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A new general analytical approach for modeling patterns of genetic differentiation and effective size of subdivided populations over time
Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Faculty of Science, Department of Zoology.
Stockholm University, Faculty of Science, Department of Zoology.
2014 (English)In: Mathematical Biosciences, ISSN 0025-5564, E-ISSN 1879-3134, Vol. 258, 113-133 p.Article in journal (Refereed) Published
Abstract [en]

The main purpose of this paper is to develop a theoretical framework for assessing effective population size and genetic divergence in situations with structured populations that consist of various numbers of more or less interconnected subpopulations. We introduce a general infinite allele model for a diploid, monoecious and subdivided population, with subpopulation sizes varying overtime, including local subpopulation extinction and recolonization, bottlenecks, cyclic census size changes or exponential growth. Exact matrix analytic formulas are derived for recursions of predicted (expected) gene identities and gene diversities, identity by descent and coalescence probabilities, and standardized variances of allele frequency change. This enables us to compute and put into a general framework a number of different types of genetically effective population sizes (N-e) including variance, inbreeding, nucleotide diversity, and eigenvalue effective size. General expressions for predictions (g(ST)) of the coefficient of gene differentiation G(ST) are also derived. We suggest that in order to adequately describe important properties of a subdivided population with respect to allele frequency change and maintenance of genetic variation over time, single values of g(ST) and N-e are not enough. Rather, the temporal dynamic patterns of these properties are important to consider. We introduce several schemes for weighting subpopulations that enable effective size and expected genetic divergence to be calculated and described as functions of time, globally for the whole population and locally for any group of subpopulations. The traditional concept of effective size is generalized to situations where genetic drift is confounded by external sources, such as immigration and mutation. Finally, we introduce a general methodology for state space reduction, which greatly decreases the computational complexity of the matrix analytic formulas.

Place, publisher, year, edition, pages
2014. Vol. 258, 113-133 p.
Keyword [en]
Effective population size, Coefficient of gene differentiation, Matrix analytic methods, Subpopulation weights, State space reduction
National Category
Biological Sciences Mathematics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:su:diva-113969DOI: 10.1016/j.mbs.2014.10.001ISI: 000348020700012OAI: oai:DiVA.org:su-113969DiVA: diva2:789810
Note

AuthorCount:4;

Available from: 2015-02-20 Created: 2015-02-16 Last updated: 2017-12-04Bibliographically approved
In thesis
1. Inbreeding, Effective Population Sizes and Genetic Differentiation: A Mathematical Analysis of Structured Populations
Open this publication in new window or tab >>Inbreeding, Effective Population Sizes and Genetic Differentiation: A Mathematical Analysis of Structured Populations
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of four papers on various aspects of inbreeding, effective population sizes and genetic differentiation in structured populations, that is, populations that consist of a number of subpopulations. Three of the papers concern age structured populations, where in the first paper we concentrate on calculating the variance effective population size (NeV) and how NeV depends on the time between measurements and the weighting scheme of age classes. In the third paper we develop an estimation procedure of NeV which uses age specific demographic parameters to obtain approximately unbiased estimates. A simulation method for age structured populations is presented in the fourth paper. It is applicable to models with multiallelic loci in linkage equilibrium.

In the second paper, we develop a framework for analysis of effective population sizes and genetic differentiation in geographically subdivided populations with a general migration scheme. Predictions of gene identities and gene diversities of the population are presented, which are used to find expressions for effective population sizes (Ne) and the coefficient of gene differentiation (GST). We argue that not only the asymptotic values of Ne and GST are important, but also their temporal dynamic patterns.

The models presented in this thesis are important for understanding how different age decomposition, migration and reproduction scenarios of a structured population affect quantities, such as various types of effective sizes and genetic differentiation between subpopulations.

Place, publisher, year, edition, pages
Stockholm: Department of Mathematics, Stockholm University, 2015
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:su:diva-115708 (URN)978-91-7649-147-8 (ISBN)
Public defence
2015-05-22, room 14, house 5, Kräftriket, Roslagsvägen 101, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 4: Submitted.

Available from: 2015-04-29 Created: 2015-03-27 Last updated: 2015-05-05Bibliographically approved

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Hössjer, OlaOlsson, FredrikLaikre, LindaRyman, Nils
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