Electronic ISBN:  9781470419646 
Product Code:  MEMO/233/1096.E 
List Price:  $71.00 
MAA Member Price:  $63.90 
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 233; 2015; 87 ppMSC: Primary 60; 92;
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

Chapters

1. Introduction

2. The Model

3. Main Results

4. Coupling

5. Normalized Model

6. Lumping

7. Monotonicity

8. Stochastic Bounds

9. Birth and Death Processes

10. The Neutral Phase


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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 \[\ell\to +\infty,\qquad m\to +\infty,\qquad q\to 0,\] \[{\ell q} \to a\in ]0,+\infty[, \qquad\frac{m}{\ell}\to\alpha\in [0,+\infty].\]

Chapters

1. Introduction

2. The Model

3. Main Results

4. Coupling

5. Normalized Model

6. Lumping

7. Monotonicity

8. Stochastic Bounds

9. Birth and Death Processes

10. The Neutral Phase