Dynamical Modeling of Toxic and Non-toxic Phytoplankton Competition

The study of the competitive outcome associated with two consumers of the same resource, algae, is investigated under asymmetric intraguild interactions and carrying capacities that are a function of resource (algae) availability at any time. The mathematical model is motivated by our understanding of the interactions of genus Protoperidinium (toxin producing) and Heterocapsa (non-toxic producing) phytoplankton while competing by the same resource (algae). Equilibrium stability and bifurcation analysis of a general theoretical model are carried out. Two competitive outcomes have been identified, win-win and win-lose. It is shown that the system will support coexistence (win-win) at a stable equilibrium. The win-lose situation is somewhat subtle since we have shown that initial conditions can affect the outcome.