A simple competition model involving selection

Asimple model system of two self-reproducing objects is considered. A set of equations, similar to Eigen's equation, describing competition of these objects is derived and analyzed under the effect of an ‘ecological constraint’. The relation with other constraints used in the literature is discussed.     

A statistical model of the competition curve

1. A theoretical model for the competition curve, which stands on a few simple assumptions, was proposed.
2. Some applications were done to actual data, and during these applications the validity of the present model and its assumptions was discussed.
3. From the present model it can be expected that there is a discrete competition mechanism even in the appearently continuous medium.

     

A population model for limited food competition

In this paper a deterministic differential equation system is proposed to model the population dynamics of a biological community in which two species on the same trophic level compete for a common food, taken to be in limited supply. Food limitation is assumed to be the only inhibition of the growth of the populations and food quantity is assumed to be only affected by consumption. The model is thus designed to mimic a closed experimental situation rather than a natural community.Analytical properties of the solution of the differential equation system are developed and corresponding biological interpretations suggested.Cited laboratory data on the experimental batch community consisting of the marine ciliates Euplotes vannus and Uronema marinum feeding on bacteria motivated the model and supported its analytic properties.     

A general model of local competition for space

Local competition for space across a wide array of taxa typically involves three mechanisms that we denote here as expansion (spreading into unoccupied habitat), lottery (replacing dead competitors), and overgrowth (encroaching on competitors along zones of contact). By formulating and analysing a simple, general model incorporating these features, we identify ecological conditions and life‐history features that lead to stable coexistence or competitive exclusion (with or without initial‐condition dependence) and gain insight by linking these to case studies in the literature. We demonstrate the importance of contact inhibition, a little‐studied feature of overgrowth, and we show how life‐history tradeoffs may influence and be influenced by local competition for space. The general model we present can help indicate whether local interactions are sufficient to explain patterns of coexistence or exclusion and can serve as the foundation for more specific, realistic models of spatial competition.     

A competition model with dynamically allocated inhibitor production

The chemostat is a basic model for competition in an open system and a model for the laboratory bio-reactor (CSTR). Inhibitors in open systems are studied with a view of detoxification in natural systems and of control in bio-reactors. This study allows the amount of resource devoted to inhibitor production to depend on the state of the system. The feasibility of one dependence is provided by quorum sensing. In contrast to the constant allocation case, a much wider set of outcomes is possible including interior, stable rest points and stable limit cycles. These outcomes are important contrasts to competitive exclusion or bistable attractors that are often the outcomes for competitive systems. The model consists of four non-linear ordinary differential equations and computer software is used for most of the stability calculations.     

A quantitative genetic competition model for sympatric speciation

I use multilocus genetics to describe assortative mating in a competition model. The intensity of competition between individuals is influenced by a quantitative character whose value is determined additively by alleles from many loci. With assortative mating based on this character, frequency- and density-dependent competition can subdivide a population with an initially unimodal character distribution. The character distribution becomes bimodal, and the subpopulations corresponding to the two modes are reproductively separated because mating is assortative. This happens if the resource distribution is unimodal, i.e. even if selection due to phenotypic carrying capacities is not disruptive. The results suggest that sympatric speciation due to frequency-dependent selection can occur in quite general ecological scenarios if mating is assortative. I also discuss the evolution of assortative mating. Since it induces bimodal phenotype distributions, assortative mating leads to a better match of the resources if their distribution is also bimodal. Moreover, in a population with a bimodal phenotype distribution, the average strength of frequency-dependent competition is lower than in a unimodal population. Therefore, assortative mating permits higher equilibrium densities than random mating even if the resource distribution is unimodal. Thus, even though it may lead to a less efficient resource use, assortative mating is favoured over random mating because it reduces frequency-dependent effects of competition.     

A competition model for a seasonally fluctuating nutrient

A model of two species consuming a single, limited, periodically added resource is discussed. The model is based on chemostat-type equations, which differ from the classical models of Lotka and Volterra. The model incorporates nonlinear functional response curves of the Holling or Michaelis-Menten type to describe the dependence of the resource-exploitation rate on the amount of resource. Coexistence of two species due to seasonal variation is indicated by numerical studies.     

A classification model for the Leiden proteomics competition

A strategy is presented to build a discrimination model in proteomics studies. The model is built using cross-validation. This cross-validation step can simply be combined with a variable selection method, called rank products. The strategy is especially suitable for the low-samples-to-variables-ratio (undersampling) case, as is often encountered in proteomics and metabolomics studies. As a classification method, Principal Component Discriminant Analysis is used; however, the methodology can be used with any classifier. A data set containing serum samples from breast cancer patients and healthy controls is analysed. Double cross-validation shows that the sensitivity of the model is 82% and the specificity 86%. Potential putative biomarkers are identified using the variable selection method. In each cross-validation loop a classification model is built. The final classification uses a majority voting scheme from the ensemble classifier.     

种间竞争的一个新的数学模型—对经典的Lotka—Vol—terra竞争方程的扩充

本文根据营养动力学理论,建立了一类种间竞争的新的数学模型:它是单种群增长的Cui-Lawson模型,在种间竞争上的推广。新的种间竞争模型克服了经典的种间竞争的Lotka-Volteira方程的局限与不足,具有更广泛和复杂的行为,并在特殊条件下以Lotka-Volterra竞争方程为其特例。因此,新的种间竞争的数学模型是更一般的解释性模型,是对经典的Lotka-Voterra竞争方程的扩充。     

A competition model for viral inhibition of host cell proliferation

Some viruses encode proteins that promote cell proliferation while others, such as the human immunodeficiency virus (HIV), encode proteins that prevent cell division. It has been hypothesized that the selective advantage determining which strategy evolves depends on the ability of the virus to induce a cellular environment which maximizes both virus production and cell life span. In HIV, the protein that causes cell cycle arrest is Vpr. In this paper, we develop a mathematical model, based on difference equations, to study the competition between two genotypes of HIV - one that encodes this protein (Vpr+) and one that does not (Vpr-). In particular, we are interested in parameters that could be different between the in vitro condition, where the Vpr- genotype dominates, and the in vivo condition, where the Vpr+ genotype dominates. Our model indicates that the infected cell death-rate, the viral half-life, and the dynamics of the target cell population all effect the competition dynamics between the Vpr+ and Vpr- viral genotypes. Perturbing any of these parameters from the in vitro estimates while holding the others fixed has no affect on the competition outcome, i. e., the Vpr- genotype dominates. Perturbing the infected cell death-rate and the target cell source causes a switch in competitive outcome, although not necessarily at values, which represent the in vivo condition. Adding a perturbation in the viral half-life from in vitro to in vivo condition results in a switch of the competitive advantage from the Vpr- genotype to the Vpr+ genotype with parameters for all three mechanisms set to estimated in vivo values.     

The gradostat: A model of competition along a nutrient gradient

The general mathematical theory of the gradostat is presented for two competitors. The gradostat provides a mechanism for studying competition along a nutrient gradient. In the two vessel case, the results are complete and the conditions are testable. In then-vessel case, the relevant conditions are stated in terms of the stability modulii of certain matrices and are testable for any specific case.     

A discrete stage-structured two-species competition model with sexual and clonal reproduction

In this paper, we analyse a discrete stage-structured model which is a generalization of the two-species competition model studied in [2]. Motivated by plant populations, each species is assumed to reproduce both sexually and clonally. We show that this model has a dynamical behaviour that is similar to that of the classical continuous two-dimensional Lotka-Volterra model under weak nonlinearities of the Beverton-Holt type. By allowing the species to have different competition efficiencies, we show that it is possible to obtain different dynamics including coexistence, bistability and competitive exclusion, in contrast with the model studied in [2], which exhibits only competitive exclusion behaviour.     

Density dependent selection incorporating intraspecific competition 1. A haploid model

A haploid model is introduced and analyzed in which intraspecific competition is incorporated within a density dependent framework. It is assumed that each genotype has a unique carrying capacity corresponding to the equilibrium population size when fixed for that type. Each genotypic fitness at a single multi-allelic locus is a function of a distinctive effective population size formed by adding the numbers of each genotype present, weighted by an intraspecific competition coefficient. As a result, the fitnesses depend upon the relative frequencies of the various genotypes as well as the total population size. Intergenotypic interactions can have a profound effect upon the outcome of the population. In particular, when the density effect of one individual upon another depends upon their respective genotypes, a unique stable interior equilibrium is possible in which all alleles are present. This stands in contrast to the purely density dependent haploid system in which the only possible stable state corresponds to fixation for the type with the highest carrying capacity. In the present model selective advantage is determined by a balance between carrying capacity and sensitivity to density pressures from other genotypes. Fixation for the genotype with the highest carrying capacity, for instance, will not be stable if it exerts a sufficiently weak competitive effect upon the other genotypes. In the diallelic case, maintenance of both alleles at a stable equilibrium requires that the net intragenotypic competition between individuals of like genotype be stronger than that between unlike types. As for purely density regulated systems, there may be no stable equilibria and/or regular and chaotic cycling may occur. The results may also be interpreted in terms of a discrete time model of interspecific competition with each haplotype representing a different species.     

A model for molecular mechanisms of synaptic competition for a finite resource

Ca(2+)/calmodulin-dependent protein kinase II (CaMKII) undergoes Ca(2+)/calmodulin-dependent autophosphorylation of threonine-286/287 (Thr(286/287)). Extremely high concentration of CaMKII in the postsynaptic spine indicates that increase in the Ca(2+) concentration in the spine induced by synaptic activation results in Thr(286/287) autophosphorylation of this enzyme. It has recently been shown that the K(d) value of CaMKII for Ca(2+)/calmodulin (Ca(2+)/CaM) drastically decreases after Thr(286/287) autophosphorylation. Therefore, Ca(2+)/CaM associated with CaMKII becomes tightly bound to this kinase after Thr(286/287) autophosphorylation. This has been called 'Ca(2+)/CaM trapping'. We discussed the functional significance of Ca(2+)/CaM trapping in the neuronal system by a mathematical-modelling approach. We considered neighbouring synapses formed on the same dendrite and different increase in the Ca(2+) concentration in each spine. CaMKII undergoing Thr(286/287) autophosphorylation in each spine is eager to recruit nearby calmodulin in the dendrite for Ca(2+)/CaM trapping. Since the amount of calmodulin is limited, recruiting calmodulin to each spine causes competition among synapses for this finite resource. The results of our computer simulation show that this competition leads to 'winner-take-all': almost all calmodulin is taken by a few synapses to which relatively large increases in the Ca(2+) concentration are assigned. These results suggest a novel form of synaptic encoding of information.     

A spatial model for the spread of invading organisms subject to competition

 A spatially explicit integrodifference equation model is studied for the spread of an invading organism against an established competitor. Provided the invader is initially confined to a bounded region, the invasion spreads asymptotically as a travelling wave whose speed depends on the strength of the competitive interaction and on the dispersal characteristics of the invader. Even an inferior, but established, competitor can significantly reduce the invasion speed. The invasion speed is also influenced by the exact shape of the dispersal kernel (especially the thickness of the tail) as well as the mean dispersal distance for each generation. Received 10 April 1996; received in revised form 21 August 1996     

Analysis of a model for random competition

A random competition model is reformulated as an urn model and its behavior is analysed.     

A methodology for evaluation of parent-mutant competition using a generalized non-linear ecosystem model

A generalized, non-linear population dynamics model of an ecosystem is used to investigate the direction of selective pressures upon a mutant by studying the competition between parent and mutant populations. The model has the advantages of considering selection as operating on the phenotype, of retaining the interaction of the mutant population with the ecosystem as a whole, and of setting a reasonable balance between theoretical manageability and quantitative testability.The model is used to make generalizations about several aspects of evolution in a terminal consumer (e.g. top carnivore). Mutations which avoid over exploitation of the prey species or introduce intra-specific population regulators will be selected against.Application of the method is limited primarily by the assumptions of a non-fluctuating environment, an asymptotically stable steady state before the mutation, absence of genetic drift, and uniformity of selective pressure on the mutant population.The method described in this paper is well suited for handling the high degree of complexity experienced in most ecosystems. Thus the methodology present may become a powerful tool in the approach to certain evolutionary questions.