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

Raphaël Cerf Université Paris Sud, Orsay, France
Available Formats:
Electronic ISBN: 978-1-4704-1964-6
Product Code: MEMO/233/1096.E
List Price: $71.00 MAA Member Price:$63.90
AMS Member Price: $42.60 Click above image for expanded view Critical Population and Error Threshold on the Sharp Peak Landscape for a Moran Model Raphaël Cerf Université Paris Sud, Orsay, France Available Formats:  Electronic ISBN: 978-1-4704-1964-6 Product Code: MEMO/233/1096.E  List Price:$71.00 MAA Member Price: $63.90 AMS Member Price:$42.60
• Book Details

Memoirs of the American Mathematical Society
Volume: 2332015; 87 pp
MSC: 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 $\ell\to +\infty,\qquad m\to +\infty,\qquad q\to 0,$ ${\ell q} \to a\in ]0,+\infty[, \qquad\frac{m}{\ell}\to\alpha\in [0,+\infty].$

• 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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Volume: 2332015; 87 pp
MSC: 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 $\ell\to +\infty,\qquad m\to +\infty,\qquad q\to 0,$ ${\ell q} \to a\in ]0,+\infty[, \qquad\frac{m}{\ell}\to\alpha\in [0,+\infty].$

• 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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