Allele Frequency Spectra for 1-Dimensional Circular Populations Open Access

Arani, Akash (Spring 2021)

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The natural limit on geographic genetic dispersal given through isolation by distance encourages the use of spatial structure to analyze genetic diversity, commonly analyzed using allele frequency spectra. This paper aims to analyze the spectra of one of the simplest forms of discrete population structure: 1-dimensional circular populations. Msprime was used to model the genetic variation of a 1-dimensional circular population and create genealogical trees using coalescent theory. As mutations were assumed to have no effect on fitness, neutral mutations were applied post coalescent simulation. These genealogical trees were then converted to allele frequency spectra by counting the number of single nucleotide polymorphisms (SNPS) per branch group.

The results focused on strong structured 1-dimensional circular populations, where the configuration of the demes and the intra-deme migration rate had a significant impact on genetic variation. Simulation results showed that the expected allele frequency spectra of strong-structured 1-dimensional circular populations matched the predicted allele frequency spectra for populations of census size at low frequencies and transitioned to match the predicted allele frequency spectra for populations of effective size at higher frequencies. These results indicate that 1-dimensional circular populations undergo changes in genetic variation at different frequencies and populations need to be deeply sampled to analyze a population’s genetic variation. Further research is needed to identify if this behavior translates to higher-dimensional structures and continuous space.

Table of Contents

Introduction 7

Model 11

Results 14

Allele frequency spectra: 1< 16

Allele frequency spectral : m⍴<19

Transition frequencies 22

Discussion 26

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