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Using multitype branching models to analyze bacterial pathogenicity
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.ORCID iD: 0000-0002-7672-190X
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.ORCID iD: 0000-0002-5816-4345
Institute of Medical Biology, Polish Academy of Sciences, Poland.
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(English)In: Article in journal (Refereed) Submitted
Abstract [en]

We apply multitype, continuous time Markov branching models to study pathogenicity in E. coli, a bacterium belonging to the genus Escherichia. First, we examine briefly the properties of multitype branching processes and we also survey some fundamental limit theorems regarding the behavior of such models under various conditions. These theorems are then applied to discrete, state dependent models in order to analyze pathogenicity in a published clinical data set consisting of 251 strains of E. coli. We use well established methods, incorporating maximum likelihood techniques, to estimate speciation rates as well as the rates of transition between different states of the models. From the analysis, we not only derive new results, we also verify some preexisting notions about virulent behavior in bacterial strains.

Keywords [en]
Markov models, branching processes, limit theorems, virulence factors, E. coli strains.
National Category
Mathematics Biological Sciences
Identifiers
URN: urn:nbn:se:uu:diva-380966OAI: oai:DiVA.org:uu-380966DiVA, id: diva2:1301720
Available from: 2019-04-02 Created: 2019-04-02 Last updated: 2019-04-25
In thesis
1. Multi-trait Branching Models with Applications to Species Evolution
Open this publication in new window or tab >>Multi-trait Branching Models with Applications to Species Evolution
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis provides an analysis of the evolution of discrete traits and their effect on the birth and survival of species using the theory of supercritical, continuous time Markov branching processes. We present a branching modeling framework that incorporates multi-trait diversification processes associated with the emergence of new species, death of existing species, and transition of species carrying one type of a trait to another. The trait-dependent speciation, extinction, and transition help in interpreting the relationships between traits on one hand, and linking together the diversification process with molecular evolution on the other. Various multitype species branching models are applied in order to examine the evolutionary patterns in known data sets, such as the impact of outcrossing and selfing mating systems on the diversification rates of species, and the analysis of virulent behavior of pathogenic bacterial strains in different environments. Stochastic equations and limit theorems for branching processes help scrutinize the long time asymptotics of the models under an asymmetry in change of types, and under various schemes of rescaling. In addition, we explore diversity-dependent processes in which, instead of allowing supercritical growth of population sizes, the increase in species numbers is regulated by modifying the species branching rates. The use of probabilistic methods in a setting of population genetics leads to an analogy between biallelic frequency models and binary trait species tree models. To obtain an approximation for a Markov branching process of species evolution over a long geological time scale, we methodically utilize the theory of diffusion processes. Overall, our results show that branching models can be effectively used to seek to comprehend the diversification patterns in species during the process of evolution.

Place, publisher, year, edition, pages
Uppsala: Department of Mathematics, 2019. p. 55
Series
Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 115
Keywords
Markov models, branching processes, density dependence, discrete traits, species trees, diversification rates, diffusion approximation
National Category
Mathematics Evolutionary Biology
Identifiers
urn:nbn:se:uu:diva-380975 (URN)978-91-506-2765-7 (ISBN)
Public defence
2019-06-14, Room 80101, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 13:15 (English)
Opponent
Supervisors
Available from: 2019-05-23 Created: 2019-04-25 Last updated: 2019-05-23

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Tahir, DaniahKaj, IngemarBartoszek, Krzysztof

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