Pioneer exclusion in a one-hump discrete pioneer-climax competitive system

One-hump maps as single species pioneer and climax ecological models confirm the expected pioneer exclusion in an uninterrupted two dimensional discrete pioneer-climax competition model. Other dynamic situations occur in such models. In particular a mutual exclusion principle is presented as a mathematical theorem.     

Extinction of species in age-structured, discrete noncooperative systems

Using a multi-species model of Ebenman for the dynamics of a discretely reproducing population that consists of noncooperation between juveniles and adults, we obtain exclusion principles by Lyapunov function methods. In the very general age-structured model, we show that, if there is an adult whose growth function is always larger than that of all the other species in the system, then it dominates the system by driving all the others to extinction. This result confirms a general folklore. We also develop a quasi-dominance concept and show that it implies the extinction of all the quasi-dominated species. The quasi-dominance concept applies even if there is no species whose adults always grow faster than all the others. In addition, a notion of weak dominance is developed. We show with specific examples that weak dominance does not necessarily imply extinction of species. If all the growth functions are exponential functions, then weak dominance is equivalent to quasi-dominance.     

Global exponential stability of positive periodic solution of the n-species impulsive Gilpin–Ayala competition model with discrete and distributed time delays

In this paper, we study the n-species impulsive Gilpin–Ayala competition model with discrete and distributed time delays. The existence of positive periodic solution is proved by employing the fixed point theorem on cones. By constructing appropriate Lyapunov functional, we also obtain the global exponential stability of the positive periodic solution of this system. As an application, an interesting example is provided to illustrate the validity of our main results.     

A delay differential equation model for tumor growth

We present a competition model of tumor growth that includes the immune system response and a cycle-phase-specific drug. The model considers three populations: Immune system, population of tumor cells during interphase and population of tumor during mitosis. Delay differential equations are used to model the system to take into account the phases of the cell cycle. We analyze the stability of the system and prove a theorem based on the argument principle to determine the stability of a fixed point and show that the stability may depend on the delay. We show theoretically and through numerical simulations that periodic solutions may arise through Hopf Bifurcations.Send offprint requests to:Minaya Villasana     

Stability in a class of discrete time models of interacting populations

Summary Effective Lyapunov and Lyapunov-like functions for a class of discrete time models of interacting populations are presented. These functions are constructed on the biologically meaningful principle that a viable population must absorb energy from external sources when its density is low and it must dissipate energy to the environment when its density is high. These functions can be used to establish that a discrete time model is globally stable or that its solutions are ultimately confined to an acceptable region of the state space. The latter is especially interesting when the model has chaotic solutions. These methods are applied to a single species model and a model of competition between two species.     

Changes in Individual Allometry Can Lead to Species Coexistence without Niche Separation

The principle of competitive exclusion is a fundamental tenet of ecology. Commonly used competition models predict that at most only one species per limiting resource can coexist in the same environment at steady state; hence, the upper limit to species diversity depends only on the number of limiting resources and not on the rates of resource supply. We demonstrate that such model behavior is the result of both the growth and biomass turnover functions being proportional to the population biomass. We argue that at least the growth function should be a nonlinear, concave downward function of biomass. This form for the growth function should arise simply because of changes in the allometry of individuals in the population. With this change in model structure, we show that any number of species can coexist at an asymptotically stable steady state, even where there is only one limiting resource. Furthermore, if growth increases nonlinearly with biomass, the steady-state resource concentration and hence the potential for biodiversity increases as the resource supply rate increases. Received 31 August 2001; accepted 10 April 2002.     

Mathematical models of microbial growth and competition in the chemostat regulated by cell-bound extracellular enzymes

A mathematical model of growth and competitive interaction of microorganisms in the chemostat is analyzed. The growth-limiting nutrient is not in a form that can be directly assimilated by the microorganisms, and must first be transformed into an intermediate product by cell-bound extracellular enzymes. General monotone functions, including Michaelis-Menten and sigmoidal response functions, are used to describe nutrient conversion and growth due to consumption of the intermediate product. It is shown that the initial concentration of the species is an important determining factor for survival or washout. When there are two species whose growth is limited by the same nutrient, three different modes of competition are described. Competitive coexistence steady states are shown to be possible in two of them, but they are always unstable. In all of our numerical simulations, the system approaches a steady state corresponding to the washout of one or both of the species from the chemostat.Research supported by NSF grant DMS-90-96279Research supported by NSERC grant A-9358     

Coexistence of pathogens in sexually-transmitted disease models

We present a sexually-transmitted disease (STD) model for two strains of pathogen in a one-sex, heterogeneously-mixing population, where the dynamics are of SIS (susceptible/infected/susceptible) type, and there are two different groups of individuals. We analyze all equilibria for the case where contacts are modeled via proportionate (random) mixing. We find that both strains may under suitable circumstances coexist, and that it is the heterogeneous mixing that creates refuges for each strain as each population group favors one particular strain. This author was partially supported under Chinese NSF grant 19971066.This author was partially supported by The Research Center for Sciences, Xian Jiaotong University, while visiting Xian Jiaotong University, Xian, China.The authors thank two anonymous reviewers for their valuable comments and suggestions.     

Competitive exclusion and persistence in models of resource and sexual competition

 We study a combined mathematical model of resource and sexual competition. The population dynamics in this model is analyzed through a coupled system of reaction-diffusion equations. It is shown that strong sexual competition and low birth rate lead to competitive exclusion of the biological species. If sexual competition is weak, then the persistence of the species is possible, depending on the initial density functions and the growth rates of the species. When sexual competition affects both species, persistence and competitive exclusion results are also obtained in terms of the ecological data in the model. Received 1 November 1995; received in revised form 13 January 1996     

Large amplification in stage-structured models: Arnol’d tongues revisited

The coexistence of periodic and point attractors has been confirmed for a range of stage-structured discrete time models. The periodic attractor cycles have large amplitude, with the populations cycling between extremely low and surprisingly high values when compared to the equilibrium level. In this situation a stable state can be shocked by noise of sufficient strength into a state of high volatility. We found that the source of these large amplitude cycles are Arnold tongues, special regions of parameter space where the system exhibits periodic behaviour. Most of these tongues lie entirely in that part of parameter space where the system is unstable, but there are exceptions and these exceptions are the tongues that lead to attractor coexistence. Similarity in the geometry of Arnold tongues over the range of models considered might suggest that this is a common feature of stage-structured models but in the absence of proof this can only be a useful working hypothesis. The analysis shows that although large amplitude cycles might exist mathematically they might not be accessible biologically if biological constraints, such as non-negativity of population densities and vital rates, are imposed. Accessibility is found to be highly sensitive to model structure even though the mathematical structure is not. This highlights the danger of drawing biological conclusions from particular models. Having a comprehensive view of the different mechanisms by which periodic states can arise in families of discrete time models is important in the debate on whether the causes of periodicity in particular ecological systems are intrinsic, environmental or trophic. This paper is a contribution to that continuing debate.     

Effects of Nitrogen Exponential Fertilization on Growth and Nutrient Concentration of <i>Hydrangea macrophylla</i> Seedlings

Slow growth rate restricts the development and growth of seedlings due to nutrients deficiency or nutrient imbalance. Exponential fertilization can enhance the internal nutrient reserves in seedlings at the nursery-stage and strengthen their resistance to adverse conditions. In this study, nitrogen requirements for producing Hydrangea macrophylla ‘Hanatemari’ that robust seedlings, nutrient dynamics, biomass and growth, was examined utilizing exponential fertilization. The potted seedlings were fertilized with urea under exponential regime at rates of 0.5, 1.5 and 2.0 g nitrogen/plant (EF1, EF2, and EF3), respectively. In addition, an unfertilized group treated with equal volume of deionized water was used as control. The results showed that seedlings under 1.5 g N/plant (EF2) had the highest plant growth index and total biomass. The nutrient concentrations of different organs varied in different fertilization treatments. Based on the results of current study, it is concluded that 1.5 g N/plant (EF2) is suitable exponential fertilization treatment for the culture of hydrangea seedlings. Our treatments results showed that 2.0 g N/plant is not suitable for seedling culturing, because of serious nutrient toxicity. These findings will help to improve seedling quality and strengthen the production of H. macrophylla for plantation.     

Stability of a Ricker-type competition model and the competitive exclusion principle

Our main objective is to study a Ricker-type competition model of two species. We give a complete analysis of stability and bifurcation and determine the centre manifolds, as well as stable and unstable manifolds. It is shown that the autonomous Ricker competition model exhibits subcritical bifurcation, bubbles, period-doubling bifurcation, but no Neimark–Sacker bifurcations. We exhibit the region in the parameter space where the competition exclusion principle applies.     

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.     

珍稀植物华木莲的现代濒危机制:探析与展望

华木莲(Sinomanglietia glauca)在探讨木兰科系统演化与被子植物起源等方面具有重要科学价值,但其分布区域狭窄、种群规模较小,被列为我国濒危植物和极小种群植物。该文在系统综述华木莲生物生态学特性和更新维持机制的基础上,对华木莲的现代濒危原因进行了总结:(1)华木莲属古老残遗濒危植物,环境变迁、瓶颈效应、高频自交和遗传漂变,导致其遗传多样性下降、适应性差;(2)喜光喜肥的生物生态学特性和群落种间竞争驱赶作用,"林—窗"游击式更新是华木莲种群延续的重要方式,然而当前人类干扰导致有效林窗供给不足、种子传播效率下降、"游击"机会减少,更新难以完成;(3)毛竹扩张与林下箬竹过度增长严重影响华木莲开花结实,并妨碍其幼苗更新。今后应加强华木莲谱系地理与群落系统发育、群落环境对华木莲生长发育的影响及其应答、林窗更新机制与种子长距传播、群落结构调整与保护技术、遗传复壮与迁地保护等方面研究,为华木莲以及相似生物生态学特征的濒危植物保护提供理论指导。     

Using exclusion rate to unify niche and neutral perspectives on coexistence

The competitive exclusion principle is one of the most influential concepts in ecology. The classical formulation suggests a correlation between competitor species similarity and competition severity, leading to rapid competitive exclusion where species are very similar; yet neutral models show that identical species can persist in competition for long periods. Here, we resolve the conflict by examining two components of similarity – niche overlap and competitive similarity – and modeling the effects of each on exclusion rate (defined as the inverse of time to exclusion). Studying exclusion rate, rather than the traditional focus on binary outcomes (coexistence versus exclusion), allows us to examine classical niche and neutral perspectives using the same currency. High niche overlap speeds exclusion, but high similarity in competitive ability slows it. These predictions are confirmed by a well‐known model of two species competing for two resources. Under ecologically plausible scenarios of correlation between these two factors, the strongest exclusion rates may be among moderately similar species, while very similar and highly dissimilar competitors have very low exclusion rates. Adding even small amounts of demographic stochasticity to the model blurs the line between deterministic and probabilistic coexistence still further. Thus, focusing on exclusion rate, instead of on the binary outcome of coexistence versus exclusion, allows a variety of outcomes to result from competitive interactions. This approach may help explain species coexistence in diverse competitive communities and raises novel issues for future work.     

PWP2, a member of the WD-repeat family of proteins, is an essentialSaccharomyces cerevisiae gene involved in cell separation

WD-repeat proteins contain four to eight copies of a conserved motif that usually ends with a tryptophan-aspartate (WD) dipeptide. TheSaccharomyces cerevisiae PWP2 gene, identified by sequencing of chromosome III, is predicted to contain eight so-called WD-repeats, flanked by nonhomologous extensions. This gene is expressed as a 3.2-kb mRNA in all cell types and encodes a protein of 104 kDa. ThePWP2 gene is essential for growth because spores carrying thepwp21::HIS3 disruption germinate before arresting growth with one or two large buds. The growth defect ofpwp21::HIS3 cells was rescued by expression ofPWP2 or epitope-taggedHA-PWP2 using the galactose-inducibleGAL1 promoter. In the absence of galactose, depletion of Pwp2p resulted in multibudded cells with defects in bud site selection, cytokinesis, and hydrolysis of the septal junction between mother and daughter cells. In cell fractionation studies, HA-Pwp2p was localized in the particulate component of cell lysates, from which it would be solubulized by high salt and alkaline buffer but not by nonionic detergents or urea. Indirect immunofluorescence microscopy indicated that HA-Pwp2p was clustered at multiple points in the cytoplasm. These results suggest that Pwp2p exists in a proteinaceous complex, possibly associated with the cytoskeleton, where it functions in control of cell growth and separation.     

Impacts of environmental variability in open populations and communities: "inflation" in sink environments

Ecological communities are typically open to the immigration and emigration of individuals, and also variable through time. In this paper we argue that interesting and potentially important effects arise when one splices together spatial fluxes and temporal variability. The particular system we examine is a sink habitat, where a species faces deterministic extinction but is rescued by recurrent immigration. We have shown, using a simple extension of the canonical exponential growth model in a time-varying environment, that variation "inflates" the average abundance of sink populations. We can analytically quantify the magnitude of this effect in several special cases (square-wave temporal variation and Gaussian stochastic variation). The inflationary effect can be large in "intermittent" sinks (where there are periods with positive growth), and when temporal variation is strongly autocorrelated. The effect appears to be robust to incorporation of demographic stochasticity (due to discrete birth-death-immigration processes), and to direct density dependence. With discrete generations, however, one can observe a wide range of effects of temporal variation, including depression as well as inflation. We argue that the inflationary effect of temporal variation in sink habitats can have important implications for community structure, because it can increase the average abundance (and hence local impacts) of species that on average are being excluded from a local community. We illustrate the latter effect using a familiar model of exploitative competition for a single limiting resource. We demonstrate that temporal variation can reverse local competitive dominance, even to the extent of allowing an inferior competitor maintained by immigration to exclude a competing species that would be locally superior in a constant environment.     

Production of recombinant protein C in serum-containing and serum-free perfusion culture

For the development of a perfusion culture producing recombinant human protein C, the effects of fetal calf serum and growth factors on cell growth and recombinant protein production were investigated. Although the growth of recombinant cells was stimulated by serum in a dose-dependent manner, a lower concentration of serum (2%) could support both synthesis and post-translational modification of protein C as efficiently as 10% serum. Among the growth factors tested, transferrin enhanced protein C production to the level comparable with 10% serum, while insulin was effective in maintaining cellular metabolism. Based on these results, a perfusion culture for a scale-up production of recombinant protein C was done using an Opticell culture system. A good productivity of the recombinant protein was obtained in low serum or serum-free medium for more than one month. Address for offprints: Laboratory for Molecular Biology, Pharma Research Laboratories, Hoechst Japan Ltd., 1-3-2, Minamidai, Kawagoe, Saitama 350, Japan     

Multiline varieties and disease control

Summary A general model for the evolution of pathogen populations on mixtures or multilines is developed. This model is used to extend previous analyses of the effects of the widespread cultivation of multilines on the evolution of virulence in obligate parasites to mixtures of lines carrying different numbers of resistance genes. It is concluded that the composition of an equilibrium pathogen population growing on a multiline may vary within wide limits and the prinicipal determinant of its composition is the number of components in the multiline and the resistance genes they carry. Other factors of importance are (i) the relative contribution made by each host class (with different numbers of resistance genes) to the pathogen spore pool each generation; (ii) the levels of stabilizing selection against unnecessary virulence genes; and (iii) the way in which unnecessary genes for virulence combine to reduce pathogen fitness. Conditions for the fixation of avirulent biotypes in the pathogen population and the evolution of a pathogen superrace are given for multilines of various compositions.Paper No. 9246 of the Journal Series of the North Carolina Agricultural Research Service, Raleigh, North Carolina. This investigation was supported in part by NIH Research Grant No. GM 11546 from the National Institute of General Medical Sciences     

Homogenization of Heterogeneously Coupled Bistable ODE's—Applied to Excitation Waves in Pancreatic Islets of Langerhans

We consider a lattice of coupled identical differential equations. The coupling is between nearest neighbors and of resistance type, but the strength of coupling varies from site to site. Such a lattice can, for example, model an islet of Langerhans, where the sites in the lattice model individual but identical -cells, and the coupling between cells is made of gap junctions.By using a homogenization technique we approximate the coupled discrete equations by a PDE, basically a nonlinear heat equation (a Fisher equation). For appropriate parameters this equation is known to have wave-solutions. Of importance is the fact, that the resulting diffusion coefficient does not only depend on the average of the coupling, but also on the variance of the strength. This means that the heterogeneity of the coupling strength influences the wave velocity—the greater the variance, the slower is the wave. This result is illustrated by simulations, both of a simple prototype equation, and for a full model of coupled beta-cells in both one and two dimensions, and implies that the natural heterogeneity in the islets of Langerhans should be taken into account.