**1. Introduction**

Industrial ecologists have established material flow analysis (MFA) as a premier tool for assessing the metabolism of human society. While an MFA can be a highly effective tool for optimizing resource allocation, researchers can easily overlook the relationships between a system under study and other related systems. Failing to understand the interdependencies of systems could lead to sub-optimal decision making when considering broader system boundaries for analyses. One such example is the shock in global automobile production following the 2011 earthquake in Japan, which revealed to many major automakers that parts of their upstream supply chains depended on a pigment produced by only one factory in the world, near Fukushima. Automakers could have hedged their supply chain risks if they had a full understanding of how their networks of lower-tier suppliers (lower-level systems) integrated with networks that include higher-tier suppliers (higher-level systems). The current framework for MFA works well at helping researchers identify opportunities for optimizing systems at a single system level but is not well suited for optimizing material flows across nested systems interacting with one another. One idea to address this limitation is to approach MFA using the holarchy framework. The holarchy concept aims to examine systems holistically by acknowledging the systems nature of the modern material-based society.

The holarchy framework was proposed by Koestler [1] as an alternative to hierarchy in recognizing the semi-autonomous characteristic of components of biological and social systems, including organizations, organisms, and cells. Each of these entities is considered a holon since each is a complex system with operational and managerial independence wherein each system is seeking to optimize objectives at its respective holarchic level [2]. As such, a holon is simultaneously a part and a whole in itself and arises from the collaboration of its complex sub-systems and super-systems. This framework has been commonly applied to information systems of intelligent manufacturing systems [3–5] and of supply chain managemen<sup>t</sup> systems [6–8] and, more recently, to energy systems such as microgrids [9]. Holarchy has also been used to analyze the means for improving the resilience of social-ecological systems [10,11], including how to alleviate congestion, ine ffective distribution of resources, and environmental pollution in cities [12]. Holarchy was introduced to industrial ecology by the works of Kay [13] and Spiegelman [14] to study socio-economic systems as self-organizing, holarchic, open (SOHO) systems.

It is widely recognized that quantifying the material flows into and from a jurisdictional region such as a city or country is not a simple matter. The challenge is one of data availability, which could result from (1) a simple lack of e ffort in data collection, (2) data collected but in insu fficient detail for the intended purpose, or (3) the di fficulty of monitoring flows across porous jurisdictional boundaries. In principle, a promising way of addressing the data challenge is by focusing on islands, which have clearly defined physical boundaries and, often, a small number of locations (ports, airports) where material flows need to be monitored [15]. The methodological utility of island boundaries was, of course, recognized by Darwin in his studies of finches in the Galapagos Archipelago. A nice summary of his work is given by Grant and Estes [16]. Examples of island-based MFAs that demonstrate this efficacy include those of Singh et al. [17], Lenzen [18], Krausmann et al. [19], Nielsen and Jørgensen [20], and Cecchin [21].

Anthropogenic activities on islands become segments of economies larger and smaller. In this vein, the sum of human activities on Planet Earth related to material flows represents the sum of flows into and from Earth's regions. The regional flows are those related to cities, industries, and other activities, extending down to smaller entities. Nonetheless, it is not easy to demonstrate the features of a modern, multi-level material system. Islands may provide a potential end-run around this challenge because island archipelagoes are themselves generally self-contained and are also connected with their individual islands (a lower level) and with flows to and from continental and global systems (higher levels).

An archipelago and its connections form an example of a holarchy, or what engineers call a system of systems [2] and ecologists call a panarchy [22,23]. In such a system, a higher-level holon is, in part, a result of activities of holons below it in the hierarchy. Similarly, an upper-level holon may constrain the behaviors of lower-level holons. One can, therefore, picture a material flow holarchy ranging from the lowest level holon to the highest level holon defined in this paper as (1) an industrial activity on an island by one or more enterprises, (2) a city on the island that contains that industrial activity, (3) the island itself, (4) the archipelago of which the island is part, and (5) the planet that contains the archipelago. The holarchy framework can also be applied to conceptualize non-island socio-economic systems.

In practice, a holarchic study in industrial ecology would consist of the collective examination of material flow accounts of a particular holon and its lower- and higher-level holons which form a holarchy (Figure 1). This article synthesizes research by faculty and graduate students from the Yale School of Forestry and Environmental Studies and explores some of the benefits and challenges of examining material flows for Hawaii using the holarchy framework. The material flow accounts presented in this study were not compiled with the idea of holons in mind, but it subsequently occurred to us that the islands were part of a holarchic system. Our previous objective had been to compare material flows on islands that were each a political unit (typically a county) of the same state, Hawaii, thereby allowing us to examine variations in metabolism while controlling for di fferences in the regulatory system. Because of limitations in scope and data availability, the results are indicative rather than comprehensive, revealing some of the challenges and achievements of applying the holarchic perspective within industrial ecology. The value of the activity is that it demonstrates the potential of a holarchic approach to MFA, and thereby encourages further research based on that perspective.

**Figure 1.** Conceptual diagram of a holarchic system for integrated material flow analyses. The entire Earth system and each circle denote individual holons, and their borders represent system boundaries for individual material flow analyses. Holarchic levels are indicated by shades of blue. Black arrows represent flows of materials between holons in the same holarchic level, and blue arrows represent flows between holarchic levels.

#### **2. Materials and Methods**

The Hawaiian Island Archipelago consists of six principal islands (Figure 2) and a number of smaller, largely uninhabited islands. During the years 2006–2013, faculty and graduate students from the Yale School of Forestry and Environmental Studies conducted projects related to quantifying and analyzing flows of materials through the islands, organized by authors of the present study. MFAs, energy analyses, and targeted studies of various kinds were conducted for a selection of industries, cities, and islands in the archipelago [24–47]. These activities were pursued with diverse analytic aims in mind, with the result that the individual studies were interesting and useful, but the sum of the studies did not comprise a fully integrated specification of the interlinked material flows related to the Hawaiian Archipelago. Nonetheless, the results provide examples of metabolism at the different holarchic levels, thereby enabling us to demonstrate the potential value of a complete holarchic evaluation centered on anthropogenic flows of materials.

The analysis in the present work is directed at the five-level holarchy shown in Figure 3. As the holarchy framework views each holon as a semi-autonomous system, our study treats each holon as an individual system of analysis, effectively constructing a tiered system of MFAs consisting of multiple levels connected by material input and output flows. We present the multi-layer analysis of material flows by providing examples of standalone MFAs for holons drawing on our previous works (see the Supplementary Materials for additional examples of such MFAs). The compiled material flows are compared across individual holons to yield insights that are not apparent when examining each holon in isolation.

**Figure 2.** The Hawaiian Archipelago, picturing the six islands under study and several principal cities.

**Figure 3.** The Hawaiian Islands holarchic system. Arrows represent material flows between holarchic levels. Lower-level holons are nested within higher-level holons. Flows between higher-level holons are larger than those between lower-level holons. In addition, flows from higher to lower holons are depicted as larger than those from lower to higher holons to indicate that material stocks in Hawaii are gradually increasing over time as island infrastructure is further developed.

The material flow accounts at each holarchic level were compiled based on Eurostat's methodology for economy-wide material flow accounts (EW-MFA; see the Supplementary Materials for the compiled material flow data) [48]. Imports and exports for each holon were calculated using data on inbound and outbound ocean shipments by port from the U.S. Army Corps of Engineers Waterborne Commerce Statistics Center [49]. The accounts for domestic extraction drew primarily on state-level harvest and mining data from the U.S. Department of Agriculture's National Agricultural Statistics Service [50]

and the U.S. Geological Survey's National Minerals Information Center [51]. State-level material accounts were disaggregated to the island and municipality levels based on information including the distributions of crop area, retail sales, population, and man-hours worked in mines, provided by the State of Hawaii Databook [52], a publication of the State of Hawaii's Department of Business, Economic Development and Tourism (DBEDT), the U.S. Census Bureau's Economic Census [53], and the U.S. Department of Labor's Mine Safety and Health Administration [54], among others. For analyses of island and industry-level holons, data from these sources were enhanced by in-person interviews conducted in Hawaii by Yale graduate students and by personal communication with individuals at local organizations. Apparent consumption, or formally direct material consumption, is calculated as the sum of used domestic extraction and imports, minus exports.

Material shipments by air are not accounted for in this study. Approximately 98% of imports to Hawaii were ocean deliveries [37], and this ratio was assumed to be similar for exports. Therefore, values for ocean shipments were treated as all shipments in the calculations. Furthermore, the terms "import" and "export" are used in this document to describe inbound and outbound material flows for a defined system as used by Eurostat [48] and do not strictly indicate international flows. Imports and exports for the entire State of Hawaii can be calculated from port-level data because all ocean shipments to and from the Hawaiian Islands pass through Oahu [37]. Our analysis does not include unused extraction, indirect flows, or sectoral disaggregation of material flows. We present the results of MFAs for individual holons by holarchic level in order of increasing spatial scale and explore their relationships.
