Mutualistic relationships between phytoplankton and bacteria caused by carbon excretion from phytoplankton

For the competition system of phytoplankton and bacteria through inorganic phosphorus, our mathematical model showed that mutualistic relationships between them could occur due to production and consumption of extracellular organic carbon by phytoplankton and bacteria. In our model, phytoplankton are limited in their growth by light and phosphorus, and bacteria are limited in their growth by phosphorus and carbon released from phytoplankton. We adopted 'permanence' as a criterion of the coexistence in mathematical analysis, and led necessary conditions of permanence in the model. Under these coexistence conditions, we estimated the strength of total effects of interactions between phytoplankton and bacteria at the steady state by press perturbation method. The results of this estimation indicated the mutualistic interactions between phytoplankton and bacteria. This suggests that mutualistic situation could occur due to the introduction of carbon flow from phytoplankton to bacteria, even if phytoplankton and bacteria compete with each other through common resource, inorganic phosphorus.