An ecosystem can be viewed as an energy flow system in which various species are connected by energy flows along food web links. To understand the co-evolution of the fast dynamics of energy flows and slow dynamics of food web structure, a simple reaction diffusion equation is presented in this paper. Some statistical indicators such as total system throughflow (TST) and Shannon entropy are designed to describe the macro-level evolution of the system. The positive correlation between time series of TST and Shannon entropy is mainly shown. That means the diversity of the species may accelerate the total energy flows in the system. This conclusion may help us to understand general phenomena of flows and diversity in other complex systems.
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