Estimating the normal background rate of species extinction.

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

Hundreds of studies have been dedicated to estimating speciation and extinction from phylogenies of extant species. Although it has long been known that estimates of extinction rates using trees of extant organisms are often uncertain, an influential paper by Rabosky (2010) suggested that when birth rates vary continuously across the tree, estimates of the extinction fraction (i.e., extinction rate/speciation rate) will appear strongly bimodal, with a peak suggesting no extinction and a peak implying speciation and extinction rates are approaching equality. On the basis of these results, and the realistic nature of this form of rate variation, it is now generally assumed by many practitioners that extinction cannot be understood from molecular phylogenies alone. Here, we reevaluated and extended the analyses of Rabosky (2010) and come to the opposite conclusion-namely, that it is possible to estimate extinction from molecular phylogenies, even with model violations due to heritable variation in diversification rate. Note that while it may be tempting to interpret our study as advocating the application of simple birth-death models, our goal here is to show how a particular model violation does not necessitate the abandonment of an entire field: use prudent caution, but do not abandon all hope.

The topic of this thesis is the latitudinal diversity gradient: the general increase in numbers of species from high latitudes towards the equator. Although it is a well-documented and very general pattern, there is little consensus among biologists as to the causes of high tropical species richness. In Chapter 1 I give an overview of the latitudinal diversity gradient and hypotheses proposed to explain it, and outline a framework for developing and testing hypotheses. The emphasis in this thesis is on non-equilibrium hypotheses, and in particular on the idea that rates of species diversification are higher at low latitudes. In Chapter 2 I directly test the hypothesis that rates of species diversification increase towards the equator, using the phylogenetic method of sister-group comparisons. For birds and butterflies, 1 show that there does indeed appear to be an increase in rates of diversification towards lower latitudes. One possible explanation for this pattern links climatic conditions at low latitudes to faster speciation, via a causal chain which includes a higher rate of molecular evolution. In Chapter 3 I test the prediction that rates of molecular evolution are faster at low latitudes, using phylogenies reconstructed from DNA sequence data for birds. Although the results provide no evidence for a latitudinal effect on rates of cytb and ND2 evolution in birds, this chapter demonstrates a way in which further tests on a wider range of genes and taxa can be carried out as more sequence data becomes available. If rates of diversification are higher in the tropics, this may result from latitudinal gradients in life history traits which could influence rates of speciation or extinction. However, previous attempts to test for such patterns have rarely controlled for phylogenetic relationships among species, and have never controlled for geographic range overlap. In Chapter 4 I present a method for analyzing latitudinal variation in life history traits which takes both of these problems into account. For birds, this method indicates strong latitudinal variation in geographic range size and clutch size, less strong variation in body size and niche width, and no variation in the strength of sexual selection. While this does not prove that life history plays a part in generating the latitudinal diversity gradient, a robust demonstration of latitudinal variation in life history traits is an important prerequisite for any hypotheses which link life history with high tropical species richness. Speciation and extinction rates are believed to vary with species' life history and ecology. If speciation or extinction rates also vary with latitude, we should expect species with certain traits to show stronger latitudinal diversity gradients than others. We should also expect to see latitudinal variation in the macroecological structure of species assemblages. Chapters 5 and 6 confirm these expectations. In Chapter 5 I show that smaller-bodied bird species have steeper latitudinal diversity gradients than larger species. This is reflected in systematic latitudinal variation in the shape of body size frequency distributions, usually thought to be relatively consistent across regions. In Chapter 6 I show that body size - abundance relationships in the Australian marsupial fauna differ considerably between temperate and tropical subsets of the fauna. Whereas the temperate species display the typical negative relationship, the tropical species show no significant relationship. This pattern is consistent with the explanation that extinction rates vary with respect to body size, abundance and the latitude in which a species occurs. Together, the results of the analyses presented in this thesis provide evidence in favour of the non-equilibrium view that there are more species in the tropics because rates of species diversification are higher. It seems likely that this is due to latitudinal variation in environmental conditions, leading to latitudinal variation in species' life histories and the structure of species assemblages, and to latitudinal variation in rates of speciation or extinction. However, it is still difficult to judge whether it is variation in speciation rate (cradle model) or extinction rate (museum model) which is of primary importance, or if both are equally important. Further work on this question, applying the large-scale comparative methodology used here, will be necessary to progress towards a full understanding of the high species richness of the tropics.

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.

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

The Proteaceae is a large angiosperm family displaying the common pattern of uneven distribution of species among genera. Previous studies have shown that this disparity is a result of variation in diversification rates across lineages, but the reasons for this variation are still unclear. Here, we tested the impact of floral symmetry and occurrence in Mediterranean climate regions on speciation and extinction rates in the Proteaceae. A rate shift analysis was conducted on dated genus-level phylogenetic trees of the Proteaceae. Character-dependent analyses were used to test for differences in diversification rates between actinomorphic and zygomorphic lineages and between lineages located within or outside Mediterranean climate regions. The rate shift analysis identified 5-10 major diversification rate shifts in the Proteaceae tree. The character-dependent analyses showed that speciation rates, extinction rates and net diversification rates of the Proteaceae were significantly higher for lineages occurring in Mediterranean hotspots. Higher speciation and extinction rates were also detected for zygomorphic species, but net diversification rates appeared to be similar in actinomorphic and zygomorphic Proteaceae. Presence in Mediterranean hotspots favors Proteaceae diversification. In contrast with observations at the scale of angiosperms, floral symmetry is not a trait that strongly influences their evolutionary success.

Birth-death models are widely used to describe the diversification process which leads to the observed species and phylogenies. When integrated into Bayesian phylogenetic inference, birth-death models allow the joint inference of the phylogeny and the diversification parameters from molecular information. Two major classes of extensions of the birth-death process are considered in this article. The first extends the phylogenetic tree to include fossil samples alongside extant species, allowing the inference to integrate information about the past diversity. This type of inference uses either morphological or taxonomic information to place fossils in the phylogeny. The second extension models diversification rates which can vary between lineages, and is thus able to infer patterns of variation in speciation or extinction rates. In this work, we combine these two types of extension into a multi-type fossilized birth-death (MTFBD) process, which can perform the joint inference of a phylogeny including extinct and extant samples, and lineage-specific diversification and fossil sampling rates in a Bayesian framework. The MTFBD model is implemented as part of the phylogenetic inference framework BEAST2. Using simulated and empirical datasets, we demonstrate the performance and accuracy of the new model compared to a model with rate heterogeneity but using only extant samples, and compared to a model without rate variation including fossils. We demonstrate that including fossils improves the accuracy of the phylogeny and diversification rates, especially extinction rates, provided that the inference includes detailed morphological information to accurately place the fossil samples. When this information is not available however, MTFBD estimates are strongly driven by the priors and are thus no better or even worse than estimates obtained only with extant samples. With informative fossil characters, the MTFBD model provides accurate phylogenies, and precisely characterizes how speciation, extinction and fossil sampling rates vary as diversification proceeds.

Understanding the origin of diversity is a fundamental problem in biology. Evolutionary diversification has been intensely explored during the last years due to the development of molecular tools and the comparative method. However, most studies are conducted using only information from extant species. This approach probably leads to misleading conclusions, especially because of inaccuracy in the estimation of extinction rates. It is critical to integrate the information generated by extant organisms with the information obtained from the fossil record. Unfortunately, this integrative approach has been seldom performed, and thus, our understanding of the factors fueling diversification is still deficient. Ecological interactions are a main factor shaping evolutionary diversification by influencing speciation and extinction rates. Most attention has focused on the effect of antagonistic interactions on evolutionary diversification. In contrast, the role of mutualistic interactions in shaping diversification has been much less explored. In this study, by combining phylogenetic, neontological, and paleontological information, we show that a facultative mutualistic plant-animal interaction emerging from frugivory and seed dispersal has most likely contributed to the diversification of our own lineage, the primates. We compiled diet and seed dispersal ability in 381 extant and 556 extinct primates. Using well-established molecular phylogenies, we demonstrated that mutualistic extant primates had higher speciation rates, lower extinction rates, and thereby higher diversification rates than nonmutualistic ones. Similarly, mutualistic fossil primates had higher geological durations and smaller per capita rates of extinction than nonmutualistic ones. As a mechanism underlying this pattern, we found that mutualistic extinct and extant primates have significantly larger geographic ranges, which promotes diversification by hampering extinction and increasing geographic speciation. All these outcomes together strongly suggest that the establishment of a facultative mutualism with plants has greatly benefited primate evolution and fueled its taxonomic diversification.

According to when they attained high diversity, major taxa of marine animals have been clustered into three groups, the Cambrian, Paleozoic, and Modern Faunas. Because the Cambrian Fauna was a relatively minor component of the total fauna after mid-Ordovician time, the Phanerozoic history of marine animal diversity is largely a matter of the fates of the Paleozoic and Modern Faunas. The fact that most late Cenozoic genera belong to taxa that have been radiating for tens of millions of years indicates that the post-Paleozoic increase in diversity indicated by fossil data is real, rather than an artifact of improvement of the fossil record toward the present.Assuming that ecological crowding produced the so-called Paleozoic plateau for family diversity, various workers have used the logistic equation of ecology to model marine animal diversification as damped exponential increase. Several lines of evidence indicate that this procedure is inappropriate. A plot of the diversity of marine animal genera through time provides better resolution than the plot for families and has a more jagged appearance. Generic diversity generally increased rapidly during the Paleozoic, except when set back by pulses of mass extinction. In fact, an analysis of the history of the Paleozoic Fauna during the Paleozoic Era reveals no general correlation between rate of increase for this fauna and total marine animal diversity. Furthermore, realistically scaled logistic simulations do not mimic the empirical pattern. In addition, it is difficult to imagine how some fixed limit for diversity could have persisted throughout the Paleozoic Era, when the ecological structure of the marine ecosystem was constantly changing. More fundamentally, the basic idea that competition can set a limit for marine animal diversity is incompatible with basic tenets of marine ecology: predation, disturbance, and vagaries of recruitment determine local population sizes for most marine species. Sparseness of predators probably played a larger role than weak competition in elevating rates of diversification during the initial (Ordovician) radiation of marine animals and during recoveries from mass extinctions. A plot of diversification against total diversity for these intervals yields a band of points above the one representing background intervals, and yet this band also displays no significant trend (if the two earliest intervals of the initial Ordovician are excluded as times of exceptional evolutionary innovation). Thus, a distinctive structure characterized the marine ecosystem during intervals of evolutionary radiation—one in which rates of diversification were exceptionally high and yet increases in diversity did not depress rates of diversification.Particular marine taxa exhibit background rates of origination and extinction that rank similarly when compared with those of other taxa. Rates are correlated in this way because certain heritable traits influence probability of speciation and probability of extinction in similar ways. Background rates of origination and extinction were depressed during the late Paleozoic ice age for all major marine invertebrate taxa, but remained correlated. Also, taxa with relatively high background rates of extinction experienced exceptionally heavy losses during biotic crises because background rates of extinction were intensified in a multiplicative manner; decimation of a large group of taxa of this kind in the two Permian mass extinctions established their collective identity as the Paleozoic Fauna.Characteristic rates of origination and extinction for major taxa persisted from Paleozoic into post-Paleozoic time. Because of the causal linkage between rates of origination and extinction, pulses of extinction tended to drag down overall rates of origination as well as overall rates of extinction by preferentially eliminating higher taxa having relatively high background rates of extinction. This extinction/origination ratchet depressed turnover rates for the residual Paleozoic Fauna during the Mesozoic Era. A decline of this fauna's extinction rate to approximately that of the Modern Fauna accounts for the nearly equal fractional losses experienced by the two faunas in the terminal Cretaceous mass extinction.Viewed arithmetically, the fossil record indicates slow diversification for the Modern Fauna during Paleozoic time, followed by much more rapid expansion during Mesozoic and Cenozoic time. When viewed more appropriately as depicting geometric—or exponential—increase, however, the empirical pattern exhibits no fundamental secular change: the background rate of increase for the Modern Fauna—the fauna that dominated post-Paleozoic marine diversity—simply persisted, reflecting the intrinsic origination and extinction rates of constituent taxa. Persistence of this overall background rate supports other evidence that the empirical record of diversification for marine animal life since Paleozoic time represents actual exponential increase. This enduring rate makes it unnecessary to invoke environmental change to explain the post-Paleozoic increase of marine diversity.Because of the resilience of intrinsic rates, an empirically based simulation that entails intervals of exponential increase for the Paleozoic and Modern Faunas, punctuated by mass extinctions, yields a pattern that is remarkably similar to the empirical pattern. It follows that marine animal genera and species will continue to diversify exponentially long into the future, barring disruption of the marine ecosystem by human-induced or natural environmental changes.

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.

The taxonomic evolution of Jurassic and Cretaceous calcareous nannofossil species is described using the following indices: species diversity, rate of speciation, rate of extinction, rate of diversification, rate of turnover, survivorship, and species accretion. The Jurassic prior to the late Oxfordian is characterized by positive diversification rates, that is, rates of speciation exceeded rates of extinction. Highest rates of diversification occurred in the late Lias and early Oxfordian. During the generally regressive latest Jurassic, diversification rates remained low and rates of extinctions exceed rates of speciation. In the early Cretaceous, rates of diversification are positive and peak in the early Valanginian, early Aptian, and middle Albian, after which time rates of extinction generally exceed rates of speciation. Such peaks in rate of evolution coincide with times of increased accumulation of organic carbon in the ocean (“anoxic events”). Peaks in rates of extinction result in very high rates of turnover during times of major regressions, in particular, in the Tithonian and Maastrichtian. Survivorship analyses for three datum planes (74.5, 144, and 160 Ma) show relatively constant extinction rates with some stepping in the older part; they are best explained by a temporally fluctuating abiotic environment causing changes in the probability of extinction. Species accretion curves are also relatively linear with some indication of changing rates of speciation. The coincidences of major changes in evolutionary rates with major paleoceanographic events are indicative of a predominantly abiotic control of nannoplankton evolution. Relationships of evolutionary rates of calcareous nannoplankton with deep ocean ventilation, sea level, and ocean fertility indicates that global tectonic processes are the ultimate causes of evolutionary change.

Corrigendum for Rojas etal. (2018) DOI: 10.1111/ele.12911.

Can extinction rates be estimated without fossils?

Author SummaryWhy are there more species in the tropics? This question has fascinated ecologists and evolutionary biologists for decades, generating hundreds of hypotheses, yet basic questions remain: Are rates of speciation higher in the tropics? Are rates of extinction higher in temperate regions? Do the tropics act as a source of diversity for temperate regions? We estimated rates of speciation, extinction, and range expansion associated with mammals living in tropical and temperate regions, using an almost complete mammalian phylogeny. Contrary to what has been suggested before for this class of vertebrates, we found that diversification rates are strikingly consistent with diversity patterns, with latitudinal peaks in species richness being associated with high speciation rates, low extinction rates, or both, depending on the mammalian order (rodents, bats, primates, etc.). We also found evidence for an asymmetry in range expansion, with more expansion “out of” than “into” the tropics. Taken together, these results suggest that tropical regions are not only a reservoir of biodiversity, but also the main place where biodiversity is generated.

Biodiversity arises from the balance between speciation and extinction. Fossils record the origins and disappearance of organisms, and the branching patterns of molecular phylogenies allow estimation of speciation and extinction rates, but the patterns of diversification are frequently incongruent between these two data sources. I tested two hypotheses about the diversification of primates based on ∼600 fossil species and 90% complete phylogenies of living species: (1) diversification rates increased through time; (2) a significant extinction event occurred in the Oligocene. Consistent with the first hypothesis, analyses of phylogenies supported increasing speciation rates and negligible extinction rates. In contrast, fossils showed that while speciation rates increased, speciation and extinction rates tended to be nearly equal, resulting in zero net diversification. Partially supporting the second hypothesis, the fossil data recorded a clear pattern of diversity decline in the Oligocene, although diversification rates were near zero. The phylogeny supported increased extinction ∼34 Ma, but also elevated extinction ∼10 Ma, coinciding with diversity declines in some fossil clades. The results demonstrated that estimates of speciation and extinction ignoring fossils are insufficient to infer diversification and information on extinct lineages should be incorporated into phylogenetic analyses.