Mathematical Modelling of Tropical Rain Forest Biodiversity.

Abstract

The biodiversity of tropical rain forests is very rich in terms of number of species growing in the forest. In order to illustrate the dynamic of those species, the Tilman model was modified. The modified models were called : the exploitative competition and the colonization models. Based on analysis conducted, we obtained that the colonization model showed more diverse than the exploitative competition model, given that the rate of colonization species and the mortality were positively constant. The result of simulation using the software of MATLAB 6.5, the exploitative competition model showed that for the number of species were 2, 6, and 180, the time length required for the species would grow together were 162, 255, and 10.870 years respectively. For the colonization model, the time length required for the species would grow together were 312, 8.980, and 92.951 years respectively. It can be concluded that in the colonization model the time length required is longer than the exploitative competition model. The colonization model showed longer time compared to the exploitative competition model. This might due to an assumption that different species does not cause difference in terms of ability in competition. They were merely different in terms of the ability of gap creation in the site. In the exploitative competition model, it was assumed that the superior species would be dominant. Keywords : biodiversity, mathematical model, rain forest.