Mathematical Modelling on the Effects of Acid Rain on a Fresh-Water Ecosystem

Mareta W. Ardyani

acid rain, interacting species, predator-prey model, quasi steady state, hydrogen ions model

The pH of a lake can be altered through the effects of acid rain (caused by pollution), and also can be seen to fluctuate over a period of time. This can have serious consequences on the ecosystem of the lakes and the biological species supported by the ecosystem are unable to survive if the pH level falls too low. This situation is of particular concern in lakes around the world because of pollution, and it is particularly serious in the Adirondack region in north eastern part of New York state. Most fresh-water ecosystems involve hundreds of interacting species, and modelling such a system is a rather difficult task. The objective of this project is to develop a fundamental understanding of the role of pH in a fresh-water ecosystem. A reasonably tractable prototype system could involve three species consisting of algae (chlorella), a herbivore (daphnia), and a predator (pumpkinseed sunfish). In this report we present the dynamics of the three species using logistic growth predator-prey model and perform stability analysis on the system with a quasi-steady state assumption. We model these interactions with a simple hydrogen ions model and perform simulation onto the coupled model with varied levels of the pH value.

https://dx.doi.org/10.31873/IJEAS.8.4.09