Effects of allelochemicals produced by one population in a chemostat-like environment.

In this paper, we study some general models suggested to describe the effects of chemical compounds produced by an algal population on its survival in a chemostat-like environment. The conditions for its persistence and extinction are found. In particular, in the first model we make very general assumptions to represent the uptake, the regulative and the inhibiting functions, and analyze its global stability completely. In the second one we specify the first two functions and leave general the third one. Here the regulative function has different property from that in the first model, and a saddle-node bifurcation phenomenon occurs. In addition, according to the experimental data reported in DellaGreca et al. [2010. Fatty acids released by Clorella vulgaris and their role in interference with Pseudokirchneriella subcapitata: experiments and modelling. J. Chem. Ecol. 36, 339-349], we present a further model in which a new inhibiting function gives rise to a complex dynamics. The three models exhibit different dynamical behaviors, in particular the number of positive equilibria associated with each model varies resulting one, two and three, respectively. We also point out that the main differences exhibited by these models result from different specializations of the regulative and the inhibiting functions.

Fatty acids released by Chlorella vulgaris and their role in interference with Pseudokirchneriella subcapitata: experiments and modelling.

The role of extracellular fatty acids in the interference between two algae, Chlorella vulgaris Beijerink and Pseudokirchneriella subcapitata (Korshikov) Hindak, was assessed by the co-cultivation of the two selected strains, as well as by the chemical analysis of exudates from the culture media of single strain cultures. The effect of culture age and phosphate limitation was evaluated. The experiments showed that the composition and amount of fatty acids, released by C. vulgaris and by P. subcapitata, both in a batch and in a continuous monoculture, depend on the culture age and on the phosphate concentration in the culture medium. We also found that the amount of chlorellin generated in the two algae co-culture increased and was almost exclusively constituted by a mixture of C18 fatty acids. By using the evaluated concentrations of these fatty acids, an artificial chlorellin was prepared. The toxicity of this mixture to P. subcapitata appears to be similar to that of the natural chlorellin. For both algae, a stimulation of growth was observed at low concentrations of the natural chlorellin, whereas higher concentrations produced inhibitory effects on both species. However, P. subcapitata was much more sensitive than C. vulgaris. By using some of these new experimental results, two new mathematical models have been used to describe the toxicity of chlorellin to C. vulgaris and to the interference between C. vulgaris and P. subcapitata, respectively.

An allelopathic competition model with quorum sensing and delayed toxicant production.

The dynamics of a differential functional equation system representing an allelopathic competition is analyzed. The delayed allelochemical production process is represented by means of a distributed delay term in a linear quorum-sensing model. Sufficient conditions for local asymptotic stability properties of biologically meaningful steady-state solutions are given in terms of the parameters of the system. A global asymptotic stability result is also proved by constructing a suitable Lyapunov functional. Some simulations confirm the analytical results.