Alfonso Ramos

Bisexual Galton‐Watson Branching Process in Varying Environments

Abstract In this paper we introduce a bisexual Galton‐Watson branching process (BGWP) in which the offspring probability distribution is different in each generation. We obtain some relations among the probability generating functions (pgf) involved in the model and, making use of mean growth rates and fractional linear functions (flf), we provide sufficient and necessary conditions for its almost sure extinction.

Workshop on Branching Processes and Their Applications

Part I Population Growth Models in Random and Varying Environments.- Part II Special Branching Processes.- Part III Limit Theorems and Statistics.- Part IV Applications in Cell Kinetics and Genetics.- Part V Applications in Epidemiology.- Part VI Two-sex Branching Models.

Limiting behaviour for superadditive bisexual Galton-Watson processes in varying environments

In this paper, the class of superadditive bisexual Galton-Watson processes in varying environments is considered and the limiting behaviour of the number of mating units per generation, suitably normalized, is investigated. Two sequences of normalizing constants are considered and, for each one of them, limit theorems are established. In particular, conditions for the almost sure,L1 andL2 convergence to a non degenerate at 0 random variable are determined.

FCERI and Histamine Metabolism Gene Variability in Selective Responders to NSAIDS

The high-affinity IgE receptor (Fcε RI) is a heterotetramer of three subunits: Fcε RIα, Fcε RIβ, and Fcε RIγ (αβγ2) encoded by three genes designated as FCER1A, FCER1B (MS4A2), and FCER1G, respectively. Recent evidence points to FCERI gene variability as a relevant factor in the risk of developing allergic diseases. Because Fcε RI plays a key role in the events downstream of the triggering factors in immunological response, we hypothesized that FCERI gene variants might be related with the risk of, or with the clinical response to, selective (IgE mediated) non-steroidal anti-inflammatory (NSAID) hypersensitivity. From a cohort of 314 patients suffering from selective hypersensitivity to metamizole, ibuprofen, diclofenac, paracetamol, acetylsalicylic acid (ASA), propifenazone, naproxen, ketoprofen, dexketoprofen, etofenamate, aceclofenac, etoricoxib, dexibuprofen, indomethacin, oxyphenylbutazone, or piroxicam, and 585 unrelated healthy controls that tolerated these NSAIDs, we analyzed the putative effects of the FCERI SNPs FCER1A rs2494262, rs2427837, and rs2251746; FCER1B rs1441586, rs569108, and rs512555; FCER1G rs11587213, rs2070901, and rs11421. Furthermore, in order to identify additional genetic markers which might be associated with the risk of developing selective NSAID hypersensitivity, or which may modify the putative association of FCERI gene variations with risk, we analyzed polymorphisms known to affect histamine synthesis or metabolism, such as rs17740607, rs2073440, rs1801105, rs2052129, rs10156191, rs1049742, and rs1049793 in the HDC, HNMT, and DAO genes. No major genetic associations with risk or with clinical presentation, and no gene-gene interactions, or gene-phenotype interactions (including age, gender, IgE concentration, antecedents of atopy, culprit drug, or clinical presentation) were identified in patients. However, logistic regression analyses indicated that the presence of antecedents of atopy and the DAO SNP rs2052129 (GG) were strongly related (P < 0.001 and P = 0.005, respectively) with selective hypersensitivity to ibuprofen. With regard to patients with selective hypersensitivity to ASA, men were more prone to develop such a reaction than women (P = 0.011), and the detrimental DAO SNP rs10156191 in homozygosity increased the risk of developing such hypersensitivity (P = 0.039).

Investigations into the seasonal presence of Mycoplasma species in fattening lambs.

The presence of infection with Mycoplasma species in association with lung consolidation, environmental temperature and relative humidity was investigated in 410 clinically healthy fattening lambs from five different feedlots in Extremadura (southwestern Spain). Isolates of Mycoplasma species were obtained (n= 117), including Mycoplasma ovipneumoniae (n = 18) and Mycoplasma arginini (n = 99). Two seasonal periods were identified. The first period, which included February, March, September, October, and November, had an average temperature of 17.5 ± 4.7 °C and a relative humidity of 61.3 ± 15.8%. The second seasonal period, which included the months from April to August, had an average temperature of 22.9 ± 5.5 °C and a relative humidity of 48.4 ± 10.7%. Most Mycoplasma species were isolated from the second seasonal period, indicating that higher temperatures and lower relative humidity favour the presence of Mycoplasma species. M. arginini was also associated with lung consolidation.

Stochastic modeling in biological populations with sexual reproduction through branching models: Application to Coho salmon populations

The motivation behind this research is to develop appropriate mathematical models to describe the demographic dynamics of animal populations with sexual reproduction. We introduce a new class of two-sex branching models where several mating strategies between females and males and a variety of possibilities for the process of reproduction are taken into account. Unlike other classes of two-sex models which assume that mating and reproduction are influenced by the number of couples in the population, we now consider the most realistic case where both biological processes are affected by the numbers of females and males in the population, which may differ. Under a general parametric setting, we deal with inferential questions about the main parameters affecting the reproduction process. By considering the observation over time of the numbers of females and males up to when a certain pre-set generation is reached, we derive Bayes estimators for such parameters. With the purpose of determining highest posterior density credibility sets, we also propose a computational algorithm. As illustration, we include an application to Coho salmon populations.

Mathematical Modeling in Biological Populations with Reproduction in a Non-predictable Environment

In order to mathematically model the demographic dynamics of biological populations with sexual reproduction, we consider the more realistic situation where the reproductive process occurs in a non-predictable environment. We also assume that both biological processes, mating and reproduction, are influenced by the number of couples in the population. In this framework, a class of discrete-time two-sex branching models has been introduced in (A class of two-sex branching processes with reproduction phase in a random environment. Stochastics 88:147–161) [10]. In this work, we continue the research about such a class of stochastic models, investigating the time to extinction and some applications.

Branching Processes and Their Applications

We define a dynamical simple symmetric random walk in one dimension, and show that there almost surely exist exceptional times at which the walk tends to infinity. In fact the set of such times has Hausdorff dimension 1/2 almost surely. This is in contrast to the usual dynamical simple symmetric random walk in one dimension, for which such exceptional times are known not to exist. This is joint work with Martin Prigent.

Two-Sex Branching Processes with Several Mating and Reproduction Strategies: Extinction Versus Survival

This work deals with stochastic modeling in biological populations. We develop a two-sex branching process as an appropriate mathematical model to describe the demographic dynamics of biological populations with sexual reproduction. We assume several mating and reproduction strategies. Moreover, unlike other classes of two-sex branching processes where mating and reproduction are influenced by the number of couples in the population, we now consider the most realistic case where both (mating and reproduction) are affected by the numbers of females and males in the population. We study the extinction/survival of populations modeled by such two-sex branching process.

Mathematical modeling in biological populations through branching processes. Application to salmonid populations

This work deals with mathematical modeling through branching processes. We consider sexually reproducing animal populations where, in each generation, the number of progenitor couples is determined in a non-predictable environment. By using a class of two-sex branching processes, we describe their demographic dynamics and provide several probabilistic and inferential contributions. They include results about the extinction of the population and the estimation of the offspring distribution and its main moments. We also present an application to salmonid populations.