Bisexual branching processes in a genetic context: The extinction problem for Y-linked genes

González, Miguel; Hull, David M.; Martı́nez, Rodrigo; Mota, M.

doi:10.1016/j.mbs.2006.03.010

Cited by 15 publications

(15 citation statements)

References 17 publications

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“…The model introduced here shares some basic properties with the model with mating preference presented in González et al (2006). These are properties which do not depend on the way the females choose their mates, and were proved in that paper.…”

Section: The Modelmentioning

confidence: 68%

“…This symmetry is the main difference between the present model and that with preference in the mating introduced in González et al (2006). In that model, the genetic character controlled by the gene does appear in the phenotype, and females prefer males carrying one of the alleles of the gene.…”

Section: The Modelmentioning

confidence: 72%

“…To relax this assumption, other mating options could have been considered, such as polygamous mating or population-sizedependent number of couples. It seems likely that these other types of mating would lead to different results, as indeed is the case in the monogamous mating model with preference of females for males carrying one of the alleles of the m a n u s c r i p t gene, studied in González et al (2006), in relation to the simultaneous survival of the two genotypes.…”

Section: Two Biological Questions Have Been the Motivation Of This Comentioning

confidence: 99%

“…But more accurate models are needed in which all the phases of sexual reproduction can be considered, including the interaction between females and males in producing offspring. In González et al (2006), a model was presented that describes the evolution of the number of carriers of the two alleles of a Y-linked gene in a two-sex monogamic population. In that paper, it was considered that the characters controlled by such a gene can have some influence on the mating process of the species, with females having a preference for males carrying one of the alleles of the gene.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Bisexual branching processes to model extinction conditions for Y-linked genes

González

Martínez

Mota

2009

Journal of Theoretical Biology

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In a two-sex monogamic population, the evolution of the number of carriers of the two alleles of a Y-linked gene is considered. To this end, a multitype bisexual branching model is presented in which it is assumed that the gene has no influence on the mating process. It is deduced from this model that the average numbers of female and male descendants per mating unit constitute the key to determining the extinction or survival of each allele. Moreover, the destiny of each allele in the population is found not to depend on the behaviour of the other.

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Section: The Modelmentioning

confidence: 68%

Section: The Modelmentioning

confidence: 72%

Section: Two Biological Questions Have Been the Motivation Of This Comentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Bisexual branching processes to model extinction conditions for Y-linked genes

González

Martínez

Mota

2009

Journal of Theoretical Biology

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“…This may be due to the fact that the population size is considered constant in these models which constrains the modes of long-term behaviour. However, even with varying population size a different limiting behaviour is possible and indeed observed, for example, for Y-linked genes modeled by bisexual branching processes with preferential mating (see González et al (2006) and González et al (2008)), where the behaviour of one genotype depends on the survival of the other.…”

Section: Discussionmentioning

confidence: 99%

Limiting genotype frequencies of Y-linked genes through bisexual branching processes with blind choice

Alsmeyer

Gutiérrez

Martínez

2011

Journal of Theoretical Biology

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The limiting genotype growth rates and the limiting genotype frequencies of Y-linked genes are studied in a two-sex monogamous population. To this end, the evolution of the numbers of females, males, and mating units of each genotype is modeled by a multitype bisexual branching process in which it assumed that the gene has no influence on the mating process. It is deduced from this model that the average numbers of female and male descendants per mating unit of a genotype determine its growth rate, which does not depend on the behaviour of the other genotypes. Hence, the dominant genotype is found. Conditions for the simultaneous survival of genotypes to have positive probability are also investigated. Finally, the main results are illustrated by means of examples.

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