Expanded and Practical Use of Logistic Equations in Eco-Toxicity Evaluation: Cases of Lethal Metal Toxicity Curves in Green Paramecia with Minimal-Sized Experiments

Abstract

In ecological systems, living organisms are surrounded by a number of chemicals, among which certain portion may be toxic to organisms. Therefore, from the environment-centric point of view, importance of accurate eco-toxicological analyses is increasing day-by-day. Eco-toxicity responses in animals and other organisms against chemicals can be scored by several parameters such as median lethal concentration (LC₅₀) and median lethal dose (LD₅₀), for examples. In the present study, we attempted to perform simulations of eco-toxicological nature of given chemicals based on limited data size (showing apparently incomplete curves of toxicity response) through model experiments performed with green paramecia (Paramecium bursaria) exposed to toxic metal ions, by using practically re-arranged logistic equation and Hill-type equations with an aid by graphical elucidation of Gauss-Newton algorithm determining the constants and/or coefficients.