Mathematical investigations into fundamental population-genetic statistics and models
Abstract/Contents
- Abstract
- This dissertation explores three projects that take a theoretical approach to studying the underlying models and statistics that are used in population genetics research. Each focuses on a fundamental model or statistic in population genetics, building on the long history of theoretical research in the field while relating the quantity of interest to current research in population genetics. The first two projects relate to the fundamental population genetic model, the coalescent, and the third project explores Wright's FST. The first project consists of modeling a biological process to understand the signature it leaves in data. "A Markov Model of the Coalescent with Recombination and Population Substructure", develops an extension of the coalescent model that incorporates recombination and population substructure. This project serves to offer a framework to simulate random neutral processes that could produce similar genomic signatures to another biological phenomenon, horizontal gene transfer. The second project uses probability theory to study the random genealogies invoked in the coalescent process: coalescent trees. A better understanding of the coalescent model itself can inform the development and use of the statistics derived from the coalescent. "On the Joint Distribution of Height and Length of Trees Under the Coalescent" explores the joint distribution of coalescent tree height, Hn, and length, Ln. Understanding the relationship of height and length is important to the development and analysis of statistics that estimate the length from observed data as a proxy for the height. The third project relates to understanding the properties of a biological statistic, FST. "FST and the Triangle Inequality for Biallelic Markers" explores the use of FST as a measure of distance. FST is not a true distance metric because it does not satisfy the triangle inequality and we show that biallelic FST fails the triangle inequality everywhere. We also show that biallelic FST always fails to be a tree-like distance for distinct allele frequencies. We explore the consequences for analyses that take in a distance matrix, such as spatial analyses, like multidimensional scaling, and tree-building algorithms, like neighbor-joining.
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource. |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2018; ©2018 |
| Publication date | 2018; 2018 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Arbisser, Ilana Marisa |
|---|---|
| Degree supervisor | Rosenberg, Noah |
| Thesis advisor | Rosenberg, Noah |
| Thesis advisor | Feldman, Marcus W |
| Thesis advisor | Palacios Roman, Julia Adela |
| Degree committee member | Feldman, Marcus W |
| Degree committee member | Palacios Roman, Julia Adela |
| Associated with | Stanford University, Department of Biology. |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Ilana Arbisser. |
|---|---|
| Note | Submitted to the Department of Biology. |
| Thesis | Thesis Ph.D. Stanford University 2018. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2018 by Ilana Marisa Arbisser
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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