Global dynamics of a chemostat competition model with distributed delay

 We study the global dynamics of n-species competition in a chemostat with distributed delay describing the time-lag involved in the conversion of nutrient to viable biomass. The delay phenomenon is modelled by the gamma distribution. The linear chain trick and a fluctuation lemma are applied to obtain the global limiting behavior of the model. When each population can survive if it is cultured alone, we prove that at most one competitor survives. The winner is the population that has the smallest delayed break-even concentration, provided that the orders of the delay kernels are large and the mean delays modified to include the washout rate (which we call the virtual mean delays) are bounded and close to each other, or the delay kernels modified to include the washout factor (which we call the virtual delay kernels) are close in L ¹-norm. Also, when the virtual mean delays are relatively small, it is shown that the predictions of the distributed delay model are identical with the predictions of the corresponding ODEs model without delay. However, since the delayed break-even concentrations are functions of the parameters appearing in the delay kernels, if the delays are sufficiently large, the prediction of which competitor survives, given by the ODEs model, can differ from that given by the delay model. Received: 9 August 1997 / Revised version: 2 July 1998     

Bridging parametric and nonparametric measures of species interactions unveils new insights of non-equilibrium dynamics

A central theme in ecological research is to understand how species interactions contribute to community dynamics. Species interactions are the basis of parametric (model-driven) and nonparametric (model-free) approaches in theoretical and empirical work. However, despite their different interpretations across these approaches, these measures have occasionally been used interchangeably, limiting our opportunity to use their differences to gain new insights about ecological systems. Here, we revisit two of the most used measures across these approaches: species interactions measured as constant direct effects (typically used in parametric approaches) and local aggregated effects (typically used in nonparametric approaches). We show two fundamental properties of species interactions that cannot be revealed without bridging these definitions. First, we show that the local aggregated intraspecific effect summarizes all potential pathways through which one species impacts itself, which are likely to be negative even without any constant direct self-regulation mechanism. This property has implications for the long-held debate on how communities can be stabilized when little evidence of self-regulation has been found among higher-trophic species. Second, we show that a local aggregated interspecific effect between two species is correlated with the constant direct interspecific effect if and only if the population dynamics do not have any higher-order direct effects. This other property provides a rigorous methodology to detect direct higher-order effects in the field and experimental data. Overall, our findings illustrate a practical route to gain further insights about non-equilibrium ecological dynamics and species interactions.     

A newly discovered role of evolution in previously published consumer–resource dynamics

Consumer–resource interactions are fundamental components of ecological communities. Classic features of consumer–resource models are that temporal dynamics are often cyclic, with a ¼‐period lag between resource and consumer population peaks. However, there are few published empirical examples of this pattern. Here, we show that many published examples of consumer–resource cycling show instead patterns indicating eco‐evolutionary dynamics. When prey evolve along a trade‐off between defence and competitive ability, two‐species consumer–resource cycles become longer and antiphase (half‐period lag, so consumer maxima coincide with minima of the resource species). Using stringent criteria, we identified 21 two‐species consumer–resource time series, published between 1934 and 1997, suitable to investigate for eco‐evolutionary dynamics. We developed a statistical method to probe for a transition from classic to eco‐evolutionary cycles, and find evidence for eco‐evolutionary type cycles in about half of the studies. We show that rapid prey evolution is the most likely explanation for the observed patterns.     

Population dynamics of a polychaete during three El Niño events: disentangling biotic and abiotic factors

The macrobenthic community in shallow soft-bottom areas in the Bay of Ancón, Peru, is characterised by low biodiversity due to low oxygen concentrations. During El Niño events, higher temperature and higher concentrations of dissolved oxygen induce a temporary increase in biodiversity. However, the structure and dynamics of the emerging communities vary strongly among events. The reasons for this variation are poorly understood, in particular the relative influence of abiotic vs biotic factors. To disentangle the roles of abiotic and biotic factors, population models based on detailed monitoring data of three El Niño events were developed focused on the population dynamics of one species in the community, the polychaete Sigambra bassi , which showed different responses in different El Niño events. Calculated and observed population dynamics are compared using root mean square deviation (RMSD). The results show that S. bassi abundance can be determined by abiotic environmental conditions. Besides, three biotic factors improved model performance in different El Niño events: negative density dependence in larval settlement, lower carrying capacity in the presence of other species and positive density dependence in adult survival. The results demonstrate how population models can be used to decode information hidden in long-term monitoring data of abiotic and biotic community parameters about factors driving population dynamics.     

Disentangling spatiotemporal dynamics in metacommunities through a species-patch network approach

Colonization and extinction at local and regional scales, and gains and losses of patches are important processes in the spatiotemporal dynamics of metacommunities. However, analytical challenges remain in quantifying such spatiotemporal dynamics when species extinction-colonization and patch gain and loss processes act simultaneously. Recent advances in network analysis show great potential in disentangling the roles of colonization, extinction, and patch dynamics in metacommunities. Here, we developed a species-patch network approach to quantify metacommunity dynamics including (i) temporal changes in network structure, and (ii) temporal beta diversity of species-patch links and its components that reflect species extinction-colonization and patch gain and loss. Application of the methods to simulated datasets demonstrated that the approach was informative about metacommunity assembly processes. Based on three empirical datasets, our species-patch network approach provided additional information about metacommunity dynamics through distinguishing the effects of species colonization and extinction at different scales from patch gains and losses and how specific environmental factors related to species-patch network structure. In conclusion, our species-patch network framework provides effective methods for monitoring and revealing long-term metacommunity dynamics by quantifying gains and losses of both species and patches under local and global environmental change.     

What happens if density increases? Conservation implications of population influx into refuges

Sudden catastrophic events like fires, hurricanes, tsunamis, landslides and deforestation increase population densities in habitat fragments, as fleeing animals encroach into these refuges. Such sudden overcrowding will trigger transient fluctuations in population size in the refuges, which may expose refuge populations to an increased risk of extinction. Until recently, detailed information about the operation of density dependence in stage-structured populations, and tools for quantifying the effects of transient dynamics, have not been available, so that exploring the extinction risk of such transient fluctuations has been intractable. Here, we use such recently developed tools to show that extinction triggered by overcrowding can threaten populations in refuges. Apart from situations where density dependence acts on survival, our results indicate that short-lived species may be more at risk than longer-lived species. Because dynamics in local populations may be critical for the preservation of metapopulations and rare species, we argue that this aspect warrants further attention from conservation biologists.     

具有不连续抗生素输入和时滞效应的两菌群模型的动力学性质研究

研究了不连续的抗生素输入以及时滞效应对栖生的两菌群的影响,获得了菌群灭绝和持续生存的条件.结果表明抗生素的不连续输入对系统的动力学行为带来很大影响,而抗生素的时滞作用是无害的.     

Competition between microorganisms for a single limiting resource with cell quota structure and spatial variation

Microbial populations compete for nutrient resources, and the simplest mathematical models of competition neglect differences in the nutrient content of individuals. The simplest models also assume a spatially uniform habitat. Here both of these assumptions are relaxed. Nutrient content of individuals is assumed proportional to cell size, which varies for populations that reproduce by division, and the habitat is taken to be an unstirred chemostat where organisms and nutrients move by simple diffusion. In a spatially uniform habitat, the size-structured model predicts competitive exclusion, such that only the species with lowest break-even concentration persists. In the unstirred chemostat, coexistence of two competitors is possible, if one has a lower break-even concentration and the other can grow more rapidly. In all habitats, the calculation of competitive outcomes depends on a principal eigenvalue that summarizes relationships among cell growth, cell division, and cell size.     

Trophic interaction modifications: an empirical and theoretical framework

Consumer–resource interactions are often influenced by other species in the community. At present these ‘trophic interaction modifications’ are rarely included in ecological models despite demonstrations that they can drive system dynamics. Here, we advocate and extend an approach that has the potential to unite and represent this key group of non‐trophic interactions by emphasising the change to trophic interactions induced by modifying species. We highlight the opportunities this approach brings in comparison to frameworks that coerce trophic interaction modifications into pairwise relationships. To establish common frames of reference and explore the value of the approach, we set out a range of metrics for the ‘strength’ of an interaction modification which incorporate increasing levels of contextual information about the system. Through demonstrations in three‐species model systems, we establish that these metrics capture complimentary aspects of interaction modifications. We show how the approach can be used in a range of empirical contexts; we identify as specific gaps in current understanding experiments with multiple levels of modifier species and the distributions of modifications in networks. The trophic interaction modification approach we propose can motivate and unite empirical and theoretical studies of system dynamics, providing a route to confront ecological complexity.     

A general multi-trait-based framework for studying the effects of biodiversity on ecosystem functioning

Environmental change is as multifaceted as are the species and communities that respond to these changes. Current theoretical approaches to modeling ecosystem response to environmental change often deal only with single environmental drivers or single species traits, simple ecological interactions, and/or steady states, leading to concern about how accurately these approaches will capture future responses to environmental change in real biological systems. To begin addressing this issue, we generalize a previous trait-based framework to incorporate aspects of frequency dependence, functional complementarity, and the dynamics of systems composed of species that are defined by multiple traits that are tied to multiple environmental drivers. The framework is particularly well suited for analyzing the role of temporal environmental fluctuations in maintaining trait variability and the resultant effects on community response to environmental change. Using this framework, we construct simple models to investigate two ecological problems. First, we show how complementary resource use can significantly enhance the nutrient uptake of plant communities through two different mechanisms related to increased productivity (over-yielding) and larger trait variability. Over-yielding is a hallmark of complementarity and increases the total biomass of the community and, thus, the total rate at which nutrients are consumed. Trait variability also increases due to the lower levels of competition associated with complementarity, thus speeding up the rate at which more efficient species emerge as conditions change. Second, we study systems in which multiple environmental drivers act on species defined by multiple, correlated traits. We show that correlations in these systems can increase trait variability within the community and again lead to faster responses to environmental change. The methodological advances provided here will apply to almost any function that relates species traits and environmental drivers to growth, and should prove useful for studying the effects of climate change on the dynamics of biota.     

Habitat structure mediates biodiversity effects on ecosystem properties

Much of what we know about the role of biodiversity in mediating ecosystem processes and function stems from manipulative experiments, which have largely been performed in isolated, homogeneous environments that do not incorporate habitat structure or allow natural community dynamics to develop. Here, we use a range of habitat configurations in a model marine benthic system to investigate the effects of species composition, resource heterogeneity and patch connectivity on ecosystem properties at both the patch (bioturbation intensity) and multi-patch (nutrient concentration) scale. We show that allowing fauna to move and preferentially select patches alters local species composition and density distributions, which has negative effects on ecosystem processes (bioturbation intensity) at the patch scale, but overall positive effects on ecosystem functioning (nutrient concentration) at the multi-patch scale. Our findings provide important evidence that community dynamics alter in response to localized resource heterogeneity and that these small-scale variations in habitat structure influence species contributions to ecosystem properties at larger scales. We conclude that habitat complexity forms an important buffer against disturbance and that contemporary estimates of the level of biodiversity required for maintaining future multi-functional systems may need to be revised.     

Bacterial adaptation to sublethal antibiotic gradients can change the ecological properties of multitrophic microbial communities

Antibiotics leak constantly into environments due to widespread use in agriculture and human therapy. Although sublethal concentrations are well known to select for antibiotic-resistant bacteria, little is known about how bacterial evolution cascades through food webs, having indirect effect on species not directly affected by antibiotics (e.g. via population dynamics or pleiotropic effects). Here, we used an experimental evolution approach to test how temporal patterns of antibiotic stress, as well as migration within metapopulations, affect the evolution and ecology of microcosms containing one prey bacterium, one phage and two protist predators. We found that environmental variability, autocorrelation and migration had only subtle effects for population and evolutionary dynamics. However, unexpectedly, bacteria evolved greatest fitness increases to both antibiotics and enemies when the sublethal levels of antibiotics were highest, indicating positive pleiotropy. Crucially, bacterial adaptation cascaded through the food web leading to reduced predator-to-prey abundance ratio, lowered predator community diversity and increased instability of populations. Our results show that the presence of natural enemies can modify and even reverse the effects of antibiotics on bacteria, and that antibiotic selection can change the ecological properties of multitrophic microbial communities by having indirect effects on species not directly affected by antibiotics.     

Shrubs, granivores and annual plant community stability in an arid ecosystem

Compensatory population dynamics among species stabilise aggregate community variables. Inter-specific competition is thought to be stabilising as it promotes asynchrony among populations. However, we know little about other inter-specific interactions, such as facilitation and granivory. Such interactions are also likely to influence population synchrony and community stability, especially in harsh environments where they are thought to have relatively strong effects in plant communities. We use a manipulative experiment to test the effects of granivores (harvester ants) and nurse plants (dwarf shrubs) on annual plant community dynamics in the Negev desert, Israel. We present evidence for weak and inconsistent effects of harvester ants on plant abundance and on population and community stability. By contrast, we show that annual communities under shrubs were more species rich, had higher plant density and were temporally less variable than communities in the inter-shrub matrix. Species richness and plant abundance were also more resistant to drought in the shrub under-storey compared with the inter-shrub matrix, although population dynamics in both patch types were synchronised. Hence, we show that inter-specific interactions other than competition affect community stability, and that hypothesised mechanisms linking compensatory dynamics and community stability may not operate to the same extent in arid plant communities.     

Invasive aquarium fish transform ecosystem nutrient dynamics

Trade of ornamental aquatic species is a multi-billion dollar industry responsible for the introduction of myriad fishes into novel ecosystems. Although aquarium invaders have the potential to alter ecosystem function, regulation of the trade is minimal and little is known about the ecosystem-level consequences of invasion for all but a small number of aquarium species. Here, we demonstrate how ecological stoichiometry can be used as a framework to identify aquarium invaders with the potential to modify ecosystem processes. We show that explosive growth of an introduced population of stoichiometrically unique, phosphorus (P)-rich catfish in a river in southern Mexico significantly transformed stream nutrient dynamics by altering nutrient storage and remineralization rates. Notably, changes varied between elements; the P-rich fish acted as net sinks of P and net remineralizers of nitrogen. Results from this study suggest species-specific stoichiometry may be insightful for understanding how invasive species modify nutrient dynamics when their population densities and elemental composition differ substantially from native organisms. Risk analysis for potential aquarium imports should consider species traits such as body stoichiometry, which may increase the likelihood that an invasion will alter the structure and function of ecosystems.     

Intraseasonal predictability of natural phytoplankton population dynamics

It is difficult to make skillful predictions about the future dynamics of marine phytoplankton populations. Here, we use a 22‐year time series of monthly average abundances for 198 phytoplankton taxa from Station L4 in the Western English Channel (1992–2014) to test whether and how aggregating phytoplankton into multi‐species assemblages can improve predictability of their temporal dynamics. Using a non‐parametric framework to assess predictability, we demonstrate that the prediction skill is significantly affected by how species data are grouped into assemblages, the presence of noise, and stochastic behavior within species. Overall, we find that predictability one month into the future increases when species are aggregated together into assemblages with more species, compared with the predictability of individual taxa. However, predictability within dinoflagellates and larger phytoplankton (>12 μm cell radius) is low overall and does not increase by aggregating similar species together. High variability in the data, due to observational error (noise) or stochasticity in population growth rates, reduces the predictability of individual species more than the predictability of assemblages. These findings show that there is greater potential for univariate prediction of species assemblages or whole‐community metrics, such as total chlorophyll or biomass, than for the individual dynamics of phytoplankton species.     

Mechanism of protection of peroxidase activity by oscillatory dynamics.

The peroxidase-oxidase reaction is known to involve reactive oxygen species as intermediates. These intermediates inactivate many types of biomolecules, including peroxidase itself. Previously, we have shown that oscillatory dynamics in the peroxidase-oxidase reaction seem to protect the enzyme from inactivation. It was suggested that this is due to a lower average concentration of reactive oxygen species in the oscillatory state compared to the steady state. Here, we studied the peroxidase-oxidase reaction with either 4-hydroxybenzoic acid or melatonin as cofactors. We show that the protective effect of oscillatory dynamics is present in both cases. We also found that the enzyme degradation depends on the concentration of the cofactor and on the pH of the reaction mixture. We simulated the oscillatory behaviour, including the oscillation/steady state bistability observed experimentally, using a detailed reaction scheme. The computational results confirm the hypothesis that protection is due to lower average concentrations of superoxide radical during oscillations. They also show that the shape of the oscillations changes with increasing cofactor concentration resulting in a further decrease in the average concentration of radicals. We therefore hypothesize that the protective effect of oscillatory dynamics is a general effect in this system.     

Natural enemy specialization and the period of population cycles

The dynamical consequences of multiple‐species interactions remain an elusive and fiercely debated topic. Recently, Murdoch and colleagues proposed a general rule for the dynamics of generalist natural enemies: when periodic, they exhibit single generation cycles (SGCs), similar to single species systems. This contrasts markedly with specialists, which tend to show classic (longer period) consumer–resource cycles. Using a well‐studied laboratory system, we show that this general rule is contradicted when we consider resource age‐structure.