Biomedical subjects

J F Selgrade

Publications and source records attributed to J F Selgrade.

6 recordsLinked to original sources

PubMed2000

Dynamical analysis of density-dependent selection in a discrete one-island migration model.

A system of non-linear difference equations is used to model the effects of density-dependent selection and migration in a population characterized by two alleles at a single gene locus. Results for the existence and stability of polymorphic equilibria are established. Properties for a genetically important class of equilibria associated with complete dominance in fitness are described. The birth of an unusual chaotic attractor is also illustrated. This attractor is produced when migration causes chaotic dynamics on a boundary of phase space to bifurcate into the interior of phase space, resulting in bistable genetic polymorphic behavior.

Alleles↗

PubMed2000

A model of gonadotropin regulation during the menstrual cycle in women: qualitative features.

Increasing concerns that environmental contaminants may disrupt the endocrine system require development of mathematical tools to predict the potential for such compounds to significantly alter human endocrine function. The endocrine system is largely self-regulating, compensating for moderate changes in dietary phytoestrogens (e.g., in soy products) and normal variations in physiology. However, severe changes in dietary or oral exposures or in health status (e.g., anorexia), can completely disrupt the menstrual cycle in women. Thus, risk assessment tools should account for normal regulation and its limits. We present a mathematical model for the synthesis and release of luteinizing hormone (LH) and follicle-stimulating hormone (FSH) in women as a function of estrogen, progesterone, and inhibin blood levels. The model reproduces the time courses of LH and FSH during the menstrual cycle and correctly predicts observed effects of administered estrogen and progesterone on LH and FSH during clinical studies. The model should be useful for predicting effects of hormonally active substances, both in the pharmaceutical sciences and in toxicology and risk assessment.

Adult↗

PubMed1996

Lumped-density population models of pioneer-climax type and stability analysis of Hopf bifurcations.

The effects of population density on the survival and growth of an individual species are modeled by assuming that the species per capita growth rate (i.e., fitness) is a function of a weighted total density. A species is called a pioneer population if it thrives at low density but its fitness decreases monotonically with increasing density. A species is called a climax population if its fitness increases up to a maximum value and then decreases as a function of its total density. Hopf bifurcations for deterministic models of the interaction of pioneer and climax populations are discussed. Stability properties for the Hopf invariant curves in the discrete models are compared to the stability properties of the Hopf periodic orbits in the corresponding continuous models. Examples illustrate that stability may be more common in the discrete models.

Animals↗

PubMed1987

Convergence to equilibrium in a genetic model with differential viability between the sexes.

A single locus, diallelic selection model with female and male viability differences is studied. If the variables are ratios of allele frequencies in each sex, a 2-dimensional difference equation describes the model. Because of the strong monotonicity of the resulting map, every initial genotypic structure converges to an equilibrium structure assuming that no equilibrium has eigenvalues on the unit circle.

Alleles↗

PubMed1986

Examples of the effect of genetic variation on competing species.

An ordinary differential equation model for two competing populations with genetic variation in one population is presented. The degree of frequency dependence needed to produce various configurations of stable equilibria is discussed. For example, if the fitnesses are frequency independent then there may exist stable polymorphism although the genetically varying population becomes extinct in each fixation plane. Stable polymorphism where the genetically invariant population becomes extinct in each fixation plane requires frequency dependence in the fitness of the genetically invariant population.

Alleles↗

PubMed1986

Frequency-dependent selection in logistic growth models.

This paper describes the dynamics of a continuously reproducing diploid population with two alleles at one locus. The dependent variables are allele frequency and population density. We modify the basic density-dependent logistic growth model by inserting three possible types of frequency dependence in the fitness functions. These models are analyzed and contrasted with the purely density-dependent situation. Examples are given of periodic fluctuations in allele frequency and population density, which would be impossible for purely density-dependent fitness functions.

Animals↗