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.     

Qualitative stability and ambiguity in model ecosystems

Qualitative analysis of stability in model ecosystems has previously been limited to determining whether a community matrix is sign stable or not with little analytical means to assess the impact of complexity on system stability. Systems are seen as either unconditionally or conditionally stable with little distinction and therefore much ambiguity in the likelihood of stability. First, we reexamine Hurwitz's principal theorem for stability and propose two "Hurwitz criteria" that address different aspects of instability: positive feedback and insufficient lower-level feedback. Second, we derive two qualitative metrics based on these criteria: weighted feedback (wF(n)) and weighted determinants (wDelta(n)). Third, we test the utility of these qualitative metrics through quantitative simulations in a random and evenly distributed parameter space in models of various sizes and complexities. Taken together they provide a practical means to assess the relative degree to which ambiguity has entered into calculations of stability as a result of system structure and complexity. From these metrics we identify two classes of models that may have significant relevance to system research and management. This work helps to resolve some of the impasse between theoretical and empirical discussions on the complexity and stability of natural communities.     

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.     

Response diversity determines the resilience of ecosystems to environmental change

A growing body of evidence highlights the importance of biodiversity for ecosystem stability and the maintenance of optimal ecosystem functionality. Conservation measures are thus essential to safeguard the ecosystem services that biodiversity provides and human society needs. Current anthropogenic threats may lead to detrimental (and perhaps irreversible) ecosystem degradation, providing strong motivation to evaluate the response of ecological communities to various anthropogenic pressures. In particular, ecosystem functions that sustain key ecosystem services should be identified and prioritized for conservation action. Traditional diversity measures (e.g. ‘species richness’) may not adequately capture the aspects of biodiversity most relevant to ecosystem stability and functionality, but several new concepts may be more appropriate. These include ‘response diversity’, describing the variation of responses to environmental change among species of a particular community. Response diversity may also be a key determinant of ecosystem resilience in the face of anthropogenic pressures and environmental uncertainty. However, current understanding of response diversity is poor, and we see an urgent need to disentangle the conceptual strands that pervade studies of the relationship between biodiversity and ecosystem functioning. Our review clarifies the links between response diversity and the maintenance of ecosystem functionality by focusing on the insurance hypothesis of biodiversity and the concept of functional redundancy. We provide a conceptual model to describe how loss of response diversity may cause ecosystem degradation through decreased ecosystem resilience. We explicitly explain how response diversity contributes to functional compensation and to spatio‐temporal complementarity among species, leading to long‐term maintenance of ecosystem multifunctionality. Recent quantitative studies suggest that traditional diversity measures may often be uncoupled from measures (such as response diversity) that may be more effective proxies for ecosystem stability and resilience. Certain conclusions and recommendations of earlier studies using these traditional measures as indicators of ecosystem resilience thus may be suspect. We believe that functional ecology perspectives incorporating the effects and responses of diversity are essential for development of management strategies to safeguard (and restore) optimal ecosystem functionality (especially multifunctionality). Our review highlights these issues and we envision our work generating debate around the relationship between biodiversity and ecosystem functionality, and leading to improved conservation priorities and biodiversity management practices that maximize ecosystem resilience in the face of uncertain environmental change.     

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.     

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.     

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.     

Soil moisture determines the recovery time of ecosystems from drought

Recovery time, the time it takes for ecosystems to return to normal states after experiencing droughts, is critical for assessing the response of ecosystems to droughts; however, the spatial dominant factors determining recovery time are poorly understood. We identify the global patterns of terrestrial ecosystem recovery time based on remote sensed vegetation indices, analyse the affecting factors of recovery time using random forest regression model, and determine the spatial distribution of the dominant factors of recovery time based on partial correlation. The results show that the global average recovery time is approximately 3.3 months, and that the longest recovery time occurs in mid-latitude drylands. Analysis of affecting factors of recovery time suggests that the most important environmental factor affecting recovery time is soil moisture during the recovery period, followed by temperature and vapour pressure deficit (VPD). Recovery time shortens with increasing soil moisture and prolongs with increasing VPD; however, the response of recovery time to temperature is nonmonotonic, with colder or hotter temperatures leading to longer recovery time. Soil moisture dominates the drought recovery time over 58.4% of the assessed land area, mostly in the mid-latitudes. The concern is that soil moisture is projected to decline in more than 65% regions in the future, which will lengthen the drought recovery time and exacerbate drought impacts on terrestrial ecosystems, especially in southwestern United States, the Mediterranean region and southern Africa. Our research provides methodological insights for quantifying recovery time and spatially identifies dominant factors of recovery time, improving our understanding of ecosystem response to drought.     

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.     

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.     

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.     

Vegetation type determines heterotrophic respiration in subalpine Australian ecosystems

Soils are the largest store of carbon in the biosphere and cool‐cold climate ecosystems are notable for their carbon‐rich soils. Characterizing effects of future climates on soil‐stored C is critical to elucidating feedbacks to changes in the atmospheric pool of CO₂. Subalpine vegetation in south‐eastern Australia is characterized by changes over short distances (scales of tens to hundreds of metres) in community phenotype (woodland, shrubland, grassland) and in species composition. Despite common geology and only slight changes in landscape position, we measured striking differences in a range of soil properties and rates of respiration among three of the most common vegetation communities in subalpine Australian ecosystems. Rates of heterotrophic respiration in bulk soil were fastest in the woodland community with a shrub understorey, slowest in the grassland, and intermediate in woodland with grass understorey. Respiration rates in surface soils were 2.3 times those at depth in soils from woodland with shrub understorey. Surface soil respiration in woodlands with grass understorey and in grasslands was about 3.5 times that at greater depth. Both Arrhenius and simple exponential models fitted the data well. Temperature sensitivity (Q₁₀) varied and depended on the model used as well as community type and soil depth – highlighting difficulties associated with calculating and interpreting Q₁₀. Distributions of communities in these subalpine areas are dynamic and respond over relatively short time‐frames (decades) to changes in fire regime and, possibly, to changes in climate. Shifts in boundaries among communities and possible changes in species composition as a result of both direct and indirect (e.g. via fire regime) climatic effects will significantly alter rates of respiration through plant‐mediated changes in soil chemistry. Models of future carbon cycles need to take into account changes in soil chemistry and rates of respiration driven by changes in vegetation as well as those that are temperature‐ and moisture‐driven.     

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.     

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.