ORCID Profile
0000-0002-9938-3499
Current Organisation
Western Sydney University
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In Research Link Australia (RLA), "Research Topics" refer to ANZSRC FOR and SEO codes. These topics are either sourced from ANZSRC FOR and SEO codes listed in researchers' related grants or generated by a large language model (LLM) based on their publications.
Biological Mathematics | Group Theory and Generalisations | Applied Mathematics | Pure Mathematics | Biological Mathematics | Combinatorics and Discrete Mathematics (excl. Physical Combinatorics) | Stochastic Analysis and Modelling | Epidemiology | Population And Ecological Genetics | Algebra and Number Theory | Population, Ecological and Evolutionary Genetics
Expanding Knowledge in the Biological Sciences | Expanding Knowledge in the Mathematical Sciences | Climate change | Disease distribution and transmission | Livestock | Infectious diseases | Biological sciences |
Publisher: Oxford University Press (OUP)
Date: 11-06-2015
Publisher: Elsevier BV
Date: 2005
DOI: 10.1016/J.MEEGID.2004.06.001
Abstract: Genotypic data from pathogenic isolates are often used to measure the extent of infectious disease transmission. These methods include phylogenetic reconstruction and the evaluation of clustering indices. The first aim of this paper is to critique current methods used to analyse genotypic data from molecular epidemiological studies of tuberculosis. In particular, by not accounting for the mutation rate of markers, errors arise in making inferences about outbreaks based on genotypic information. The second aim is to suggest a new way to represent genotypic data visually, involving graphs and trees. We also discuss some interpretations and modifications of existing indices. Although our focus is tuberculosis, the methods we discuss are generally applicable to any directly transmissible clonal pathogen.
Publisher: IOP Publishing
Date: 21-07-2017
Publisher: Springer Science and Business Media LLC
Date: 16-11-2018
Publisher: Oxford University Press (OUP)
Date: 07-2006
DOI: 10.1534/GENETICS.106.055574
Abstract: Tuberculosis can be studied at the population level by genotyping strains of Mycobacterium tuberculosis isolated from patients. We use an approximate Bayesian computational method in combination with a stochastic model of tuberculosis transmission and mutation of a molecular marker to estimate the net transmission rate, the doubling time, and the reproductive value of the pathogen. This method is applied to a published data set from San Francisco of tuberculosis genotypes based on the marker IS6110. The mutation rate of this marker has previously been studied, and we use those estimates to form a prior distribution of mutation rates in the inference procedure. The posterior point estimates of the key parameters of interest for these data are as follows: net transmission rate, 0.69/year [95% credibility interval (C.I.) 0.38, 1.08] doubling time, 1.08 years (95% C.I. 0.64, 1.82) and reproductive value 3.4 (95% C.I. 1.4, 79.7). These figures suggest a rapidly spreading epidemic, consistent with observations of the resurgence of tuberculosis in the United States in the 1980s and 1990s.
Publisher: Bernoulli Society for Mathematical Statistics and Probability
Date: 02-11-2017
DOI: 10.3150/16-BEJ839
Publisher: Elsevier BV
Date: 2015
DOI: 10.1016/J.MBS.2014.10.008
Abstract: Hybrid evolution and horizontal gene transfer (HGT) are processes where evolutionary relationships may more accurately be described by a reticulated network than by a tree. In such a network, there will often be several paths between any two extant species, reflecting the possible pathways that genetic material may have been passed down from a common ancestor to these species. These paths will typically have different lengths but an 'average distance' can still be calculated between any two taxa. In this article, we ask whether this average distance is able to distinguish reticulate evolution from pure tree-like evolution. We consider two types of reticulation networks: hybridisation networks and HGT networks. For the former, we establish a general result which shows that average distances between extant taxa can appear tree-like, but only under a single hybridisation event near the root in all other cases, the two forms of evolution can be distinguished by average distances. For HGT networks, we demonstrate some analogous but more intricate results.
Publisher: Elsevier BV
Date: 06-2018
DOI: 10.1016/J.JTBI.2018.03.011
Abstract: Phylogenetic networks are an extension of phylogenetic trees which are used to represent evolutionary histories in which reticulation events (such as recombination and hybridization) have occurred. A central question for such networks is that of identifiability, which essentially asks under what circumstances can we reliably identify the phylogenetic network that gave rise to the observed data? Recently, identifiability results have appeared for networks relative to a model of sequence evolution that generalizes the standard Markov models used for phylogenetic trees. However, these results are quite limited in terms of the complexity of the networks that are considered. In this paper, by introducing an alternative probabilistic model for evolution along a network that is based on some ground-breaking work by Thatte for pedigrees, we are able to obtain an identifiability result for a much larger class of phylogenetic networks (essentially the class of so-called tree-child networks). To prove our main theorem, we derive some new results for identifying tree-child networks combinatorially, and then adapt some techniques developed by Thatte for pedigrees to show that our combinatorial results imply identifiability in the probabilistic setting. We hope that the introduction of our new model for networks could lead to new approaches to reliably construct phylogenetic networks.
Publisher: Springer Science and Business Media LLC
Date: 17-02-2020
Publisher: Elsevier BV
Date: 05-2021
Publisher: Wiley
Date: 19-05-2010
Abstract: In this manuscript, we investigate the importance that must be placed on the selection of standard compounds when undertaking studies to optimize the performance of 2-D-HPLC separations. A geometric approach to factor analysis and a measure of peak density across the separation space were applied to assess localized measures of component distributions within the 2-D separation plane. The results of this analysis of data showed that the measure of separation quality varied markedly, depending on the elution zone for which the test was undertaken. The study concluded that if standards cannot be obtained that adequately describe the entire s le matrix, the s le itself should be used, and also, the separation should be optimized for regions of interest, not necessarily the separation as a whole.
Publisher: Springer Science and Business Media LLC
Date: 13-12-2017
DOI: 10.1007/S11538-017-0381-3
Abstract: Phylogenetic networks are a generalization of phylogenetic trees that are used to represent non-tree-like evolutionary histories that arise in organisms such as plants and bacteria, or uncertainty in evolutionary histories. An unrooted phylogenetic network on a non-empty, finite set X of taxa, or network , is a connected, simple graph in which every vertex has degree 1 or 3 and whose leaf set is X . It is called a phylogenetic tree if the underlying graph is a tree. In this paper we consider properties of tree-based networks , that is, networks that can be constructed by adding edges into a phylogenetic tree. We show that although they have some properties in common with their rooted analogues which have recently drawn much attention in the literature, they have some striking differences in terms of both their structural and computational properties. We expect that our results could eventually have applications to, for ex le, detecting horizontal gene transfer or hybridization which are important factors in the evolution of many organisms.
Publisher: Informa UK Limited
Date: 21-03-2001
Publisher: Springer Science and Business Media LLC
Date: 25-04-2023
DOI: 10.1007/S11538-023-01157-0
Abstract: Phylogenetic networks are mathematical representations of evolutionary history that are able to capture both tree-like evolutionary processes (speciations) and non-tree-like ‘reticulate’ processes such as hybridization or horizontal gene transfer. The additional complexity that comes with this capacity, however, makes networks harder to infer from data, and more complicated to work with as mathematical objects. In this paper, we define a new, large class of phylogenetic networks, that we call labellable, and show that they are in bijection with the set of ‘expanding covers’ of finite sets. This correspondence is a generalisation of the encoding of phylogenetic forests by partitions of finite sets. Labellable networks can be characterised by a simple combinatorial condition, and we describe the relationship between this large class and other commonly studied classes. Furthermore, we show that all phylogenetic networks have a quotient network that is labellable.
Publisher: Public Library of Science (PLoS)
Date: 12-02-2010
Publisher: Springer Science and Business Media LLC
Date: 04-10-2018
DOI: 10.1007/S11538-018-0514-3
Abstract: Modellers of large-scale genome rearrangement events, in which segments of DNA are inverted, moved, swapped, or even inserted or deleted, have found a natural syntax in the language of permutations. Despite this, there has been a wide range of modelling choices, assumptions and interpretations that make navigating the literature a significant challenge. Indeed, even authors of papers that use permutations to model genome rearrangement can struggle to interpret each others' work, because of subtle differences in basic assumptions that are often deeply ingrained (and consequently sometimes not even mentioned). In this paper, we describe the different ways in which permutations have been used to model genomes and genome rearrangement events, presenting some features and limitations of each approach, and show how the various models are related. This paper will help researchers navigate the landscape of permutation-based genome rearrangement models and make it easier for authors to present clear and consistent models.
Publisher: Oxford University Press (OUP)
Date: 07-02-2017
Abstract: Consensus methods are widely used for combining phylogenetic trees into a single estimate of the evolutionary tree for a group of species. As more taxa are added, the new source trees may begin to tell a different evolutionary story when restricted to the original set of taxa. However, if the new trees, restricted to the original set of taxa, were to agree exactly with the earlier trees, then we might hope that their consensus would either agree with or resolve the original consensus tree. In this article, we ask under what conditions consensus methods exist that are "future proof" in this sense. While we show that some methods (e.g., Adams consensus) have this property for specific types of input, we also establish a rather surprising "no-go" theorem: there is no "reasonable" consensus method that satisfies the future-proofing property in general. We then investigate a second notion of "future proofing" for consensus methods, in which trees (rather than taxa) are added, and establish some positive and negative results. We end with some questions for future work.
Publisher: Springer Science and Business Media LLC
Date: 11-12-2015
DOI: 10.1007/S00285-014-0852-1
Abstract: Establishing a distance between genomes is a significant problem in computational genomics, because its solution can be used to establish evolutionary relationships including phylogeny. The "double cut and join" (DCJ) model of chromosomal rearrangement proposed by Yancopoulos et al. (Bioinformatics 21:3340-3346, 2005) has received attention as it can model inversions, translocations, fusion and fission on a multichromosomal genome that may contain both linear and circular chromosomes. In this paper, we realize the DCJ operator as a group action on the space of multichromosomal genomes. We study this group action, deriving some properties of the group and finding group-theoretic analogues for the key results in the DCJ theory.
Publisher: Proceedings of the National Academy of Sciences
Date: 10-10-2006
Abstract: The W-Beijing strain of tuberculosis has been identified in many molecular epidemiological studies as being particularly prevalent. This identification has been made possible through the development of a number of genotyping technologies including spoligotyping. Highly prevalent genotypes associated with outbreaks, such as the W-Beijing strain, are implicitly regarded as fast spreading. Here we present a quantitative method to identify “emerging” strains, those that are spreading faster than the background rate inferred from spoligotype data. The approach uses information about the mutation process specific to spoligotypes, combined with a model of both transmission and mutation. The core principle is that if two comparable strains have the same number of isolates, then the strain with fewer inferred mutation events must have spread faster if the mutation process is common. Applying this method to four different data sets, we find not only the W-Beijing strain, but also a number of other strains, to be emerging in this sense. Importantly, the strains that are identified as emerging are not simply those with the largest number of cases. The use of this method should facilitate the targeting of in idual genotypes in intervention programs.
Publisher: Springer Science and Business Media LLC
Date: 2012
Publisher: Elsevier BV
Date: 04-2014
Publisher: Proceedings of the National Academy of Sciences
Date: 25-08-2009
Abstract: The emergence of antibiotic resistance in Mycobacterium tuberculosis has raised the concern that pathogen strains that are virtually untreatable may become widespread. The acquisition of resistance to antibiotics results in a longer duration of infection in a host, but this resistance may come at a cost through a decreased transmission rate. This raises the question of whether the overall fitness of drug-resistant strains is higher than that of sensitive strains—essential information for predicting the spread of the disease. Here, we directly estimate the transmission cost of drug resistance, the rate at which resistance evolves, and the relative fitness of resistant strains. These estimates are made by using explicit models of the transmission and evolution of sensitive and resistant strains of M. tuberculosis , using approximate Bayesian computation, and molecular epidemiology data from Cuba, Estonia, and Venezuela. We find that the transmission cost of drug resistance relative to sensitivity can be as low as 10%, that resistance evolves at rates of ≈0.0025–0.02 per case per year, and that the overall fitness of resistant strains is comparable with that of sensitive strains. Furthermore, the contribution of transmission to the spread of drug resistance is very high compared with acquired resistance due to treatment failure (up to 99%). Estimating such parameters directly from in vivo data will be critical to understanding and responding to antibiotic resistance. For instance, projections using our estimates suggest that the prevalence of tuberculosis may decline with successful treatment, but the proportion of cases associated with resistance is likely to increase.
Publisher: Springer Science and Business Media LLC
Date: 27-11-2008
Publisher: Elsevier BV
Date: 02-2018
Publisher: Springer Berlin Heidelberg
Date: 2014
Publisher: Springer Science and Business Media LLC
Date: 07-06-2006
Abstract: Infectious diseases are often studied by characterising the population structure of the pathogen using genetic markers. An unresolved problem is the effective quantification of the extent of transmission using genetic variation data from such pathogen isolates. It is important that transmission indices reflect the growth of the infectious population as well as account for the mutation rate of the marker and the effects of s ling. That is, while responding to this growth rate, indices should be unresponsive to the s le size and the mutation rate. We use simulation methods taking into account both the mutation and s ling processes to evaluate indices designed to quantify transmission of tuberculosis. Previously proposed indices generally perform inadequately according to the above criteria, with the partial exception of the recently proposed Transmission-Mutation Index. Any transmission index needs to take into account mutation of the marker and the effects of s ling. Simple indices are unlikely to capture the full complexity of the underlying processes.
Publisher: Elsevier BV
Date: 03-2014
Publisher: Elsevier BV
Date: 03-2008
DOI: 10.1016/J.MEEGID.2007.12.004
Abstract: Molecular techniques such as IS6110-RFLP typing and spacer oligonucleotide typing (spoligotyping) have aided in understanding the transmission patterns of Mycobacterium tuberculosis. The degree of clustering of isolates on the basis of genotypes is informative of the extent of transmission in a given geographic area. We analyzed 130 published data sets of M. tuberculosis isolates, each representing a s le of bacterial isolates from a specific geographic region, typed with either or both of the IS6110-RFLP and spoligotyping methods. We explored common features and differences among these s les. Using population models, we found that the presence of large clusters (typically associated with recent transmission) as well as a large number of singletons (genotypes found exactly once in the data set) is consistent with an expanding infectious population. We also estimated the mutation rate of spoligotype patterns relative to IS6110 patterns and found the former rate to be about 10-26% of the latter. This study illustrates the utility of examining the full distribution of genotype cluster sizes from a given region, in the light of population genetic models.
Publisher: Elsevier BV
Date: 11-1999
Publisher: World Scientific Pub Co Pte Lt
Date: 10-2019
DOI: 10.1142/S1793830919500599
Abstract: Many models of genome rearrangement involve operations that are self-inverse, and hence generate a group acting on the space of genomes. This gives a correspondence between genome arrangements and the elements of a group, and consequently, between evolutionary paths and walks on the Cayley graph. Many common methods for phylogenetic reconstruction rely on calculating the minimal distance between two genomes this omits much of the other information available from the Cayley graph. In this paper, we begin an exploration of some of this additional information, in particular describing the phylogeny as a Steiner tree within the Cayley graph, and exploring the “interval” between two genomes. While motivated by problems in systematic biology, many of these ideas are of independent group-theoretic interest.
Publisher: Elsevier BV
Date: 2023
Publisher: World Scientific Pub Co Pte Lt
Date: 06-2003
Publisher: Elsevier BV
Date: 12-2006
Publisher: Springer Science and Business Media LLC
Date: 23-06-2013
DOI: 10.1007/S00285-013-0702-6
Abstract: The variation in genome arrangements among bacterial taxa is largely due to the process of inversion. Recent studies indicate that not all inversions are equally probable, suggesting, for instance, that shorter inversions are more frequent than longer, and those that move the terminus of replication are less probable than those that do not. Current methods for establishing the inversion distance between two bacterial genomes are unable to incorporate such information. In this paper we suggest a group-theoretic framework that in principle can take these constraints into account. In particular, we show that by lifting the problem from circular permutations to the affine symmetric group, the inversion distance can be found in polynomial time for a model in which inversions are restricted to acting on two regions. This requires the proof of new results in group theory, and suggests a vein of new combinatorial problems concerning permutation groups on which group theorists will be needed to collaborate with biologists. We apply the new method to inferring distances and phylogenies for published Yersinia pestis data.
Publisher: Elsevier BV
Date: 06-2017
DOI: 10.1016/J.JTBI.2017.04.015
Abstract: Accurate estimation of evolutionary distances between taxa is important for many phylogenetic reconstruction methods. Distances can be estimated using a range of different evolutionary models, from single nucleotide polymorphisms to large-scale genome rearrangements. Corresponding corrections for genome rearrangement distances fall into 3 categories: Empirical computational studies, Bayesian/MCMC approaches, and combinatorial approaches. Here, we introduce a maximum likelihood estimator for the inversion distance between a pair of genomes, using a group-theoretic approach to modelling inversions introduced recently. This MLE functions as a corrected distance: in particular, we show that because of the way sequences of inversions interact with each other, it is quite possible for minimal distance and MLE distance to differently order the distances of two genomes from a third. The second aspect tackles the problem of accounting for the symmetries of circular arrangements. While, generally, a frame of reference is locked, and all computation made accordingly, this work incorporates the action of the dihedral group so that distance estimates are free from any a priori frame of reference. The philosophy of accounting for symmetries can be applied to any existing correction method, for which ex les are offered.
Publisher: Elsevier BV
Date: 07-2005
Publisher: Springer Science and Business Media LLC
Date: 29-12-2013
DOI: 10.1007/S00285-013-0747-6
Abstract: Rearrangements of bacterial chromosomes can be studied mathematically at several levels, most prominently at a local, or sequence level, as well as at a topological level. The biological changes involved locally are inversions, deletions, and transpositions, while topologically they are knotting and catenation. These two modelling approaches share some surprising algebraic features related to braid groups and Coxeter groups. The structural approach that is at the core of algebra has long found applications in sciences such as physics and analytical chemistry, but only in a small number of ways so far in biology. And yet there are ex les where an algebraic viewpoint may capture a deeper structure behind biological phenomena. This article discusses a family of biological problems in bacterial genome evolution for which this may be the case, and raises the prospect that the tools developed by algebraists over the last century might provide insight to this area of evolutionary biology.
Publisher: Springer Science and Business Media LLC
Date: 06-2020
Publisher: Springer Science and Business Media LLC
Date: 23-08-2017
Publisher: The Royal Society
Date: 06-2022
Abstract: We introduce a correspondence between phylogenetic trees and Brauer diagrams, inspired by links between binary trees and matchings described by Diaconis and Holmes (1998 Proc. Natl Acad. Sci. USA 95 , 14 600–14 602. ( doi:10.1073 nas.95.25.14600 )). This correspondence gives rise to a range of semigroup structures on the set of phylogenetic trees, and opens the prospect of many applications. We furthermore extend the Diaconis–Holmes correspondence from binary trees to non-binary trees and to forests, showing for instance that the set of all forests is in bijection with the set of partitions of finite sets.
Publisher: Oxford University Press (OUP)
Date: 18-08-2008
DOI: 10.1093/BIOINFORMATICS/BTN434
Abstract: spolTools is a collection of online programs designed to manipulate and analyze spoligotype datasets of the Mycobacterium tuberculosis complex. These tools are integrated into a repository currently containing 1179 spoligotypes and 6278 isolates across 30 datasets. Users can search this database to export for external use or to pass on to the integrated tools. These tools include the computation of basic population genetic quantities, the visualization of clusters of spoligotype patterns based on an estimated evolutionary history and a procedure to predict emerging strains – genotypes associated with elevated transmission. Availability: Database, programs and documentation may be accessed online at www.emi.unsw.edu.au/spolTools. Contact: j.reyes@student.unsw.edu.au m.tanaka@unsw.edu.au
Publisher: Cold Spring Harbor Laboratory
Date: 03-04-2020
DOI: 10.1101/2020.03.31.20049312
Abstract: The spread of COVID-19 is expected to put a large strain on many hospital resources, including ICU bed space, and mortuary capacity. In this report we study the possible demands on ICU and mortuary capacity in Sydney, Australia, using an adapted SEIR epidemiological model.
Publisher: Elsevier BV
Date: 02-2009
Publisher: Elsevier BV
Date: 09-2020
Start Date: 2005
End Date: 12-2008
Amount: $265,000.00
Funder: Australian Research Council
View Funded ActivityStart Date: 2009
End Date: 12-2014
Amount: $614,870.00
Funder: Australian Research Council
View Funded ActivityStart Date: 12-2010
End Date: 06-2015
Amount: $670,732.00
Funder: Australian Research Council
View Funded ActivityStart Date: 05-2018
End Date: 06-2022
Amount: $338,178.00
Funder: Australian Research Council
View Funded ActivityStart Date: 2013
End Date: 12-2015
Amount: $330,000.00
Funder: Australian Research Council
View Funded Activity