Speed of evolution with spatial structure and interacting mutations Open Access

Otwinowski, Jakub (2012)

Permanent URL: https://etd.library.emory.edu/concern/etds/z029p484q?locale=en
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Abstract

Abstract
Speed of evolution with spatial structure and interacting mutations
Perhaps the simplest question about long term evolutionary adaptation is how quickly do
populations adapt to a new environment by incorporating mutations? This question is
approached from several different angles. Chapter 1 investigates the speed of evolution
when there is a large supply of beneficial mutations and the population has spatial structure.
For large system sizes, a speed limit is found on the rate adaptation. The model is analyzed as
a surface growth model in physics, which reveals universal properties of the model, such as
the distribution of fitnesses. However, neglecting spatial structure, the speed of evolution
also depends on how mutations interact with each other. This may be quantified by a fitness
landscape, or a genotype-phenotype-fitness map. In chapter 2, the fitness landscape and
genotype-phenotype map of an E. coli lac promoter is inferred from a large dataset with
100,000 sequences and fluorescence measurements. The interactions between mutations are
quantified using a simple quadratic model, similar to a spin glass Hamiltonian. Chapter 3
describes a toy model based on an overdamped particle in a potential, which demonstrates
how a fitness landscape with time dependent interactions between mutations determines the
speed of evolution.

Table of Contents

Introduction
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Evolution of large populations . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Evolution with spatial structure . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 Epistasis and fitness landscapes . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.5 Fluctuating selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.6 Final thoughts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 Speed of evolution in spatially structured populations
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Wright-Fisher model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Periodic selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4 Model with spatial structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.5 Speed of evolution with spatial competition . . . . . . . . . . . . . . . . . . 14
2.6 Surface growth and universal fitness distributions . . . . . . . . . . . . . . . 17
2.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3 Inference of a genotype-phenotype map
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2.1 Inferring the non-epistatic genotype to phenotype map . . . . . . . 27
3.2.2 Inferring epistatic contributions to fitness . . . . . . . . . . . . . . . 29
3.2.3 Properties of the inferred genomic landscape . . . . . . . . . . . . . 31
3.2.4 Landscape in two environments . . . . . . . . . . . . . . . . . . . . . 34
3.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4 Speeding up evolutionary search by small fitness fluctuations
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.2 The model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.2.1 Rescaling of the equation of motion . . . . . . . . . . . . . . . . . . 44
4.3 Fluctuating potentials enhances diffusion and drift . . . . . . . . . . . . . . 45
4.3.1 Building intuition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.3.2 Analytical treatment at β → ∞ . . . . . . . . . . . . . . . . . . . . . 47
4.4 Fluctuating potential shortens the fitness barrier crossing time . . . . . . . 49
4.4.1 Fluctuation-activated escape from the minimum is possible even at
zero internal diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.4.2 Fluctuations enhance escape even for steep barriers . . . . . . . . . . 51
4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
A Fisher's Fundamental Theorem 55
B Diffusion and drift in the no-noise limit 57
Bibliography 58

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