Tree measures and the number of segregating sites in time-structured population samples

BACKGROUND: Time-structured genetic samples are a valuable source of information in population genetics because they provide several correlated observations of the underlying evolutionary processes. In this paper we study basic properties of the genetic variation in time-structured samples as reflected in the genealogies relating individuals and the number of segregating sites observed. Our emphasis is on "measurably evolving populations" i.e. populations from which it is possible to obtain time-structured samples that span a significant interval of evolutionary time. RESULTS: We use results from the coalescent process to derive properties of time-structured samples. In the first section we extend existing results to attain measures on coalescent trees relating time-structured samples. These include the expected time to a most recent common ancestor, the expected total branch length and the expected length of branches subtending only ancient individuals. The effect of different sampling schemes on the latter measure is studied. In the second section we study the special case where the full sample consists of a group of contemporary extant samples and a group of contemporary ancient samples. As regards this case, we present results and applications concerning the probability distribution of the number of segregating sites where a mutation is unique to the ancient individuals and the number of segregating sites where a mutation is shared between ancient and extant individuals. CONCLUSION: The methodology and results presented here is of use to the design and interpretation of ancient DNA experiments. Furthermore, the results may be useful in further development of statistical tests of e.g. population dynamics and selection, which include temporal information

Recoverability of Ancestral Recombination Graph Topologies

Recombination is a powerful evolutionary process that shapes the genetic diversity observed in the populations of many species. Reconstructing genealogies in the presence of recombination from sequencing data is a very challenging problem, as this relies on mutations having occurred on the correct lineages in order to detect the recombination and resolve the placement of edges in the local trees. We investigate the probability of recovering the true topology of ancestral recombination graphs (ARGs)under the coalescent with recombination and gene conversion. We explore how sample size and mutation rate affect the inherent uncertainty in reconstructed ARGs; this sheds light on the theoretical limitations of ARG reconstruction methods. We illustrate our results using estimates of evolutionary rates for several biological organisms; in particular, we find that for parameter values that are realistic for SARS-CoV-2, the probability of reconstructing genealogies that are close to the truth is low

Reticular alignment: A progressive corner-cutting method for multiple sequence alignment

<p>Abstract</p> <p>Background</p> <p>In this paper, we introduce a progressive corner cutting method called Reticular Alignment for multiple sequence alignment. Unlike previous corner-cutting methods, our approach does not define a compact part of the dynamic programming table. Instead, it defines a set of optimal and suboptimal alignments at each step during the progressive alignment. The set of alignments are represented with a network to store them and use them during the progressive alignment in an efficient way. The program contains a threshold parameter on which the size of the network depends. The larger the threshold parameter and thus the network, the deeper the search in the alignment space for better scored alignments.</p> <p>Results</p> <p>We implemented the program in the Java programming language, and tested it on the BAliBASE database. Reticular Alignment can outperform ClustalW even if a very simple scoring scheme (BLOSUM62 and affine gap penalty) is implemented and merely the threshold value is increased. However, this set-up is not sufficient for outperforming other cutting-edge alignment methods. On the other hand, the reticular alignment search strategy together with sophisticated scoring schemes (for example, differentiating gap penalties for hydrophobic and hydrophylic amino acids) overcome FSA and in some accuracy measurement, even MAFFT. The program is available from <url>http://phylogeny-cafe.elte.hu/RetAlign/</url></p> <p>Conclusions</p> <p>Reticular alignment is an efficient search strategy for finding accurate multiple alignments. The highest accuracy achieved when this searching strategy is combined with sophisticated scoring schemes.</p

Investigating selection on viruses: a statistical alignment approach

<p>Abstract</p> <p>Background</p> <p>Two problems complicate the study of selection in viral genomes: Firstly, the presence of genes in overlapping reading frames implies that selection in one reading frame can bias our estimates of neutral mutation rates in another reading frame. Secondly, the high mutation rates we are likely to encounter complicate the inference of a reliable alignment of genomes. To address these issues, we develop a model that explicitly models selection in overlapping reading frames. We then integrate this model into a statistical alignment framework, enabling us to estimate selection while explicitly dealing with the uncertainty of individual alignments. We show that in this way we obtain un-biased selection parameters for different genomic regions of interest, and can improve in accuracy compared to using a fixed alignment.</p> <p>Results</p> <p>We run a series of simulation studies to gauge how well we do in selection estimation, especially in comparison to the use of a fixed alignment. We show that the standard practice of using a ClustalW alignment can lead to considerable biases and that estimation accuracy increases substantially when explicitly integrating over the uncertainty in inferred alignments. We even manage to compete favourably for general evolutionary distances with an alignment produced by GenAl. We subsequently run our method on HIV2 and Hepatitis B sequences.</p> <p>Conclusion</p> <p>We propose that marginalizing over all alignments, as opposed to using a fixed one, should be considered in any parametric inference from divergent sequence data for which the alignments are not known with certainty. Moreover, we discover in HIV2 that double coding regions appear to be under less stringent selection than single coding ones. Additionally, there appears to be evidence for differential selection, where one overlapping reading frame is under positive and the other under negative selection.</p

Dynamics based alignment of proteins: an alternative approach to quantify dynamic similarity

<p>Abstract</p> <p>Background</p> <p>The dynamic motions of many proteins are central to their function. It therefore follows that the dynamic requirements of a protein are evolutionary constrained. In order to assess and quantify this, one needs to compare the dynamic motions of different proteins. Comparing the dynamics of distinct proteins may also provide insight into how protein motions are modified by variations in sequence and, consequently, by structure. The optimal way of comparing complex molecular motions is, however, far from trivial. The majority of comparative molecular dynamics studies performed to date relied upon prior sequence or structural alignment to define which residues were equivalent in 3-dimensional space.</p> <p>Results</p> <p>Here we discuss an alternative methodology for comparative molecular dynamics that does not require any prior alignment information. We show it is possible to align proteins based solely on their dynamics and that we can use these dynamics-based alignments to quantify the dynamic similarity of proteins. Our method was tested on 10 representative members of the PDZ domain family.</p> <p>Conclusions</p> <p>As a result of creating pair-wise dynamics-based alignments of PDZ domains, we have found evolutionarily conserved patterns in their backbone dynamics. The dynamic similarity of PDZ domains is highly correlated with their structural similarity as calculated with Dali. However, significant differences in their dynamics can be detected indicating that sequence has a more refined role to play in protein dynamics than just dictating the overall fold. We suggest that the method should be generally applicable.</p

Comparison of Coding DNA

We discuss a model for the evolutionary distance between two coding DNA sequences which specializes to the DNA/protein model proposed in Hein [3]. We discuss the DNA/protein model in details and present a quadratic time algorithm that computes an optimal alignment of two coding DNA sequences in the model under the assumption of affine gap cost. The algorithm solves a conjecture in [3] and we believe that the constant factor of the running time is sufficiently small to make the algorithm feasible in practice

A characterisation of the genealogy of a birth-death process through time rescaling

The dynamics of a population exhibiting exponential growth can be modelled as a birth-death process, which naturally captures the stochastic variation in population size over time. In this article, we consider a supercritical birth-death process, started at a random time in the past, and conditioned to have n sampled individuals at the present. The genealogy of individuals sampled at the present time is then described by the reversed reconstructed process (RRP), which traces the ancestry of the sample backwards from the present. We show that a simple, analytic, time rescaling of the RRP provides a straightforward way to derive its inter-event times. The same rescaling characterises other distributions underlying this process, obtained elsewhere in the literature via more cumbersome calculations. We also consider the case of incomplete sampling of the population, in which each leaf of the genealogy is retained with an independent Bernoulli trial with probability \psi, and we show that corresponding results for Bernoulli-sampled RRPs can be derived using time rescaling, for any values of the underlying parameters. A central result is the derivation of a scaling limit as \psi approaches 0, corresponding to the underlying population growing to infinity, using the time rescaling formalism. We show that in this setting, after a linear time rescaling, the event times are the order statistics of n logistic random variables with mode \log(1/\psi); moreover, we show that the inter-event times are approximately exponentially distributed