Feeding the world’s population within sustainable land, water, and nutrient footprints is a daunting challenge [1]. Climate change further threatens the capability of food production to keep pace with growing demand [2]. Thermodynamically efficient aquaculture of lower-trophic level species may provide a larger share of future protein requirements; however, the production of feeds for and generation of organic pollutants from intensive aquaculture raise sustainability concerns [3]. Hybrid agriculture/aquaculture, or co-culture, can intensify food production while alleviating environmental footprints by capitalizing on ecological engineering principles. For example, rice cultivation provides opportunities for the co-culture of aquatic animals in paddy fields [4]. Ecological network analysis (ENA) can be useful for understanding interactions among wild and domesticated organisms within co-culture systems [5]. Most ENA methods, such as the ubiquitous Ecopath model, are based on linear systems of equations that reflect mass and energy balances in trophic linkages [6]. They are widely used for ecosystem management because of their ability to describe complex interactions among species [7,8]. However, such models are rarely used for optimization purposes [9], or for ensuring system resilience (i.e., ability to maintain production while internal or external conditions change).
We develop a new approach for the identification of resilient and productive co-culture systems using a socio-ecological process graph model. This modelling approach is an extension of process graph methodology to ENA [10]. The process graph method was originally developed for engineering design problems but has been applied to a broader range of analogous problems [11]. The socio-ecological process graph uses bipartite graphs to represent ecosystem components and their interactions; three component algorithms are then used to generate and optimize network structures (see Methods). We use the rice-crayfish co-culture system (Figure 1 in Supporting Information) described by Dong et al. [5] to illustrate the additional insights that can be drawn from our technique. The system consists of thirteen different species, with crayfish feeding on eleven of them. The socio-ecological process graph is used to perform a combinatorially complete search of ecological interactions to generate candidate ecological networks. The search procedure automatically considers structural feasibility from ecological interactions. The resulting structures can serve as a skeletal framework for subsequent detailed analysis that considers the magnitudes of the flows and interactions. The search algorithms use constraints that include mass balances and the existence of known ecological interactions. The search domain for finding feasible ecological interactions in the ecosystem can be reduced by eliminating or replacing species. No feasible ecological interactions are lost in this enumeration process. The details of the process graph approach to ENA are described in the Methods section.
The co-culture system simultaneously produces rice and crayfish using the same land area without an external supply of supplements. Instead, the diverse ecosystem which includes aquatic plants, phytoplankton, benthic animals, and zooplankton provides an environment for crayfish co-production with rice. We assume that the crayfish has a flexible diet [12]. Selected interactions among functional groups or species are illustrated in the Supporting Information. Simulations were performed to maximize crayfish production per unit of rice. Solving the socio-ecological process graph model generates alternative optimal and near-optimal solutions from a maximal structure that contains all possible network linkages (see Supporting Information). For this co-culture system, 60 feasible structures were identified. The most productive network is shown in Figure 1 in both conventional and process graph forms. Note that the network is much sparser than the maximal one, whose structure can be seen in the grayed-out parts of the figure. The other top fifteen networks in terms of productivity are shown in the Supporting Information.
Figure 2 shows the trends with changing ecosystem structure against the number of species present and productivity based on the mass of crayfish per unit of rice, the latter being a proxy for land area. The key result is that there are families of ecosystem structures that differ in the number and type of biological species, but have nearly identical productivity. For example, Structures 1 to 4 have similar levels (~0.12 kg crayfish/kg rice), but the number of species sequentially varies from 5 to 9. All 60 structures contain crayfish, plants, rice, phytoplankton, and detritus, with Structures 1 and 4 having only these 5 species. Structure 2 includes rotifera, bacteria, and bacterioplankton, and Structure 3 additionally has cladocera. These are biologically different ecosystems with similar productivity. Note that there are several sequences or families of structures where productivity is resilient and varies minimally while the species present significantly change. These 15 solutions structures are shown in more detail in the Supporting Information.
For the family of Structures 5 to 15, the productivity varies from 0.095 kg/kg to 0.097 kg/kg, or about 20 % lower than the optimal solution, while the number and type of species varies from 4 to 10. All the ecosystem structures include crayfish, plants, rice, and phytoplankton. Different combinations of the other species are present in these solutions. The biological functions of the missing species are again presumably taken by the remaining species. Note that snails, worms, and larvae occupy ecosystem niches which are not entirely different, and the same can be said for copepoda, cladocera, and rotifera. One could suspect that Structure 14, having the largest number of species and the most redundancy is possibly the most resilient.
Our results demonstrate how the analysis of alternative network structures can be used to ensure resilient and productive co-culture systems. Rather than identifying a unique (and possibly brittle) optimum, the process graph approach is used to identify families of solutions. These translate into options that give good productivity while being resilient to disruptions. Note that these solutions serve only to provide performance benchmarks for actual co-culture operations, since in practice it may not be possible to fully control which species will be present. This approach has general applicability to a wide range of networks beyond the class of co-culture systems examined here.