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.

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.

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.

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.

scholarly journals Does diploidy increase the rate of adaptation?

Genetics ◽  
1994 ◽  
Vol 136 (4) ◽  
pp. 1475-1480 ◽  
Author(s):  
H A Orr ◽  
S P Otto
Keyword(s):  
Population Size ◽  
Genome Size ◽  
Mutation Rate ◽  
Alternative Theory ◽  
Recent Theory ◽  
Deleterious Alleles

Abstract Explanations of the evolution of diploidy have focused on the advantages gained from masking deleterious alleles. Recent theory has shown, however, that masking does not always provide an advantage to diploidy and would never favor diploidy in predominantly asexual organisms. We explore a neglected alternative theory which posits that, by doubling the genome size, diploids double the rate at which favorable mutations arise. Consequently, the rate of adaptation in diploids is presumed to be faster than in haploids. The rate of adaptation, however, depends not only on the rate of appearance of new favorable mutations but also on the rate at which these mutations are incorporated (which depends on the population size and on the dominance of favorable mutations). We show that, in both asexuals and sexuals, doubling the mutation rate via diploidy often does not accelerate the rate of adaptation. Indeed, under many conditions, diploidy slows adaptation.

scholarly journals A phylogenetic estimator of effective population size or mutation rate.

Genetics ◽  
1994 ◽  
Vol 136 (2) ◽  
pp. 685-692 ◽  
Author(s):  
Y X Fu
Keyword(s):  
Population Size ◽  
Effective Population Size ◽  
Mutation Rate ◽  
Dna Sequences ◽  
High Efficiency ◽  
Minimum Variance ◽  
Population Subdivision ◽  
Effective Population ◽  
Fisher Model ◽  
Mitochondrial Sequences

Abstract A new estimator of the essential parameter theta = 4Ne mu from DNA polymorphism data is developed under the neutral Wright-Fisher model without recombination and population subdivision, where Ne is the effective population size and mu is the mutation rate per locus per generation. The new estimator has a variance only slightly larger than the minimum variance of all possible unbiased estimators of the parameter and is substantially smaller than that of any existing estimator. The high efficiency of the new estimator is achieved by making full use of phylogenetic information in a sample of DNA sequences from a population. An example of estimating theta by the new method is presented using the mitochondrial sequences from an American Indian population.

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