arXiv subjects

Cristina Gutiérrez

Publications and source records attributed to Cristina Gutiérrez.

2 recordsLinked to original sources

arXiv2024

Predator-prey density-dependent branching processes

Two density-dependent branching processes are considered to model predator-prey populations. For both models, preys are considered to be the main food supply of predators. Moreover, in each generation the number of individuals of each species is distributed according to a binomial distribution with size given by the species population size and probability of success depending on the density of preys per predator at the current generation. The difference between the two proposed processes lies in the food supply of preys. In the first one, we consider that preys have all the food they need at their disposal while in the second one, we assume that the natural resources of the environment are limited and therefore there exists a competition among preys for food supplies. Results on the fixation and extinction of both species as well as conditions for the coexistence are provided for the first model. On the event of coexistence of both populations and on the prey fixation event, the limiting growth rates are obtained. For the second model, we prove that the extinction of the entire system occurs almost surely. Finally, the evolution of both models over the generations is illustrated by simulated examples. Those examples validate our analytical findings.

math.PR↗

arXiv2018

Bayesian inference in Y-linked two-sex branching processes with mutations: ABC approach

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.

stat.CO↗