Ecologyʹs AWFUL theorem: sustaining sustainability

Many momentarily important concepts in science pass after a time with little enduring consequence. Sustainability has the potential to become a really significant idea, but it could also disappear if it never becomes formally implemented to make it operational. To do this requires clarifying its various meanings, then integrating these into a measure or model, preferably quantitative. This paper makes a start at this employing propositional logic—first to establish that the success of any species requires proportional disadvantage to others in a zero-sum world (the AWFUL theorem), and then to explore three possible properties of sustainability (stability, continuation, and longevity) at two different levels of system organization (whole and part). The following conclusions are reached and discussed: at a given scale of organization, for sustainability (1) stability is a necessary but not sufficient condition, (2) continuation is sufficient but not necessary, and (3) longevity is also sufficient but not necessary. Across scales, between wholes and parts: (1a) part stability is sufficient for whole system sustainability, and part instability can be compensated by system design to achieve sustainability; (1b) system instability is sufficient for part unsustainability; (2a) part continuation is sufficient for system continuation, and therefore system sustainability; (2b) part noncontinuation is necessary for system unsustainability; (3a) part longevity is sufficient for system longevity, and therefore system sustainability; and (3b) failure of parts to achieve longevity is a necessary condition for system-level unsustainability. These attributes of sustainability in the part–whole context do not exhaust the possibilities. There are also comparisons to be made of relations between different sustainability attributes. The examples given indicate that sustainability is not a simple concept and that considerable development will be necessary to mold it into a permanently useful scientific tool.