Parametric Bayesian inference for Y-linked two-sex branching models

González, Miguel; Gutiérrez, Cristina; Martínez, R.

doi:10.1007/s11222-012-9342-8

Cited by 7 publications

(4 citation statements)

References 16 publications

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“…We are interested in finding a sufficiently informative sampling scheme observing the minimum amount of information that leads us to obtain good estimates. Related to this question, as we also indicated at the Introduction, the authors published (see González et al (2013a)) a study about the estimation of the main parameters of a Y-BBP (without considering mutations) based on a sample where only the total number of females and males (without knowing the genotype of the males) up to some generation N as well as the different types of males only in the last generation N were assumed to be observed. Following these ideas, initially we set out in this paper the Bayesian estimation of the parameters of the Y-BBP with mutations based on that same sample.…”

Section: Description Of the Modelmentioning

confidence: 99%

“…However, to observe such quantity of information is hard in practice. In this sense, the authors published in a previous work a study about the inference of the parameters of a Y-BBP model without mutations (see González et al (2013a)), based on a more realistic sampling scheme where the total number of females and males up to some generation as well as the number of males of each genotype in the last generation is observed. Carrying on with these ideas, in this paper and for the Y-BBP with mutations, we consider firstly the same sample.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, in the Bayesian framework, a Markov chain Monte Carlo (MCMC) method was used for the model without mutations in González et al (2013a), with very good results. However, although in general MCMC method works well in many substantive problems, it can perform poorly when is applied to large data sets or complex models, as the model presented in this paper.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian Inference in Y-Linked Two-Sex Branching Processes with Mutations: ABC Approach

González

Gutiérrez

Martı́nez

2021

IEEE/ACM Trans. Comput. Biol. and Bioinf.

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A Y-linked two-sex branching process with mutations and blind choice of males is a suitable model for analyzing the evolution of the number of carriers of an allele and its mutations of a Y-linked gene. Considering a two-sex monogamous population, in this model each female chooses her partner from among the male population without caring about his type (i.e., the allele he carries).In this work, we deal with the problem of estimating the main parameters of such model developing the Bayesian inference in a parametric framework. Firstly, we consider, as sample scheme, the observation of the total number of females and males up to some generation as well as the number of males of each genotype at last generation. Later, we introduce the information of the mutated males only in the last generation obtaining in this way a second sample scheme. For both samples, we apply the Approximate Bayesian Computation (ABC) methodology to approximate the posterior distributions of the main parameters of this model. The accuracy of the procedure based on these samples is illustrated and discussed by way of simulated examples.

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Section: Description Of the Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Bayesian Inference in Y-Linked Two-Sex Branching Processes with Mutations: ABC Approach

González

Gutiérrez

Martı́nez

2021

IEEE/ACM Trans. Comput. Biol. and Bioinf.

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“…The reason is that the total numbers of females and of each type of male are unknown. This also implies that the inferential methods developed in [27][28][29][30][31] are inadequate to quantify the presence of the different alleles of the gene within the Y-linked pedigree. Female, male without the target allele, and male with the target allele.…”

Section: Introductionmentioning

confidence: 99%

Modeling Y-Linked Pedigrees through Branching Processes

González¹,

Gutiérrez²,

Martínez³

2020

Mathematics

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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.

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