**Memoirs of the American Mathematical Society**

2015;
87 pp;
Softcover

MSC: Primary 60; 92;

Print ISBN: 978-1-4704-0967-8

Product Code: MEMO/233/1096

List Price: $71.00

AMS Member Price: $42.60

MAA Member Price: $63.90

**Electronic ISBN: 978-1-4704-1964-6
Product Code: MEMO/233/1096.E**

List Price: $71.00

AMS Member Price: $42.60

MAA Member Price: $63.90

# Critical Population and Error Threshold on the Sharp Peak Landscape for a Moran Model

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*Raphaël Cerf*

The goal of this work is to propose a finite population counterpart to Eigen's model, which incorporates stochastic effects. The author considers a Moran model describing the evolution of a population of size \(m\) of chromosomes of length \(\ell\) over an alphabet of cardinality \(\kappa\). The mutation probability per locus is \(q\). He deals only with the sharp peak landscape: the replication rate is \(\sigma>1\) for the master sequence and \(1\) for the other sequences. He studies the equilibrium distribution of the process in the regime where \[\ell\to +\infty,\qquad m\to +\infty,\qquad q\to 0,\] \[{\ell q} \to a\in ]0,+\infty[, \qquad\frac{m}{\ell}\to\alpha\in [0,+\infty].\]

#### Table of Contents

# Table of Contents

## Critical Population and Error Threshold on the Sharp Peak Landscape for a Moran Model

- Cover Cover11 free
- Title page i2 free
- Chapter 1. Introduction 18 free
- Chapter 2. The Model 916 free
- Chapter 3. Main Results 1320
- Chapter 4. Coupling 1926
- Chapter 5. Normalized Model 2128
- Chapter 6. Lumping 2532
- Chapter 7. Monotonicity 3340
- Chapter 8. Stochastic Bounds 3946
- Chapter 9. Birth and Death Processes 4754
- Chapter 10. The Neutral Phase 5562
- Chapter 11. Synthesis 7986
- Appendix A. Appendix on Markov Chains 8188
- Bibliography 8592
- Index 8794 free
- Back Cover Back Cover1100