The phylogenetic signal of diversification rates

Hypotheses to explain the causes of diversity gradients have increasingly focused on the factors that actually change species numbers, namely speciation, extinction and dispersal. A common assumption of many of these hypotheses is that there should be phylogenetic signal in diversification rates, yet this assumption has rarely been tested explicitly. In this study, we compile a large data set including 328,219 species of plants, mammals, amphibians and squamates to assess the level of phylogenetic signal in their diversification rates. Significant phylogenetic signal was detected in all data sets, except for squamates, suggesting not only that closely related clades indeed might share similar diversification rates, but also that the level of phylogenetic signal might vary considerably between them. Moreover, there were intriguing differences among taxa in the rate of decay in phylogenetic autocorrelation over time, underscoring the existence of taxon-specific patterns of phylogenetic autocorrelation. These results have important implications for the development of more realistic models of species diversification.     

Reconstructing shifts in diversification rates on phylogenetic trees

Few issues in evolutionary biology have received as much attention over the years or have generated as much controversy as those involving evolutionary rates. One unresolved issue is whether or not shifts in speclation and/or extinction rates are closely tied to the origin of 'key' innovations in evolution. This discussion has long been dominated by 'time-based' methods using data from the fossil record. Recently, however, attention has shifted to 'tree-based' methods, in which time, if It plays any role at all, is incorporated secondarily, usually based on molecular data. Tests of hypotheses about key innovations do require Information about phylogenetic relationships, and some of these tests can be implemented without any information about time. However, every effort should be made to obtain information about time, which greatly increases the power of such tests.     

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 diversification rates for higher taxa: BAMM can give problematic estimates of rates and rate shifts

Estimates of diversification rates are invaluable for many macroevolutionary studies. Recently, an approach called BAMM (Bayesian Analysis of Macro‐evolutionary Mixtures) has become widely used for estimating diversification rates and rate shifts. At the same time, several articles have concluded that estimates of net diversification rates from the method‐of‐moments (MS) estimators are inaccurate. Yet, no studies have compared the ability of these two methods to accurately estimate clade diversification rates. Here, we use simulations to compare their performance. We found that BAMM yielded relatively weak relationships between true and estimated diversification rates. This occurred because BAMM underestimated the number of rates shifts across each tree, and assigned high rates to small clades with low rates. Errors in both speciation and extinction rates contributed to these errors, showing that using BAMM to estimate only speciation rates is also problematic. In contrast, the MS estimators (particularly using stem group ages), yielded stronger relationships between true and estimated diversification rates, by roughly twofold. Furthermore, the MS approach remained relatively accurate when diversification rates were heterogeneous within clades, despite the widespread assumption that it requires constant rates within clades. Overall, we caution that BAMM may be problematic for estimating diversification rates and rate shifts.     

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 rates of behavior from Hansen frequencies

Occurrences of a behavior pattern are sometimes recorded by tabulating, for each time period in the sample, whether the behavior occurred at least once in that period. Since repeated occurrences are not included, the tabulation does not furnish an estimate of the true rate at which the behavior is occurring. Nevertheless, under certain conditions, the rate can be estimated from such data, using the Poisson distribution.Research supported by Grant FR-00165 from the National Institutes of Health and by Grant GB-8287 from the National Science Foundation.     

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.     

Predicting rates of interspecific interaction from phylogenetic trees

Integrating phylogenetic information can potentially improve our ability to explain species' traits, patterns of community assembly, the network structure of communities, and ecosystem function. In this study, we use mathematical models to explore the ecological and evolutionary factors that modulate the explanatory power of phylogenetic information for communities of species that interact within a single trophic level. We find that phylogenetic relationships among species can influence trait evolution and rates of interaction among species, but only under particular models of species interaction. For example, when interactions within communities are mediated by a mechanism of phenotype matching, phylogenetic trees make specific predictions about trait evolution and rates of interaction. In contrast, if interactions within a community depend on a mechanism of phenotype differences, phylogenetic information has little, if any, predictive power for trait evolution and interaction rate. Together, these results make clear and testable predictions for when and how evolutionary history is expected to influence contemporary rates of species interaction.     

Carotenogenesis diversification in phylogenetic lineages of Rhodophyta

Carotenoid composition is very diverse in Rhodophyta. In this study, we investigated whether this variation is related to the phylogeny of this group. Rhodophyta consists of seven classes, and they can be divided into two groups on the basis of their morphology. The unicellular group (Cyanidiophyceae, Porphyridiophyceae, Rhodellophyceae, and Stylonematophyceae) contained only β‐carotene and zeaxanthin, “ZEA‐type carotenoids.” In contrast, within the macrophytic group (Bangiophyceae, Compsopogonophyceae, and Florideophyceae), Compsopogonophyceae contained antheraxanthin in addition to ZEA‐type carotenoids, “ANT‐type carotenoids,” whereas Bangiophyceae contained α‐carotene and lutein along with ZEA‐type carotenoids, “LUT‐type carotenoids.” Florideophyceae is divided into five subclasses. Ahnfeltiophycidae, Hildenbrandiophycidae, and Nemaliophycidae contained LUT‐type carotenoids. In Corallinophycidae, Hapalidiales and Lithophylloideae in Corallinales contained LUT‐type carotenoids, whereas Corallinoideae in Corallinales contained ANT‐type carotenoids. In Rhodymeniophycidae, most orders contained LUT‐type carotenoids; however, only Gracilariales contained ANT‐type carotenoids. There is a clear relationship between carotenoid composition and phylogenetics in Rhodophyta. Furthermore, we searched open genome databases of several red algae for references to the synthetic enzymes of the carotenoid types detected in this study. β‐Carotene and zeaxanthin might be synthesized from lycopene, as in land plants. Antheraxanthin might require zeaxanthin epoxydase, whereas α‐carotene and lutein might require two additional enzymes, as in land plants. Furthermore, Glaucophyta contained ZEA‐type carotenoids, and Cryptophyta contained β‐carotene, α‐carotene, and alloxanthin, whose acetylenic group might be synthesized from zeaxanthin by an unknown enzyme. Therefore, we conclude that the presence or absence of the four enzymes is related to diversification of carotenoid composition in these three phyla.     

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 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.     

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 predation rates from molecular gut content analysis

Several methods have been published to estimate per capita predation rates from molecular gut content analysis relying on intuitive understanding of predation, but none have been formally derived. We provide a theoretical framework for estimating predation rates to identify an accurate method and lay bare its assumptions. Per capita predation can be estimated by multiplying the prey decay rate and the prey quantity in the predators. This assumes that variation in per capita predation rate is approximately normally distributed, prey decay occurs exponentially, and predation is in steady state. We described several ways to estimate steady state predation, including using only qualitative presence-absence data to estimate the decay rate and in addition, we provided a method for estimating per capita predation rate when predation is not in steady state. We used previously published data on aphid consumption by a ladybird beetle in a feeding trial to calculate the predation rate and compare published methods with this theoretically derived method. The estimated predation rate (3.29 ± 0.27 aphids/h) using our derived method was not significantly different from the actual predation rate, 3.11 aphids/h. In contrast, previously published methods were less accurate, underestimating the predation rate (0.33 ± 0.02 to 1.66 ± 0.8 aphids/h) or overestimating it (3.64 ± 0.30 aphids/h). In summary, we provide methods to estimate predation rates even when variation in predation rates is not exactly normally distributed and not in steady state and demonstrate that the prey decay rate, and not the prey detection period, is required.     

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.     

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.     

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.     

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.     

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.