scholarly journals A Duality Approach to the Genealogies of Discrete Nonneutral Wright-Fisher Models

2009 ◽  
Vol 2009 ◽  
pp. 1-22 ◽  
Author(s):  
Thierry E. Huillet
Keyword(s):  
Population Genetics ◽  
Population Dynamics ◽  
Large Class ◽  
Elementary Algebra ◽  
Evolutionary Mechanisms ◽  
Potential Interest ◽  
Completely Monotone ◽  
Duality Approach ◽  
Neutral Case

Discrete ancestral problems arising in population genetics are investigated. In the neutral case, the duality concept has been proved of particular interest in the understanding of backward in time ancestral process from the forward in time branching population dynamics. We show that duality formulae still are of great use when considering discrete nonneutral Wright-Fisher models. This concerns a large class of nonneutral models with completely monotone (CM) bias probabilities. We show that most classical bias probabilities used in the genetics literature fall within this CM class or are amenable to it through some “reciprocal mechanism” which we define. Next, using elementary algebra on CM functions, some suggested novel evolutionary mechanisms of potential interest are introduced and discussed.

Vector Control, Optimal Control, and Vector-Borne Disease Dynamics

2020 ◽  
pp. 267-288
Author(s):  
Michael B. Bonsall
Keyword(s):  
Optimal Control ◽  
Population Genetics ◽  
Population Dynamics ◽  
Vector Control ◽  
Cost Effective ◽  
Disease Suppression ◽  
Medical Interventions ◽  
Vector Borne Disease ◽  
Vector Borne

Understanding methods of vector control is essential to vector-borne disease (VBD) management. Vaccines or standard medical interventions for many VDBs do not exist or are poorly developed so disease control is focused on managing vector numbers and dynamics. This involves understanding not only the population dynamics but also the population genetics of vectors. Using mosquitoes as a case study, in this chapter, the modern genetics-based methods of vector control (self-limiting, self-sustaining) on mosquito population and disease suppression will be reviewed. These genetics-based methods highlight the importance of understanding the interplay between genetics and ecology to develop optimal, cost-effective solutions for control. The chapter focuses on how these genetics-based methods can be integrated with other interventions, and concludes with a summary of regulatory and policy perspectives about the use of these approaches in the management of VBDs.

Robustness results for the coalescent

1998 ◽  
Vol 35 (2) ◽  
pp. 438-447 ◽  
Author(s):  
M. Möhle
Keyword(s):  
Population Genetics ◽  
Large Class ◽  
Common Ancestor ◽  
Population Models ◽  
Convergence Results

A variety of convergence results for genealogical and line-of-descendent processes are known for exchangeable neutral population genetics models. A general convergence-to-the-coalescent theorem is presented, which works not only for a larger class of exchangeable models but also for a large class of non-exchangeable population models. The coalescence probability, i.e. the probability that two genes, chosen randomly without replacement, have a common ancestor one generation backwards in time, is the central quantity to analyse the ancestral structure.

Partition structures and sufficient statistics

1998 ◽  
Vol 35 (03) ◽  
pp. 622-632
Author(s):  
Paul Joyce
Keyword(s):  
Population Genetics ◽  
Large Class ◽  
Mutation Rate ◽  
Parameter Family ◽  
Sufficient Statistics ◽  
Sufficient Statistic ◽  
Urn Scheme ◽  
Parametric Families ◽  
Necessary And Sufficient ◽  
General Conditions

Is the Ewens distribution the only one-parameter family of partition structures where the total number of types sampled is a sufficient statistic? In general, the answer is no. It is shown that all counterexamples can be generated via an urn scheme. The urn scheme need only satisfy two general conditions. In fact, the conditions are both necessary and sufficient. However, in particular, for a large class of partition structures that naturally arise in the infinite alleles theory of population genetics, the Ewens distribution is the only one in this class where the total number of types is sufficient for estimating the mutation rate. Finally, asymptotic sufficiency for parametric families of partition structures is discussed.

scholarly journals POPULATION DYNAMICS OF THE SEGREGATION DISTORTER POLYMORPHISM OF DROSOPHILA MELANOGASTER

Genetics ◽  
1978 ◽  
Vol 89 (1) ◽  
pp. 171-192 ◽  
Author(s):  
Brian Charlesworth ◽  
Daniel L Hartl
Keyword(s):  
Population Genetics ◽  
Population Dynamics ◽  
Drosophila Melanogaster ◽  
The Other ◽  
The Core ◽  
Segregation Distorter ◽  
Tight Linkage ◽  
Highly Oscillatory ◽  
Approximate Treatment ◽  
Special Case

ABSTRACT Two two-locus models of the population dynamics of the segregation distortion (SD) polymorphism of Drosophila melanogaster are described. One model is appropriate for understanding the population genetics of SD in nature, whereas the other is a special case appropriate for understanding an artificial population that has been extensively analysed. The models incorporate the general features of the Sd and Rsp loci which form the core of the SD system. It is shown that the SD polymorphism can be established only when there is sufficiently tight linkage between Sd and Rsp. An approximate treatment, valid for tight linkage, is given of all the equilibria of the system and their stabilities. It is shown that the observed composition of natural and artificial populations with respect to the Sd and Rsp loci is predicted well by the model, provided that restrictions are imposed on the fertilities of certain genotypes. Highly oscillatory paths towards equilibrium are usually to be expected on the basis of this model. The selection pressures on inversions introduced into this system are also investigated.

Molecular Population Genetics

2020 ◽  
pp. 179-224
Author(s):  
Daniel L. Hartl
Keyword(s):  
Population Genetics ◽  
Population Dynamics ◽  
Amino Acid ◽  
Frequency Spectrum ◽  
Demographic History ◽  
Human Populations ◽  
Noncoding Dna ◽  
Molecular Population Genetics ◽  
Amino Acid Divergence ◽  
Site Frequency Spectrum

Chapter 7 is an introduction to molecular population genetics that includes the principal concepts of nucleotide polymorphism and divergence, the site frequency spectrum, and tests of selection and their limitations. Highlighted are rates of nucleotide substitution in coding and noncoding DNA, nucleotide and amino acid divergence between species, corrections for multiple substitutions, and the molecular clock. Discussion of the folded and unfolded site frequency spectrum includes the strengths and limitations of Tajima’s D, Fay and Wu’s H, and other measures. The chapter also discusses an emerging consensus to resolve the celebrated selection–neutrality controversy. It also includes examination of demographic history through the use of ancient DNA with special emphasis on the surprising findings in regard to the ancestral makeup of contemporary human populations. Also discussed are the population dynamics of transposable elements in prokaryotes and eukaryotes.

Robustness results for the coalescent

1998 ◽  
Vol 35 (02) ◽  
pp. 438-447 ◽  
Author(s):  
M. Möhle
Keyword(s):  
Population Genetics ◽  
Large Class ◽  
Common Ancestor ◽  
Population Models ◽  
Convergence Results

A variety of convergence results for genealogical and line-of-descendent processes are known for exchangeable neutral population genetics models. A general convergence-to-the-coalescent theorem is presented, which works not only for a larger class of exchangeable models but also for a large class of non-exchangeable population models. The coalescence probability, i.e. the probability that two genes, chosen randomly without replacement, have a common ancestor one generation backwards in time, is the central quantity to analyse the ancestral structure.

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