scholarly journals Limiting Genotype Frequencies of Y-Linked Genes with a Mutant Allele in a Two-Sex Population

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 131
Author(s):  
Miguel González ◽  
Cristina Gutiérrez ◽  
Rodrigo Martínez

A two-type two-sex branching process is considered to model the evolution of the number of carriers of an allele and its mutations of a Y-linked gene. The limiting growth rates of the different types of couples and males (depending on the allele, mutated or not, that they carry on) on the set of coexistence of both alleles and on the fixation set of the mutant allele are obtained. In addition, the limiting genotype of the Y-linked gene and the limiting sex frequencies on those sets are established. Finally, the main results have been illustrated with simulated studies contextualized in problems of population genetics.

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 256
Author(s):  
Miguel González ◽  
Cristina Gutiérrez ◽  
Rodrigo Martínez

A multidimensional two-sex branching process is introduced to model the evolution of a pedigree originating from the mutation of an allele of a Y-linked gene in a monogamous population. The study of the extinction of the mutant allele and the analysis of the dominant allele in the pedigree is addressed on the basis of the classical theory of multi-type branching processes. The asymptotic behavior of the number of couples of different types in the pedigree is also derived. Finally, using the estimates of the mean growth rates of the allele and its mutation provided by a Gibbs sampler, a real Y-linked pedigree associated with hearing loss is analyzed, concluding that this mutation will persist in the population although without dominating the pedigree.


Genetics ◽  
2000 ◽  
Vol 154 (1) ◽  
pp. 437-446 ◽  
Author(s):  
Lisa Girard ◽  
Michael Freeling

Abstract Insertions of Mutator transposons into maize genes can generate suppressible alleles. Mu suppression is when, in the absence of Mu activity, the phenotype of a mutant allele reverts to that of its progenitor. Here we present the characterization of five dominant Mu-suppressible alleles of the knox (knotted1-like homeobox) genes liguleless3 and rough sheath1, which exhibit neomorphic phenotypes in the leaves. RNA blot analysis suggests that Mu suppression affects only the neomorphic aspect of the allele, not the wild-type aspect. Additionally, Mu suppression appears to be exerting its effects at the level of transcription or transcript accumulation. We show that truncated transcripts are produced by three alleles, implying a mechanism for Mu suppression of 5′ untranslated region insertion alleles distinct from that which has been described previously. Additionally, it is found that Mu suppression can be caused by at least three different types of Mutator elements. Evidence presented here suggests that whether an allele is suppressible or not may depend upon the site of insertion. We cite previous work on the knox gene kn1, and discuss our results in the context of interactions between Mu-encoded products and the inherently negative regulation of neomorphic liguleless3 and rough sheath1 transcription.


Genetics ◽  
2001 ◽  
Vol 159 (2) ◽  
pp. 853-867 ◽  
Author(s):  
Peter Donnelly ◽  
Magnus Nordborg ◽  
Paul Joyce

Abstract Methods for simulating samples and sample statistics, under mutation-selection-drift equilibrium for a class of nonneutral population genetics models, and for evaluating the likelihood surface, in selection and mutation parameters, are developed and applied for observed data. The methods apply to large populations in settings in which selection is weak, in the sense that selection intensities, like mutation rates, are of the order of the inverse of the population size. General diploid selection is allowed, but the approach is currently restricted to models, such as the infinite alleles model and certain K-models, in which the type of a mutant allele does not depend on the type of its progenitor allele. The simulation methods have considerable advantages over available alternatives. No other methods currently seem practicable for approximating likelihood surfaces.


2021 ◽  
Vol 53 (1) ◽  
pp. 251-278
Author(s):  
Adrián González Casanova ◽  
Juan Carlos Pardo ◽  
José Luis Pérez

AbstractIn this paper, we introduce a family of processes with values on the nonnegative integers that describes the dynamics of populations where individuals are allowed to have different types of interactions. The types of interactions that we consider include pairwise interactions, such as competition, annihilation, and cooperation; and interactions among several individuals that can be viewed as catastrophes. We call such families of processes branching processes with interactions. Our aim is to study their long-term behaviour under a specific regime of the pairwise interaction parameters that we introduce as the subcritical cooperative regime. Under such a regime, we prove that a process in this class comes down from infinity and has a moment dual which turns out to be a jump-diffusion that can be thought as the evolution of the frequency of a trait or phenotype, and whose parameters have a classical interpretation in terms of population genetics. The moment dual is an important tool for characterizing the stationary distribution of branching processes with interactions whenever such a distribution exists; it is also an interesting object in its own right.


1986 ◽  
Vol 23 (02) ◽  
pp. 283-296 ◽  
Author(s):  
Peter Donnelly

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.


1995 ◽  
Vol 32 (3) ◽  
pp. 591-608 ◽  
Author(s):  
Chinsan Lee ◽  
Grace L. Yang

Asymptotic formulas for means and variances of a multitype decomposable age-dependent supercritical branching process are derived. This process is a generalization of the Kendall–Neyman–Scott two-stage model for tumor growth. Both means and variances have exponential growth rates as in the case of the Markov branching process. But unlike Markov branching, these asymptotic moments depend on the age of the original individual at the start of the process and the life span distribution of the progenies.


1978 ◽  
Vol 201 (1143) ◽  
pp. 217-217

One of the most striking results of recent theoretical research in population genetics is the sampling formula associated with the name of W. J. Ewens, who enunciated it in 1972, since which time it has been shown to hold for many different population models. This asserts that, if a sample of n gametes is taken from a population, and classified according to the gene at a particular locus, then the probability that there are a 1 alleles represented once in the sample, a 2 represented twice, a 3 thrice, and so on, is given for some positive value of θ by the expression P n (a 1 ,a 2 ..., a n ) = n !/θ(θ+1)...(θ+ n ─1) ∏ n j=1 ﴾θ aj /j aj a j !﴿. Most of the models for which this has been established share three broad features: ( a ) the size of the population is large compared with n , and the expected total number of mutations per generation is moderate (and in fact differs from θ by a constant factor depending on the reproductive mechanism), ( b ) the population is in statistical equilibrium under mutation and genetic drift, with selection at the locus playing a negligible rôle, and ( c ) mutation is non-recurrent, so that every mutant allele is a completely novel one.


1986 ◽  
Vol 23 (2) ◽  
pp. 283-296 ◽  
Author(s):  
Peter Donnelly

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.


Author(s):  
Anya Plutynski

Huxley coined the phrase, the ‘modern synthesis’ to refer to the acceptance by a vast majority of biologists in the mid-twentieth century of a ‘synthetic’ view of evolution. According to its main chroniclers, Mayr and Provine, the ‘synthesis’ consisted in the acceptance of natural selection acting on minor hereditary variation as the primary cause of both adaptive change within populations and major changes, such as speciation, and the evolution of higher taxa (e.g. families and genera). However, the dating and substance of the synthesis is controversial. The evolutionary synthesis may be broken down into two periods, the ‘early’ synthesis from 1918 to 1932, and the later, ‘modern synthesis’ from 1936 to 1947. The authors most commonly associated with the early synthesis are J. B. S. Haldane, R. A. Fisher, and S. Wright. These three authored a number of important advances; first, they demonstrated the compatibility of a Mendelian theory of inheritance with the results of Biometry, a study of the correlations of measures of traits between relatives. Second, they developed the theoretical framework for evolutionary biology, classical population genetics. This is a family of mathematical models representing evolution as change in genotype frequencies, from one generation to the next, as a product of selection, mutation, migration, and drift, or chance. Third, there was a broader synthesis of population genetics with cytology (cell biology), genetics, and biochemistry, as well as both empirical and mathematical demonstrations to the effect that very small selective forces acting over a relatively long time were able to generate substantial evolutionary change. The later ‘modern’ synthesis is most often identified with the work of Mayr, Dobzhansky and Simpson. There was a major institutional change in biology at this stage, insofar as different subdisciplines formerly housed in different departments, and using different methods, were united under the institutional umbrella of ‘evolutionary biology’. Mayr played an important role as a community architect, in founding the Society for the Study of Evolution, and the journal Evolution, which drew together work in systematics, biogeography, paleontology, and theoretical population genetics. The synthesis presents an occasion for addressing a number of important philosophical questions about the nature of theories, explanation, progress in science, theory unification, and reduction.


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