Inferring population history with DIY ABC: a user-friendly approach to approximate Bayesian computation

Genetic data obtained on population samples convey information about their evolutionary history. Inference methods can extract part of this information but they require sophisticated statistical techniques that have been made available to the biologist community (through computer programs) only for simple and standard situations typically involving a small number of samples. We propose here a computer program (DIY ABC) for inference based on approximate Bayesian computation (ABC), in which scenarios can be customized by the user to fit many complex situations involving any number of populations and samples. Such scenarios involve any combination of population divergences, admixtures and population size changes. DIY ABC can be used to compare competing scenarios, estimate parameters for one or more scenarios and compute bias and precision measures for a given scenario and known values of parameters (the current version applies to unlinked microsatellite data). This article describes key methods used in the program and provides its main features. The analysis of one simulated and one real dataset, both with complex evolutionary scenarios, illustrates the main possibilities of DIY ABC.

Phylogenetic utility of more axillary growth (MAX4 ) - like genes: a case study in Digitalis / Isoplexis (Plantaginaceae)

We present the first assessment of phylogenetic utility of a potential novel low-copy nuclear gene region in flowering plants. A fragment of the MORE AXILLARY GROWTH 4 gene (MAX4, also known as RAMOSUS1 and DECREASED APICAL DOMINANCE1), predicted to span two introns, was isolated from members of Digitalis/Isoplexis. Phylogenetic analyses, under both maximum parsimony and Bayesian inference, were performed and revealed evidence of putative MAX4-like paralogues. The MAX4-like trees were compared with those obtained for Digitalis/Isoplexis using ITS and trnL-F, revealing a high degree of incongruence between these different DNA regions. Network analyses indicate complex patterns of evolution between the MAX4 sequences, which cannot be adequately represented on bifurcating trees. The incidence of paralogy restricts the use of MAX4 in phylogenetic inference within the study group, although MAX4 could potentially be used in combination with other DNA regions for resolving species relationships in cases where paralogues can be clearly identified.

Phylogenetic utility of MORE AXILLARY GROWTH4 (MAX4)-like genes: a case study in Digitalis/Isoplexis (Plantaginaceae)

We present the first assessment of phylogenetic utility of a potential novel low-copy nuclear gene region in flowering plants. A fragment of the MORE AXILLARY GROWTH 4 gene (MAX4, also known as RAMOSUS1 and DECREASED APICAL DOMINANCE1), predicted to span two introns, was isolated from members of Digitalis/Isoplexis. Phylogenetic analyses, under both maximum parsimony and Bayesian inference, were performed and revealed evidence of putative MAX4-like paralogues. The MAX4-like trees were compared with those obtained for Digitalis/Isoplexis using ITS and trnL-F, revealing a high degree of incongruence between these different DNA regions. Network analyses indicate complex patterns of evolution between the MAX4 sequences, which cannot be adequately represented on bifurcating trees. The incidence of paralogy restricts the use of MAX4 in phylogenetic inference within the study group, although MAX4 could potentially be used in combination with other DNA regions for resolving species relationships in cases where paralogues can be clearly identified.

Estimation following selection of the largest of two normal means

This paper considers the problem of estimation when one of a number of populations, assumed normal with known common variance, is selected on the basis of it having the largest observed mean. Conditional on selection of the population, the observed mean is a biased estimate of the true mean. This problem arises in the analysis of clinical trials in which selection is made between a number of experimental treatments that are compared with each other either with or without an additional control treatment. Attempts to obtain approximately unbiased estimates in this setting have been proposed by Shen [2001. An improved method of evaluating drug effect in a multiple dose clinical trial. Statist. Medicine 20, 1913–1929] and Stallard and Todd [2005. Point estimates and confidence regions for sequential trials involving selection. J. Statist. Plann. Inference 135, 402–419]. This paper explores the problem in the simple setting in which two experimental treatments are compared in a single analysis. It is shown that in this case the estimate of Stallard and Todd is the maximum-likelihood estimate (m.l.e.), and this is compared with the estimate proposed by Shen. In particular, it is shown that the m.l.e. has infinite expectation whatever the true value of the mean being estimated. We show that there is no conditionally unbiased estimator, and propose a new family of approximately conditionally unbiased estimators, comparing these with the estimators suggested by Shen.

Phylogenetic mixture models can reduce node-density artifacts

We investigate the performance of phylogenetic mixture models in reducing a well-known and pervasive artifact of phylogenetic inference known as the node-density effect, comparing them to partitioned analyses of the same data. The node-density effect refers to the tendency for the amount of evolutionary change in longer branches of phylogenies to be underestimated compared to that in regions of the tree where there are more nodes and thus branches are typically shorter. Mixture models allow more than one model of sequence evolution to describe the sites in an alignment without prior knowledge of the evolutionary processes that characterize the data or how they correspond to different sites. If multiple evolutionary patterns are common in sequence evolution, mixture models may be capable of reducing node-density effects by characterizing the evolutionary processes more accurately. In gene-sequence alignments simulated to have heterogeneous patterns of evolution, we find that mixture models can reduce node-density effects to negligible levels or remove them altogether, performing as well as partitioned analyses based on the known simulated patterns. The mixture models achieve this without knowledge of the patterns that generated the data and even in some cases without specifying the full or true model of sequence evolution known to underlie the data. The latter result is especially important in real applications, as the true model of evolution is seldom known. We find the same patterns of results for two real data sets with evidence of complex patterns of sequence evolution: mixture models substantially reduced node-density effects and returned better likelihoods compared to partitioning models specifically fitted to these data. We suggest that the presence of more than one pattern of evolution in the data is a common source of error in phylogenetic inference and that mixture models can often detect these patterns even without prior knowledge of their presence in the data. Routine use of mixture models alongside other approaches to phylogenetic inference may often reveal hidden or unexpected patterns of sequence evolution and can improve phylogenetic inference.

The automation and evaluation of nested clade phylogeographic analysis

Nested clade phylogeographic analysis (NCPA) is a popular method for reconstructing the demographic history of spatially distributed populations from genetic data. Although some parts of the analysis are automated, there is no unique and widely followed algorithm for doing this in its entirety, beginning with the data, and ending with the inferences drawn from the data. This article describes a method that automates NCPA, thereby providing a framework for replicating analyses in an objective way. To do so, a number of decisions need to be made so that the automated implementation is representative of previous analyses. We review how the NCPA procedure has evolved since its inception and conclude that there is scope for some variability in the manual application of NCPA. We apply the automated software to three published datasets previously analyzed manually and replicate many details of the manual analyses, suggesting that the current algorithm is representative of how a typical user will perform NCPA. We simulate a large number of replicate datasets for geographically distributed, but entirely random-mating, populations. These are then analyzed using the automated NCPA algorithm. Results indicate that NCPA tends to give a high frequency of false positives. In our simulations we observe that 14% of the clades give a conclusive inference that a demographic event has occurred, and that 75% of the datasets have at least one clade that gives such an inference. This is mainly due to the generation of multiple statistics per clade, of which only one is required to be significant to apply the inference key. We survey the inferences that have been made in recent publications and show that the most commonly inferred processes (restricted gene flow with isolation by distance and contiguous range expansion) are those that are commonly inferred in our simulations. However, published datasets typically yield a richer set of inferences with NCPA than obtained in our random-mating simulations, and further testing of NCPA with models of structured populations is necessary to examine its accuracy.

Three-level main-effects designs exploiting prior information about model uncertainty

To explore the projection efficiency of a design, Tsai, et al [2000. Projective three-level main effects designs robust to model uncertainty. Biometrika 87, 467-475] introduced the Q criterion to compare three-level main-effects designs for quantitative factors that allow the consideration of interactions in addition to main effects. In this paper, we extend their method and focus on the case in which experimenters have some prior knowledge, in advance of running the experiment, about the probabilities of effects being non-negligible. A criterion which incorporates experimenters' prior beliefs about the importance of each effect is introduced to compare orthogonal, or nearly orthogonal, main effects designs with robustness to interactions as a secondary consideration. We show that this criterion, exploiting prior information about model uncertainty, can lead to more appropriate designs reflecting experimenters' prior beliefs. (c) 2006 Elsevier B.V. All rights reserved.

Evolutionary history of vegetative reproduction in Porpidia s. l. (lichen-forming ascomycota)

The evolutionary history of gains and losses of vegetative reproductive propagules (soredia) in Porpidia s.l., a group of lichen-forming ascomycetes, was clarified using Bayesian Markov chain Monte Carlo (MCMC) approaches to monophyly tests and a combined MCMC and maximum likelihood approach to ancestral character state reconstructions. The MCMC framework provided confidence estimates for the reconstructions of relationships and ancestral character states, which formed the basis for tests of evolutionary hypotheses. Monophyly tests rejected all hypotheses that predicted any clustering of reproductive modes in extant taxa. In addition, a nearest-neighbor statistic could not reject the hypothesis that the vegetative reproductive mode is randomly distributed throughout the group. These results show that transitions between presence and absence of the vegetative reproductive mode within Porpidia s.l. occurred several times and independently of each other. Likelihood reconstructions of ancestral character states at selected nodes suggest that - contrary to previous thought - the ancestor to Porpidia s.l. already possessed the vegetative reproductive mode. Furthermore, transition rates are reconstructed asymmetrically with the vegetative reproductive mode being gained at a much lower rate than it is lost. A cautious note has to be added, because a simulation study showed that the ancestral character state reconstructions were highly dependent on taxon sampling. However, our central conclusions, particularly the higher rate of change from vegetative reproductive mode present to absent than vice versa within Porpidia s.l., were found to be broadly independent of taxon sampling. [Ancestral character state reconstructions; Ascomycota, Bayesian inference; hypothesis testing; likelihood; MCMC; Porpidia; reproductive systems]

Detecting the node-density artifact in phylogeny reconstruction

The node-density effect is an artifact of phylogeny reconstruction that can cause branch lengths to be underestimated in areas of the tree with fewer taxa. Webster, Payne, and Pagel (2003, Science 301:478) introduced a statistical procedure (the "delta" test) to detect this artifact, and here we report the results of computer simulations that examine the test's performance. In a sample of 50,000 random data sets, we find that the delta test detects the artifact in 94.4% of cases in which it is present. When the artifact is not present (n = 10,000 simulated data sets) the test showed a type I error rate of approximately 1.69%, incorrectly reporting the artifact in 169 data sets. Three measures of tree shape or "balance" failed to predict the size of the node-density effect. This may reflect the relative homogeneity of our randomly generated topologies, but emphasizes that nearly any topology can suffer from the artifact, the effect not being confined only to highly unevenly sampled or otherwise imbalanced trees. The ability to screen phylogenies for the node-density artifact is important for phylogenetic inference and for researchers using phylogenetic trees to infer evolutionary processes, including their use in molecular clock dating. [Delta test; molecular clock; molecular evolution; node-density effect; phylogenetic reconstruction; speciation; simulation.]

A phylogenetic mixture model for detecting pattern-heterogeneity in gene sequence or character-state data

We describe a general likelihood-based 'mixture model' for inferring phylogenetic trees from gene-sequence or other character-state data. The model accommodates cases in which different sites in the alignment evolve in qualitatively distinct ways, but does not require prior knowledge of these patterns or partitioning of the data. We call this qualitative variability in the pattern of evolution across sites "pattern-heterogeneity" to distinguish it from both a homogenous process of evolution and from one characterized principally by differences in rates of evolution. We present studies to show that the model correctly retrieves the signals of pattern-heterogeneity from simulated gene-sequence data, and we apply the method to protein-coding genes and to a ribosomal 12S data set. The mixture model outperforms conventional partitioning in both these data sets. We implement the mixture model such that it can simultaneously detect rate- and pattern-heterogeneity. The model simplifies to a homogeneous model or a rate- variability model as special cases, and therefore always performs at least as well as these two approaches, and often considerably improves upon them. We make the model available within a Bayesian Markov-chain Monte Carlo framework for phylogenetic inference, as an easy-to-use computer program.

Phylogenomics of eukaryotes: Impact of missing data on large alignments

Resolving the relationships between Metazoa and other eukaryotic groups as well as between metazoan phyla is central to the understanding of the origin and evolution of animals. The current view is based on limited data sets, either a single gene with many species (e.g., ribosomal RNA) or many genes but with only a few species. Because a reliable phylogenetic inference simultaneously requires numerous genes and numerous species, we assembled a very large data set containing 129 orthologous proteins (similar to30,000 aligned amino acid positions) for 36 eukaryotic species. Included in the alignments are data from the choanoflagellate Monosiga ovata, obtained through the sequencing of about 1,000 cDNAs. We provide conclusive support for choanoflagellates as the closest relative of animals and for fungi as the second closest. The monophyly of Plantae and chromalveolates was recovered but without strong statistical support. Within animals, in contrast to the monophyly of Coelomata observed in several recent large-scale analyses, we recovered a paraphyletic Coelamata, with nematodes and platyhelminths nested within. To include a diverse sample of organisms, data from EST projects were used for several species, resulting in a large amount of missing data in our alignment (about 25%). By using different approaches, we verify that the inferred phylogeny is not sensitive to these missing data. Therefore, this large data set provides a reliable phylogenetic framework for studying eukaryotic and animal evolution and will be easily extendable when large amounts of sequence information become available from a broader taxonomic range.

Estimation of population growth or decline in genetically monitored populations

This article introduces a new general method for genealogical inference that samples independent genealogical histories using importance sampling (IS) and then samples other parameters with Markov chain Monte Carlo (MCMC). It is then possible to more easily utilize the advantages of importance sampling in a fully Bayesian framework. The method is applied to the problem of estimating recent changes in effective population size from temporally spaced gene frequency data. The method gives the posterior distribution of effective population size at the time of the oldest sample and at the time of the most recent sample, assuming a model of exponential growth or decline during the interval. The effect of changes in number of alleles, number of loci, and sample size on the accuracy of the method is described using test simulations, and it is concluded that these have an approximately equivalent effect. The method is used on three example data sets and problems in interpreting the posterior densities are highlighted and discussed.

Phylogenetic relationships within the moss family Bryaceae based on chloroplast DNA evidence

The Bryaceae are a large cosmopolitan family of mosses containing genera of considerable taxonomic difficulty. Phylogenetic relationships within the family were inferred using data from chloroplast DNA sequences (rps4 and trnL-trnF region). Parsimony and maximum likelihood optimality criteria, and Bayesian phylogenetic inference procedures were employed to reconstruct relationships. The genera Bryum and Brachymenium are not monophyletic groups. A clade comprising Plagiobryum, Acidodontium, Mielichhoferia macrocarpa, Bryum sects. Bryum, Apalodictyon, Limbata, Leucodontium, Caespiticia, Capillaria (in part: sect. Capillaria), and Brachymenium sect. Dicranobryum, is well supported in all analyses and represents a major lineage within the family. Section Dicranobryum of Brachymenium is more closely related to section Bryum than to the other sections of Brachymenium, as are Mielichhoferia macrocarpa and M. himalayana. Species of Acidodontium form a clade with Anomobryum julaceum. The grouping of species with a rosulate gametophytic growth form suggests the presence of a 'rosulate' clade similar in circumscription to the genus Rosulabryum. Mielichhoferia macrocarpa and M. himalayana are transferred to Bryum as B. porsildii and B. caucasicum, respectively.

Population subdivision and molecular sequence variation: Theory and analysis of Drosophila ananassae data

Population subdivision complicates analysis of molecular variation. Even if neutrality is assumed, three evolutionary forces need to be considered: migration, mutation, and drift. Simplification can be achieved by assuming that the process of migration among and drift within subpopulations is occurring fast compared to Mutation and drift in the entire population. This allows a two-step approach in the analysis: (i) analysis of population subdivision and (ii) analysis of molecular variation in the migrant pool. We model population subdivision using an infinite island model, where we allow the migration/drift parameter Theta to vary among populations. Thus, central and peripheral populations can be differentiated. For inference of Theta, we use a coalescence approach, implemented via a Markov chain Monte Carlo (MCMC) integration method that allows estimation of allele frequencies in the migrant pool. The second step of this approach (analysis of molecular variation in the migrant pool) uses the estimated allele frequencies in the migrant pool for the study of molecular variation. We apply this method to a Drosophila ananassae sequence data set. We find little indication of isolation by distance, but large differences in the migration parameter among populations. The population as a whole seems to be expanding. A population from Bogor (Java, Indonesia) shows the highest variation and seems closest to the species center.

Assessing reading at Key Stage 2: SATs as measures of children's inferential abilities

This article describes two studies. The first study was designed to investigate the ways in which the statutory assessments of reading for 11-year-old children in England assess inferential abilities. The second study was designed to investigate the levels of performance achieved in these tests in 2001 and 2002 by 11-year-old children attending state-funded local authority schools in one London borough. In the first study, content and questions used in the reading papers for the Standard Assessment Tasks (SATs) in the years 2001 and 2002 were analysed to see what types of inference were being assessed. This analysis suggested that the complexity involved in inference making and the variety of inference types that are made during the reading process are not adequately sampled in the SATs. Similar inadequacies are evident in the ways in which the programmes of study for literacy recommended by central government deal with inference. In the second study, scripts of completed SATs reading papers for 2001 and 2002 were analysed to investigate the levels of inferential ability evident in scripts of children achieving different SATs levels. The analysis in this article suggests that children who only just achieve the 'target' Level 4 do so with minimal use of inference skills. They are particularly weak in making inferences that require the application of background knowledge. Thus, many children who achieve the reading level (Level 4) expected of 11-year-olds are entering secondary education with insecure inference-making skills that have not been recognised.