Recent diversification rates in North American tiger beetles estimated from a dated mtDNA phylogenetic tree

Species-level phylogenies derived from DNA sequence data provide a tool for estimating diversification rates and how these rates change over time, but to date there have been few empirical studies, particularly on insect groups. We use a densely sampled phylogenetic tree based on mitochondrial DNA to investigate diversification rates in the North American tiger beetles (genus Cicindela). Using node ages estimated from sequence data and calibrated by biogeographical evidence, we estimate an average per-lineage diversification rate of at least 0.22 +/- 0.08 species/Myr over the time interval since the most recent colonization that led to a radiation within the continent. In addition, we find evidence for a weak, recent increase in the net diversification rate. This is more consistent with a late Pleistocene increase in the speciation rate than with a constant rate of background extinction, but the results are sensitive to the dating method and taxon sampling. We discuss practical limitations to phylogenetic studies of diversification rates.     

Estimating death rates from transect counts

Abstract.

• 1 The time course of abundance of adult insects emerging in discrete generations is modelled, assuming the absence of net migration and a constant death rate. The time till emergence is assumed to be logistically distributed.
• 2 The qualitative features of the model depend on one dimensionless parameter only, namely the product of the death rate and a dispersion measure for the symmetric emergence distribution.
• 3 The model is fitted to data on the abundance of five butterfly species. The tit is excellent; moreover, the estimated death rates are well within the range given in the literature (mostly 0.1–0.2 day^-1). Death rates are generally obtained by mark-recapture methods. The present model gives the opportunity to evaluate some assumptions of these methods.

     

Estimating recombination rates from population-genetic data

Obtaining an accurate measure of how recombination rates vary across the genome has implications for understanding the molecular basis of recombination, its evolutionary significance and the distribution of linkage disequilibrium in natural populations. Although measuring the recombination rate is experimentally challenging, good estimates can be obtained by applying population-genetic methods to DNA sequences taken from natural populations. Statistical methods are now providing insights into the nature and scale of variation in the recombination rate, particularly in humans. Such knowledge will become increasingly important owing to the growing use of population-genetic methods in biomedical research.     

Estimating hypermutation rates from clonal tree data

To understand the mechanisms underlying the varying patterns of mutations that occur during immune and autoimmune responses, estimates of the somatic hypermutation rate are critical. However, despite its significance, precise estimates of the mutation rate do not currently exist. Microdissection studies of mutating B cell clones provide an opportunity to measure this rate more accurately than previously possible. Each microdissection provides a number of clonally related sequences that, through the analysis of shared mutations, can be genealogically related to each other. The shape of these clonal trees is influenced by many processes, including the hypermutation rate. We have developed two different methods to estimate the mutation rate based on these data. These methods are applied to two sets of experimental data, one from an autoimmune response and one from the antihapten response to (4-hydroxy-3-nitrophenyl)acetyl (NP). Comparable mutation rates are estimated for both responses, 0.7-0.9 x 10(-3) and 0.9-1.1 x 10(-3) bp(-1) division(-1) for the autoimmune and NP responses, respectively. In addition to comparing the results of the two procedures, we investigate the effect on our estimate of assumptions, such as the fraction of lethal mutations.     

Estimating surface growth rates from changes in curvature

The shape of a biological surface may be regarded as an observable. Here a method is given for deriving growth parameters from the change in shape of such a surface. Isotropy is assumed, and implies a conformal relationship between initial and final surfaces. One further assumption is necessary to specify the growth regime: in the case of radially symmetric surfaces, this is that the process is similarly symmetric; in the general case the assumption is that the Dirichlet integral of scale factors is miminized.     

Estimating population growth rates from stochastic Leslie matrices

Stochastic versions of exponential growth models predict that even when r or λ values calculated from mean vital statistics indicate exponential growth, most of the individual populations may become extinct. Several recent papers have considered this problem and some misunderstanding has arisen due to the difference between mathematical expectation of population size and most likely course of population growth. We replicated Boyce's (1977, 1979) simulations of population growth with age structure and a single randomly varying vital statistic, and reconciled some of these differences. Mean number can be projected using the dominant eigenvalue of the mean Leslie matrix, but the modal number may be considerably lower. We compared several measures of the rate of growth of the geometric mean or median of numbers and conclude that Tuljapurkar's α is an acceptable measure.     

Estimating recombination rates from population genetic data.

We introduce a new method for estimating recombination rates from population genetic data. The method uses a computationally intensive statistical procedure (importance sampling) to calculate the likelihood under a coalescent-based model. Detailed comparisons of the new algorithm with two existing methods (the importance sampling method of Griffiths and Marjoram and the MCMC method of Kuhner and colleagues) show it to be substantially more efficient. (The improvement over the existing importance sampling scheme is typically by four orders of magnitude.) The existing approaches not infrequently led to misleading results on the problems we investigated. We also performed a simulation study to look at the properties of the maximum-likelihood estimator of the recombination rate and its robustness to misspecification of the demographic model.     

Estimating growth and mortality rates from size data

Summary A method is presented for estimating rates of individual growth and population mortality utilizing average individual size at two times during a year. The model assumes a constant rate of mortality, Brody-Bertalanffy growth, a stationary age distribution, and recruitment confined to one month each year. A hypothetical example is presented to show the interrelationships of the growth and mortality constants, size at recruitment, asymptotic size and average individual size. Three examples are presented using data from the literature: Flathead sole (Hippoglossoides elassodon), a sea urchin(Echinus esculentus), and the crown-of-thorns starfish(Acanthaster planci). The method appears to be a means of obtaining reasonable approximations of growth and mortality rates for a variety of organisms.     

Global diversification rates of passerine birds

The distribution of species richness in families of passerine birds suggests that the net rate of diversification was significantly higher than average in as many as 7 out of 47 families. However, the absence of excess species richness among the 106 tribes within these families indicates that these high rates were transient, perhaps associated in some cases with tectonic movements or dispersal events that extended geographical ranges. Thus, large clade size among passerine birds need not represent intrinsic key innovations that influence the rate of diversification. Approximately 17 families and 30 tribes have too few species relative to other passerine taxa. Many of these are ecologically or geographically marginal, being especially overrepresented in the Australasian region. Observed intervals between lineage splitting suggest that extinction has occurred ca. 90% as frequently as speciation (waiting times of 1.03 and 0.93 Myr) and that the 47 modern families comprising 5712 species descended from approximately 430 passerine lineages extant 24 Myr ago. Speciation and extinction rates among small, marginal families might be 1-2 orders of magnitude lower.     

Incorporating information from length-mutational events into phylogenetic analysis

With the growing number of phylogenetic studies that use length variable DNA sequences, incorporating information from length-mutational events into phylogenetic analysis is becoming increasingly important. A new method, modified complex indel coding is described that aims at maximizing the phylogenetic information retained from unambiguously aligned sequence regions or regions where the principal relative position of gaps to one another can be safely established. An algorithm is described that allows application of the method to all theoretically possible gap-nucleotide patterns. A platform-independent computer program is introduced that automates the new method as well as several previously published coding schemes. Differences to previously published indel coding approaches as well as to the integration of ambiguously aligned regions into phylogenetic analysis are discussed.     

Ecology predicts large-scale patterns of phylogenetic diversification in birds

One of the most striking patterns in evolutionary biology is that clades may differ greatly in the number of species they contain. Numerous hypotheses have been put forward to explain this phenomenon, and several have been tested using phylogenetic methods. Remarkably, however, all such tests performed to date have been characterized by modest explanatory power, which has generated an interest in explanations stressing the importance of random processes. Here we make use of phylogenetic methods to test whether ecological variables, typically ignored in previous models, may explain phylogenetic tree imbalance in birds. We show that diversification rate possesses an intermediate phylogenetic signal across families. Using phylogenetic comparative methods, we then build a multipredictor model that explains more than 50% of the variation in diversification rate among clades. High annual dispersal is identified as the strongest predictor of high rates of diversification. In addition, high diversification rate is strongly associated with feeding generalization. In all but one instance, these key findings remain qualitatively unchanged when we use an alternative phylogeny and methodology and when small clades, containing five species or less, are excluded. Taken together, these results suggest that large-scale patterns in avian diversification can be explained by variation in intrinsic biology.     

Estimating meiotic gene conversion rates from population genetic data

Gene conversion plays an important part in shaping genetic diversity in populations, yet estimating the rate at which it occurs is difficult because of the short lengths of DNA involved. We have developed a new statistical approach to estimating gene conversion rates from genetic variation, by extending an existing model for haplotype data in the presence of crossover events. We show, by simulation, that when the rate of gene conversion events is at least comparable to the rate of crossover events, the method provides a powerful approach to the detection of gene conversion and estimation of its rate. Application of the method to data from the telomeric X chromosome of Drosophila melanogaster, in which crossover activity is suppressed, indicates that gene conversion occurs approximately 400 times more often than crossover events. We also extend the method to estimating variable crossover and gene conversion rates and estimate the rate of gene conversion to be approximately 1.5 times higher than the crossover rate in a region of human chromosome 1 with known recombination hotspots.     

Estimating recombination rates from single-nucleotide polymorphisms using summary statistics

We describe a novel method for jointly estimating crossing-over and gene-conversion rates from population genetic data using summary statistics. The performance of our method was tested on simulated data sets and compared with the composite-likelihood method of R. R. Hudson. For several realistic parameter values, the new method performed similarly to the composite-likelihood approach for estimating crossing-over rates and better when estimating gene-conversion rates. We used our method to analyze a human data set recently genotyped by Perlegen Sciences.     

Analysis of diversification: combining phylogenetic and taxonomic data

The estimation of diversification rates using phylogenetic data has attracted a lot of attention in the past decade. In this context, the analysis of incomplete phylogenies (e.g. phylogenies resolved at the family level but unresolved at the species level) has remained difficult. I present here a likelihood-based method to combine partly resolved phylogenies with taxonomic (species-richness) data to estimate speciation and extinction rates. This method is based on fitting a birth-and-death model to both phylogenetic and taxonomic data. Some examples of the method are presented with data on birds and on mammals. The method is compared with existing approaches that deal with incomplete phylogenies. Some applications and generalizations of the approach introduced in this paper are further discussed.     

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.     

Detecting shifts in diversification rates without fossils

Studies of shifts in diversification rates and adaptive radiations are difficult when there are no fossils because past events cannot be inferred. The phylogenies of recent species, however, allow one to infer the patterns of past diversifications. I present a new method for estimating the diversification rate of a lineage, provided that a phylogeny of recent species, constructed, for instance, with molecular data, is available. This method was inspired by survival models and takes into account species that are not included in detailed phylogenetic data, provided that approximate dates of origin of these species are known. Likelihood ratio tests and Akaike Information Criterion make it possible to test for differences in diversification among lineages or groups of lineages and, thus, to evaluate adaptive radiation hypotheses. The present modeling approach can easily be extended to include temporal variations in diversification rates. A simulation study showed that the method is statistically consistent, avoiding Type I and Type II errors, and that it is robust to periodic or random fluctuations in the speciation rate. An example is presented with a composite phylogeny of primates.     

Whole-tree methods for detecting differential diversification rates

Prolific cladogenesis, adaptive radiation, species selection, key innovations, and mass extinctions are a few examples of biological phenomena that lead to differential diversification among lineages. Central to the study of differential diversification rates is the ability to distinguish chance variation from that which requires deterministic explanation. To detect diversification rate variation among lineages, we propose a number of methods that incorporate information on the topological distribution of species diversity from all internal nodes of a phylogenetic tree. These whole-tree methods (M(Pi), M(Sigma), and M(R)) are explicitly connected to a null model of random diversification--the equal-rates Markov (ERM) random branching model--and an alternative model of differential diversification: M(Pi) is based on the product of individual nodal ERM probabilities; M(Sigma) is based on the sum of individual nodal ERM probabilities, and M(R) is based on a transformation of ERM probabilities that corresponds to a formalized system that orders trees by their relative symmetry. These methods have been implemented in a freely available computer program, SYMMETREE, to detect clades with variable diversification rates, thereby allowing the study of biological processes correlated with and possibly causal to shifts in diversification rate. Application of these methods to several published phylogenies demonstrates their ability to contend with relatively large, incompletely resolved trees. These topology-based methods do not require estimates of relative branch lengths, which should facilitate the analysis of phylogenies, such as supertrees, for which such data are unreliable or unavailable.     

Estimating divergence times in large phylogenetic trees

A new method, PATHd8, for estimating ultrametric trees from trees with edge (branch) lengths proportional to the number of substitutions is proposed. The method allows for an arbitrary number of reference nodes for time calibration, each defined either as absolute age, minimum age, or maximum age, and the tree need not be fully resolved. The method is based on estimating node ages by mean path lengths from the node to the leaves but correcting for deviations from a molecular clock suggested by reference nodes. As opposed to most existing methods allowing substitution rate variation, the new method smoothes substitution rates locally, rather than simultaneously over the whole tree, thus allowing for analysis of very large trees. The performance of PATHd8 is compared with other frequently used methods for estimating divergence times. In analyses of three separate data sets, PATHd8 gives similar divergence times to other methods, the largest difference being between crown group ages, where unconstrained nodes get younger ages when analyzed with PATHd8. Overall, chronograms obtained from other methods appear smoother, whereas PATHd8 preserves more of the heterogeneity seen in the original edge lengths. Divergence times are most evenly spread over the chronograms obtained from the Bayesian implementation and the clock-based Langley-Fitch method, and these two methods produce very similar ages for most nodes. Evaluations of PATHd8 using simulated data suggest that PATHd8 is slightly less precise compared with penalized likelihood, but it gives more sensible answers for extreme data sets. A clear advantage with PATHd8 is that it is more or less instantaneous even with trees having several thousand leaves, whereas other programs often run into problems when analyzing trees with hundreds of leaves. PATHd8 is implemented in freely available software.     

Estimating phylogenetic trees from pairwise likelihoods and posterior probabilities of substitution counts

The field of phylogenetic tree estimation has been dominated by three broad classes of methods: distance-based approaches, parsimony and likelihood-based methods (including maximum likelihood (ML) and Bayesian approaches). Here we introduce two new approaches to tree inference: pairwise likelihood estimation and a distance-based method that estimates the number of substitutions along the paths through the tree. Our results include the derivation of the formulae for the probability that two leaves will be identical at a site given a number of substitutions along the path connecting them. We also derive the posterior probability of the number of substitutions along a path between two sequences. The calculations for the posterior probabilities are exact for group-based, symmetric models of character evolution, but are only approximate for more general models.     

Estimating selfing rates from reconstructed pedigrees using multilocus genotype data

Several methods have been developed to estimate the selfing rate of a population from a sample of individuals genotyped for several marker loci. These methods can be based on homozygosity excess (or inbreeding), identity disequilibrium, progeny array (PA) segregation or population assignment incorporating partial selfing. Progeny array-based method is generally the best because it is not subject to some assumptions made by other methods (such as lack of misgenotyping, absence of biparental inbreeding and presence of inbreeding equilibrium), and it can reveal other facets of a mixed-mating system such as patterns of shared paternity. However, in practice, it is often difficult to obtain PAs, especially for animal species. In this study, we propose a method to reconstruct the pedigree of a sample of individuals taken from a monoecious diploid population practicing mixed mating, using multilocus genotypic data. Selfing and outcrossing events are then detected when an individual derives from identical parents and from two distinct parents, respectively. Selfing rate is estimated by the proportion of selfed offspring in the reconstructed pedigree of a sample of individuals. The method enjoys many advantages of the PA method, but without the need of a priori family structure, although such information, if available, can be utilized to improve the inference. Furthermore, the new method accommodates genotyping errors, estimates allele frequencies jointly and is robust to the presence of biparental inbreeding and inbreeding disequilibrium. Both simulated and empirical data were analysed by the new and previous methods to compare their statistical properties and accuracies.