Exploring simple structural configurations for optimal network mutualism

There is a great interest in understanding how ecosystems organize into structural patterns they exhibit. The acquisition and utilization of energy has long been identified as one of the key issues of life; as the famous physicist Ludwig von Boltzmann once stated “life is the struggle for free energy”. Adopting the premise that energy flow is a primary organizing principle in ecological systems, here we explore an ecological goal function based on the net energy flow between system compartments. This approach, called network utility analysis, proposes that the integral utility (direct plus indirect) in well-developed systems tends to contain more positive relations than negative ones. In this research we use utility analysis to determine specific relationship types between compartments for several basic network structures. Simple networks exhibit relations that are fixed for that particular structure, whereas for more complex cases the system may be classified into utility regimes depending on the energy flow values in the system. Lastly, we present candidate structural configurations having the least and greatest utility values. This research contributes to the overall discipline of ecological network analysis.