Modeling symbiosis by a Lotka-Volterra-type system of differential equations
Biological symbiosis is necessary for life on earth. However, population based models of symbiosis are rare in literature. One problem is defining symbiosis, and whether is includes mutualism, commensalism and parasitism, or only mutualism. Additionally, there are obligate and facultative types. Another problem is that basic models of symbiosis have relied on a variation of the Lotka-Volterra competition equation, which can lead to unrealistic results, such as unlimited population growth. Several stable models have limited the growth by using equations for carrying capacity which are functions of the symbiont species. In this work a new model is proposed which uses a modified Holling Type II functional response for the carrying capacities. The broadest definition of symbiosis for thoroughness is used. This new model has stable equilibria for many different types of symbiosis.