Tandem repeats are repetitive structures present in some DNA sequences, consisting of many repeated copies of a single motif. They can serve as important markers for phylogenetic and population genetic studies, due to the high polymorphism in the number of motif copies as well as variations in the motif. The first step in using tandem repeats for phylogenetic studies is to estimate the evolutionary distance between a pair D1 and D2 of tandem repeat sequences with homologous motifs. This problem can be broken into two sub-problems: 1) Construct the most recent common ancestor of the sequences. 2) Calculate the evolutionary distance between each sequence and the hypothesised common ancestor. We present an algorithm that estimates the solution to the second problem. This takes the form of an asymmetric alignment algorithm to estimate the evolutionary distance between two tandem repeat sequences A and D, where D is assumed to have descended from A, under a model that allows block duplication, deletion, and variant substitution. The algorithm is asymmetric in the sense that the two input sequences A and D play different roles in the calculations, reflecting the assumption that D descends from A. Our model assumes static motif boundaries, meaning that motif duplication and deletion events must respect the motif boundaries. The algorithm may also be applied without modification to more complex repetitive structures with two or more motifs, such as nested tandem repeats.

Since Jacob and Monod's characterization of the role of DNA elements in gene control, it has been recognized that the linear organization of genome structure is important for the regulation of gene transcription and hence the manifestation of phenotypes. Similarly, it has long been hypothesized that the spatial organization (in three dimensions evolving through time), as part of the epigenome, makes a significant contribution to the genotype-phenotype transition. Proximity ligation assays commonly known as chromosome conformation capture (3C) and 3C based methodologies (e.g., GCC, HiC and ChIA-Pet) are increasingly being incorporated into empirical studies to investigate the role that three-dimensional genome structure plays in the regulation of phenotype. The apparent simplicity of these methodologies-crosslink chromatin, digest, dilute, ligate, detect interactions-belies the complexity of the data and the considerations that should be taken into account to ensure the generation and accurate interpretation of reliable data. Here we discuss the probabilistic nature of these methodologies and how this contributes to their endogenous limitations.

At macroevolutionary time scales, and for a constant mutation rate, there is an expected linear relationship between time and the number of inferred neutral mutations (the "molecular clock"). However, at shorter time scales, a number of recent studies have observed an apparent acceleration in the rate of molecular evolution. We study this apparent acceleration under a Jukes-Cantor model applied to a randomly mating population, and show that, under the model, it arises as a consequence of ignoring short-term effects due to existing diversity within the population. The acceleration can be accounted for by adding the correction term h(0)e(-4μt/3) to the usual Jukes-Cantor formula p(t) = 3/4(1 - e (-(-4μt/3), where h(0) is the expected heterozygosity in the population at time t = 0. The true mutation rate μ may then be recovered, even if h(0) is not known, by estimating μ and h(0) simultaneously using least squares. Rate estimates made without the correction term (i.e., incorrectly assuming the population to be homogeneous) will result in a divergent rate curve of the form μ(div) = μ + C/t, so that the mutation rate appears to approach infinity as the time scale approaches zero. Although our quantitative results apply only to the Jukes-Cantor model, it is reasonable to suppose that the qualitative picture that emerges also applies to more complex models. Our study, therefore, demonstrates the importance of properly accounting for any ancestral diversity, because it may otherwise play a dominant role in rate overestimation.

A characteristic feature of eukaryote and prokaryote genomes is the co-occurrence of nucleotide substitution and insertion/deletion (indel) mutations. Although similar observations have also been made for chloroplast DNA, genome-wide associations have not been reported. We determined the chloroplast genome sequences for two morphotypes of taro (Colocasia esculenta; family Araceae) and compared these with four publicly available aroid chloroplast genomes. Here, we report the extent of genome-wide association between direct and inverted repeats, indels, and substitutions in these aroid chloroplast genomes. We suggest that alternative but not mutually exclusive hypotheses explain the mutational dynamics of chloroplast genome evolution.

In many applications of tandem repeats the outcome depends critically on the choice of boundaries (beginning and end) of the repeated motif: for example, different choices of pattern boundaries can lead to different duplication history trees. However, the best choice of boundaries or parsing of the tandem repeat is often ambiguous, as the flanking regions before and after the tandem repeat often contain partial approximate copies of the motif, making it difficult to determine where the tandem repeat (and hence the motif) begins and ends. We define the parsing problem for tandem repeats to be the problem of discriminating among the possible choices of parsing. In this paper we propose and compare three heuristic methods for solving the parsing problem, under the assumption that the parsing is fixed throughout the duplication history of the tandem repeat. The three methods are PAIR, which minimises the number of pairs of common adjacent mutations which span a boundary; VAR, which minimises the total number of variants of the motif; and MST, which minimises the length of the minimum spanning tree connecting the variants, where the weight of each edge is the Hamming distance of the pair of variants. We test the methods on simulated data over a range of motif lengths and relative rates of substitutions to duplications, and show that all three perform better than choosing the parsing arbitrarily. Of the three MST typically performs the best, followed by VAR then PAIR.

We introduce the software tool NTRFinder to search for a complex repetitive structure in DNA we call a nested tandem repeat (NTR). An NTR is a recurrence of two or more distinct tandem motifs interspersed with each other. We propose that NTRs can be used as phylogenetic and population markers. We have tested our algorithm on both real and simulated data, and present some real NTRs of interest. NTRFinder can be downloaded from http://www.maths.otago.ac.nz/~aamatroud/.

1. ABSTRACT 1.1. Motivation: We introduce the algorithm NTRFinder to find a complex repetitive structure in DNA we call a nested tandem repeat (NTR). An NTR is a recurrence of two distinct tandem motifs interspersed with each other. We propose that nested tandem repeats can be used as phylogenetic and population markers. A major issue is the parsing problem, which is the problem of fi nding the optimal boundaries of the respective motifs. There has been little discus sion about determining the best boundaries of the repeated motifs in tandem repeats. For nested tandem repeats, parsing is a significant issue. 1.2. Results: An algorithm for finding Nested Tandem Repeats and a criterio n for solving the parsing problem are introduced. We have tested our algorithm on both real and simulated data, and present some real nested tandem repeats of interest. We discuss how one of these may assist in determining the cultivation prehistory of the ancient staple food crop taro (Colocasia esculenta). 1.3. Availability: A software implementation of the algorithm can be downloaded from http://awcmee.massey.ac.nz/downloads.htm.

Suppose a trial has r possible outcomes, with the i-th outcome having probability p(i), Sigma(r)(i=1) pi = 1 and p = (p(1), ..., p(r)). The outcome of n independent trials can be described by the frequencies k = (k(1), ..., k(r)), Sigma(r)(i=1) k(i) = n, where outcome i was selected with frequency k(i) is an element of N. A mode (there can be multiple modes) is an outcome with maximal likelihood over all possible outcomes.Despite the ubiquity of multinomial distributions in statistical applications, the best algorithm to date for finding modes has unknown computational complexity and highly variable performance in practice. It is also vulnerable to precision problems due to accumulated roundoff error.We propose a new algorithm, GreedyModeFind, for calculating the mode(s) of this distribution, given n and p. GreedyModeFind is simple, efficient and numerically robust, requiring O(r log r) time and O(r) space to find one mode. A concise representation of the full set of joint modes can be found for an additional time cost of O(r log r). In practice this algorithm drastically improves on the performance of earlier algorithms. We provide a freely available C++ implementation of GreedyModeFind. (C) 2009 Elsevier B.V. All rights reserved.

Commonly used phylogenetic models assume a homogeneous process through time in all parts of the tree. However, it is known that these models can be too simplistic as they do not account for nonhomogeneous lineage-specific properties. In particular, it is now widely recognized that as constraints on sequences evolve, the proportion and positions of variable sites can vary between lineages causing heterotachy. The extent to which this model misspecification affects tree reconstruction is still unknown. Here, we evaluate the effect of changes in the proportions and positions of variable sites on model fit and tree estimation. We consider 5 current models of nucleotide sequence evolution in a Bayesian Markov chain Monte Carlo framework as well as maximum parsimony (MP). We show that for a tree with 4 lineages where 2 nonsister taxa undergo a change in the proportion of variable sites tree reconstruction under the best-fitting model, which is chosen using a relative test, often results in the wrong tree. In this case, we found that an absolute test of model fit is a better predictor of tree estimation accuracy. We also found further evidence that MP is not immune to heterotachy. In addition, we show that increased sampling of taxa that have undergone a change in proportion and positions of variable sites is critical for accurate tree reconstruction.

An approximate nested tandem repeat (NTR) in a string T is a complex repetitive structure consisting of many approximate copies of two substrings x and X (“motifs”) interspersed with one another. NTRs have been found in real DNA sequences and are expected to have applications for evolutionary studies, both as a tool to understand concerted evolution, and as a potential marker in population studies. In this paper we describe software tools developed for database searches for NTRs. After a first program NTRFinder identifies putative NTR motifs, a confirmation step requires the application of the alignment of the putative NTR against exact NTRs built from the putative template motifs x and X. In this paper we describe an algorithm to solve this alignment problem in O(|T|(| x| + | X|)) space and time. Our alignment algorithm is based on Fischetti et al.’s wrap-around dynamic programming.

Presented here are the most recent results of our studies of Rattus exulans, one of the main commensal animals transported across the Pacific by Lapita peoples and their descendants. We sampled several locations in Near Oceania to determine distribution of R. exulans mitochondrial DNA (mtDNA) haplotypes in the region. We also obtained data regarding distribution of other introduced Rattus species to several islands in the Bismarck Archipelago. Our results Suggest that there were multiple introductions of R. exulans to the region, which may Suggest a more complex history for Lapita populations in Near Oceania.

We present a mathematical model of mitochondrial inheritance evolving under neutral evolution to interpret the heteroplasmies observed at some sites. A comparison of the levels of heteroplasmies transmitted from mother to her offspring allows us to estimate the number N(x) of inherited mitochondrial genomes (segregating units). The model demonstrates the necessity of accounting for both the multiplicity of an unknown number N(x), and the threshold , below which heteroplasmy cannot be detected reliably, in order to estimate the mitochondrial mutation rate mu(m) in the maternal line of descent. Our model is applicable to pedigree studies of any eukaryotic species where site heteroplasmies are observed in regions of the mitochondria, provided neutrality can be assumed. The model is illustrated with an analysis of site heteroplasmies in the first hypervariable region of mitochondrial sequence data sampled from Adélie penguin families, providing an estimate N(x) and mu(m). This estimate of mu(m) was found to be consistent with earlier estimates from ancient DNA analysis.

We report three developments toward resolving the challenge of the apparent basal polytomy of neoavian birds. First, we describe improved conditional down-weighting techniques to reduce noise relative to signal for deeper divergences and find increased agreement between data sets. Second, we present formulae for calculating the probabilities of finding predefined groupings in the optimal tree. Finally, we report a significant increase in data: nine new mitochondrial (mt) genomes (the dollarbird, New Zealand kingfisher, great potoo, Australian owlet-nightjar, white-tailed trogon, barn owl, a roadrunner [a ground cuckoo], New Zealand long-tailed cuckoo, and the peach-faced lovebird) and together they provide data for each of the six main groups of Neoaves proposed by Cracraft J (2001). We use his six main groups of modern birds as priors for evaluation of results. These include passerines, cuckoos, parrots, and three other groups termed "WoodKing" (woodpeckers/rollers/kingfishers), "SCA" (owls/potoos/owlet-nightjars/hummingbirds/swifts), and "Conglomerati." In general, the support is highly significant with just two exceptions, the owls move from the "SCA" group to the raptors, particularly accipitrids (buzzards/eagles) and the osprey, and the shorebirds may be an independent group from the rest of the "Conglomerati". Molecular dating mt genomes support a major diversification of at least 12 neoavian lineages in the Late Cretaceous. Our results form a basis for further testing with both nuclear-coding sequences and rare genomic changes.

Under a stochastic model of molecular sequence evolution the probability of each possible pattern of a characters is well defined. The Kimura's three-substitution-types (K3ST) model of evolution, allows analytical expression for these probabilities of by means of the Hadamard conjugation as a function of the phylogeny T and the substitution probabilities on each edge of TM . In this paper we produce a direct combinatorial proof of these results, using pathset distances which generalise pairwise distances between sequences. This interpretation provides us with tools that were proved useful in related problems in the mathematical analysis of sequence evolution.

Precise estimations of molecular rates are fundamental to our understanding of the processes of evolution. In principle, mutation and evolutionary rates for neutral regions of the same species are expected to be equal. However, a number of recent studies have shown that mutation rates estimated from pedigree material are much faster than evolutionary rates measured over longer time periods. To resolve this apparent contradiction, we have examined the hypervariable region (HVR I) of the mitochondrial genome using families of Adélie penguins (Pygoscelis adeliae) from the Antarctic. We sequenced 344 bps of the HVR I from penguins comprising 508 families with 915 chicks, together with both their parents. All of the 62 germline heteroplasmies that we detected in mothers were also detected in their offspring, consistent with maternal inheritance. These data give an estimated mutation rate (micro) of 0.55 mutations/site/Myrs (HPD 95% confidence interval of 0.29-0.88 mutations/site/Myrs) after accounting for the persistence of these heteroplasmies and the sensitivity of current detection methods. In comparison, the rate of evolution (k) of the same HVR I region, determined using DNA sequences from 162 known age sub-fossil bones spanning a 37,000-year period, was 0.86 substitutions/site/Myrs (HPD 95% confidence interval of 0.53 and 1.17). Importantly, the latter rate is not statistically different from our estimate of the mutation rate. These results are in contrast to the view that molecular rates are time dependent.

Background: Publicly available DNA sequence databases such as GenBank are large, and are growing at an exponential rate. The sheer volume of data being dealt with presents serious storage and data communications problems. Currently, sequence data is usually kept in large "flat files," which are then compressed using standard Lempel-Ziv (gzip) compression - an approach which rarely achieves good compression ratios. While much research has been done on compressing individual DNA sequences, surprisingly little has focused on the compression of entire databases of such sequences. In this study we introduce the sequence database compression software coil.Results: We have designed and implemented a portable software package, coil, for compressing and decompressing DNA sequence databases based on the idea of edit-tree coding. coil is geared towards achieving high compression ratios at the expense of execution time and memory usage during compression - the compression time represents a "one-off investment" whose cost is quickly amortised if the resulting compressed file is transmitted many times. Decompression requires little memory and is extremely fast. We demonstrate a 5% improvement in compression ratio over state-of-the-art general-purpose compression tools for a large GenBank database file containing Expressed Sequence Tag (EST) data. Finally, coil can efficiently encode incremental additions to a sequence database.Conclusion: coil presents a compelling alternative to conventional compression of flat files for the storage and distribution of DNA sequence databases having a narrow distribution of sequence lengths, such as EST data. Increasing compression levels for databases having a wide distribution of sequence lengths is a direction for future work.