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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
Critical Population and Error Threshold on the Sharp Peak Landscape for a Moran Model
eBook 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
Critical Population and Error Threshold on the Sharp Peak Landscape for a Moran Model
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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
eBook 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 \[\ell\to +\infty,\qquad m\to +\infty,\qquad q\to 0,\] \[{\ell q} \to a\in ]0,+\infty[, \qquad\frac{m}{\ell}\to\alpha\in [0,+\infty].\]

  • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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