Abstract: We will introduce a biological model called Lotka-Volterra competition system. We construct an N-shaped constrained region. By using this region we give an a priori estimate for this system and show that the total population of this 2-species system has a nontrivial lower bound. Finally, we know that one of the important issues in ecology is biodiversity. By using this estimate, we find necessary conditions for coexistence of 3-species Lotka-Volterra system.
