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Inbreeding, Effective Population Sizes and Genetic Differentiation: A Mathematical Analysis of Structured Populations
Stockholm University, Faculty of Science, Department of Mathematics.
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: urn:nbn:se:su:diva-115708ISBN: 978-91-7649-147-8 (print)OAI: oai:DiVA.org:su-115708DiVA: diva2:798994
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At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 4: Submitted.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
List of papers
1. Characteristics of the variance effective population size over time using an age structured model with variable size
Open this publication in new window or tab >>Characteristics of the variance effective population size over time using an age structured model with variable size
2013 (English)In: Theoretical Population Biology, ISSN 0040-5809, E-ISSN 1096-0325, Vol. 90, 91-103 p.Article in journal (Refereed) Published
Abstract [en]

The variance effective population size (N-ev) is a key concept in population biology, because it quantifies the microevolutionary process of random genetic drift, and understanding the characteristics of N-ev is thus of central importance. Current formulas for Nev for populations with overlapping generations weight age classes according to their reproductive values (i.e. reflecting the contribution of genes from separate age classes to the population growth) to obtain a correct measure of genetic drift when computing the variance of the allele frequency change over time. In this paper, we examine the effect of applying different weights to the age classes using a novel analytical approach for exploring N-ev. We consider a haploid organism with overlapping generations and populations of increasing, declining, or constant expected size and stochastic variation with respect to the number of individuals in the separate age classes. We define Nov, as a function of how the age classes are weighted, and of the span between the two points in time, when measuring allele frequency change. With this model, time profiles for N-ev can be calculated for populations with various life histories and with fluctuations in life history composition, using different weighting schemes. We examine analytically and by simulations when Nei, using a weighting scheme with respect to reproductive contribution of separate age classes, accurately reflect the variance of the allele frequency change due to genetic drift over time. We show that the discrepancy of N-ev, calculated with reproductive values as weights, compared to when individuals are weighted equally, tends to a constant when the time span between the two measurements increases. This constant is zero only for a population with a constant expected population size. Our results confirm that the effect of ignoring overlapping generations, when empirically assessing Nell from allele frequency shifts, gets smaller as the time interval between samples increases. Our model has empirical applications including assessment of (i) time intervals necessary to permit ignoring the effect of overlapping generations for N-ev estimation by means of the temporal method, and (ii) effects of life table manipulation on N-ev over varying time periods.

Keyword
Variance effective population size, Fluctuating size of age classes, Overlapping generations, Temporal method
National Category
Mathematics Biological Sciences
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:su:diva-98288 (URN)10.1016/j.tpb.2013.09.014 (DOI)000327925000009 ()
Funder
Swedish Research CouncilSwedish Environmental Protection Agency
Note

AuthorCount:4;

Available from: 2014-01-08 Created: 2014-01-03 Last updated: 2017-12-06Bibliographically approved
2. A new general analytical approach for modeling patterns of genetic differentiation and effective size of subdivided populations over time
Open this publication in new window or tab >>A new general analytical approach for modeling patterns of genetic differentiation and effective size of subdivided populations over time
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.

Keyword
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:nbn:se:su:diva-113969 (URN)10.1016/j.mbs.2014.10.001 (DOI)000348020700012 ()
Note

AuthorCount:4;

Available from: 2015-02-20 Created: 2015-02-16 Last updated: 2017-12-04Bibliographically approved
3. Estimation of the variance effective population size in age structured populations
Open this publication in new window or tab >>Estimation of the variance effective population size in age structured populations
2015 (English)In: Theoretical Population Biology, ISSN 0040-5809, E-ISSN 1096-0325, Vol. 101, 9-23 p.Article in journal (Refereed) Published
Abstract [en]

The variance effective population size for age structured populations is generally hard to estimate and the temporal method often gives biased estimates. Here, we give an explicit expression for a correction factor which, combined with estimates from the temporal method, yield approximately unbiased estimates. The calculation of the correction factor requires knowledge of the age specific offspring distribution and survival probabilities as well as possible correlation between survival and reproductive success. In order to relax these requirements, we show that only first order moments of these distributions need to be known if the time between samples is large, or individuals from all age classes which reproduce are sampled. A very explicit approximate expression for the asymptotic coefficient of standard deviation of the estimator is derived, and it can be used to construct confidence intervals and optimal ways of weighting information from different markers. The asymptotic coefficient of standard deviation can also be used to design studies and we show that in order to maximize the precision for a given sample size, individuals from older age classes should be sampled since their expected variance of allele frequency change is higher and easier to estimate. However, for populations with fluctuating age class sizes, the accuracy of the method is reduced when samples are taken from older age classes with high demographic variation. We also present a method for simultaneous estimation of the variance effective and census population size.

Keyword
Variance effective population size, Temporal method, Effective number of independent alleles, Overlapping generations, Confidence interval
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:su:diva-115417 (URN)10.1016/j.tpb.2015.02.003 (DOI)000352828400002 ()
Available from: 2015-03-24 Created: 2015-03-24 Last updated: 2017-12-04Bibliographically approved
4. Simulation methods for age structured populations
Open this publication in new window or tab >>Simulation methods for age structured populations
(English)In: Mathematical Biosciences, ISSN 0025-5564, E-ISSN 1879-3134Article in journal (Refereed) Submitted
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:su:diva-115617 (URN)
Available from: 2015-03-27 Created: 2015-03-27 Last updated: 2017-12-04

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