Socio-Ecological Network Structures from Process Graphs

Abstract

We propose a process graph (P-graph) approach to develop ecosystem networks from knowledge of the properties of the component species. Originally developed as a process engineering tool for designing industrial plants, the P-graph framework has key advantages over conventional ecological network analysis (ENA) techniques. A P-graph is a bipartite graph consisting of two types of nodes, which we propose to represent components of an ecosystem. Compartments within ecosystems (e.g., organism species) are represented by one class of nodes, while the roles or functions that they play relative to other compartments are represented by a second class of nodes. This bipartite graph representation enables a powerful, unambiguous representation of relationships among ecosystem compartments, which can come in tangible (e.g., mass flow in predation) or intangible form (e.g., symbiosis). For example, within a P-graph, the distinct roles of bees as pollinators for some plants and as prey for some animals can be explicitly represented, which would not otherwise be possible using conventional ENA. After a discussion of the mapping of ecosystems into P-graph, we also discuss how this framework can be used to guide understanding of complex networks that exist in nature. Two component algorithms of P-graph, namely maximal structure generation (MSG) and solution structure generation (SSG), are shown to be particularly useful for ENA. This method can be used to determine the (a) effects of loss of specific ecosystem compartments due to extinction, (b) potential efficacy of ecosystem reconstruction efforts, and (c) maximum sustainable exploitation of human ecosystem services by humans. We illustrate the use of P-graph for the analysis of ecosystem compartment loss using a small-scale stylized case study, and further propose a new criticality index that can be easily derived from SSG results. Author summaryIn this study, we propose the novel application of the process graph (P-graph) methodology to the analysis of ecological networks. P-graph was originally developed for engineering design problems; in our work, we show how its five axioms and two algorithms - maximal structure generation (MSG) and solution structure generation (SSG) can be adapted to the problem of understanding complex interactions in ecosystems. The methodology allows multiple types of interactions among ecosystem components to be handled simultaneously based on representation as a bipartite graph. Complete network structures can be deduced from knowledge of local interactions of components using MSG. Finally, all structurally feasible networks of viable ecosystems can be identified with SSG. We illustrate the features of the P-graph methodology with a stylized illustrative example.