Table 1.

The five original axioms of PNS (left column) [14] and the equivalent formulation for ecosystems (right column) [17].

Process Engineering	Socio-Ecological Systems
(S1) Every final product is represented in the structure	(SE1) There should be at least one well-defined terminal ecosystem service in the ecosystem structure.
(S2) A material represented in the structure is a raw material if and only if it is not an output of any operating unit represented in the structure	(SE2) An ecosystem service represented in the structure is exogenous if and only if it is not an output of a functional unit defined in the ecosystem structure.
(S3) Every operating unit represented in the structure is defined in the synthesis problem	(SE3) Every ecosystem functional unit in the ecosystem structure is well defined.
(S4) Any operating unit represented in the structure has at least one path leading to a product	(SE4) Any ecosystem functional unit has at least one path leading to a terminal ecosystem service.
(S5) If a material belongs to the structure, it must be an input to or output from at least one operating unit represented in the structure	(SE5) If an ecosystem service belongs to the ecosystem structure, it must be an input to or output from at least one ecosystem functional unit represented in the structure.
Assumption: capital is available to pay for operating units and operating costs.	Assumption: energy is available to keep the ecosystem structure functioning
Goals: (1) meet production goal at (2) minimum cost for the structure and operation	Goals: (1) meet ecosystem services goal; and (2) minimize a cost metric (e.g., money, ecological footprint, energy, etc.) for the structure, management, functioning, and operations of the ecosystem services