• ECOLOGICAL AMMENSALISM WITH FOUR SPECIES AT THREE LEVELS-A NUMERICAL APPROACH

Abstract

The present paper aims to discuss on an ecological Ammensal model with Four Species (A,P,E,H) Syn Eco-System of Ammensal-Prey(A),Predator-Ammensal(P),Enemy-Ammensal(E) and malice(M) species. The System constitutes of an Ammensal –prey(A) , a Predator –Ammensal(P) that endures on Ammensal –prey(A), enemy-Ammensal(E) and malice(M) for which A, P are Ammensal respectively i.e., E and M adversely effect on A and P without themselves getting effected in any manner. Further E is Ammensal for M and M is harming for E. The pair (A, E) may be referred as First level Ammensalism, the pair (P, H) as the second level Ammensalism and (E, H) as third level Ammensalism. The model equations of the system establishes a set of four first order non-linear ordinary differential coupled equations.Sixteen equilibrium points are identified. The interactions among the four species are investigated in view of change in natural growth rate of Ammensal-Prey by employing the classical R-K method of Fourth order.