Analysis and dynamics of an elephant-tree ecosystem having abundant and rare tree species

A model is developed and parameterized to represent an ecological system consisting of elephants, abundant trees and rare trees, which represents a reasonable approximation of ecosystem scenarios in which elephants are found. Parameters are set in realistic bounds and model simulation results are consistent with elephant densities measured in the wild. Parameter variations alter population densities in explainable ways. The model is considered from the perspective of tree species that are rare and could be in danger of local extinction because of damage caused by elephant. The model appears to summarize the basic components of an elephant-tree system where one plant species dominates in the elephant diet. Elephant and tree densities reach a limit cycle. The range in density variations for tree and elephant species in the final limit cycle are small and, for the ecology, these effectively do not represent cycling solutions. Significant cycles are however found during the transients to the final limit cycle and these could be important for a successful understanding of elephant ecology and management of such ecosystems. Analysis of the dynamics resulted in a set of conditions that set bounds on permissible elephant densities to avoid the extinction of the rare tree. An important implication is that the rare tree species can survive in the system under specific conditions expressed in terms of elephant and abundant tree densities. It is interesting to note that in the case of competition between the tree species, the simulations indicate that if the elephant die out the same may happen to the rare trees. Thus, an unexpected implication is that, for certain situations, it is possible that elephant stabilize rare tree densities and prevent, rather than cause (as previously thought), their extinction.