Likelihood Inference of Non-Constant Diversification Rates with Incomplete Taxon Sampling

Large-scale phylogenies provide a valuable source to study background diversification rates and investigate if the rates have changed over time. Unfortunately most large-scale, dated phylogenies are sparsely sampled (fewer than 5% of the described species) and taxon sampling is not uniform. Instead, taxa are frequently sampled to obtain at least one representative per subgroup (e.g. family) and thus to maximize diversity (diversified sampling). So far, such complications have been ignored, potentially biasing the conclusions that have been reached. In this study I derive the likelihood of a birth-death process with non-constant (time-dependent) diversification rates and diversified taxon sampling. Using simulations I test if the true parameters and the sampling method can be recovered when the trees are small or medium sized (fewer than 200 taxa). The results show that the diversification rates can be inferred and the estimates are unbiased for large trees but are biased for small trees (fewer than 50 taxa). Furthermore, model selection by means of Akaike''s Information Criterion favors the true model if the true rates differ sufficiently from alternative models (e.g. the birth-death model is recovered if the extinction rate is large and compared to a pure-birth model). Finally, I applied six different diversification rate models – ranging from a constant-rate pure birth process to a decreasing speciation rate birth-death process but excluding any rate shift models – on three large-scale empirical phylogenies (ants, mammals and snakes with respectively 149, 164 and 41 sampled species). All three phylogenies were constructed by diversified taxon sampling, as stated by the authors. However only the snake phylogeny supported diversified taxon sampling. Moreover, a parametric bootstrap test revealed that none of the tested models provided a good fit to the observed data. The model assumptions, such as homogeneous rates across species or no rate shifts, appear to be violated.     

Phylogenetically patterned speciation rates and extinction risks change the loss of evolutionary history during extinctions

If we are to plan conservation strategies that minimize the loss of evolutionary history through human-caused extinctions, we must understand how this loss is related to phylogenetic patterns in current extinction risks and past speciation rates. Nee & May (1997, Science 278, 692-694) showed that for a randomly evolving clade (i) a single round of random extinction removed relatively little evolutionary history, and (ii) extinction management (choosing which taxa to sacrifice) offered only marginal improvement. However, both speciation rates and extinction risks vary across lineages within real clades. We simulated evolutionary trees with phylogenetically patterned speciation rates and extinction risks (closely related lineages having similar rates and risks) and then subjected them to several biologically informed models of extinction. Increasing speciation rate variation increases the extinction-management pay-off. When extinction risks vary among lineages but are uncorrelated with speciation rates, extinction removes more history (compared with random trees), but the difference is small. When extinction risks vary and are correlated with speciation rates, history loss can dramatically increase (negative correlation) or decrease (positive correlation) with speciation rate variation. The loss of evolutionary history via human-caused extinctions may therefore be more severe, yet more manageable, than first suggested.     

Evolutionary distance estimation under heterogeneous substitution pattern among lineages

Most of the sophisticated methods to estimate evolutionary divergence between DNA sequences assume that the two sequences have evolved with the same pattern of nucleotide substitution after their divergence from their most recent common ancestor (homogeneity assumption). If this assumption is violated, the evolutionary distance estimated will be biased, which may result in biased estimates of divergence times and substitution rates, and may lead to erroneous branching patterns in the inferred phylogenies. Here we present a simple modification for existing distance estimation methods to relax the assumption of the substitution pattern homogeneity among lineages when analyzing DNA and protein sequences. Results from computer simulations and empirical data analyses for human and mouse genes are presented to demonstrate that the proposed modification reduces the estimation bias considerably and that the modified method performs much better than the LogDet methods, which do not require the homogeneity assumption in estimating the number of substitutions per site. We also discuss the relationship of the substitution and mutation rate estimates when the substitution pattern is not the same in the lineages leading to the two sequences compared.     

Fossil biogeography: a new model to infer dispersal,extinction and sampling from palaeontological data

Methods in historical biogeography have revolutionized our ability to infer the evolution of ancestral geographical ranges from phylogenies of extant taxa, the rates of dispersals, and biotic connectivity among areas. However, extant taxa are likely to provide limited and potentially biased information about past biogeographic processes, due to extinction, asymmetrical dispersals and variable connectivity among areas. Fossil data hold considerable information about past distribution of lineages, but suffer from largely incomplete sampling. Here we present a new dispersal–extinction–sampling (DES) model, which estimates biogeographic parameters using fossil occurrences instead of phylogenetic trees. The model estimates dispersal and extinction rates while explicitly accounting for the incompleteness of the fossil record. Rates can vary between areas and through time, thus providing the opportunity to assess complex scenarios of biogeographic evolution. We implement the DES model in a Bayesian framework and demonstrate through simulations that it can accurately infer all the relevant parameters. We demonstrate the use of our model by analysing the Cenozoic fossil record of land plants and inferring dispersal and extinction rates across Eurasia and North America. Our results show that biogeographic range evolution is not a time-homogeneous process, as assumed in most phylogenetic analyses, but varies through time and between areas. In our empirical assessment, this is shown by the striking predominance of plant dispersals from Eurasia into North America during the Eocene climatic cooling, followed by a shift in the opposite direction, and finally, a balance in biotic interchange since the middle Miocene. We conclude by discussing the potential of fossil-based analyses to test biogeographic hypotheses and improve phylogenetic methods in historical biogeography.     

EXTINCTION RATES SHOULD NOT BE ESTIMATED FROM MOLECULAR PHYLOGENIES

Molecular phylogenies contain information about the tempo and mode of species diversification through time. Because extinction leaves a characteristic signature in the shape of molecular phylogenetic trees, many studies have used data from extant taxa only to infer extinction rates. This is a promising approach for the large number of taxa for which extinction rates cannot be estimated from the fossil record. Here, I explore the consequences of violating a common assumption made by studies of extinction from phylogenetic data. I show that when diversification rates vary among lineages, simple estimators based on the birth–death process are unable to recover true extinction rates. This is problematic for phylogenetic trees with complete taxon sampling as well as for the simpler case of clades with known age and species richness. Given the ubiquity of variation in diversification rates among lineages and clades, these results suggest that extinction rates should not be estimated in the absence of fossil data.     

Effect of sampling strategy on estimation of fine‐scale spatial genetic structure in Androsace tapete (Primulaceae), an alpine plant endemic to Qinghai‐Tibetan Plateau

Abstract The fine‐scale spatial genetic structure (SGS) of alpine plants is receiving increasing attention, from which seed and pollen dispersal can be inferred. However, estimation of SGS may depend strongly on the sampling strategy, including the sample size and spatial sampling scheme. Here, we examined the effects of sample size and three spatial schemes, simple‐random, line‐transect, and random‐cluster sampling, on the estimation of SGS in Androsace tapete, an alpine cushion plant endemic to Qinghai‐Tibetan Plateau. Using both real data and simulated data of dominant molecular markers, we show that: (i) SGS is highly sensitive to sample strategy especially when the sample size is small (e.g., below 100); (ii) the commonly used SGS parameter (the intercept of the autocorrelogram) is more susceptible to sample error than a newly developed Sp statistic; and (iii) the random‐cluster scheme is susceptible to obvious bias in parameter estimation even when the sample size is relatively large (e.g., above 200). Overall, the line‐transect scheme is recommendable, in that it performs slightly better than the simple‐random scheme in parameter estimation and is more efficient to encompass broad spatial scales. The consistency between simulated data and real data implies that these findings might hold true in other alpine plants and more species should be examined in future work.     

Testing metapopulation concepts: effects of patch characteristics and neighborhood occupancy on the dynamics of an endangered lagomorph

Metapopulation ecology is a field that is richer in theory than in empirical results. Many existing empirical studies use an incidence function approach based on spatial patterns and key assumptions about extinction and colonization rates. Here we recast these assumptions as hypotheses to be tested using 18 years of historic detection survey data combined with four years of data from a new monitoring program for the Lower Keys marsh rabbit. We developed a new model to estimate probabilities of local extinction and colonization in the presence of nondetection, while accounting for estimated occupancy levels of neighboring patches. We used model selection to identify important drivers of population turnover and estimate the effective neighborhood size for this system. Several key relationships related to patch size and isolation that are often assumed in metapopulation models were supported: patch size was negatively related to the probability of extinction and positively related to colonization, and estimated occupancy of neighboring patches was positively related to colonization and negatively related to extinction probabilities. This latter relationship suggested the existence of rescue effects. In our study system, we inferred that coastal patches experienced higher probabilities of extinction and colonization than interior patches. Interior patches exhibited higher occupancy probabilities and may serve as refugia, permitting colonization of coastal patches following disturbances such as hurricanes and storm surges. Our modeling approach should be useful for incorporating neighbor occupancy into future metapopulation analyses and in dealing with other historic occupancy surveys that may not include the recommended levels of sampling replication.     

Taxon sampling effects on the quantification and comparison of community phylogenetic diversity

Ecologists are increasingly making use of molecular phylogenies, especially in the fields of community ecology and conservation. However, these phylogenies are often used without full appreciation of their underlying assumptions and uncertainties. A frequent practice in ecological studies is inferring a phylogeny with molecular data from taxa only within the community of interest. These “inferred community phylogenies” are inherently biased in their taxon sampling. Despite the importance of comprehensive sampling in constructing phylogenies, the implications of using inferred community phylogenies in ecological studies have not been examined. Here, we evaluate how taxon sampling affects the quantification and comparison of community phylogenetic diversity using both simulated and empirical data sets. We demonstrate that inferred community trees greatly underestimate phylogenetic diversity and that the probability of incorrectly ranking community diversity can reach up to 25%, depending on the dating methods employed. We argue that to reach reliable conclusions, ecological studies must improve their taxon sampling and generate the best phylogeny possible.     

The quality of the fossil record and the accuracy of phylogenetic inferences about sampling and diversity

Because phylogenies can be estimated without stratigraphic data and because estimated phylogenies also infer gaps in sampling, some workers have used phylogeny estimates as templates for evaluating sampling from the fossil record and for "correcting" historical diversity patterns. However, it is not known how sampling intensity (the probability of sampling taxa per unit time) and completeness (the proportion of taxa sampled) affect the accuracy of phylogenetic inferences, nor how phylogenetically inferred estimates of sampling and diversity respond to inaccurate estimates of phylogeny. Both issues are addressed with a series of simulations using simple models of character evolution, varying speciation patterns, and various rates of speciation, extinction, character change, and preservation. Parsimony estimates of simulated phylogenies become less accurate as sampling decreases, and inaccurate trees chronically underestimate sampling. Biotic factors such as rates of morphologic change and extinction both affect the accuracy of phylogenetic estimates and thus affect estimated gaps in sampling, indicating that differences in implied sampling need not reflect actual differences in sampling. Errors in inferred diversity are concentrated early in the history of a clade. This, coupled with failure to account for true extinction times (i.e., the Signor-Lipps effect), inflates relative diversity levels early in clade histories. Because factors other than differences in sampling predict differences in the numbers of gaps implied by phylogeny estimates, inferred phylogenies can be misleading templates for evaluating sampling or historical diversity patterns.     

Trees of unusual size: biased inference of early bursts from large molecular phylogenies

An early burst of speciation followed by a subsequent slowdown in the rate of diversification is commonly inferred from molecular phylogenies. This pattern is consistent with some verbal theory of ecological opportunity and adaptive radiations. One often-overlooked source of bias in these studies is that of sampling at the level of whole clades, as researchers tend to choose large, speciose clades to study. In this paper, we investigate the performance of common methods across the distribution of clade sizes that can be generated by a constant-rate birth-death process. Clades which are larger than expected for a given constant-rate branching process tend to show a pattern of an early burst even when both speciation and extinction rates are constant through time. All methods evaluated were susceptible to detecting this false signature when extinction was low. Under moderate extinction, both the [Formula: see text]-statistic and diversity-dependent models did not detect such a slowdown but only because the signature of a slowdown was masked by subsequent extinction. Some models which estimate time-varying speciation rates are able to detect early bursts under higher extinction rates, but are extremely prone to sampling bias. We suggest that examining clades in isolation may result in spurious inferences that rates of diversification have changed through time.     

Does migration promote or inhibit diversification? A case study involving the dominant radiation of temperate Southern Hemisphere freshwater fishes

Although theory predicts that dispersal has a pivotal influence on speciation and extinction rates, it can have contradictory effects on each, such that empirical quantification of its role is required. In many studies, dispersal reduction appears to promote diversification, although some comparisons of migratory and nonmigratory species suggest otherwise. We tested for a relationship between migratory status and diversification rate within the dominant radiation of temperate Southern Hemisphere freshwater fishes, the Galaxiidae. We reconstructed a molecular phylogeny comprising >95% of extant taxa, and applied State-dependent Speciation Extinction models to estimate speciation, extinction, and diversification rates. In contrast to some previous studies, we revealed higher diversification rates in nonmigratory lineages. The reduced gene flow experienced by nonmigratory galaxiids appears to have increased diversification under conditions of allopatry or local adaptation. Migratory galaxiid lineages, by contrast, are genetically homogeneous within landmasses, but may also be rarely able to diversify by colonizing other landmasses in the temperate Southern Hemisphere. Apparent contradictions among studies of dispersal-diversification relationships may be explained by the spatial context of study systems relative to species dispersal abilities, by means of the “intermediate dispersal” model; the accurate quantification of dispersal abilities will aid in the understanding of these proposed interactions.     

Understanding angiosperm diversification using small and large phylogenetic trees

How will the emerging possibility of inferring ultra-large phylogenies influence our ability to identify shifts in diversification rate? For several large angiosperm clades (Angiospermae, Monocotyledonae, Orchidaceae, Poaceae, Eudicotyledonae, Fabaceae, and Asteraceae), we explore this issue by contrasting two approaches: (1) using small backbone trees with an inferred number of extant species assigned to each terminal clade and (2) using a mega-phylogeny of 55473 seed plant species represented in GenBank. The mega-phylogeny approach assumes that the sample of species in GenBank is at least roughly proportional to the actual species diversity of different lineages, as appears to be the case for many major angiosperm lineages. Using both approaches, we found that diversification rate shifts are not directly associated with the major named clades examined here, with the sole exception of Fabaceae in the GenBank mega-phylogeny. These agreements are encouraging and may support a generality about angiosperm evolution: major shifts in diversification may not be directly associated with major named clades, but rather with clades that are nested not far within these groups. An alternative explanation is that there have been increased extinction rates in early-diverging lineages within these clades. Based on our mega-phylogeny, the shifts in diversification appear to be distributed quite evenly throughout the angiosperms. Mega-phylogenetic studies of diversification hold great promise for revealing new patterns, but we will need to focus more attention on properly specifying null expectation.     

Accounting for Sampling Error When Inferring Population Synchrony from Time-Series Data: A Bayesian State-Space Modelling Approach with Applications

Background

Data collected to inform time variations in natural population size are tainted by sampling error. Ignoring sampling error in population dynamics models induces bias in parameter estimators, e.g., density-dependence. In particular, when sampling errors are independent among populations, the classical estimator of the synchrony strength (zero-lag correlation) is biased downward. However, this bias is rarely taken into account in synchrony studies although it may lead to overemphasizing the role of intrinsic factors (e.g., dispersal) with respect to extrinsic factors (the Moran effect) in generating population synchrony as well as to underestimating the extinction risk of a metapopulation.

Methodology/Principal findings

The aim of this paper was first to illustrate the extent of the bias that can be encountered in empirical studies when sampling error is neglected. Second, we presented a space-state modelling approach that explicitly accounts for sampling error when quantifying population synchrony. Third, we exemplify our approach with datasets for which sampling variance (i) has been previously estimated, and (ii) has to be jointly estimated with population synchrony. Finally, we compared our results to those of a standard approach neglecting sampling variance. We showed that ignoring sampling variance can mask a synchrony pattern whatever its true value and that the common practice of averaging few replicates of population size estimates poorly performed at decreasing the bias of the classical estimator of the synchrony strength.

Conclusion/Significance

The state-space model used in this study provides a flexible way of accurately quantifying the strength of synchrony patterns from most population size data encountered in field studies, including over-dispersed count data. We provided a user-friendly R-program and a tutorial example to encourage further studies aiming at quantifying the strength of population synchrony to account for uncertainty in population size estimates.     

Effects of sample size on estimates of population growth rates calculated with matrix models

Background

Matrix models are widely used to study the dynamics and demography of populations. An important but overlooked issue is how the number of individuals sampled influences estimates of the population growth rate (λ) calculated with matrix models. Even unbiased estimates of vital rates do not ensure unbiased estimates of λ–Jensen''s Inequality implies that even when the estimates of the vital rates are accurate, small sample sizes lead to biased estimates of λ due to increased sampling variance. We investigated if sampling variability and the distribution of sampling effort among size classes lead to biases in estimates of λ.

Methodology/Principal Findings

Using data from a long-term field study of plant demography, we simulated the effects of sampling variance by drawing vital rates and calculating λ for increasingly larger populations drawn from a total population of 3842 plants. We then compared these estimates of λ with those based on the entire population and calculated the resulting bias. Finally, we conducted a review of the literature to determine the sample sizes typically used when parameterizing matrix models used to study plant demography.

Conclusions/Significance

We found significant bias at small sample sizes when survival was low (survival = 0.5), and that sampling with a more-realistic inverse J-shaped population structure exacerbated this bias. However our simulations also demonstrate that these biases rapidly become negligible with increasing sample sizes or as survival increases. For many of the sample sizes used in demographic studies, matrix models are probably robust to the biases resulting from sampling variance of vital rates. However, this conclusion may depend on the structure of populations or the distribution of sampling effort in ways that are unexplored. We suggest more intensive sampling of populations when individual survival is low and greater sampling of stages with high elasticities.     

Phylogenetically clustered extinction risks do not substantially prune the Tree of Life

Anthropogenic activities have increased the rate of biological extinction many-fold. Recent empirical studies suggest that projected extinction may lead to extensive loss to the Tree of Life, much more than if extinction were random. One suggested cause is that extinction risk is heritable (phylogenetically patterned), such that entire higher groups will be lost. We show here with simulation that phylogenetically clustered extinction risks are necessary but not sufficient for the extensive loss of phylogenetic diversity (PD) compared to random extinction. We simulated Yule trees and evolved extinction risks at various levels of heritability (measured using Pagel's λ). At most levels of heritability (λ in range of 0 to 10), mean values of extinction risk (range 0.25 to 0.75), tree sizes (64 to 128 tips), tree balance and temporal heterogeneity of diversification rates (Yule and coalescent trees), extinction risks do not substantially increase the loss of PD in these trees when compared to random extinction. The maximum loss of PD (20% above random) was only associated with the combination of extremely excessive values of phylogenetic signal, high mean species' extinction probabilities, and extreme (coalescent) tree shapes. Interestingly, we also observed a decline in the rate of increase in the loss of PD at high phylogenetic clustering (λ → 10) of extinction risks. Our results suggest that the interplay between various aspects of tree shape and a predisposition of higher extinction risks in species-poor clades is required to explain the substantial pruning of the Tree of Life.     

Phylogeny of Helicobacter felis sp. nov., Helicobacter mustelae, and related bacteria.

Strain CS1T (T = type strain) is a gram-negative, microaerophilic, urease-positive, spiral-shaped bacterium that was isolated from the gastric mucosa of a cat. Additional strains which possessed biochemical and ultrastructural characteristics similar to those of strain CS1T were isolated from the gastric mucosa of cats and dogs. The guanine-plus-cytosine content of the DNA of strain CS1T was 42.5 mol%. The 16S rRNA sequences of strain CS1T, strain DS3 (a spiral-shaped isolate from a dog), and Helicobacter mustelae were determined by direct RNA sequencing, using a modified Sanger method. These sequences were compared with the 16S rRNA sequences of Helicobacter pylori, "Flexispira rappini," Wolinella succinogenes, and 11 species of campylobacters. A dendrogram was constructed based upon sequence similarities. Strains CS1T and DS3 were very closely related (level of similarity, 99.3%). Two major phylogenetic groups were formed; one group consisted of strains CS1T and DS3, H. mustelae, H. pylori, "F. rappini," and W. succinogenes, and the other group contained the true campylobacters. The average level of similarity between members of these two groups was 84.9%. Within the first group, strains CS1T and DS3, H. pylori, and H. mustelae formed a cluster of organisms with an interspecies similarity level of 94.5%. The phylogenetic positions of W. succinogenes and "F. rappini" were just outside this cluster. On the basis of the results of this study, we believe that strains CS1T (= ATCC 49179T) and DS3 represent a new species of the genus Helicobacter, for which we propose the name Helicobacter felis.     

Prolonging the past counteracts the pull of the present: protracted speciation can explain observed slowdowns in diversification

Phylogenetic trees show a remarkable slowdown in the increase of number of lineages towards the present, a phenomenon which cannot be explained by the standard birth-death model of diversification with constant speciation and extinction rates. The birth-death model instead predicts a constant or accelerating increase in the number of lineages, which has been called the pull of the present. The observed slowdown has been attributed to nonconstancy of the speciation and extinction rates due to some form of diversity dependence (i.e., species-level density dependence), but the mechanisms underlying this are still unclear. Here, we propose an alternative explanation based on the simple concept that speciation takes time to complete. We show that this idea of "protracted" speciation can be incorporated in the standard birth-death model of diversification. The protracted birth-death model predicts a realistic slowdown in the rate of increase of number of lineages in the phylogeny and provides a compelling fit to four bird phylogenies with realistic parameter values. Thus, the effect of recognizing the generally accepted fact that speciation is not an instantaneous event is significant; even if it cannot account for all the observed patterns, it certainly contributes substantially and should therefore be incorporated into future studies.     

Continental faunal exchange and the asymmetrical radiation of carnivores

Lineages arriving on islands may undergo explosive evolutionary radiations owing to the wealth of ecological opportunities. Although studies on insular taxa have improved our understanding of macroevolutionary phenomena, we know little about the macroevolutionary dynamics of continental exchanges. Here we study the evolution of eight Carnivora families that have migrated across the Northern Hemisphere to investigate if continental invasions also result in explosive diversification dynamics. We used a Bayesian approach to estimate speciation and extinction rates from a substantial dataset of fossil occurrences while accounting for the incompleteness of the fossil record. Our analyses revealed a strongly asymmetrical pattern in which North American lineages invading Eurasia underwent explosive radiations, whereas lineages invading North America maintained uniform diversification dynamics. These invasions into Eurasia were characterized by high rates of speciation and extinction. The radiation of the arriving lineages in Eurasia coincide with the decline of established lineages or phases of climate change, suggesting differences in the ecological settings between the continents may be responsible for the disparity in diversification dynamics. These results reveal long-term outcomes of biological invasions and show that the importance of explosive radiations in shaping diversity extends beyond insular systems and have significant impact at continental scales.     

Did hard substrate taxa diversify prior to the Great Ordovician Biodiversification Event?

The Great Ordovician Biodiversification Event (GOBE) refers to one of the greatest increases in biodiversity during the Phanerozoic. Recent studies have shown that this taxonomic increase can be attributed to elevated origination rates around the Dapingian–Darriwilian boundary in the Middle Ordovician, while extinction rates stayed relatively constant throughout the Ordovician. Even though this global pattern of origination and extinction appears similar across diverse groups and geographical areas, earlier studies suggested that hard substrate taxa may have diversified prior to the GOBE, during the Early Ordovician. Here, we quantify Ordovician diversification dynamics of hard substrate taxa while simultaneously accounting for temporally varying sampling probabilities. Diversification rates of hard substrate taxa, both as a whole and when analysed as separate groups, appear to be very similar to those of free-living benthic taxa. The observation that the diversification dynamics of many different taxonomic and ecological groups show the same temporal pattern, suggests a common cause of Ordovician diversification dynamics.     

EXPLOSIVE EVOLUTIONARY RADIATIONS: DECREASING SPECIATION OR INCREASING EXTINCTION THROUGH TIME?

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.