A new hypothesis to explain the coexistence of n species in the presence of a single resource

Interspecific density-dependent model of predator–prey relationship in the chemostat

The objective of this study is to analyze a model of competition for one resource in the chemostat with general interspecific density-dependent growth rates, taking into account the predator–prey relationship. This relationship is characterized by the fact that the prey species promotes the growth of the predator species which in turn inhibits the growth of the first species. The model is a three-dimensional system of ordinary differential equations. With the same dilution rates, the model can be reduced to a planar system where the two models have the same local and even global behavior. The existence and stability conditions of all steady states of the reduced model in the plane are determined according to the operating parameters. Using the nullcline method, we present a geometric characterization of the existence and stability of all equilibria showing the multiplicity of coexistence steady states. The bifurcation diagrams illustrate that the steady states can appear or disappear only through saddle-node or transcritical bifurcations. Moreover, the operating diagrams describe the asymptotic behavior of this system by varying the control parameters and show the effect of the inhibition of predation on the emergence of the bistability region and the reduction until the disappearance of the coexistence region by increasing this inhibition parameter.

Increased Temperature Disrupts the Biodiversity-Ecosystem Functioning Relationship

Gaining knowledge of how ecosystems provide essential services to humans is of primary importance, especially with the current threat of climate change. Yet little is known about how increased temperature will impact the biodiversity-ecosystem functioning (BEF) relationship. We tackled this subject theoretically and experimentally. We developed a BEF theory based on mechanistic population dynamic models, which allows the inclusion of the effect of temperature. Using experimentally established relationships between attack rate and temperature, the model predicts that temperature increase will intensify competition, and consequently the BEF relationship will flatten or even become negative. We conducted a laboratory experiment with natural microbial microcosms, and the results were in agreement with the model predictions. The experimental results also revealed that an increase in both temperature average and variation had a more intense effect than an increase in temperature average alone. Our results indicate that under climate change, high diversity may not guarantee high ecosystem functioning.

A density-dependent model of competition for one resource in the chemostat

This paper deals with a two-microbial species model in competition for a single-resource in the chemostat including general intra- and interspecific density-dependent growth rates with distinct removal rates for each species. In order to understand the effects of intra- and interspecific interference, this general model is first studied by determining the conditions of existence and local stability of steady states. With the same removal rate, the model can be reduced to a planar system and then the global stability results for each steady state are derived. The bifurcations of steady states according to interspecific interference parameters are analyzed in a particular case of density-dependent growth rates which are usually used in the literature. The operating diagrams show how the model behaves by varying the operating parameters and illustrate the effect of the intra- and interspecific interference on the disappearance of coexistence region and the occurrence of bi-stability region. Concerning the small enough interspecific interference terms, we would shed light on the global convergence towards the coexistence steady state for any positive initial condition. When the interspecific interference pressure is large enough this system exhibits bi-stability where the issue of the competition depends on the initial condition.

Competition for a single resource and coexistence of several species in the chemostat

We study a model of the chemostat with several species in competition for a single resource. We take into account the intra-specific interactions between individuals of the same population of micro-organisms and we assume that the growth rates are increasing and the dilution rates are distinct. Using the concept of steady-state characteristics, we present a geometric characterization of the existence and stability of all equilibria. Moreover, we provide necessary and sufficient conditions on the control parameters of the system to have a positive equilibrium. Using a Lyapunov function, we give a global asymptotic stability result for the competition model of several species. The operating diagram describes the asymptotic behavior of this model with respect to control parameters and illustrates the effect of the intra-specific competition on the coexistence region of the species.

Population dynamics and competitive outcome derive from resource allocation statistics: The governing influence of the distinguishability of individuals

Model predictions for species competition outcomes highly depend on the assumed form of the population growth function. In this paper we apply an alternative inferential method based on statistical mechanics, maximizing Boltzmann entropy, to predict resource-constrained population dynamics and coexistence. Within this framework, population dynamics and competition outcome can be determined without assuming any particular form of the population growth function. The dynamics of each species is determined by two parameters: the mean resource requirement θ (related to the mean metabolic rate) and individual distinguishability Dr (related to intra- compared to interspecific functional variation). Our theory clarifies the condition for the energetic equivalence rule (EER) to hold, and provide a statistical explanation for the importance of species functional variation in determining population dynamics and coexistence patterns.

The genetic requirements for fast and slow growth in mycobacteria

Mycobacterium tuberculosis infects a third of the world's population. Primary tuberculosis involving active fast bacterial replication is often followed by asymptomatic latent tuberculosis, which is characterised by slow or non-replicating bacteria. Reactivation of the latent infection involving a switch back to active bacterial replication can lead to post-primary transmissible tuberculosis. Mycobacterial mechanisms involved in slow growth or switching growth rate provide rational targets for the development of new drugs against persistent mycobacterial infection. Using chemostat culture to control growth rate, we screened a transposon mutant library by Transposon site hybridization (TraSH) selection to define the genetic requirements for slow and fast growth of Mycobacterium bovis (BCG) and for the requirements of switching growth rate. We identified 84 genes that are exclusively required for slow growth (69 hours doubling time) and 256 genes required for switching from slow to fast growth. To validate these findings we performed experiments using individual M. tuberculosis and M. bovis BCG knock out mutants. We have demonstrated that growth rate control is a carefully orchestrated process which requires a distinct set of genes encoding several virulence determinants, gene regulators, and metabolic enzymes. The mce1 locus appears to be a component of the switch to slow growth rate, which is consistent with the proposed role in virulence of M. tuberculosis. These results suggest novel perspectives for unravelling the mechanisms involved in the switch between acute and persistent TB infections and provide a means to study aspects of this important phenomenon in vitro.

Practical coexistence of two species in the chemostat - a slow-fast characterization

We show that the chemostat model with two species having different but close break-even concentrations exhibits a slow-fast dynamics. Considering small perturbations about the dilution rate for which break-even concentrations are identical, we use the Fenichel theory to show the coexistence of species for large times. Then we determine the reduced dynamics, which is non-trivial and characterized by the slopes of the growth functions about their break-even concentrations.

Long run coexistence in the chemostat with multiple species

In this work we analyze the transient behavior of the dynamics of multiple species competing in a chemostat for a single resource, presenting slow/fast characteristics. We prove that coexistence among a subset of species, with growth functions close to each other, can last for a substantially long time. For these cases, we also show that the proportion of non-dominant species can be increasing before decreasing, under certain conditions on the initial distribution.

Characterization of a three bacteria mixed culture in a chemostat: Evaluation and application of a quantitative terminal-restriction fragment length polymorphism (T-RFLP) analysis for absolute and species specific cell enumeration

Growth dynamics of Pseudomonas aeruginosa, Burkholderia cepacia, and Staphylococcus aureus in a batch and chemostat, were investigated as a laboratory model system for persistent infections in cystic fibrosis. Most species-specific enumeration methods for mixed cultures are laborious or only qualitative, and therefore impede generation of quantitative data required for validation of mathematical models. Here, a quantitative T-RFLP method was evaluated and applied for specific and absolute cell number enumerations. The method was tested to be unbiased by quantitative sample composition and allowed reproducible enumerations of mixed cultures. For assay validation, samples of defined concentration containing one, two or three species were quantified. Logarithmically transformed absolute cell numbers of single-species dilutions were linear within a lower working range of 10(4)-10(6) cfu/mL (species-dependent) and an upper working range of 10(10) cfu/mL. Quantifications of single species (10(6)-10(10) cfu/mL) spiked with one or two other species agreed well with single species controls. Differences between slopes of first order linear regression of spiked and pure dilution series were insignificant. Coefficient of variation of defined mixed replicates was maximum 4.39%, of a three-species chemostat it was maximum 1.76%. T-RFLP monitoring of pure cultures in parallel shake flasks and of a three-species mixed chemostat gave very consistent results. Coexistence of at least two species after a time period equivalent to more than 33 volume exchanges was found. This result was not predicted from pure cultures clearly indicating the need for quantitative mixed culture experiments to better understand microbial growth dynamics and for mathematical model validation.