Large-deviation properties of the extended Moran model

  title={Large-deviation properties of the extended Moran model},
  author={Alexander K. Hartmann and Thierry Huillet},
  journal={Physical Review E},
The distributions of the times to the first common ancestor t_mrca is numerically studied for an ecological population model, the extended Moran model. This model has a fixed population size N. The number of descendants is drawn from a beta distribution Beta(alpha, 2-alpha) for various choices of alpha. This includes also the classical Moran model (alpha->0) as well as the uniform distribution (alpha=1). Using a statistical mechanics-based large-deviation approach, the distributions can be… 
1 Citations

Figures from this paper

Cannings models, population size changes and multiple-merger coalescents

  • F. Freund
  • Mathematics
    Journal of mathematical biology
  • 2020
This article gives a more general construction of time-changed Λ - n -coalescents as limits of specific Cannings models with rather arbitrary time changes.



High-precision work distributions for extreme nonequilibrium processes in large systems.

  • A. Hartmann
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2014
It is verified that the resulting distributions of work for forward and backward processes fulfill Crooks theorem with high precision, and the free energy for the Ising magnet as a function of the field strength is obtained.

Random walk Green kernels in the neutral Moran model conditioned on survivors at a random time to origin

ABSTRACT In the theory of finite discrete-time birth and death chains with absorbing endpoint boundaries, the evaluation of both additive and multiplicative path functionals is made possible by their

Coalescent Processes When the Distribution of Offspring Number Among Individuals Is Highly Skewed

A complex set of scaling relationships between mutation and reproduction in a simple model of a population suggests the presence of rare reproduction events in which ∼8% of the population is replaced by the offspring of a single individual.

Coalescent Processes with Skewed Offspring Distributions and Nonequilibrium Demography

An extended Moran model with exponential population growth is developed, and it is demonstrated that the underlying ancestral process converges to a time-inhomogeneous psi-coalescent, and both can be estimated accurately from whole-genome data.

Large-deviation properties of largest component for random graphs

Abstract Distributions of the size of the largest component, in particular the large-deviation tail, are studied numerically for two graph ensembles, for Erdös-Rényi random graphs with finite

The general coalescent with asynchronous mergers of ancestral lines

  • S. Sagitov
  • Mathematics
    Journal of Applied Probability
  • 1999
Take a sample of individuals in the fixed-size population model with exchangeable family sizes. Follow the ancestral lines for the sampled individuals backwards in time to observe the ancestral

Coalescents with multiple collisions

k−2 � 1 − xb−k � � dx� . Call this process a � -coalescent. Discrete measure-valued processes derived from the � -coalescent model a system of masses undergoing coalescent collisions. Kingman's