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Multi-trait Branching Models with Applications to Species Evolution
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Description
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 [en]
Markov models, branching processes, density dependence, discrete traits, species trees, diversification rates, diffusion approximation
National Category
Mathematics Evolutionary Biology
Identifiers
URN: urn:nbn:se:uu:diva-380975ISBN: 978-91-506-2765-7 (print)OAI: oai:DiVA.org:uu-380975DiVA, id: diva2:1306824
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
List of papers
1. Modeling a trait-dependent diversification process coupled with molecular evolution on a random species tree
Open this publication in new window or tab >>Modeling a trait-dependent diversification process coupled with molecular evolution on a random species tree
2019 (English)In: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 461, p. 189-203Article in journal (Refereed) Published
Abstract [en]

Understanding the evolution of binary traits, which affects the birth and survival of species and also the rate of molecular evolution, remains challenging. In this work, we present a probabilistic modeling framework for binary trait, random species trees, in which the number of species and their traits are represented by an asymmetric, two-type, continuous time Markov branching process. The model involves a number of different parameters describing both character and molecular evolution on the so-called 'reduced' tree, consisting of only extant species at the time of observation. We expand our model by considering the impact of binary traits on dN/dS, the normalized ratio of nonsynonymous to synonymous substitutions. We also develop mechanisms which enable us to understand the substitution rates on a phylogenetic tree with regards to the observed traits. The properties obtained from the model are illustrated with a phylogeny of outcrossing and selfing plant species, which allows us to investigate not only the branching tree rates, but also the molecular rates and the intensity of selection.

Keywords
Branching processes, Irreversible transitions, Binary traits, Phylogenetic trees, Mutation rates
National Category
Evolutionary Biology Probability Theory and Statistics
Identifiers
urn:nbn:se:uu:diva-372749 (URN)10.1016/j.jtbi.2018.10.032 (DOI)000452245900018 ()30340056 (PubMedID)
Available from: 2019-01-15 Created: 2019-01-15 Last updated: 2019-04-25
2. Using multitype branching models to analyze bacterial pathogenicity
Open this publication in new window or tab >>Using multitype branching models to analyze bacterial pathogenicity
Show others...
(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
Markov models, branching processes, limit theorems, virulence factors, E. coli strains.
National Category
Mathematics Biological Sciences
Identifiers
urn:nbn:se:uu:diva-380966 (URN)
Available from: 2019-04-02 Created: 2019-04-02 Last updated: 2019-04-25
3. Stochastic equations and limit results for some two-type branching models
Open this publication in new window or tab >>Stochastic equations and limit results for some two-type branching models
2019 (English)In: Statistics and Probability Letters, ISSN 0167-7152, E-ISSN 1879-2103, Vol. 150, p. 35-46Article in journal (Refereed) Published
Abstract [en]

A class of binary state, asymmetric, continuous time Markov branching processes are analyzed under supercritical conditions. Stochastic equations are provided, and limit results for the long time asymptotics as well as for the behavior of the model under rescaling are reviewed. Extensions are presented for model variations, such as population size dependence, with the purpose of promoting further use of these models for applications.

Keywords
Continuous time branching process, Asymmetric model, Population size dependence, Functional limit theory, Central limit theory
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:uu:diva-380960 (URN)10.1016/j.spl.2019.02.011 (DOI)000466623900006 ()
Available from: 2019-04-02 Created: 2019-04-02 Last updated: 2019-06-25Bibliographically approved
4. Analysis of diversity-dependent species evolution using concepts in population genetics
Open this publication in new window or tab >>Analysis of diversity-dependent species evolution using concepts in population genetics
(English)Manuscript (preprint) (Other academic)
Abstract [en]

In this work, we consider a two-type species model with trait dependent speciation, extinction and transition rates under an evolutionary time scale. The scaling approach and the diffusion approximation techniques which are widely used in mathematical population genetics provide background and tools to assist in the study of species dynamics, and help explore the analogy between trait dependent species diversication and the evolution of allele frequencies in the population genetics setting. The analytical framework specied is then applied to models incorporating diversity-dependence, in order to infer effective results from processes in which the net growth of species depends on their current population sizes.

National Category
Evolutionary Biology
Identifiers
urn:nbn:se:uu:diva-380961 (URN)
Available from: 2019-04-02 Created: 2019-04-02 Last updated: 2019-04-25

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