scholarly journals Diffusion approximation of the Wright-Fisher model of population genetics: Single-locus two alleles

2000 ◽  
Vol 52 (3) ◽  
pp. 388-399 ◽  
Author(s):  
R. W. Coad
Keyword(s):  
Population Genetics ◽  
Diffusion Approximation ◽  
Single Locus ◽  
Fisher Model

A genealogical approach to variable-population-size models in population genetics

1986 ◽  
Vol 23 (02) ◽  
pp. 283-296 ◽  
Author(s):  
Peter Donnelly
Keyword(s):  
Population Genetics ◽  
Branching Process ◽  
Sufficient Conditions ◽  
Process Models ◽  
Moran Model ◽  
Fisher Model ◽  
Variable Population ◽  
Exchangeable Model ◽  
Necessary And Sufficient ◽  
Variable Population Size

A general exchangeable model is introduced to study gene survival in populations whose size changes without density dependence. Necessary and sufficient conditions for the occurrence of fixation (that is the proportion of one of the types tending to 1 with probability 1) are obtained. These are then applied to the Wright–Fisher model, the Moran model, and conditioned branching-process models. For the Wright–Fisher model it is shown that certain fixation is equivalent to certain extinction of one of the types, but that this is not the case for the Moran model.

scholarly journals A measure valued diffusion process describing an n locus model incorporating gene conversion

1990 ◽  
Vol 119 ◽  
pp. 81-92 ◽  
Author(s):  
Akinobu Shimizu
Keyword(s):  
Population Genetics ◽  
Probability Measure ◽  
Diffusion Process ◽  
Gene Conversion ◽  
Random Sampling ◽  
Diffusion Processes ◽  
Single Locus ◽  
Locus Model

Probability measure valued diffusion processes have been discussed by many authors, in connection with population genetics. Most papers studying probability measure valued diffusions are mainly concerned with the ones describing single locus models. In this paper, we will discuss a measure valued diffusion describing an n locus model. Random sampling, mutation and gene conversion, a kind of interaction between loci, which was introduced and investigated by T. Ohta in [5], [6], will be taken into consideration.

Population genetics of C4 with the use of complementary DNA probes

1984 ◽  
Vol 306 (1129) ◽  
pp. 405-417 ◽  
Keyword(s):  
Population Genetics ◽  
Protein Level ◽  
Dna Probes ◽  
Single Locus ◽  
Haemolytic Activity ◽  
Complementary Dna ◽  
Restriction Sites

The C4 system is unusually variant both in the number of expressed genes and in the variety of those expressed. It is also closely linked to two other complement loci ( C2 and Bf ), which are structurally distinct but not linked to the two complement loci ( C3 and C5 ) which are structurally similar. The C2, Bf, C4 segment lies within the MHC system, and their closeness to one another, and to the surrounding recognition loci ( HLA-A,-B, -C, -DR ) makes it difficult to attribute benefit or handicap, in relation to any disease, to any single locus by simple comparisons. The variation at the protein level, expressed by specificity, or charge, or size, or haemolytic activity, can now be supplemented by variation at restriction sites, or in the length of DNA between sites. The latter may be either causally or coincidentally related to the variant proteins. These data provide information on the evolutionary relations of the variants, both within and between species, and on the determinants related to inadequate or inappropriate defence against disease. They also provide evidence relevant to the sufficiency of the classical explanations of mutation, recombination and misalignment with recombination, and selection as explanations for what exists now.

A genealogical approach to variable-population-size models in population genetics

1986 ◽  
Vol 23 (2) ◽  
pp. 283-296 ◽  
Author(s):  
Peter Donnelly
Keyword(s):  
Population Genetics ◽  
Branching Process ◽  
Sufficient Conditions ◽  
Process Models ◽  
Moran Model ◽  
Fisher Model ◽  
Variable Population ◽  
Exchangeable Model ◽  
Necessary And Sufficient ◽  
Variable Population Size

A general exchangeable model is introduced to study gene survival in populations whose size changes without density dependence. Necessary and sufficient conditions for the occurrence of fixation (that is the proportion of one of the types tending to 1 with probability 1) are obtained. These are then applied to the Wright–Fisher model, the Moran model, and conditioned branching-process models. For the Wright–Fisher model it is shown that certain fixation is equivalent to certain extinction of one of the types, but that this is not the case for the Moran model.

scholarly journals Diffusion approximations in population genetics and the rate of Muller's ratchet

2021 ◽  
Author(s):  
Matteo Smerlak ◽  
Camila Braeutigam
Keyword(s):  
Population Genetics ◽  
Diffusion Theory ◽  
Diffusion Equations ◽  
Muller's Ratchet ◽  
Expected Time ◽  
Parameters Selection ◽  
Fisher Model ◽  
Muller’S Ratchet ◽  
Fixation Probabilities ◽  
Modern Population

Diffusion theory is a central tool of modern population genetics, yielding simple expressions for fixation probabilities and other quantities that are not easily derived from the underlying Wright-Fisher model. Unfortunately, the textbook derivation of diffusion equations as scaling limits requires evolutionary parameters (selection coefficients, mutation rates) to scale like the inverse population size---a severe restriction that does not always reflect biological reality. Here we note that the Wright-Fisher model can be approximated by diffusion equations under more general conditions, including in regimes where selection and/or mutation are strong compared to genetic drift. As an illustration, we use a diffusion approximation of the Wright-Fisher model to improve estimates for the expected time to fixation of a strongly deleterious allele, i.e. the rate of Muller's ratchet.

scholarly journals Stochasticity-induced stabilization in ecology and evolution

2019 ◽  
Author(s):  
Antony Dean ◽  
Nadav M. Shnerb
Keyword(s):  
Population Genetics ◽  
Species Richness ◽  
Diffusion Approximation ◽  
Generation Time ◽  
Overlapping Generations ◽  
Storage Effect ◽  
Asymmetric Competition ◽  
Bet Hedging ◽  
Qualitative And Quantitative ◽  
Hedging Strategies

AbstractThe ability of random environmental variation to stabilize competitor coexistence was pointed out long ago and, in recent years, has received considerable attention. Here we suggest a novel and generic synthesis of stochasticity-induced stabilization (SIS) phenomena. The storage effect in the lottery model, together with other well-known examples drawn from population genetics, microbiology and ecology, are placed together, reviewed, and explained within a clear, coherent and transparent theoretical framework. Implementing the diffusion approximation we show that in all these systems (including discrete and continuous dynamics, with overlapping and non-overlapping generations) the ratio between the expected growth and its variance governs both qualitative and quantitative features of persistence and invasibility. We further clarify the relationships between bet-hedging strategies, generation time and SIS, study the dynamics of extinction when SIS fails and the explain effects of species richness and asymmetric competition on the stabilizing mechanism.

scholarly journals A non-zero variance of Tajima’s estimator for two sequences even for infinitely many unlinked loci

2016 ◽  
Author(s):  
Léandra King ◽  
John Wakeley ◽  
Shai Carmi
Keyword(s):  
Population Genetics ◽  
Large Scale ◽  
Weak Correlation ◽  
Effective Population ◽  
Statistical Population ◽  
Demographic Models ◽  
Empirical Estimates ◽  
Fisher Model ◽  
Pairwise Differences ◽  
Coalescence Times

AbstractThe population-scaled mutation rate, θ, is informative on the effective population size and is thus widely used in population genetics. We show that for two sequences and n unlinked loci, Tajima’s estimator (), which is the average number of pairwise differences, is not consistent and therefore its variance does not vanish even as n → ∞. The non-zero variance of results from a (weak) correlation between coalescence times even at unlinked loci, which, in turn, is due to the underlying fixed pedigree shared by all genealogies. We derive the correlation coefficient under a diploid, discrete-time, Wright-Fisher model, and we also derive a simple, closed-form lower bound. We also obtain empirical estimates of the correlation of coalescence times under demographic models inspired by large-scale human genealogies. While the effect we de scribe is small , it is important to recognize this feature of statistical population genetics, which runs counter to commonly held notions about unlinked loci.

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