Robustness of the Ewens sampling formula

1995 ◽  
Vol 32 (3) ◽  
pp. 609-622 ◽  
Author(s):  
Paul Joyce
Keyword(s):  
Mutation Rate ◽  
Direct Result ◽  
Ewens Sampling Formula ◽  
Asymptotically Normal ◽  
Sampling Formula ◽  
Selective Neutrality ◽  
Infinite Alleles Model ◽  
Asymptotically Normal Estimator

Under the assumptions of the neutral infinite alleles model, K (the total number of alleles present in a sample) is sufficient for estimating θ (the mutation rate). This is a direct result of the Ewens sampling formula, which gives a consistent, asymptotically normal estimator for θ based on K. It is shown that the same estimator used to estimate θ under neutrality is consistent and asymptotically normal, even when the assumption of selective neutrality is violated.

Robustness of the Ewens sampling formula

1995 ◽  
Vol 32 (03) ◽  
pp. 609-622 ◽  
Author(s):  
Paul Joyce
Keyword(s):  
Mutation Rate ◽  
Direct Result ◽  
Ewens Sampling Formula ◽  
Asymptotically Normal ◽  
Sampling Formula ◽  
Selective Neutrality ◽  
Infinite Alleles Model ◽  
Asymptotically Normal Estimator

Under the assumptions of the neutral infinite alleles model, K (the total number of alleles present in a sample) is sufficient for estimating θ (the mutation rate). This is a direct result of the Ewens sampling formula, which gives a consistent, asymptotically normal estimator for θ based on K. It is shown that the same estimator used to estimate θ under neutrality is consistent and asymptotically normal, even when the assumption of selective neutrality is violated.

A stability property of the Ewens sampling formula

1983 ◽  
Vol 20 (03) ◽  
pp. 449-459
Author(s):  
Stanley Sawyer
Keyword(s):  
Population Size ◽  
Error Bound ◽  
Mutation Rate ◽  
Stability Property ◽  
Ewens Sampling Formula ◽  
Sampling Formula ◽  
Deleterious Alleles

An error bound for convergence to the Ewens sampling formula is given where the population size or mutation rate may vary from generation to generation, or the population is not yet at equilibrium. An application is given to a model of Hartl and Campbell about selectively-equivalent subtypes within a class of deleterious alleles, and a theorem is proven showing that the size of the deleterious class stays within bounds sufficient to apply the first result. Generalizations are discussed.

Weak limit for the stationary distribution of the infinite-alleles model

1979 ◽  
Vol 16 (3) ◽  
pp. 459-472
Author(s):  
Haim Avni
Keyword(s):  
Laplace Transform ◽  
Order Statistics ◽  
Frequency Spectrum ◽  
Stationary Distribution ◽  
Weak Limit ◽  
Limit Behavior ◽  
Ewens Sampling Formula ◽  
Sampling Formula ◽  
Spectrum Density ◽  
Infinite Alleles Model

The limit behavior of the stationary distribution of the infinite-alleles model is reduced to a single Laplace transform formula. Some known results, such as Ewens' sampling formula, the distribution of the order-statistics and the frequency spectrum density are shown to follow from this relation. All the results are obtained within the framework of the configuration process, without recourse to finite alleles models.In view of some recent results by Kingman (1977), the results apply wherever the Ewens' sampling formula is valid.

Weak limit for the stationary distribution of the infinite-alleles model

1979 ◽  
Vol 16 (03) ◽  
pp. 459-472
Author(s):  
Haim Avni
Keyword(s):  
Laplace Transform ◽  
Order Statistics ◽  
Frequency Spectrum ◽  
Stationary Distribution ◽  
Weak Limit ◽  
Limit Behavior ◽  
Ewens Sampling Formula ◽  
Sampling Formula ◽  
Spectrum Density ◽  
Infinite Alleles Model

The limit behavior of the stationary distribution of the infinite-alleles model is reduced to a single Laplace transform formula. Some known results, such as Ewens' sampling formula, the distribution of the order-statistics and the frequency spectrum density are shown to follow from this relation. All the results are obtained within the framework of the configuration process, without recourse to finite alleles models. In view of some recent results by Kingman (1977), the results apply wherever the Ewens' sampling formula is valid.

A stability property of the Ewens sampling formula

1983 ◽  
Vol 20 (3) ◽  
pp. 449-459 ◽  
Author(s):  
Stanley Sawyer
Keyword(s):  
Population Size ◽  
Error Bound ◽  
Mutation Rate ◽  
Stability Property ◽  
Ewens Sampling Formula ◽  
Sampling Formula ◽  
Deleterious Alleles

An error bound for convergence to the Ewens sampling formula is given where the population size or mutation rate may vary from generation to generation, or the population is not yet at equilibrium. An application is given to a model of Hartl and Campbell about selectively-equivalent subtypes within a class of deleterious alleles, and a theorem is proven showing that the size of the deleterious class stays within bounds sufficient to apply the first result. Generalizations are discussed.

The infinitely-many-neutral-alleles diffusion model by ages

1990 ◽  
Vol 22 (01) ◽  
pp. 1-24 ◽  
Author(s):  
S. N. Ethier
Keyword(s):  
Diffusion Model ◽  
Probability Distributions ◽  
Ewens Sampling Formula ◽  
Sample Paths ◽  
Sampling Formula ◽  
Frequent Allele

We discuss two formulations of the infinitely-many-neutral-alleles diffusion model that can be used to study the ages of alleles. The first one, which was introduced elsewhere, assumes values in the set of probability distributions on the set of alleles, and the ages of the alleles can be inferred from its sample paths. We illustrate this approach by proving a result of Watterson and Guess regarding the probability that the most frequent allele is oldest. The second diffusion model, which is new, assumes values in the set of probability distributions on the set of pairs (x, a), where x is an allele and a is its age. We illustrate this second approach by proving an extension of the Ewens sampling formula to age-ordered samples due to Donnelly and Tavaré.

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