INTERACTION BETWEEN WATER AND PLANTS: RICH DYNAMICS IN A SIMPLE MODEL

An ordinary differential equation model describing interaction of water and plants in ecosystem is proposed. Despite its simple looking, it is shown that the model possesses surprisingly rich dynamics including multiple stable equilibria, backward bifurcation of positive equilibria, supercritical or subcritical Hopf bifurcations, bubble loop of limit cycles, homoclinic bifurcation and Bogdanov-Takens bifurcation. We classify bifurcation diagrams of the system using the rain-fall rate as bifurcation parameter. In the transition from global stability of bare-soil state for low rain-fall to the global stability of high vegetation state for high rain-fall rate, oscillatory states or multiple equilibrium states can occur, which can be viewed as a new indicator of catastrophic environmental shift

Improvement of antibiotic activity of Xenorhabdus bovienii by medium optimization using response surface methodology

<p>Abstract</p> <p>Background</p> <p>The production of secondary metabolites with antibiotic properties is a common characteristic to entomopathogenic bacteria <it>Xenorhabdus</it> spp. These metabolites not only have diverse chemical structures but also have a wide range of bioactivities with medicinal and agricultural interests such as antibiotic, antimycotic and insecticidal, nematicidal and antiulcer, antineoplastic and antiviral. It has been known that cultivation parameters are critical to the secondary metabolites produced by microorganisms. Even small changes in the culture medium may not only impact the quantity of certain compounds but also the general metabolic profile of microorganisms. Manipulating nutritional or environmental factors can promote the biosynthesis of secondary metabolites and thus facilitate the discovery of new natural products. This work was conducted to evaluate the influence of nutrition on the antibiotic production of <it>X. bovienii</it> YL002 and to optimize the medium to maximize its antibiotic production.</p> <p>Results</p> <p>Nutrition has high influence on the antibiotic production of <it>X. bovienii</it> YL002. Glycerol and soytone were identified as the best carbon and nitrogen sources that significantly affected the antibiotic production using one-factor-at-a-time approach. Response surface methodology (RSM) was applied to optimize the medium constituents (glycerol, soytone and minerals) for the antibiotic production of <it>X. bovienii</it> YL002. Higher antibiotic activity (337.5 U/mL) was obtained after optimization. The optimal levels of medium components were (g/L): glycerol 6.90, soytone 25.17, MgSO₄·7H₂O 1.57, (NH₄)₂SO₄ 2.55, KH₂PO₄ 0.87, K₂HPO₄ 1.11 and Na₂SO₄ 1.81. An overall of 37.8% increase in the antibiotic activity of <it>X. bovienii</it> YL002 was obtained compared with that of the original medium.</p> <p>Conclusions</p> <p>To the best of our knowledge, there are no reports on antibiotic production of <it>X. boviebii</it> by medium optimization using RSM. The results strongly support the use of RSM for medium optimization. The optimized medium not only resulted in a 37.8% increase of antibiotic activity, but also reduced the numbers of experiments. The chosen method of medium optimization was efficient, simple and less time consuming. This work will be useful for the development of <it>X. bovienii</it> cultivation process for efficient antibiotic production on a large scale, and for the development of more advanced control strategies on plant diseases.</p

Effect of Diffusion and Cross-Diffusion in a Predator-Prey Model with a Transmissible Disease in the Predator Species

We study a Lotka-Volterra type predator-prey model with a transmissible disease in the predator population. We concentrate on the effect of diffusion and cross-diffusion on the emergence of stationary patterns. We first show that both self-diffusion and cross-diffusion can not cause Turing instability from the disease-free equilibria. Then we find that the endemic equilibrium remains linearly stable for the reaction diffusion system without cross-diffusion, while it becomes linearly unstable when cross-diffusion also plays a role in the reaction-diffusion system; hence, the instability is driven solely from the effect of cross-diffusion. Furthermore, we derive some results for the existence and nonexistence of nonconstant stationary solutions when the diffusion rate of a certain species is small or large