Effects of Mutation and Recombination on the Rate of Evolution on a Time varying Mt. Fuji Fitness Landscape 公开
Kirkham, John (2013)
Published
Abstract
Recombination confers many positive attributes to populations of organisms, who implement it. The discovery of recombination in bacteria changed our understanding of them. Interactions of recombination, mutation and selection have been considered in diploid organisms, but this still leaves plenty of questions open about haploid organisms. Though it is commonly believed that recombination exists primarily to repair DNA and possibly increase variability, the interaction of recombination and mutation has not been well considered. In this thesis, a WrightFisher model of a population evolving on a Mt. Fuji Landscape will be explored with different values of selection, mutation, and recombination. Ultimately, the model will incorporate periodic fluctuations that completely randomize the peak of the Mt. Fuji Landscape. The goal of this thesis is to answer the following question: What are the optimal mutation and recombination rates to most rapidly improve a population's fitness given a fixed period and selection strength? It will be demonstrated that the recombination has no optimum (more recombination is always better). Further, it will be demonstrated that the mutation rate does have an optimum that is strongly affected by period and possibly weakly affected by selection.
Table of Contents
Contents
1 Introduction 1
2 Methods 3
3 Results 8
4 Discussion 30
5 Conclusion 32
Nomenclature 33
Appendices 34
A Probability Distributions 34
A.1 Preliminaries ........................................ 34
A.2 Bernoulli Distribution ................................... 35
A.3 Symmetric Bernoulli Distribution............................. 35
A.4 Geometric Distribution................................... 36
A.5 Binomial Distribution ................................... 37
A.6 Symmetric Binomial Distribution............................. 37
A.7 Normal Distribution .................................... 38
A.8 Uniform Distribution.................................... 38
A.9 Standard Uniform Distribution .............................. 39
B Population Distribution Cases 40
B.1 Initial Distribution..................................... 40
B.1.1 Ideal Sequence Distance Average ......................... 40
B.1.2 Average Sequence Variance ............................ 40
B.1.3 Approximate Best Individual ........................... 41
B.2 One Uncertain Bit in the Population........................... 43
B.2.1 Average Sequence Variance ............................ 43
B.3 Equally dispersed clones with one bit different from the ideal sequence (similar to Muller's ratchet) ...................................... 44
B.3.1 Average Sequence Variance ............................ 44
B.4 Competition between two types of clones......................... 44
B.4.1 Average Sequence Variance ............................ 44
C Code Documentation 46
C.1 Generics Library ...................................... 47
C.2 Bacteria Multiplication Library.............................. 54
C.3 Bacteria Multiplication................................... 55
C.4 Bacteria Multiplication Log Parser ............................ 56
D Algorithmic Details 57
D.1 Probability Distributions.................................. 57
D.1.1 Preliminaries .................................... 57
D.1.2 Bernoulli Distribution Mapping.......................... 57
D.1.3 Uniform Distribution Mapping .......................... 57
D.1.4 Optimized Bernoulli Distribution Mapping ................... 57
D.1.5 Geometric Distribution Mapping ......................... 58
6 References 59
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