Estimating Speciation and Extinction Rates for Phylogenies of Higher Taxa

Are polyploids really evolutionary dead-ends (again)? A critical reappraisal of Mayrose etal. ().

Palaeobiodiversity and taxonomic resolution: linking past trends with present patterns

Species traits may influence rates of speciation and extinction, affecting both the patterns of diversification among lineages and the distribution of traits among species. Existing likelihood approaches for detecting differential diversification require complete phylogenies; that is, every extant species must be present in a well-resolved phylogeny. We developed 2 likelihood methods that can be used to infer the effect of a trait on speciation and extinction without complete phylogenetic information, generalizing the recent binary-state speciation and extinction method. Our approaches can be used where a phylogeny can be reasonably assumed to be a random sample of extant species or where all extant species are included but some are assigned only to terminal unresolved clades. We explored the effects of decreasing phylogenetic resolution on the ability of our approach to detect differential diversification within a Bayesian framework using simulated phylogenies. Differential diversification caused by an asymmetry in speciation rates was nearly as well detected with only 50% of extant species phylogenetically resolved as with complete phylogenetic knowledge. We demonstrate our unresolved clade method with an analysis of sexual dimorphism and diversification in shorebirds (Charadriiformes). Our methods allow for the direct estimation of the effect of a trait on speciation and extinction rates using incompletely resolved phylogenies.

A key measure of humanity's global impact is by how much it has increased species extinction rates. Familiar statements are that these are 100-1000 times pre-human or background extinction levels. Estimating recent rates is straightforward, but establishing a background rate for comparison is not. Previous researchers chose an approximate benchmark of 1 extinction per million species per year (E/MSY). We explored disparate lines of evidence that suggest a substantially lower estimate. Fossil data yield direct estimates of extinction rates, but they are temporally coarse, mostly limited to marine hard-bodied taxa, and generally involve genera not species. Based on these data, typical background loss is 0.01 genera per million genera per year. Molecular phylogenies are available for more taxa and ecosystems, but it is debated whether they can be used to estimate separately speciation and extinction rates. We selected data to address known concerns and used them to determine median extinction estimates from statistical distributions of probable values for terrestrial plants and animals. We then created simulations to explore effects of violating model assumptions. Finally, we compiled estimates of diversification-the difference between speciation and extinction rates for different taxa. Median estimates of extinction rates ranged from 0.023 to 0.135 E/MSY. Simulation results suggested over- and under-estimation of extinction from individual phylogenies partially canceled each other out when large sets of phylogenies were analyzed. There was no evidence for recent and widespread pre-human overall declines in diversity. This implies that average extinction rates are less than average diversification rates. Median diversification rates were 0.05-0.2 new species per million species per year. On the basis of these results, we concluded that typical rates of background extinction may be closer to 0.1 E/MSY. Thus, current extinction rates are 1,000 times higher than natural background rates of extinction and future rates are likely to be 10,000 times higher.

At present there are many animal phyla that contain only a few species. The existence of these small phyla can be used to test assumptions about speciation and extinction in multicellular animals.We first model the number of species in a monophyletic clade with a birth and death process that assumes rates of speciation and extinction are constant. If no new phyla have evolved since the Cambrian and speciation and extinction rates for minor phyla are similar to or greater than those estimated from fossils, then our model shows that the probabilities of minor phyla surviving to the present are small. Random variation in extinction and speciation rates does not improve the chances for persistence. If speciation rates exceed extinction rates at the initial radiation of the clade, but before the clade becomes large, speciation rates come to equal extinction rates and both are low, persistence from before the Ordovician up to the present becomes likely. These models show that if speciation and extinction rates are independent of the number of species in a clade, then conditions before the Ordovician strongly influence today's distribution of species among taxa.We also discuss a model in which speciation and extinction rates depend on the number of species in a clade. This alternative model can account for the persistence of phyla with few species to the present and predicts a short duration for phyla that did not exceed a threshold number of species.

Latitudinal gradient in species richness

Artificial neural networks can learn to estimate extinction rates from molecular phylogenies

A common pattern in time-calibrated molecular phylogenies is a signal of rapid diversification early in the history of a radiation. Because the net rate of diversification is the difference between speciation and extinction rates, such "explosive-early" diversification could result either from temporally declining speciation rates or from increasing extinction rates through time. Distinguishing between these alternatives is challenging but important, because these processes likely result from different ecological drivers of diversification. Here we develop a method for estimating speciation and extinction rates that vary continuously through time. By applying this approach to real phylogenies with explosive-early diversification and by modeling features of lineage-accumulation curves under both declining speciation and increasing extinction scenarios, we show that a signal of explosive-early diversification in phylogenies of extant taxa cannot result from increasing extinction and can only be explained by temporally declining speciation rates. Moreover, whenever extinction rates are high, "explosive early" patterns become unobservable, because high extinction quickly erases the signature of even large declines in speciation rates. Although extinction may obscure patterns of evolutionary diversification, these results show that decreasing speciation is often distinguishable from increasing extinction in the numerous molecular phylogenies of radiations that retain a preponderance of early lineages.

Recent application of time-varying birth-death models to molecular phylogenies suggests that a decreasing diversification rate can only be observed if there was a decreasing speciation rate coupled with extremely low or no extinction. However, from a paleontological perspective, zero extinction rates during evolutionary radiations seem unlikely. Here, with a more comprehensive set of computer simulations, we show that substantial extinction can occur without erasing the signal of decreasing diversification rate in a molecular phylogeny. We also find, in agreement with the previous work, that a decrease in diversification rate cannot be observed in a molecular phylogeny with an increasing extinction rate alone. Further, we find that the ability to observe decreasing diversification rates in molecular phylogenies is controlled (in part) by the ratio of the initial speciation rate (Lambda) to the extinction rate (Mu) at equilibrium (the LiMe ratio), and not by their absolute values. Here we show in principle, how estimates of initial speciation rates may be calculated using both the fossil record and the shape of lineage through time plots derived from molecular phylogenies. This is important because the fossil record provides more reliable estimates of equilibrium extinction rates than initial speciation rates.

The integration of Geographic Information System (GIS) methodology within a phylogenetic and statistical framework provides a background against which to evaluate the relationship between biogeographic changes and evolution in the fossil record. A case study based on patterns in Middle and Late Devonian phyllocarids (Crustacea) illustrates the usefulness of this integrated approach. Using a combined approach enhances determination of rates of biodiversity change and the relationship between biogeographic and evolutionary changes. Because the interaction between speciation and extinction rates fundamentally determines biodiversity dynamics, and speciation and extinction rates are influenced by the geographic ranges of component taxa, the relationship between biogeography and evolution is important. Furthermore, GIS makes it possible to quantify paleobiogeographic ranges.Phylogenetic biogeography resolved patterns of both vicariance and geodispersal and revealed that range expansions were more abundant than range contractions in Devonian phyllocarids. In addition, statistical tests on GIS-constrained species ranges and evolutionary-rate data revealed a relationship between increasing species' ranges and increases in both speciation and extinction rates. Extinction rate, however, increased more rapidly than speciation rate in the phyllocarids. The pattern of extinction rate increasing faster than speciation rate in the phyllocarids may illuminate aspects of the Late Devonian biodiversity crisis in particular, and protracted biodiversity crises in general.

Reinventing species selection with molecular phylogenies

Can extinction rates be estimated without fossils?

The birth-death model is commonly used to infer speciation and extinction rates by fitting the model to phylogenetic trees with exclusively extant taxa. Recently, it was demonstrated that speciation and extinction rates are not identifiable if the rates are allowed to vary freely over time. The group of birth-death models that have the same likelihood is called a congruence class, and there is no statistical evidence to favor one model over the other. This issue has led researchers to question if and what patterns can reliably be inferred from phylogenies of only extant taxa and whether time-variable birth-death models should be fitted at all. We explore the congruence class in the context of several empirical phylogenies as well as hypothetical scenarios. For these empirical phylogenies, we assume that we inferred the true congruence class. Thus, our conclusions apply to any empirical phylogeny for which we robustly inferred the true congruence class. When we summarize shared patterns in the congruence class, we show that strong directional trends in speciation and extinction rates are shared among most models. Therefore, we conclude that the inference of strong directional trends is robust. Conversely, estimates of constant rates or gentle slopes are not robust and must be treated with caution. Interestingly, the space of valid speciation rates is narrower and more limited in contrast to extinction rates, which are less constrained. These results provide further evidence and insights that speciation rates can be estimated more reliably than extinction rates.

One of the most striking patterns observed among animals is that smaller-bodied taxa are generally much more diverse than larger-bodied taxa. This observation seems to be explained by the mere fact that smaller-bodied taxa tend to have an older evolutionary origin and have therefore had more time to diversify. A few studies, based on the prevailing null model of diversification (i.e. the stochastic constant-rate birth–death model), have suggested that this is indeed the correct explanation, and body-size dependence of speciation and extinction rates does not play a role. However, there are several potential shortcomings to these studies: a suboptimal statistical procedure and a relatively narrow range of body sizes in the analysed data. Here, we present a more coherent statistical approach, maximizing the likelihood of the constant-rate birth–death model with allometric scaling of speciation and extinction rates, given data on extant diversity, clade age and average body size in each clade. We applied our method to a dataset compiled from the literature that includes a wide range of Metazoan taxa (range from midges to elephants). We find that the higher diversity among small animals is indeed, partly, caused by higher clade age. However, it is also partly caused by the body-size dependence of speciation and extinction rates. We find that both the speciation rate and extinction rate decrease with body size such that the net diversification rate is close to 0. Even more interestingly, the allometric scaling exponent of speciation and extinction rates is approximately −0.25, which implies that the per generation speciation and extinction rates are independent of body size. This suggests that the observed relationship between diversity and body size pattern can be explained by clade age alone, but only if clade age is measured in generations rather than years. Thus, we argue that the most parsimonious explanation for the observation that smaller-bodied taxa are more diverse is that their evolutionary clock ticks faster.

Nee et al. (1994) presented likelihood equations for estimating speciation and extinction rates based on phylogenies of only extant species; in particular their method can infer extinction patterns without extinct species data. Meanwhile, even for the simplest model of speciation and extinction, namely, the constant rate birth–death process, a number of studies have been published using different likelihood equations (Thompson 1975; Rannala and Yang 1996; Yang and Rannala 1997; Gernhard 2008; Stadler 2009). The likelihood functions differ due to conditioning the likelihood on different quantities, like the age of the tree, survival of the tree, or the number of species in the tree. Which conditionings yield the most accurate speciation and extinction rate estimates? In order to answer this question, I present an overview of 7 likelihood functions (which have been published in previous articles), conditioning on different aspects of the tree. I investigate and discuss the impact of the different conditionings toward accuracy of the maximum-likelihood rate estimates by inferring rates based on simulated phylogenies. The second part of this article discusses a possible bias in speciation and extinction rate estimates when analyzing incomplete phylogenies, that is, phylogenies in which not all extant species are included. The analytic considerations reveal that we cannot estimate the fraction of nonsampled species, but have to know it, when estimating speciation and extinction rates. The conclusions reached in this article, assuming the simple constant rate birth–death model, will also apply when assuming the more realistic macroevolutionary models allowing for nonconstant rates (Rabosky 2007; Alfaro et al. 2009; FitzJohn et al. 2009; Morlon et al. 2011; Stadler 2011a; Silvestro et al. 2011; Etienne et al. 2012), as these general models all contain the constant rate birth– death model as a special case. This article ends with contrasting these different method implementations (Table 1) and providing some recommendations for end users in order to facilitate model comparison across packages. SEVEN TREE LIKELIHOOD FUNCTIONS