Allelopathy and competition between Chlorella vulgaris and Pseudokirchneriella subcapitata: Experiments and mathematical model

In this paper the results of several new experiments concerning the allelopathic competition between the two algal species Chlorella vulgaris (C. vulgaris) and Pseudokirchneriella subcapitata (P. subcapitata) have been reported. They show that the growth rates of the two species are different and can be modeled by the Andrews function (P. subcapitata) and Michaelis-Menten one (C. vulgaris). They also prove that the two species have different yields and that allelochemicals produced by C. vulgaris (called chlorellin) produce inhibitory effects on P. subcapitata. These results have been used to validate a mathematical modeling approach widely applied in eco-toxicology. The validation test being based on the comparison between the experimental outcome of the competition and the possible dynamical behaviors exhibited by the mathematical model. The paper consists of two parts devoted to the experiments and to the mathematical model, respectively. The mathematical analysis of the experimental results allowed to compute the numerical values of some parameters appearing in the growth-rate functions of the two species, and in the function which represents the inhibitory effect of chlorellin. The stability properties of some biologically meaningful steady-state solutions have been investigated. Moreover, by means of numerical simulations, it has been shown that the outcome of the real competition is foreseen by our model, and it can be easily simulated, provided that suitable numerical values for the parameters and initial conditions are chosen.