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Designing eco-industrial parks in a nested structure to mimic mutualistic ecological networks
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26th CIRP Life Cycle Engineering (LCE) Conference 26th CIRP Life Cycle Engineering (LCE) Conference
Designing eco-industrial parks in a nested structure to mimic mutualistic Designing eco-industrial parks in a nested structure to mimic mutualistic 28th CIRP Design Conference,networks May 2018, Nantes, France ecological ecological networks Colton Brehm, Astrid Layton* A new methodology to analyze the functional and physical architecture of ColtonTexas Brehm, Astrid Layton* Department of Mechanical Engineering, A&M University, 3123 TAMU, College Station, Texas 77843, USA existing products for anEngineering, assembly product family identification Department of Mechanical Texas A&Moriented University, 3123 TAMU, College Station, Texas 77843, USA *Corresponding author. Tel.: +1-979-458-0360. E-mail address: [email protected] *Corresponding author. Tel.: +1-979-458-0360. E-mail address: [email protected]
Paul Stief *, Jean-Yves Dantan, Alain Etienne, Ali Siadat Abstract École Nationale Supérieure d’Arts et Métiers, Arts et Métiers ParisTech, LCFC EA 4495, 4 Rue Augustin Fresnel, Metz 57078, France Abstract Industrial Ecology uses ecological systems as a guide for improving the sustainability of complex industrial systems. Eco-Industrial Parks (EIPs) have gained support as ecological a solution systems that seeks simultaneously reduce environmentalofburdens promotesystems. economic interests byParks exchanging Industrial Ecology uses as to a guide for improving the sustainability complexand industrial Eco-Industrial (EIPs) materials and energy between industries to their mutual benefit. Recent studies have focused on drawing relations between food webs (FWs) and have gained support as a solution that seeks to simultaneously reduce environmental burdens and promote economic interests by exchanging EIPs to improve the sustainability of the to latter ecological such ashave the level of cycling or average connections between materials and energy between industries theirusing mutual benefit. metrics, Recent studies focused on drawing relations between food websactors. (FWs)This and study new ecological metric, into themetrics, discussion The associationbetween of nestedness with EIPs toincorporates improve thea sustainability of the latternestedness, using ecological suchof as sustainable the level of design cyclingfor or EIPs. average connections actors. This Abstract mutualistic ecological networks supports its application EIP The work here improves of holisticofnetwork structure study incorporates a new ecological metric, nestedness, to into thedesign. discussion of sustainable designtheforunderstanding EIPs. The association nestedness with with the goal of improving future design decisions for EIPs with purposeful placement of material and energy flows. mutualistic ecological networks supports its application to EIP design. The work here improves the understanding of holistic network In today’s business environment, the trend towards more product variety and customization is unbroken. Due to this development, thestructure need of * Corresponding author. Tel.: +33 3 87 37 54 30; E-mail address: [email protected]
with and the goal of improving future design decisions for EIPs withwith purposeful of material energyToflows. agile reconfigurable production systems emerged to cope various placement products and product and families. design and optimize production c 2019 as The Authors. Published by Elsevier B.V. This is an open access articlemethods under theareCC BY-NC-ND license systems well as to choose the optimal product matches, product analysis needed. Indeed, most © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license of the known methods aim to (http://creativecommons.org/licenses/by-nc-nd/3.0/) c 2019aThe Authors. Published by Elsevier B.V. This islevel. an open accessproduct article under the however, CC BY-NC-ND license analyze product or one product family on the physical Different families, may differ largely in terms of the number and (http://creativecommons.org/licenses/by-nc-nd/3.0/) Peer-review under committee of Conference. (http://creativecommons.org/licenses/by-nc-nd/3.0/) nature of components. This fact of impedes an efficient comparison and CIRP choice of Cycle appropriate product(LCE) family combinations for the production Peer-review underresponsibility responsibility ofthe thescientific scientific committee ofthe the26th 26th CIRPLife Life CycleEngineering Engineering (LCE) Conference. Peer-review under responsibility of the scientific committee of the 26thinCIRP Life Cycle Engineering (LCE) Conference. system. A new methodology is proposed to analyze existing products viewparks of their functional and physical architecture. The aim is to cluster Keywords: nestedness; industrial ecology; network design; mutualism; eco-industrial these products in new assembly oriented product families for the optimization of existing assembly lines and the creation of future reconfigurable Keywords: nestedness; industrial ecology; network design; mutualism; eco-industrial parks assembly systems. Based on Datum Flow Chain, the physical structure of the products is analyzed. Functional subassemblies are identified, and a1.functional analysis is performed. Moreover, a hybrid functional and physical architecture graph (HyFPAG) is the outputsteam. which depicts the gas, sulfur, fly ash, sludge, and low-quality These exIntroduction similarity between product families by providing design support to both, production system planners and product designers. An illustrative changes re-purpose waste streams as imports, avoiding gas, sulfur, fly ash, sludge, and low-quality steam. Theseaddiex1. Introduction example of a nail-clipper is used to explain the proposed methodology. An industrial case study on two product families of steering columns of tions to landfills andwaste emissions to the environment [3]. StudBiologically Inspired Design (BID) implements biological changes re-purpose streams as imports, avoiding addithyssenkrupp Presta France is then carried out to give a first industrial evaluation of the proposed approach. ies oftothese complex industry networks have drawn[3]. comparsolve human problems, most notably in the field of tions landfills and emissions to the environment StudBiologically Inspired Design (BID) implements biological ©principles 2017 The to Authors. Published by Elsevier B.V. isons with the field of ecology, where complex natural systems engineering. Some product examples of BID include Leonardo ies of these complex industry networks have drawn comparprinciples to solve human problems, most notably in the field of Peer-review under responsibility of the scientific committee of the 28th CIRP Design Conference 2018.
demonstrate sustainability [4, 5]. EIPs designed in isons with theautonomous field of ecology, where complex natural systems ademonstrate food web-like structuresustainability have shown positive attributes, such autonomous [4, 5]. EIPs designed in reduced environmental burdens from materials and energy omy non-toxic depends wood on dwindling resources and is a growaasfood web-like structure have shown positive attributes, such and glue [1].finite Today’s global industrial econintake [6, 7].environmental Food web-likeburdens networkfrom structures haveand also been ing burden on on environmental health. Issues created these as reduced materials energy omy depends dwindling finite resources and is by a growshown [6, to reduce economic supplyhave chain disrupcomplex industrial networks require an equally encompassintake 7]. Food web-likedamage networkfrom structures also been ing burden on environmental health. Issues created by these 1.complex Introduction of thewhile product range and characteristics manufactured and/or tions continuing to minimize carbon emissions ing network-level andequally privateencompasscompanies shown to reduce economic damage cost fromand supply chain disrupindustrialsolution. networksCountries require an assembled this system. In thissuggest context, the main challenge in [8]. Positive results liketo these as a route for inaround the world are seekingCountries to counter these issues with the tions whileincontinuing minimize costBID and carbon emissions ing network-level solution. and private companies Due to the fast development in the domain of modelling and analysis is now not only to cope with single creasing the sustainability of industrial systems. Diverse formation Eco-Industrial (EIPs). Theissues goalswith behind [8]. Positive results like these suggest BID as a route forperinaround the of world are seekingParks to counter these the communication and ongoing digitization and products, aare limited product range or existing product spectives the required to combat misunderstandings infamilies, theperapEIPs are to of reduce rawan material use,trend emissions, andgoals waste. EIPs creasing sustainability of industrial systems. Diverse formation Eco-Industrial Parks (EIPs).of The behind digitalization, enterprises are facing important but also toof beBID able analyze and to compare products define plication totoEIPs. food web (FW) metrics used are created bymanufacturing connecting industries through mutually benefispectives are required to Namely, combat misunderstandings intothe apEIPs are to reduce raw material use, emissions, and waste. EIPs challenges in today’s market environments: a continuing new product families. It can be observed that classical existing to describe tend to focus heavily number of links cial created relationships. The concept of mutually beneficial is derived plication of EIPs BID to EIPs. Namely, food on webthe (FW) metrics used are by connecting industries through mutually benefitendency reduction product development and product families are regrouped function ofthe clients or features. between actors the on position or distribution fromrelationships. the towards field of ecology andofimplies that interactions to describe EIPswithout tend todescribing focusinheavily number of links cial The concept of mutually beneficial times ispromote derived shortened product lifecycles. In addition, there is an increasing However, assembly oriented product families are hardly to find. [6, 7, 8]. actors without describing the position or distribution the well both parties; a network primarily composed between from the being field ofofecology and implies that interactions promote demand of customization, being at the same time in a global On the product family level, products differ mainly in two of these interactions called aa mutualistic networkcomposed [2]. The [6, 7, 8]. the well being of bothis parties; network primarily competition with competitors all over the world. This trend, main characteristics: (i) the number of components and (ii) the Kalundborg EIP in Denmark successful example inof these interactions is calledis aa mutualistic networkwhere [2]. The which is inducing the development from macro to micro type of components (e.g. mechanical, electrical, electronical). dustries are EIP linked via exchanges of wastes,example such aswhere refinery Kalundborg in Denmark is a successful inmarkets, results in via diminished lotofsizes due such to augmenting Classical methodologies considering mainly single products dustries are linked exchanges wastes, as refinery product varieties (high-volume to low-volume production) [1]. or solitary, already existing product families analyze the To cope with this variety as well asThis to be structure on a physical c 2019 2212-8271 Theaugmenting Authors. Published by Elsevier B.V. is anable opento access product article under the CC BY-NC-ND licenselevel (components level) which identify possible optimization potentials in the existing causes difficulties regarding (http://creativecommons.org/licenses/by-nc-nd/3.0/) c 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license an efficient definition and 2212-8271 Peer-review under responsibility of the scientific committee of the 26th CIRP Life Cycle Engineeringof(LCE) Conference. production system, it is important to have a precise knowledge comparison different product families. Addressing this (http://creativecommons.org/licenses/by-nc-nd/3.0/) DaVincis flying machine, cells include based on leaves, engineering. Some product photovoltaic examples of BID Leonardo
and non-toxic glue [1]. Today’s global industrial econKeywords: Assembly; Design method; Family identification DaVincis flyingwood machine, photovoltaic cells based on leaves,
Peer-review under responsibility of the scientific committee of the 26th CIRP Life Cycle Engineering (LCE) Conference. 2212-8271 © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/) 2212-8271 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of scientific the scientific committee theCIRP 26thDesign CIRP Conference Life Cycle 2018. Engineering (LCE) Conference. Peer-review under responsibility of the committee of the of 28th 10.1016/j.procir.2018.12.011
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2. Methods Nomenclature
2.1. EIP and FW data sets
EIP Eco-Industrial Park FW Food Web ENA Ecological Network Analysis [A] Adjacency Matrix [F] Food Web or Community Matrix λmax Cyclicity λnorm Normalized Cyclicity S Degree of Nestedness of a bi-directional, 2-mode network
A data set of 44 EIPs was used to evaluate nestedness among realized and proposed industrial networks. The EIPs in this study span a diverse set of industries with varying material, energy, and waste flows. These EIPs were compared to a group of 57 FWs to extract similarities and differences among several ecological metrics, including nestedness, connectance, species richness, cyclicity, and normalized cyclicity [14]. Both the EIP and FW datasets are composed of matrices containing binary data describing the realized connections between actors in the network. A simple example for a simplified FW is displayed in 1 for clarity. Samples in this study however contain many more nodes. All calculations exclusively use these 101 matrices. FW analysis in the 1990s shifted when ecologists proposed to homogenize data collection methods to improve data quality [15, 16]. The FWs in this study were selected post-1993 when ecological field methods were improved, to ensure data of the highest quality was used.
Recently, the analysis of EIPs has been diversified with the use of the metric cyclicity (λmax ). Cyclicity measures the prevalence of cyclical pathways in a network and is heavily related to decomposer-type species in FWs [9]. Cycles are realized in areas of high linkage density and therefore depend to some degree on link distribution. A metric that purely describes linkage density and position however has yet to be applied to EIPs. Nestedness can help illuminate the importance of the position of exchanges in an EIP. Nestedness was originally developed by the ecologists Atmar and Patterson in 1993 to describe species distribution patterns in fragmented habitat and their predicted extinction sequences [10]. The metric has since become very popular in studying mutualistic networks, such as pollination and seed dispersal networks, which are both characterized by a high degree of nestedness [11]. Nestedness has not yet been used in the study of EIPs, which are unipartite and unidirectional networks. Ecology defines unipartite networks as communities that do not have their species categorized into distinct groups, how a plant-pollinator network would be modeled for example. Each species in a unipartite network has the potential to form a relationship with any other species in the network. Unidirectional constrains the direction of flow; in a FW this would be the direction that energy and nutrients can travel from resource to consumer. These two definitions describe the way EIPs and many FWs are modeled using an ENA. Generalized species have many interactions in a network while specialized species may only have one or two interactions [12]. Pure nestedness (a nestedness value of 1) is when 100% of actors that are more specialized than at least one other actor, connect to a proper subset of the more general actors. A proper subset would be when the actors that a specialized species are connected to, can all be found connected to the next more general actor. The structure of self-sustaining mutualistic networks has shown higher nestedness values than any other class of network [13]. Therefore studying nestedness in EIPs may not only be a helpful perspective for future studies, but could also be paramount to promoting sustainability in industrial networks.
Fig. 1. An example ecosystem (left), its FW (center), and its community matrix (right). S1 -S3 represent the three species highlighted in the ecosystem and L11 L33 represent the linkages between them. [17].
2.2. ENA metrics Ecologists use a large set of metrics as part of an Ecological Network Analysis (ENA) to draw relationships between FW network structure and behavior [11, 18]. Several ENA metrics are used in this study to uncover sources that contribute to nestedness as well as to compare fundamental features of FWs and EIPs. These ENA metrics are calculated from a FW matrix [F], which is a square matrix containing binary information on the presence and direction of interactions in the network. [F] must always be of size N x N, where (N) is defined as the species richness or the total number of actors in a network. The interactions are entered into Fi j as a one when there is an interaction from i to j and a zero otherwise. The total number of interactions is the number of links (L) and is calculated by summing all the nonzero values in [F], as seen in Eq. 1. L=
N N
Fi j
(1)
i=1 j=1
2
Connectance (c) is the number of realized predator-prey interactions, divided by the total number of possible interactions in the FW, where the number of possible interactions is the size of matrix [F] as seen in Eq. 2 below. Connectance is a good de-
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scriptor for network structure and has been found to positively correlate with nestedness in FWs [11]. c=
L N2
(UNODFc, the c standing for columns, which represent consumers in [F]). UNODFr is defined in ecology as the degree of nestedness of prey sharing consumers and UNODFc is the degree of nestedness of consumers sharing prey. Recent works have created multiple nestedness algorithms to discern nestedness in these types of ecological networks however, the study here uses only the variation in Eq. 5 [20, 21]. A qualitative perspective for the concept of nestedness is shown in Figure 2.
(2)
Cyclicity (λmax ) measures the abundance and strength of cyclic pathways in a network [18, 19]. The magnitude of nestedness and cyclicity both depend on the location, rather than just the number, of links in the network. Cyclicity is the maximum real eigenvalue solution of Eq. 3. Calculating cyclicity requires the adjacency matrix [A], which is the transpose of the FW matrix. Cyclicity is equal to either zero, one, or any value greater than one. These values respectively correspond to the qualitative descriptions of cycling absent, one simple internal cycle present, or lots of complex internal cycling. The dynamics and stability of ecosystems are significantly influenced by nutrient cycling [18]. Cyclicity does have some relationship to system size, as the network size increases cyclicity will either increase or remain the same. |A − λI| = 0
(3)
Normalized cyclicity (λnorm ), cyclicity divided by the total number of actors, is used in place of cyclicity to account for its system-size dependence. Normalized cyclicity and nestedness both have an upper bound so the values do not always increase with network size.
Fig. 2. Nestedness values (y-axis) for four unidirectional networks: (A) checkered, (B) modular, (C) random, and (D) perfectly nested. Graphic use with permission from [22].
2.3. Nestedness
Matrices A,B,C, and D in Figure 2 represent four different types of networks of the same size (N) and with the same total number of connections (L), and thus four networks with the same connectedness. This illustrates the potential for four networks with the same N, L, and c to have completely different nestedness values (as shown by the range on the y-axis) based on how the actors are connected, rather than how much they are connected. The yellow entries in the four matrices in the bottom of Fig. 2 represent realized links in the network and the black represents no link. Figure 2D shows a perfectly nested, unipartite, non-cannibalistic network in contrast to the checkered (every actor is connected to every other actor to the same degree), modular (two highly connected networks are joined by a few common actors), and random structures of A, B, and C respectively.
Nestedness (S ) was computed for 57 FWs and 44 EIPs following Eq. 4 and its adaptation in to Eq. 5 below [20, 21]. N N N 2 l=1 Ai j A jl S = N(N − 1) i j,i< j min(ki , k j ) N
UNODF =
3
N
2 N(N − 1) i j,i< j
N
(4)
l=1 (1
− δki k j )Ai j A jl min(ki , k j )
(5)
where δki k j = 0 if ki = k j , and in all other cases. The “degree” of node i is determined by ki = Ail . Conceptually degree is the number of interactions a node experiences in one direction. S checks for node overlap of the same degree such as ki = k j . The assumption of no cannibalism, or preventing an actor from interacting with itself (the diagonal of the [F] and [A] matrices will always be zero), presents the need for a variation on Eq. 4 that avoids these interactions. Thus, nestedness is calculated here using Eq. 5 for the unidirectional node overlap (UNODF). UNODF has a range of 0-1 with perfectly nested networks residing on the upper bound. EIPs and FWs are directed networks, a consumer can take from a producer without the reverse interaction needing to exist. This creates two nestedness values, one for production (UNODFr, the r standing for rows, which represent producers in [F]) and one for consumption
2.4. Null models and significance
3
The nestedness of the EIPs and FWs are given significance by calculating P-values to measure if the networks are more nested than a randomly created network of the same size and connectance would be. One thousand null models were created for each EIP and FW using the ‘null2’ function in RStudio 2018 3.5.0. The null cases form a normal distribution of UNODFr and UNODFc values [23]. The difference in nestedness between the FWs and EIPs and their corresponding null average is the ‘nestedness difference,’ which also serves as a measure of purposeful ordering of the network.
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The normal distributions of the null data allows for a Z-score describing the number of standard deviations from the mean that any element is. A Z-score is assigned to the actual UNODFr and UNODFc values to describe where any of the real-life networks lie on the null distributions. A P-value, representing the chance that a network has more nested, or anti-nested, structure than a random network of the same N and c, is also used to describe the results. A cutoff of P < 0.05 conveys a 95% confidence that the network has a nested structure beyond random chance. Networks with high nestedness difference to the null will therefore result in low P-values.
Table 1. ENA comparison of the data sets of 44 eco-industrial parks (EIPs) and 57 food webs (FWs). *Average values are underlined.
3. Results Figures 3A and 3C display the nestedness difference to the null average for each of the 57 FWs and 44 EIPs, respectively. Points around the zero line represent networks without any nestedness more than a random network of equal size and connectance would show on average. The production nestedness difference is +4.94e-2 and 3.65e-4 for the FWs and EIPs respectively. The consumption nestedness difference is +2.99e-3 and +0.169 for the FWs and EIPs respectively. Figures 3A and 3B plot nestedness vs normalized cyclicity for the FWs and EIPs. The average normalized cyclicity is 0.177 for the FWs and 0.153 for the EIPs. The average number of actors for the FWs is 37 (which have an average cyclicity of 5.34), compared to only 12 for the EIPs (which have an average cyclicity of 1.54). This suggests that the higher average cyclicity of FWs is partially due to their larger size and using normalized cyclicity helps account for this difference. Figures 3C and 3D show when comparing nestedness against normalized cyclicity, EIPs tend toward the upper right but little correlation is seen for the FWs. Most notably, the EIPs with the largest nestedness values have the largest normalized cyclicity values. Figure 3 is summarized in Table 1 alongside additional ENA metric results. Only 2 out of 44 EIPs have significantly nested consumers (UNODFc), while 40 out of 57 FWs had P-values below 0.05. UNODFr, nestedness of production, shows a similar trend with only 4 out of 44 EIPs having P-values less than 0.05 as compared to 28 out of 57 FWs. 4. Discussion EIPs seek to mimic the mutually beneficial interactions common in ecosystems but are shown here to lack the degree of nestedness seen in FWs. Although it is not yet clear if increasing the nestedness in EIPs will result in positive network behavior, industrial systems have been shown to gain positive behavioral traits when they better mimic structural characteristics of ecosystems [6-8]. The production and consumption nestedness values are shown to be significantly higher for FWs than EIPs alongside the nestedness differences to the null averages signifying that the distribution of links in these two data sets is consistently different. Almost all the EIPs studies here vary within only ± 0.10 of the nestedness of randomly structured networks.
593 4
4
Metric
EIPs (44)
FWs (57)
UNODFr UNODFc Range of data set size actors c λmax λnorm Nestedness diff. (production) Nestedness diff. (consumption) # P-values < 0.05 (rows) # P-values < 0.05 (cols)
0.174 0.185 6 – 39 ≈ 12 0.160 1.54 0.153 +3.65e-4 +2.99e-3 4 2
0.295 0.436 4 – 125 ≈ 37 0.196 5.34 0.177 +4.94e-2 +0.169 28 40
However, small EIPs could randomly display very high or low nestedness because the few nodes constrain the possible number of network combinations. Filtering the EIPs for size, removing those networks with less than 12 actors, further reduces the difference to the null group’s nestedness. Appendix Fig. ??A shows FW nestedness values further shift above the null average when a size filter of 16 species is applied. This strengthens the conclusion that these networks structure their connections much differently. FWs, as seen by the P-values listed in Table 1, also show a consistent and significant difference from the null cases. This confirmation motivates future work to test EIP network designs with higher nestedness than the 44 used here. The FWs also show more nestedness for consumption than for production while EIPs have no difference in the nestedness of consumption vs production. This could be related to the onesided mutualistic nature of these feeding interactions. It is in the consumers’ favor to reduce competition by feeding in a nested fashion, but it is not in the resources’ favor to distribute energy in a nested fashion because it sustains a healthy population of consumers. The comparison of nestedness with normalized cyclicity done here can provide some conclusion in the form of design advice for EIPs. Those EIPs with the highest degree of nestedness also showed the highest normalized cyclicity. Closer examination shows that groups of highly general nodes, in the EIPs promote nestedness more than any other actor type. Examples of these include power and water networks that not only connect to many specialized industries but also connect to each other. All networks without these generalist-to-generalist interactions fail to reach moderate or high degrees of nestedness and normalized cyclicity. While nestedness requires a proper distribution of generalist and specialist species, it appears there is most commonly a dearth of generalist-generalist interactions among EIP networks. This lack of a core group of generalist actors simultaneously decreases cyclicity and nestedness. Cyclicity and nestedness by definition do not necessarily represent the same network structure, but in application require a basic component of generalists to exist in a high degree. Ecologists have hypothesized that generalist-generalist interactions are a key foundation to support the growth of network species rich-
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Fig. 3. (TOP) Plots A & B: the difference in nestedness (production is UNODFr and consumption is UNODFc) between individual cases and their null average for a set of 48 FWs (A) and 55 EIPs (B). (BOTTOM) Plots C & D: nestedness versus normalized cyclicity (λnorm ) for a set of 48 FWs (C) and 55 EIPs (D).
Acknowledgements
ness [24], which is analogous to company growth and formation in industry. Therefore, increasing the interactions between generalist actors in an EIP could promote new industries, new interactions, and sustainable growth among a complex.
We would like to thank our colleagues from Texas AM University, who provided insight and expertise that greatly assisted with this bio-inspired exploration into EIP structure. We would also like to thank Shelby Warrington for collecting EIP data. References
5. Conclusion The history of bio-inspired design in promoting sustainability among EIPs behooves the field of industrial ecology to continue adding perspectives to ENA. The near random ordering of EIPs is rather shocking and sheds light on the importance of link placement to go along with connectance.The consistent nestedness difference from EIPs to FWs suggest a more purposeful ordering of link positions in the latter. Increasing the number of core industry connections will lead EIP designs closer to FW structure. Examples of common generalist industrial actors in this study include water treatment plants, power plants, and waste remediation facilities that are not adequately connected to support high levels of nestedness and cyclicity. One of the great advantages of an EIP is that material imports can come from multiple sources which can reduce supply chain disruptions. Industrial structures that connect actors in chains rather than nested structures simply propagate the disruption down the line to several dependent industries. While the nestedness values in FWs do not suggest it to be the chief ordering metric of these networks, a linkage distribution metric that more accurately describes unipartite systems is necessary to inspire novel EIP network designs.
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[10] Atmar, W., Patterson, B.D., 1993. The measure of order and disorder in the distribution of species in a fragmented habitat. Oecologia 96.3, 373–382. [11] Bascompte, J., Jordano, P., Melian, C.J., Olesen, J.M., 2003. The nested assembly of plant-animal mutualistic networks. Proceedings of the National Academy of Sciences 100.16, 9383–9387. [12] Havens, K., 1993. Predator-Prey relationships in natural community food webs. Oikos 68.1, 117–124. [13] Strona, G., Veech, J.A., and Poisot, T., 2015. A new measure of ecological network structure based on node overlap and segregation. Methods in Ecology and Evolution 6.8, 907–915. [14] Layton, A. 2015. Realizing Biological Inspiration for Industrial Resource Networks. Ph.D. Dissertation, Georgia Institute of Technology, Atlanta, GA [15] Cohen, J.E., Beaver, R.A., et al., 1993. Improving Food Webs. Ecology 74.1, 252–258. [16] Polis, G.A., 1991. Complex trophic interactions in deserts: An empirical critique of food web theory. American Naturalist 138.1, 123–155. [17] Layton, A., Bras, B., and Weissburg, M., 2016. Ecological Principles and Metrics for Improving Material Cycling Structures in Manufacturing Networks. ASME Journal of of Manufacturing Science and Engineering, 130(10) 101002-101014, 2016. DOI: 10.1115/1.4033689. [18] Fath, B.D. and Halnes, G., 2007. Cyclic energy pathways in ecological food webs. Ecological Modelling 208.1, 17–24. [19] Allesina, S., Bondavalli, C., and Scharler, U.M., 2005. The consequences of the aggregation of detritus pools in ecological networks. Ecological Modelling 189.1-2, 221–232. [20] Almeida-Neto M, Guimaraes, P., Guimaraes, P.R., Loyala, R.D., Ulrich, W., 2008. A consistent metric for nestedness analysis in ecological systems: reconciling concept and measurement. Oikos 117.8, 1227–1239. [21] Lee, D.S., Maeng, S.E., Lee, J.W., 2012. Scaling of Nestedness is Complex Networks. Journal of the Korean Physics Society 60.4, 648–656. [22] Cantor, M., et al., 2017. Nestedness across biological scales. PLoS ONE 12.2, e0171691. [23] Bascompte, J., 2009. Mutualistic networks. Frontiers of Ecological Environment 7.8, 429–436. [24] Pillai, P., Gonzalez, A., and Loreau, M., 2011. Metacommunity theory explains the emergence of food web complexity. Proceedings of the National Academy of Sciences 108.48, 19293–8.
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26th CIRP Life Cycle Engineering (LCE) Conference 26th CIRP Life Cycle Engineering (LCE) Conference
Designing eco-industrial parks in a nested structure to mimic mutualistic Designing eco-industrial parks in a nested structure to mimic mutualistic 28th CIRP Design Conference,networks May 2018, Nantes, France ecological ecological networks Colton Brehm, Astrid Layton* A new methodology to analyze the functional and physical architecture of ColtonTexas Brehm, Astrid Layton* Department of Mechanical Engineering, A&M University, 3123 TAMU, College Station, Texas 77843, USA existing products for anEngineering, assembly product family identification Department of Mechanical Texas A&Moriented University, 3123 TAMU, College Station, Texas 77843, USA *Corresponding author. Tel.: +1-979-458-0360. E-mail address: [email protected] *Corresponding author. Tel.: +1-979-458-0360. E-mail address: [email protected]
Paul Stief *, Jean-Yves Dantan, Alain Etienne, Ali Siadat Abstract École Nationale Supérieure d’Arts et Métiers, Arts et Métiers ParisTech, LCFC EA 4495, 4 Rue Augustin Fresnel, Metz 57078, France Abstract Industrial Ecology uses ecological systems as a guide for improving the sustainability of complex industrial systems. Eco-Industrial Parks (EIPs) have gained support as ecological a solution systems that seeks simultaneously reduce environmentalofburdens promotesystems. economic interests byParks exchanging Industrial Ecology uses as to a guide for improving the sustainability complexand industrial Eco-Industrial (EIPs) materials and energy between industries to their mutual benefit. Recent studies have focused on drawing relations between food webs (FWs) and have gained support as a solution that seeks to simultaneously reduce environmental burdens and promote economic interests by exchanging EIPs to improve the sustainability of the to latter ecological such ashave the level of cycling or average connections between materials and energy between industries theirusing mutual benefit. metrics, Recent studies focused on drawing relations between food websactors. (FWs)This and study new ecological metric, into themetrics, discussion The associationbetween of nestedness with EIPs toincorporates improve thea sustainability of the latternestedness, using ecological suchof as sustainable the level of design cyclingfor or EIPs. average connections actors. This Abstract mutualistic ecological networks supports its application EIP The work here improves of holisticofnetwork structure study incorporates a new ecological metric, nestedness, to into thedesign. discussion of sustainable designtheforunderstanding EIPs. The association nestedness with with the goal of improving future design decisions for EIPs with purposeful placement of material and energy flows. mutualistic ecological networks supports its application to EIP design. The work here improves the understanding of holistic network In today’s business environment, the trend towards more product variety and customization is unbroken. Due to this development, thestructure need of * Corresponding author. Tel.: +33 3 87 37 54 30; E-mail address: [email protected]
with and the goal of improving future design decisions for EIPs withwith purposeful of material energyToflows. agile reconfigurable production systems emerged to cope various placement products and product and families. design and optimize production c 2019 as The Authors. Published by Elsevier B.V. This is an open access articlemethods under theareCC BY-NC-ND license systems well as to choose the optimal product matches, product analysis needed. Indeed, most © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license of the known methods aim to (http://creativecommons.org/licenses/by-nc-nd/3.0/) c 2019aThe Authors. Published by Elsevier B.V. This islevel. an open accessproduct article under the however, CC BY-NC-ND license analyze product or one product family on the physical Different families, may differ largely in terms of the number and (http://creativecommons.org/licenses/by-nc-nd/3.0/) Peer-review under committee of Conference. (http://creativecommons.org/licenses/by-nc-nd/3.0/) nature of components. This fact of impedes an efficient comparison and CIRP choice of Cycle appropriate product(LCE) family combinations for the production Peer-review underresponsibility responsibility ofthe thescientific scientific committee ofthe the26th 26th CIRPLife Life CycleEngineering Engineering (LCE) Conference. Peer-review under responsibility of the scientific committee of the 26thinCIRP Life Cycle Engineering (LCE) Conference. system. A new methodology is proposed to analyze existing products viewparks of their functional and physical architecture. The aim is to cluster Keywords: nestedness; industrial ecology; network design; mutualism; eco-industrial these products in new assembly oriented product families for the optimization of existing assembly lines and the creation of future reconfigurable Keywords: nestedness; industrial ecology; network design; mutualism; eco-industrial parks assembly systems. Based on Datum Flow Chain, the physical structure of the products is analyzed. Functional subassemblies are identified, and a1.functional analysis is performed. Moreover, a hybrid functional and physical architecture graph (HyFPAG) is the outputsteam. which depicts the gas, sulfur, fly ash, sludge, and low-quality These exIntroduction similarity between product families by providing design support to both, production system planners and product designers. An illustrative changes re-purpose waste streams as imports, avoiding gas, sulfur, fly ash, sludge, and low-quality steam. Theseaddiex1. Introduction example of a nail-clipper is used to explain the proposed methodology. An industrial case study on two product families of steering columns of tions to landfills andwaste emissions to the environment [3]. StudBiologically Inspired Design (BID) implements biological changes re-purpose streams as imports, avoiding addithyssenkrupp Presta France is then carried out to give a first industrial evaluation of the proposed approach. ies oftothese complex industry networks have drawn[3]. comparsolve human problems, most notably in the field of tions landfills and emissions to the environment StudBiologically Inspired Design (BID) implements biological ©principles 2017 The to Authors. Published by Elsevier B.V. isons with the field of ecology, where complex natural systems engineering. Some product examples of BID include Leonardo ies of these complex industry networks have drawn comparprinciples to solve human problems, most notably in the field of Peer-review under responsibility of the scientific committee of the 28th CIRP Design Conference 2018.
demonstrate sustainability [4, 5]. EIPs designed in isons with theautonomous field of ecology, where complex natural systems ademonstrate food web-like structuresustainability have shown positive attributes, such autonomous [4, 5]. EIPs designed in reduced environmental burdens from materials and energy omy non-toxic depends wood on dwindling resources and is a growaasfood web-like structure have shown positive attributes, such and glue [1].finite Today’s global industrial econintake [6, 7].environmental Food web-likeburdens networkfrom structures haveand also been ing burden on on environmental health. Issues created these as reduced materials energy omy depends dwindling finite resources and is by a growshown [6, to reduce economic supplyhave chain disrupcomplex industrial networks require an equally encompassintake 7]. Food web-likedamage networkfrom structures also been ing burden on environmental health. Issues created by these 1.complex Introduction of thewhile product range and characteristics manufactured and/or tions continuing to minimize carbon emissions ing network-level andequally privateencompasscompanies shown to reduce economic damage cost fromand supply chain disrupindustrialsolution. networksCountries require an assembled this system. In thissuggest context, the main challenge in [8]. Positive results liketo these as a route for inaround the world are seekingCountries to counter these issues with the tions whileincontinuing minimize costBID and carbon emissions ing network-level solution. and private companies Due to the fast development in the domain of modelling and analysis is now not only to cope with single creasing the sustainability of industrial systems. Diverse formation Eco-Industrial (EIPs). Theissues goalswith behind [8]. Positive results like these suggest BID as a route forperinaround the of world are seekingParks to counter these the communication and ongoing digitization and products, aare limited product range or existing product spectives the required to combat misunderstandings infamilies, theperapEIPs are to of reduce rawan material use,trend emissions, andgoals waste. EIPs creasing sustainability of industrial systems. Diverse formation Eco-Industrial Parks (EIPs).of The behind digitalization, enterprises are facing important but also toof beBID able analyze and to compare products define plication totoEIPs. food web (FW) metrics used are created bymanufacturing connecting industries through mutually benefispectives are required to Namely, combat misunderstandings intothe apEIPs are to reduce raw material use, emissions, and waste. EIPs challenges in today’s market environments: a continuing new product families. It can be observed that classical existing to describe tend to focus heavily number of links cial created relationships. The concept of mutually beneficial is derived plication of EIPs BID to EIPs. Namely, food on webthe (FW) metrics used are by connecting industries through mutually benefitendency reduction product development and product families are regrouped function ofthe clients or features. between actors the on position or distribution fromrelationships. the towards field of ecology andofimplies that interactions to describe EIPswithout tend todescribing focusinheavily number of links cial The concept of mutually beneficial times ispromote derived shortened product lifecycles. In addition, there is an increasing However, assembly oriented product families are hardly to find. [6, 7, 8]. actors without describing the position or distribution the well both parties; a network primarily composed between from the being field ofofecology and implies that interactions promote demand of customization, being at the same time in a global On the product family level, products differ mainly in two of these interactions called aa mutualistic networkcomposed [2]. The [6, 7, 8]. the well being of bothis parties; network primarily competition with competitors all over the world. This trend, main characteristics: (i) the number of components and (ii) the Kalundborg EIP in Denmark successful example inof these interactions is calledis aa mutualistic networkwhere [2]. The which is inducing the development from macro to micro type of components (e.g. mechanical, electrical, electronical). dustries are EIP linked via exchanges of wastes,example such aswhere refinery Kalundborg in Denmark is a successful inmarkets, results in via diminished lotofsizes due such to augmenting Classical methodologies considering mainly single products dustries are linked exchanges wastes, as refinery product varieties (high-volume to low-volume production) [1]. or solitary, already existing product families analyze the To cope with this variety as well asThis to be structure on a physical c 2019 2212-8271 Theaugmenting Authors. Published by Elsevier B.V. is anable opento access product article under the CC BY-NC-ND licenselevel (components level) which identify possible optimization potentials in the existing causes difficulties regarding (http://creativecommons.org/licenses/by-nc-nd/3.0/) c 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license an efficient definition and 2212-8271 Peer-review under responsibility of the scientific committee of the 26th CIRP Life Cycle Engineeringof(LCE) Conference. production system, it is important to have a precise knowledge comparison different product families. Addressing this (http://creativecommons.org/licenses/by-nc-nd/3.0/) DaVincis flying machine, cells include based on leaves, engineering. Some product photovoltaic examples of BID Leonardo
and non-toxic glue [1]. Today’s global industrial econKeywords: Assembly; Design method; Family identification DaVincis flyingwood machine, photovoltaic cells based on leaves,
Peer-review under responsibility of the scientific committee of the 26th CIRP Life Cycle Engineering (LCE) Conference. 2212-8271 © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/) 2212-8271 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of scientific the scientific committee theCIRP 26thDesign CIRP Conference Life Cycle 2018. Engineering (LCE) Conference. Peer-review under responsibility of the committee of the of 28th 10.1016/j.procir.2018.12.011
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2. Methods Nomenclature
2.1. EIP and FW data sets
EIP Eco-Industrial Park FW Food Web ENA Ecological Network Analysis [A] Adjacency Matrix [F] Food Web or Community Matrix λmax Cyclicity λnorm Normalized Cyclicity S Degree of Nestedness of a bi-directional, 2-mode network
A data set of 44 EIPs was used to evaluate nestedness among realized and proposed industrial networks. The EIPs in this study span a diverse set of industries with varying material, energy, and waste flows. These EIPs were compared to a group of 57 FWs to extract similarities and differences among several ecological metrics, including nestedness, connectance, species richness, cyclicity, and normalized cyclicity [14]. Both the EIP and FW datasets are composed of matrices containing binary data describing the realized connections between actors in the network. A simple example for a simplified FW is displayed in 1 for clarity. Samples in this study however contain many more nodes. All calculations exclusively use these 101 matrices. FW analysis in the 1990s shifted when ecologists proposed to homogenize data collection methods to improve data quality [15, 16]. The FWs in this study were selected post-1993 when ecological field methods were improved, to ensure data of the highest quality was used.
Recently, the analysis of EIPs has been diversified with the use of the metric cyclicity (λmax ). Cyclicity measures the prevalence of cyclical pathways in a network and is heavily related to decomposer-type species in FWs [9]. Cycles are realized in areas of high linkage density and therefore depend to some degree on link distribution. A metric that purely describes linkage density and position however has yet to be applied to EIPs. Nestedness can help illuminate the importance of the position of exchanges in an EIP. Nestedness was originally developed by the ecologists Atmar and Patterson in 1993 to describe species distribution patterns in fragmented habitat and their predicted extinction sequences [10]. The metric has since become very popular in studying mutualistic networks, such as pollination and seed dispersal networks, which are both characterized by a high degree of nestedness [11]. Nestedness has not yet been used in the study of EIPs, which are unipartite and unidirectional networks. Ecology defines unipartite networks as communities that do not have their species categorized into distinct groups, how a plant-pollinator network would be modeled for example. Each species in a unipartite network has the potential to form a relationship with any other species in the network. Unidirectional constrains the direction of flow; in a FW this would be the direction that energy and nutrients can travel from resource to consumer. These two definitions describe the way EIPs and many FWs are modeled using an ENA. Generalized species have many interactions in a network while specialized species may only have one or two interactions [12]. Pure nestedness (a nestedness value of 1) is when 100% of actors that are more specialized than at least one other actor, connect to a proper subset of the more general actors. A proper subset would be when the actors that a specialized species are connected to, can all be found connected to the next more general actor. The structure of self-sustaining mutualistic networks has shown higher nestedness values than any other class of network [13]. Therefore studying nestedness in EIPs may not only be a helpful perspective for future studies, but could also be paramount to promoting sustainability in industrial networks.
Fig. 1. An example ecosystem (left), its FW (center), and its community matrix (right). S1 -S3 represent the three species highlighted in the ecosystem and L11 L33 represent the linkages between them. [17].
2.2. ENA metrics Ecologists use a large set of metrics as part of an Ecological Network Analysis (ENA) to draw relationships between FW network structure and behavior [11, 18]. Several ENA metrics are used in this study to uncover sources that contribute to nestedness as well as to compare fundamental features of FWs and EIPs. These ENA metrics are calculated from a FW matrix [F], which is a square matrix containing binary information on the presence and direction of interactions in the network. [F] must always be of size N x N, where (N) is defined as the species richness or the total number of actors in a network. The interactions are entered into Fi j as a one when there is an interaction from i to j and a zero otherwise. The total number of interactions is the number of links (L) and is calculated by summing all the nonzero values in [F], as seen in Eq. 1. L=
N N
Fi j
(1)
i=1 j=1
2
Connectance (c) is the number of realized predator-prey interactions, divided by the total number of possible interactions in the FW, where the number of possible interactions is the size of matrix [F] as seen in Eq. 2 below. Connectance is a good de-
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scriptor for network structure and has been found to positively correlate with nestedness in FWs [11]. c=
L N2
(UNODFc, the c standing for columns, which represent consumers in [F]). UNODFr is defined in ecology as the degree of nestedness of prey sharing consumers and UNODFc is the degree of nestedness of consumers sharing prey. Recent works have created multiple nestedness algorithms to discern nestedness in these types of ecological networks however, the study here uses only the variation in Eq. 5 [20, 21]. A qualitative perspective for the concept of nestedness is shown in Figure 2.
(2)
Cyclicity (λmax ) measures the abundance and strength of cyclic pathways in a network [18, 19]. The magnitude of nestedness and cyclicity both depend on the location, rather than just the number, of links in the network. Cyclicity is the maximum real eigenvalue solution of Eq. 3. Calculating cyclicity requires the adjacency matrix [A], which is the transpose of the FW matrix. Cyclicity is equal to either zero, one, or any value greater than one. These values respectively correspond to the qualitative descriptions of cycling absent, one simple internal cycle present, or lots of complex internal cycling. The dynamics and stability of ecosystems are significantly influenced by nutrient cycling [18]. Cyclicity does have some relationship to system size, as the network size increases cyclicity will either increase or remain the same. |A − λI| = 0
(3)
Normalized cyclicity (λnorm ), cyclicity divided by the total number of actors, is used in place of cyclicity to account for its system-size dependence. Normalized cyclicity and nestedness both have an upper bound so the values do not always increase with network size.
Fig. 2. Nestedness values (y-axis) for four unidirectional networks: (A) checkered, (B) modular, (C) random, and (D) perfectly nested. Graphic use with permission from [22].
2.3. Nestedness
Matrices A,B,C, and D in Figure 2 represent four different types of networks of the same size (N) and with the same total number of connections (L), and thus four networks with the same connectedness. This illustrates the potential for four networks with the same N, L, and c to have completely different nestedness values (as shown by the range on the y-axis) based on how the actors are connected, rather than how much they are connected. The yellow entries in the four matrices in the bottom of Fig. 2 represent realized links in the network and the black represents no link. Figure 2D shows a perfectly nested, unipartite, non-cannibalistic network in contrast to the checkered (every actor is connected to every other actor to the same degree), modular (two highly connected networks are joined by a few common actors), and random structures of A, B, and C respectively.
Nestedness (S ) was computed for 57 FWs and 44 EIPs following Eq. 4 and its adaptation in to Eq. 5 below [20, 21]. N N N 2 l=1 Ai j A jl S = N(N − 1) i j,i< j min(ki , k j ) N
UNODF =
3
N
2 N(N − 1) i j,i< j
N
(4)
l=1 (1
− δki k j )Ai j A jl min(ki , k j )
(5)
where δki k j = 0 if ki = k j , and in all other cases. The “degree” of node i is determined by ki = Ail . Conceptually degree is the number of interactions a node experiences in one direction. S checks for node overlap of the same degree such as ki = k j . The assumption of no cannibalism, or preventing an actor from interacting with itself (the diagonal of the [F] and [A] matrices will always be zero), presents the need for a variation on Eq. 4 that avoids these interactions. Thus, nestedness is calculated here using Eq. 5 for the unidirectional node overlap (UNODF). UNODF has a range of 0-1 with perfectly nested networks residing on the upper bound. EIPs and FWs are directed networks, a consumer can take from a producer without the reverse interaction needing to exist. This creates two nestedness values, one for production (UNODFr, the r standing for rows, which represent producers in [F]) and one for consumption
2.4. Null models and significance
3
The nestedness of the EIPs and FWs are given significance by calculating P-values to measure if the networks are more nested than a randomly created network of the same size and connectance would be. One thousand null models were created for each EIP and FW using the ‘null2’ function in RStudio 2018 3.5.0. The null cases form a normal distribution of UNODFr and UNODFc values [23]. The difference in nestedness between the FWs and EIPs and their corresponding null average is the ‘nestedness difference,’ which also serves as a measure of purposeful ordering of the network.
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The normal distributions of the null data allows for a Z-score describing the number of standard deviations from the mean that any element is. A Z-score is assigned to the actual UNODFr and UNODFc values to describe where any of the real-life networks lie on the null distributions. A P-value, representing the chance that a network has more nested, or anti-nested, structure than a random network of the same N and c, is also used to describe the results. A cutoff of P < 0.05 conveys a 95% confidence that the network has a nested structure beyond random chance. Networks with high nestedness difference to the null will therefore result in low P-values.
Table 1. ENA comparison of the data sets of 44 eco-industrial parks (EIPs) and 57 food webs (FWs). *Average values are underlined.
3. Results Figures 3A and 3C display the nestedness difference to the null average for each of the 57 FWs and 44 EIPs, respectively. Points around the zero line represent networks without any nestedness more than a random network of equal size and connectance would show on average. The production nestedness difference is +4.94e-2 and 3.65e-4 for the FWs and EIPs respectively. The consumption nestedness difference is +2.99e-3 and +0.169 for the FWs and EIPs respectively. Figures 3A and 3B plot nestedness vs normalized cyclicity for the FWs and EIPs. The average normalized cyclicity is 0.177 for the FWs and 0.153 for the EIPs. The average number of actors for the FWs is 37 (which have an average cyclicity of 5.34), compared to only 12 for the EIPs (which have an average cyclicity of 1.54). This suggests that the higher average cyclicity of FWs is partially due to their larger size and using normalized cyclicity helps account for this difference. Figures 3C and 3D show when comparing nestedness against normalized cyclicity, EIPs tend toward the upper right but little correlation is seen for the FWs. Most notably, the EIPs with the largest nestedness values have the largest normalized cyclicity values. Figure 3 is summarized in Table 1 alongside additional ENA metric results. Only 2 out of 44 EIPs have significantly nested consumers (UNODFc), while 40 out of 57 FWs had P-values below 0.05. UNODFr, nestedness of production, shows a similar trend with only 4 out of 44 EIPs having P-values less than 0.05 as compared to 28 out of 57 FWs. 4. Discussion EIPs seek to mimic the mutually beneficial interactions common in ecosystems but are shown here to lack the degree of nestedness seen in FWs. Although it is not yet clear if increasing the nestedness in EIPs will result in positive network behavior, industrial systems have been shown to gain positive behavioral traits when they better mimic structural characteristics of ecosystems [6-8]. The production and consumption nestedness values are shown to be significantly higher for FWs than EIPs alongside the nestedness differences to the null averages signifying that the distribution of links in these two data sets is consistently different. Almost all the EIPs studies here vary within only ± 0.10 of the nestedness of randomly structured networks.
593 4
4
Metric
EIPs (44)
FWs (57)
UNODFr UNODFc Range of data set size actors c λmax λnorm Nestedness diff. (production) Nestedness diff. (consumption) # P-values < 0.05 (rows) # P-values < 0.05 (cols)
0.174 0.185 6 – 39 ≈ 12 0.160 1.54 0.153 +3.65e-4 +2.99e-3 4 2
0.295 0.436 4 – 125 ≈ 37 0.196 5.34 0.177 +4.94e-2 +0.169 28 40
However, small EIPs could randomly display very high or low nestedness because the few nodes constrain the possible number of network combinations. Filtering the EIPs for size, removing those networks with less than 12 actors, further reduces the difference to the null group’s nestedness. Appendix Fig. ??A shows FW nestedness values further shift above the null average when a size filter of 16 species is applied. This strengthens the conclusion that these networks structure their connections much differently. FWs, as seen by the P-values listed in Table 1, also show a consistent and significant difference from the null cases. This confirmation motivates future work to test EIP network designs with higher nestedness than the 44 used here. The FWs also show more nestedness for consumption than for production while EIPs have no difference in the nestedness of consumption vs production. This could be related to the onesided mutualistic nature of these feeding interactions. It is in the consumers’ favor to reduce competition by feeding in a nested fashion, but it is not in the resources’ favor to distribute energy in a nested fashion because it sustains a healthy population of consumers. The comparison of nestedness with normalized cyclicity done here can provide some conclusion in the form of design advice for EIPs. Those EIPs with the highest degree of nestedness also showed the highest normalized cyclicity. Closer examination shows that groups of highly general nodes, in the EIPs promote nestedness more than any other actor type. Examples of these include power and water networks that not only connect to many specialized industries but also connect to each other. All networks without these generalist-to-generalist interactions fail to reach moderate or high degrees of nestedness and normalized cyclicity. While nestedness requires a proper distribution of generalist and specialist species, it appears there is most commonly a dearth of generalist-generalist interactions among EIP networks. This lack of a core group of generalist actors simultaneously decreases cyclicity and nestedness. Cyclicity and nestedness by definition do not necessarily represent the same network structure, but in application require a basic component of generalists to exist in a high degree. Ecologists have hypothesized that generalist-generalist interactions are a key foundation to support the growth of network species rich-
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Fig. 3. (TOP) Plots A & B: the difference in nestedness (production is UNODFr and consumption is UNODFc) between individual cases and their null average for a set of 48 FWs (A) and 55 EIPs (B). (BOTTOM) Plots C & D: nestedness versus normalized cyclicity (λnorm ) for a set of 48 FWs (C) and 55 EIPs (D).
Acknowledgements
ness [24], which is analogous to company growth and formation in industry. Therefore, increasing the interactions between generalist actors in an EIP could promote new industries, new interactions, and sustainable growth among a complex.
We would like to thank our colleagues from Texas AM University, who provided insight and expertise that greatly assisted with this bio-inspired exploration into EIP structure. We would also like to thank Shelby Warrington for collecting EIP data. References
5. Conclusion The history of bio-inspired design in promoting sustainability among EIPs behooves the field of industrial ecology to continue adding perspectives to ENA. The near random ordering of EIPs is rather shocking and sheds light on the importance of link placement to go along with connectance.The consistent nestedness difference from EIPs to FWs suggest a more purposeful ordering of link positions in the latter. Increasing the number of core industry connections will lead EIP designs closer to FW structure. Examples of common generalist industrial actors in this study include water treatment plants, power plants, and waste remediation facilities that are not adequately connected to support high levels of nestedness and cyclicity. One of the great advantages of an EIP is that material imports can come from multiple sources which can reduce supply chain disruptions. Industrial structures that connect actors in chains rather than nested structures simply propagate the disruption down the line to several dependent industries. While the nestedness values in FWs do not suggest it to be the chief ordering metric of these networks, a linkage distribution metric that more accurately describes unipartite systems is necessary to inspire novel EIP network designs.
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