Time lags and global stability in two-species competition

Global asymptotic stability and equilibrium coexistence is established in two species Lotka-Volterra-type competition when there are time delays in interspecific interaction terms and the intraspecies competition is stronger than the interspecies competition.     

Uniform persistence and global stability of two prey-predator pairs linked by competition

General models of two predator-prey systems are considered in which the prey are linked through competition and the predators are not directly linked. The persistence criteria based upon a technique developed by Gard is obtained. In addition, a condition for the global asymptotic stability of the interior equilibrium is discussed.     

The stability of ecosystems

Stability criteria and phase boundaries for complex ecosystems are obtained and contrasted with previously studied scenarios. The stability of such systems is determined by the behaviour of the largest eigenvalue of matrices governing the response of the system to small perturbations. As a result we show that ecosystems with unstructured cooperative interactions between arbitary species can be less stable than had been previously determined. We also examine hierarchical ecologies, and demonstrate their increased stability under certain conditions.     

Effective size and the persistence of ecosystems

Summary Ecosystems distributed in space have an effective size, reflecting both their absolute size (extent) and their fine-scale physical structure (viscosity). In this paper, a general mathematical model of a predator-prey interaction is presented via the phase-plane graphs of Rosenzweig and MacArthur (1963) to show one reason why ecosystems of larger effective size should persist longer than smaller ones: oscillations of population densities tend to be displaced farther from extinction thresholds—even in spatially homogeneous systems. Experimental results obtained by Gause and Luckinbill with protozoa and Huffaker with mites are interpreted in this context.     

On the global stability of a generalized cholera epidemiological model

In this paper, we conduct a careful global stability analysis for a generalized cholera epidemiological model originally proposed in [J. Wang and S. Liao, A generalized cholera model and epidemic/endemic analysis, J. Biol. Dyn. 6 (2012), pp. 568–589]. Cholera is a water- and food-borne infectious disease whose dynamics are complicated by the multiple interactions between the human host, the pathogen, and the environment. Using the geometric approach, we rigorously prove the endemic global stability for the cholera model in three-dimensional (when the pathogen component is a scalar) and four-dimensional (when the pathogen component is a vector) systems. This work unifies the study of global dynamics for several existing deterministic cholera models. The analytical predictions are verified by numerical simulation results.     

Thermodynamic stability of ecosystems

The stability of ecosystems during periods of stasis in their macro-evolutionary trajectory is studied from a non-equilibrium thermodynamic perspective. Individuals of the species are considered as units of entropy production and entropy exchange in an open thermodynamic system. Within the framework of the classical theory of irreversible thermodynamics, and under the condition of constant external constraints, such a system will naturally evolve toward a globally stable thermodynamic stationary state. It is thus suggested that the ecological steady state, or stasis, is a particular case of the thermodynamic stationary state, and that the evolution of community stability through natural selection is a manifestation of non-equilibrium thermodynamic directives. Furthermore, it is argued that punctuation of stasis leading to ecosystem succession, may be a manifestation of non-equilibrium "phase transitions" brought on by a change of external constraints through a thermodynamic critical point.     

On the global stability of an epidemic model of computer viruses

In this paper, we study the global properties of a computer virus propagation model. It is, interesting to note that the classical method of Lyapunov functions combined with the Volterra–Lyapunov matrix properties, can lead to the proof of the endemic global stability of the dynamical model characterizing the spread of computer viruses over the Internet. The analysis and results presented in this paper make building blocks towards a comprehensive study and deeper understanding of the fundamental mechanism in computer virus propagation model. A numerical study of the model is also carried out to investigate the analytical results.     

The stability of benthic ecosystems

Physicists have two conceptions of the stability of systems: global and neighbourhood stability. Global stability corresponds to the idea of successional changes leading to climax communities. Yet, neighbourhood stability is shown to be a more realistic model for changes in dominance of marine benthic sediment-living communities. The factors inducing state changes in dominance pattern were shown to be principally biological interactions. In order to model the stability of benthic ecosystems, much more attention must be given to natural history-type studies of biological interactions. Furthermore, mathematical models usually assume that the systems are globally stable. Should neighbourhood stability prove to be the rule for benthic systems then realistic models of such systems will be an order of magnitude more complex.     

The structure and stability of model ecosystems assembled in a variable environment

To explore how environmental variability may create non‐random community structure, we simulated the assembly of model communities under varying levels of environmental variability. We assembled communities by creating a large pool of randomly constructed species, and then added species from this pool sequentially, allowing extinctions of invading and resident species to occur until the community became saturated. Because much current research on community structure focuses on single trophic levels, we constructed species pools consisting only of competitors. To compare with more realistic communities, we also created species pools with multiple trophic levels. For both types of communities, following assembly we calculated a variety of metrics of community structure, and five measures of community stability. Communities assembled under high environmental variability had fewer species, fewer and weaker interactions among species, and greater evenness in abundance of persisting species. For single trophic‐level communities, community size was dictated primarily by competitive exclusion. In contrast, for multiple trophic‐level communities, community size was increasingly limited by dynamical instabilities as environmental variability increased. Differences in community structure resulting from assembly under high environmental variability led to differences in community stability. According to two measures of stability related to population variability – the characteristic return rate to equilibrium and the coefficient of variation in individual species densities – stability increased for communities assembled under high environmental variability. In contrast, three additional measures of stability that are not directly related to population variability showed a variety of patterns, either increasing, decreasing, or remaining constant. Thus, communities assembled in highly variable environments are not necessarily generically more stable. Our results demonstrate that environmental variability can structure communities and affect their stability properties in non‐trivial ways. Thus, when making predictions about the response of communities to future extinctions or environmental degradation, account should be given to the forces responsible for community structure.     

Within-host competition determines reproductive success of temperate bacteriophages

Within-host competition between parasites is frequently invoked as a major force for parasite evolution, yet quantitative studies on its extent in an organismal group are lacking. Temperate bacteriophages are diverse and abundant parasites of bacteria, distinguished by their ability to enter a facultative dormant state in their host. Bacteria can accumulate multiple phages that may eventually abandon dormancy in response to host stress. Host resources are then converted into phage particles, whose release requires cell death. To study within-host competition between phages, I used the bacterium Escherichia coli and 11 lambdoid phages to construct single and double lysogens. Lysogenic bacterial cultures were then induced and time to host cell lysis and productivity of phages was measured. In double lysogens, this revealed strong competitive interactions as in all cases productivity of at least one phage declined. The outcome of within-host competition was often asymmetrical, and phages were found to vary hierarchically in within-host competitive ability. In double infections, the phage with the shorter lysis time determined the timing of cell lysis, which was associated with a competitive advantage when time differences were large. The results emphasize that within-host competition greatly affects phage fitness and that multiple infections should be considered an integral part of bacteriophage ecology.     

Resource competition determines selection of B cell repertoires

Previous experiments with mouse chimeras demonstrated that cellular competition for antigen-specific survival signals plays a crucial role in the maintenance of the naive B cell repertoire. Transgenic (Tg) B cell populations in these chimeras have a shortened lifespan and poor competitive abilities as compared to more diverse non-Tg populations in the same mice. We develop a mathematical model to investigate the mechanism of B cell competition. The model allows for various B cell clones, generated in the bone marrow, to go into the peripheral circulation, where they compete specifically for various ligands providing survival signals. In the model we also find the observed poor competitive abilities of the Tg repertoire. Investigating the nature of the competition in the model, we find that most of the competition is "intraspecific" occurring largely within the clone of truly Tg B cells, and within the repertoire of leaky Tg and non-Tg B cells. This is confirmed by analysing a simplified version of the model, which only allows for intraspecific competition, and resembles a simple ecological model with density-dependent death. The fact that our model accounts for the data, casts doubt on a previous interpretation of the same data arguing that more diverse repertoires outcompete repertoires of lower diversity. Here, we conclude that most of the data can be explained with intraspecific competition, and formulate an experimental prediction that allows one to distinguish between the previous interpretation of inter-specific competition between repertoires, and the current interpretation of intraspecific competition.     

Nodal stability determines signaling range

Secreted TGFbeta proteins of the Nodal family pattern the vertebrate body axes and induce mesoderm and endoderm . Nodal proteins can act as morphogens , but the mechanisms regulating their activity and signaling range are poorly understood. In particular, it has been unclear how inefficient processing or rapid turnover of the Nodal protein influences autocrine and paracrine signaling properties . Here, we evaluate the role of Nodal processing and stability in tissue culture and zebrafish embryos. Removal of the pro domain potentiates autocrine signaling but reduces Nodal stability and signaling range. Insertion of an N-glycosylation site present in several related TGFbeta proteins increases the stability of mature Nodal. The stabilized form of Nodal acts at a longer range than the wild-type form. These results suggest that increased proteolytic maturation of Nodal potentiates autocrine signaling, whereas increased Nodal stability extends paracrine signaling.     

Plant nutrient supply determines competition between phytophagous insects

Indirect competition is often mediated by plant responses to herbivore feeding damage and is common among phytophagous insect species. Plant-mediated responses may be altered by abiotic conditions such as nutrient supply, which can affect plant growth, morphology, and the concentration of primary and secondary metabolites. Nutrient supply can be manipulated by the type and amount of fertilizer applied to a plant. Brassica oleracea plants were grown in several types of fertilizer, including those commonly used in sustainable and conventional agricultural systems. The occurrence of indirect competition between two phytophagous species from different feeding guilds (a phloem-feeder and leaf-chewer) was assessed. The leaf-chewer reduced aphid populations on plants growing in most fertilizer treatments, but not on those in the ammonium nitrate fertilizer treatment, which caused the highest concentration of foliar nitrogen. The potential consequences of our findings are discussed for phytophagous species in conventional and sustainable agricultural systems.     

Biodiversity and the productivity and stability of ecosystems

Attempts to unveil the relationships between the taxonomic diversity, productivity and stability of ecosystems continue to generate inconclusive, contradictory and controversial conclusions. New insights from recent studies support the hypothesis that species diversity enhances productivity and stability in some ecosystems, but not in others. Appreciation is growing for the ways that particular ecosystem features, such as environmental variability and nutrient stress, can influence biotic interactions. Alternatives to the diversity-stability hypothesis have been proposed, and experimental approaches are starting to evolve to test these hypotheses and to elucidate the mechanisms underlying the functional role of species diversity.     

Discrete three-stage population model: persistence and global stability results

A general three-stage discrete-time population model is studied. The inherent net reproductive number for this model is derived. Global stability of the origin is established provided that the inherent net reproductive number is less than one. If it is larger than one the existence of a unique positive fixed point is proved and the persistence of the system is established. Finally, for certain parameter ranges global stability of the positive fixed point is proved.     

Discrete three-stage population model: persistence and global stability results

A general three-stage discrete-time population model is studied. The inherent net reproductive number for this model is derived. Global stability of the origin is established provided that the inherent net reproductive number is less than one. If it is larger than one the existence of a unique positive fixed point is proved and the persistence of the system is established. Finally, for certain parameter ranges global stability of the positive fixed point is proved.