Mathematical Modeling on Competition and Cooperation of Species Using Hill-type Function

Competition and cooperation play an important role in society. It drives the species to survive and it enables to balance and maintain the biodiversity in communities. These concepts are important in many fields, such as in ethology, economics, ecology, and evolutionary theory. In this paper, we develop a mathematical model that describes the dynamics of the population of a species that simultaneously interact with a competitor and/or with a cooperator. This modeling study uses a Hill-type function rather than the classical Lotka-Volterra equations. Numerical simulations are done on this model. Heat maps are used to describe different cases by varying the competition coefficient δ and cooperation coefficient γ. Our model has demonstrated not just coexistence but also exclusion or extinction of the population of species. This means that even if competition and cooperation are done simultaneously by a species, it is not a guarantee that they will always survive in the long run. It depends on how much the strength of competition and cooperation they exerted towards its co-competitor or co-cooperator. Moreover, cooperating species are most likely to survive as compared to the competing species. This modeling study enables us to look possibly for ways to control δ and γ, and consequently, control populations in our ecosystem. This will be useful not only for biologists and ecologists but also for researchers who are interested in studying the competitive and cooperative interactions of species in societies.