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An ecological application of sustainability and sustainizability over sets

The sustainability over sets and sustainizability over sets concepts have been recently introduced as sustainable system analysis and synthesis tools, respectively, with broad flexibility in incorporating human input. In this work, these two concepts are applied to an ecological food web system, describing the flow of biomass among different organisms of an ecosystem with 10 compartments aggregated in five trophic levels. The obtained results first show that this ecosystem is not sustainable over any set, imposing upper and lower numerical bounds on the population of each species, and accounting for sinusoidal variations in plant growth. It is subsequently established that the system can be sustainized over such sets through appropriate external actions.