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Characteristics of the variance effective population size over time using an age structured model with variable size
Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Faculty of Science, Department of Zoology.ORCID iD: 0000-0001-9286-3361
Stockholm University, Faculty of Science, Department of Zoology.ORCID iD: 0000-0003-3342-8479
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.

Place, publisher, year, edition, pages
2013. Vol. 90, 91-103 p.
Keyword [en]
Variance effective population size, Fluctuating size of age classes, Overlapping generations, Temporal method
National Category
Mathematics Biological Sciences
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:su:diva-98288DOI: 10.1016/j.tpb.2013.09.014ISI: 000327925000009OAI: oai:DiVA.org:su-98288DiVA: diva2:684414
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
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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Olsson, FredrikHössjer, OlaLaikre, LindaRyman, Nils
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