Stable States of a Microbial Community Are Formed by Dynamic Metabolic Networks with Members Functioning to Achieve Both Robustness and Plasticity.

A more detailed understanding of the mechanisms underlying the formation of microbial communities is essential for the efficient management of microbial ecosystems. The stable states of microbial communities are commonly perceived as static and, thus, have not been extensively examined. The present study investigated stabilizing mechanisms, minority functions, and the reliability of quantitative ana-lyses, emphasizing a metabolic network perspective. A bacterial community, formed by batch transferred cultures supplied with phenol as the sole carbon and energy source and paddy soil as the inoculum, was analyzed using a principal coordinate ana-lysis (PCoA), mathematical models, and quantitative parameters defined as growth activity, community-changing activity, community-forming activity, vulnerable force, and resilience force depending on changes in the abundance of operational taxonomic units (OTUs) using 16S rRNA gene amplicon sequences. PCoA showed succession states until the 3rd transferred cultures and stable states from the 5th to 10th transferred cultures. Quantitative parameters indicated that the bacterial community was dynamic irrespective of the succession and stable states. Three activities fluctuated under stable states. Vulnerable and resilience forces were detected under the succession and stable states, respectively. Mathematical models indicated the construction of metabolic networks, suggesting the stabilizing mechanism of the community structure. Thirteen OTUs coexisted during stable states, and were recognized as core OTUs consisting of majorities, middle-class, and minorities. The abundance of the middle-class changed, whereas that of the others did not, which indicated that core OTUs maintained metabolic networks. Some extremely low abundance OTUs were consistently exchanged, suggesting a role for scavengers. These results indicate that stable states were formed by dynamic metabolic networks with members functioning to achieve robustness and plasticity.

Interspecies interactions are an integral determinant of microbial community dynamics.

This study investigated the factors that determine the dynamics of bacterial communities in a complex system using multidisciplinary methods. Since natural and engineered microbial ecosystems are too complex to study, six types of synthetic microbial ecosystems (SMEs) were constructed under chemostat conditions with phenol as the sole carbon and energy source. Two to four phenol-degrading, phylogenetically and physiologically different bacterial strains were used in each SME. Phylogeny was based on the nucleotide sequence of 16S rRNA genes, while physiologic traits were based on kinetic and growth parameters on phenol. Two indices, J parameter and "interspecies interaction," were compared to predict which strain would become dominant in an SME. The J parameter was calculated from kinetic and growth parameters. On the other hand, "interspecies interaction," a new index proposed in this study, was evaluated by measuring the specific growth activity, which was determined on the basis of relative growth of a strain with or without the supernatant prepared from other bacterial cultures. Population densities of strains used in SMEs were enumerated by real-time quantitative PCR (qPCR) targeting the gene encoding the large subunit of phenol hydroxylase and were compared to predictions made from J parameter and interspecies interaction calculations. In 4 of 6 SEMs tested the final dominant strain shown by real-time qPCR analyses coincided with the strain predicted by both the J parameter and the interspecies interaction. However, in SMEII-2 and SMEII-3 the final dominant Variovorax strains coincided with prediction of the interspecies interaction but not the J parameter. These results demonstrate that the effects of interspecies interactions within microbial communities contribute to determining the dynamics of the microbial ecosystem.

Mathematical Modeling of Vibrio vulnificus Infection in Korea and the Influence of Global Warming.

OBJECTIVES: To investigate the possible link between Vibrio vulnificus population size in seawater and water temperature. METHODS: We collected incidence and water temperature data in coastal regions of Korea and constructed a mathematical model that consisted of three classes; susceptible fish, infected fish available to humans, and infected humans. RESULTS: We developed a mathematical model to connect V. vulnificus incidence with water temperature using estimated bacterial population sizes and actual coastal water temperatures. CONCLUSION: Increased V. vulnificus population sizes in marine environments may increase the risk of infection in people who eat at coastal restaurants in Korea. Furthermore, we estimated the near-future number of infected patients using our model, which will help to establish a public-health policy to reduce the disease burden.

Species coexistence under resource competition with intraspecific and interspecific direct competition in a chemostat.

Competition theory has developed separately for direct competition and for exploitative competition. However, the combined effects of the two types of competition on species coexistence remain unclear. To examine how intraspecific and interspecific direct competition contributes to the coexistence of species competing for a single resource, we constructed a chemostat-type resource competition model. With general functions for intraspecific and interspecific direct competition, we derived necessary and sufficient conditions (except for a critical case that rarely occurs in a biological sense) that determine the number of stably coexisting species. From these conditions, we found that the number of coexisting species is determined just by the invasibility of each species into subcommunities with a smaller number of species. In addition, using a combination of rigorous mathematical theory and a simple graphical method, we can demonstrate how the stronger intraspecific direct competition facilitates species invasion, leading to a larger number of coexisting species.

Qualitative permanence of Lotka-Volterra equations.

In this paper, we consider permanence of Lotka-Volterra equations. We investigate the sign structure of the interaction matrix that guarantees the permanence of a Lotka-Volterra equation whenever it has a positive equilibrium point. An interaction matrix with this property is said to be qualitatively permanent. Our results provide both necessary and sufficient conditions for qualitative permanence.

Permanence of delayed population model with dispersal loss.

Permanence of a dispersal single-species population model where environment is partitioned into several patches is considered. The species not only requires some time to disperse between the patches but also has some possibility to die during its dispersion. The model is described by delay differential equations. The existence of 'super' food-rich patch is proved to be sufficient to ensure partial permanence of the model. It is also shown that partial permanence implies permanence if each food-poor patch is chained to the super food-rich patch. Furthermore, it is proven that partial persistence is ensured if there exist food-rich patches and the dispersion of the species among the patches are small. When the dispersion is large, the partial persistence is realized under relatively small dispersion time.

Prey-predator system with parental care for predators.

A stage structure is incorporated into a prey-predator model in which predators are split into immature predators and mature predators. It is assumed that immature predators are raised by their parents in the sense that they cannot catch the prey and their foods are provided by parents. Further, it is assumed that the maturation rate of immature predators is a function of the food availability for one immature individual. It is found that the model admits periodic solutions which are produced from the stage structure. Further, it is shown that two stability switches of positive equilibria may occur due to the transition rate incorporating the influence of nutrient, and that the enrichment of adult predators may lead to the catastrophe of the ecological system.

Spreading disease with transport-related infection.

Transportation among regions is found as one of the main factors which affect the outbreak of diseases. It will change the disease dynamics and break infection out even if infectious diseases will go to extinction in each city without transport-related infection. In this paper, a mathematical model is proposed to demonstrate the dynamics of such disease propagation between two regions (or cities) due to the population dispersal and infection on transports. Further, our analysis shows that transport-related infection intensifies the disease spread if infectious diseases break out to cause an endemic situation in each region, in the sense that both the absolute and relative size of patients increase. This suggests that it is very essential to strengthen restrictions of passengers once we know infectious diseases appeared.

Permanence of single-species stage-structured models.

In this paper, we consider population survival by using single-species stage-structured models. As a criterion of population survival, we employ the mathematical notation of permanence. Permanence of stage-structured models has already been studied by Cushing (1998). We generalize his result of permanence, and obtain a condition which guarantees that population survives. The condition is applicable to a wide class of stage-structured models. In particular, we apply our results to the Neubert-Caswell model, which is a typical stage-structured model, and obtain a condition for population survival of the model.