey���s model is itself equivalent to the Moran process of population genetics, which describes the dynamics of individuals as opposed to species. Hey [21] showed that the terminal branches of phylogenies generated under his model are too short to be realistic, yet generalizations of the model to the case in which the turnover rate decays over time (Model 2) may provide a better description of empirical phylogenies (e.g., [22]). Such a decay in rates is expected if species become better adapted over the course of evolution. The remaining scenarios (Models 3���6) correspond to non- saturated diversity, and they feature independent speciation and extinction events. The model with time-constant speciation and extinction rates (Model 3) is the classical constant-rate birth���death model of cladogenesis [20], which reduces to the Yule process in the absence of extinction (Model 5). The other models (Models 4a��� 4d and 6) include temporal variation in speciation and/or extinction rates [27,28,30]. Rates were assumed to vary exponen- tially through time, but generalization to any form of time variation is straightforward. The nine diversification scenarios we consider here represent the range of qualitative cladogenesis processes typically discussed in the cladogenesis literature [1,19,20,27]. These models can be divided into pairs of subsets corresponding to our competing hypotheses for diversity dynamics (Figure 1): models with expanding diversity (in red) versus models with saturated diversity models with time-varying rates (in blue) versus models with time- constant rates and models where extinction is present (green) versus models where extinction is absent. Phylogenetic trees resulting from these various diversification scenarios have distinct branch-length patterns (Figure 2). Some models produce phylogenies that can easily be distinguished from each other ������by eye,������ but others produce trees that appear similar and that can be distinguished only through quantitative statistics. Author Summary Is species diversity in equilibrium, or is it still expanding? Are there ecological limits on diversity, or will evolution always find new niches for further specialization? These are all long- standing questions about the dynamics of macro-evolution, which have been examined using the fossil record and, more recently, molecular phylogenies. Understanding these long-term dynamics is central to our knowledge of how species diversify and ultimately what controls present-day biodiversity across groups and regions. We have developed a novel approach to infer diversification dynamics from the phylogenies of present-day species. Applying our approach to a diverse set of empirical phylogenies, we demonstrate that speciation rates have decayed over time, suggesting ecological constraints to diversification. Nonetheless, we find that diversity is still expanding at present, suggesting either that these ecological constraints do not impose an upper limit to diversity or that this upper limit has not yet been reached. Ecological Limits on Diversification PLoS Biology | www.plosbiology.org 2 September 2010 | Volume 8 | Issue 9 | e1000493