Biomedical subjects

R Cressman

Publications and source records attributed to R Cressman.

9 recordsLinked to original sources

PubMed1999

Nonlinear frequency-dependent selection at a single locus with two alleles and two phenotypes.

The paper investigates the discrete frequency dynamics of two phenotype diploid models where genotypic fitness is an exponential function of the expected payoff in the matrix game. Phenotypic and genotypic equilibria are defined and their stability compared to frequency-dependent selection models based on linear fitness when there are two possible phenotypes in the population. In particular, it is shown that stable equilibria of both types can exist in the same nonlinear model. It is also shown that period-doubling bifurcations emerge when there is sufficient selection in favor of interactions between different phenotypes.

Alleles↗

PubMed1997

Spatial and density effects in evolutionary game theory.

Two models are considered for the study of game dynamics in a spatial domain. Both models are continuous in space and time and give rise to reaction-diffusion equations. The spatial domain is homogeneous but the mobility of the individuals is allowed to depend upon the strategy. The models are analysed for spatial patterns (via a Turing instability) and also for the direction of the travelling wave that replaces one strategy by another. It is shown that the qualitative behaviour of the two models is quite different. When considering the existence of spatial patterns and deciding whether increased mobility is helpful or not, it is shown that the answers depend crucially upon the model equations. Since both models (in the absence of spatial variation) are quite standard, it is clear that considerable care has to be exercised in the formulation of spatial models and in their interpretation.

Animals↗

PubMed1996

Frequency-Dependent Stability for Two-Species Interactions

Evolutionary game theory is extended to models of two-species interactions where fitnesses are based on individual characteristics (strategies) rather than on a population dynamic that assumes homogeneous species. It is shown that the coevolutionary theories in the literature that combine ecology with genetic viability selection are part of this extended theory and that the dynamic stability resulting from a separation of ecological and evolutionary processes actually follows from game-theoretic solution concepts. The main focus of the paper is to investigate the application of the ESS (evolutionarily stable strategy) solution concept to dynamic stability when fitnesses are given by random interactions between individuals as opposed to viability selection. For two-species frequency-dependent interactions, the ESS criterion that implies stability asserts that, in any system near the ESS, at least one of the species is better off (i.e., more fit) if it evolves towards the ESS. The global stability of a polymorphic two-species ESS that is shown for two-species matrix games gives a powerful tool to predict the course of evolution through static fitness comparisons.

Journal Article↗

PubMed1992

Evolutionarily stable sets in symmetric extensive two-person games.

Evolutionarily stable (ES) sets are characterized for evolutionary games in extensive form. It is shown that, for the normal form of games involving informational symmetries or repeated play, the standard approach of determining evolutionarily stable strategies (ESSs) often fails to predict the evolutionary outcome. The dynamic stability of ES sets is proved in both the pure strategy and mixed strategy models. ES sets are shown to also generalize the notion of direct ESSs (an earlier attempt to apply ESS theory to extensive games). The theory is illustrated by three examples of biological games in extensive form.

Animals↗

PubMed1990

Strong stability and density-dependent evolutionarily stable strategies.

Stability conditions for equilibria of the evolution of population strategies in a single species are developed by comparing frequency and density dependent fitnesses of pairs of strategies. Stability of such equilibria is shown for general haploid frequency and density dynamics. It is also shown that this stability is stronger than that of multispecies population dynamical systems. A biological interpretation of the conditions is provided in terms of the fitness of invading subpopulations.

Animals↗

PubMed1989

Functional analysis of DNA sequences responsible for ethylene regulation of a bean chitinase gene in transgenic tobacco.

Expression of at least two genes from bean encoding the defense-related protein chitinase has been shown previously to be transcriptionally regulated by the phytohormone ethylene. We have determined the complete nucleotide sequence of one of these genes, the CH5B gene, which resides on a 4.7-kilobase fragment of bean genomic DNA. The structural gene consists of a single open reading frame and encodes the 301 amino acids of the mature protein and a 26-amino acid signal peptide. The CH5B gene has been introduced into tobacco plants using Agrobacterium Ti-plasmid vectors. Little or no expression of the bean gene was observed when transgenic tobacco plants were grown in air; however, exposure of these plants to an atmosphere containing 50 parts per million ethylene resulted in an approximately 20-fold to 50-fold increase in the level of the bean chitinase mRNA. Ethylene-dependent expression of a chimeric gene consisting of 1.6 kilobases of 5'-flanking DNA derived from the CH5B gene fused to the coding sequence of beta-glucuronidase indicates that this region of the CH5B gene is sufficient for ethylene-regulated expression. Deletion analysis of the CH5B promoter region has allowed us to localize these DNA sequences to within a 228-base pair region situated between -422 and -195 upstream of the transcriptional start site. This region is characterized by two short DNA sequences that are exactly conserved in a second ethylene-regulated bean chitinase gene.

Chitinases↗

PubMed1988

Frequency-dependent viability selection (a single-locus, multi-phenotype model).

Frequency-dependent natural selection models are examined where the viability of an individual in the diploid population is determined by its phenotype and the frequency of other phenotypes present. The equilibria of the multi-phenotypic system are characterized through local mean fitness functions. It is shown that stability can best be analyzed by combining the principles of maximization of population mean fitness with the evolutionary stability conditions that apply when phenotypic fitnesses relative to the genetic constraints are equal.

Animals↗

PubMed1988

Complex dynamical behaviour of frequency-dependent viability selection: an example.

The model of viability selection based on a one-locus, two-allele diploid population is considered. Frequency dependence is introduced through the fitnesses of three phenotypes (strategies) exhibited by the population. Both discrete and continuous dynamics are analyzed and contrasted with the classical results of frequency-independent selection and with the more recent results of frequency-dependent selection based on two-phenotype multi-allele systems. Cycling and chaotic behaviour are shown to be easily obtained in the discrete model. Intuitive biological conditions for stability are shown to fail as well as at general equilibria of the continuous model.

Animals↗

PubMed1986

Evolutionary games and two species population dynamics.

Competition between species has long been modeled by population dynamics based on total numbers of each species. Recently, the evolution of strategy frequencies has been used successfully for competition models between individuals. In this paper, we illustrate that these two views of competition are compatible. It is shown that the rate of intra and interspecific competitions between individuals largely determines the population dynamics. Competition models over a single common resource and predator-prey models are developed from this individual competition approach. In particular, the equilibrium strategies in a co-evolving predator-prey system are shown to be more stable than the predicted strategy cycling of standard evolutionary game theory.

Animals↗