Details

Autor(en) / Beteiligte

• Labo, Philip Thomas

Titel

Yeast and Chemostats, Balls and Urns: Two Comments on the Dynamics of Adaptive Evolution

Ort / Verlag

ProQuest Dissertations & Theses

Erscheinungsjahr

2012

Quelle

ProQuest Dissertations & Theses A&I

Beschreibungen/Notizen

• Kao & Sherlock (2008) present three-color data on yeast evolutionary dynamics. Four of their experiments depict one hundred million yeast cells; four depict one billion yeast cells. Each shows the adaptive evolution of an initially neutral population for about five hundred generations. Each cell in their experimental populations fluoresces one of three colors (red, yellow, or green). Their data show subpopulations so-defined evolving through time. Our work deals with the Wright-Fisher model (Fisher 1922; Wright 1931) and its use in modeling the Kao-Sherlock data (2008). In particular we use the model in an attempt to approximate the adaptive characteristics of the subpopulations that underlie the red, yellow, and green Kao-Sherlock subpopulations. We introduce our work on these data in Chapter 2. Specifically, we describe the data in detail and review the model and its continuous time approximation. We also review briefly previous work pertinent to our work here. Chapter 3 deals with two mathematical features of the Wright-Fisher model. We bound the means of certain stopping times relating to the process. Such bounds show that the process with selection spends little time in the central part of its domain; it spends most of its time near the boundaries of such. We then discuss approximating the mean of the process with selection. We show how typical calculations break down and discuss the assumptions underlying our approximation. Chapter 4 then applies the results of Chapter 3 to the Kao-Sherlock yeast data. We discuss issues relating to data fitting and parameter estimation and arrive at an approach based on sequential non-linear regressions. We give our results in the context of additional recent results by Kvitek & Sherlock (unpublished) and discuss pros and cons relating to in silico versus experimental approaches. In the end each informs the other. Model-based results allow the direct comparison of assumptions and outcomes.In Chapter 5 we consider an urn model of simplified adaptive dynamics. Imagine an urn containing one ball. On closer inspection we see that it has a "0" printed on it. We select the ball from the urn. Seeing the "0" we return it to the urn along with a new "1" ball. We repeat this indefinitely. At each step we:1. Select a ball at random from the urn making a mental note of its number;2. Throw the selected ball back into the urn and then add a brand-new ball. The new ball sports a number one greater than that on the selected ball.In Chapter 5 we derive bounds for the expected dynamics of this process. In addition, we take pains to build a tenuous connection between this process and the process underlying our conception of adaptive evolution. We close by suggesting several possible interesting research directions involving urn models in population genetics.