Abstract:Study concerning the allelopathic inhibition of water bloom-forming algae by aquatic macrophyte is one of the hot topics in aquatic ecology. Researches on the mathematic model of allelopathic algae control received less attention so far. The present study investigated the inhibitory effects of Chara vulgaris extracts on Microcystis aeruginosa, a toxin-producing algae, and on Scenedesmus obliquus Kütz (single and combined). Mathematic models were constructed based on the data obtained during experimentation, the characteristics of data, the traditional Logistic model and Lotka-Volterra model by using the infinitestimal method in terms of the inhibitory effect of the extracts on M aeruginosa, S. obliquus and their mixtures, respectively. The results showed that, (1) C.vulgaris extracts inhibited significantly both M. aeruginosa, S. obliquus and their mixture, and M. aeruginosa was more sensitive to the inhibition of Chara vulgaris extracts than S. obliquus. (2) The constructed mathematical models can effectively characterize and predict, to a certain degree, the exposure time-dependent dynamics of algal density of M. aeruginosa, S. obliquus and their mixture in the context of Chara vulgaris extracts. According to these models the predicted value of the maximal 50% effective concentration (EC50), and the minimal inhibitory concentration (MIC) at any time point during experimentation, as well as the predicted value of algae mixture in the relatively stable microhabitat. The traditional Logistic model that describes the growth of a single population can characterize only the trend of population growth in a certain spatial scale, but can't calculate quantitatively the biomass of a population under stress at any time point. The Lotka-Volterra model can describe the quantitative relationship of two competitive populations, but can not solve thoroughly the problem of exclusion and coexistence in the context of inhibitors and other distracting agents, which makes it hard to get the biomass at any time point. Our group ever examined the inhibitory model of a single or two kinds of allelochemicals against a single algae. The present study constructed a mathematical model concerning the inhibitory effect of the etracts of aquatic macrophyte against a single algae or algae mixture by using the infinitesimal method based on the traditional Logistic model and Lotka-Volterra model mentioned above. These models can well solve the calculation problem of algal biomass of populations under stress, or two competitive populations. As a result, the study can provide valuable data support and reference for the complex biological problems and for the establishment and implementation of actual algal inhibition plan by integrating mathematics into biology.