*1.1. Social-Ecological Systems and the Application of Ecological Terminology*

This paper emphasizes the concept that humans are a part of—not separate from—nature [1], supporting views established by Berkes and Folke [2], and Berkes et al. [3], which hold that the delineation between social systems and natural systems is arbitrary and artificial. Several frameworks for understanding such social-ecological systems have been put forth (e.g., [4–6]), but some have pointed out a disconnect between the frameworks—proposed to understand social-ecological systems—and the biocultural elements that are at the foundation of such systems [7]. This research aims to bridge that gap by (a) presenting theories and methods associated with quantifying biocultural

relationships within social-ecological systems; (b) demonstrating how restoring the function of "keystone" components is essential to restoring the structure of social-ecological systems that are observed to be in decline; and (c) demonstrating how restoring the function of "redundant" components is essential to restoring the resilience of such systems. As with our other publications on social-ecological systems, we follow the Walker et al. definition of resilience as the capacity of a system to absorb disturbance and reorganize while undergoing change so as to still retain essentially the same function, structure, identity, and feedbacks [8].

Following Berkes [9], we use the terms "ecological subsystem" and "social subsystem" when discussing particular sides of the social-ecological spectrum, and will do so even when the referenced text uses the term "ecosystem". This allows us to discuss each of the two sides, while maintaining that the two subsystems are not autonomous from one another. We follow others in applying common ecological terms to set up a logical framework for understanding social-ecological systems [10–13]. This paper uses accepted terminology such as 'function', 'functional group', 'diversity', 'keystone', 'redundant', 'regime shift', and 'stable state' of Anderies and Janssen [14] in discussing social-ecological systems. This paper uses the term, 'alternative regime state', to describe alternative stable states that can exist within the same social-ecological system, such as flooded-field agriculture versus rain-fed agriculture practiced by the same culture. An 'alternative regime state' describes different stable states that can exist within the context of the same social-ecological system, whereas a 'regime shift' indicates a stable state that exists within a different social-ecological system altogether, such as a rural agricultural community being transformed into a city and inducing a concurrent shift in the dominant culture. This notion is explored in more detail below.

#### *1.2. Quantifying Biocultural Elements within Social-Ecological Systems*

Theories relating to co-evolutionary relationships between human and natural systems are not new [15]. In the 5th century BC, the Greek philosopher Herodotus voiced his observation that events shape both people and nature, and that people and nature interact and evolve together through these events. More recently, Winter and McClatchey [16,17] put forth theories to quantify these co-evolutionary relationships, and established methods for measuring fundamental units of interaction between people and plants—or linked biological-sociocultural relationships (henceforth referred to as biocultural relationships)—in a way that is scalable from simple interactions (one person and one plant) to complex relationships (all of humanity and all plants). Such an approach has been used to address hypotheses about the evolution of interactive relationships [16–18].

The Quantum Co-evolution Unit—or QCU—(Figure 1) is a unit to measure linked, co-evolving relationships such as those observed in social-ecological systems [16–18]. These relationships will henceforth be referred to as "biocultural elements" of such systems. A set of QCUs within a social-ecological system can be quantified (Figure 2, [17]) and assessments of these populations at different times can demonstrate co-evolving biocultural relationships [16,17]. As in many disciplines, units can be considered at different scales for both the ecological component (ecosystem, genus, species, etc.) and the social component (socio-cultural system, community, individual, etc.), to assess the health of diffent aspects of a social-ecological system. The research presented here contends that QCUs can be used as a unit to quantify biocultural elements, such as the following:


Possessing such an understanding can be key to informing biocultural restoration efforts.

**Figure 1.** The Quantum Co-evolution Unit (QCU), which relates to the co-evolutionary relationship between biological taxa and human cultures. It is composed of two subunits—the biological-taxa subunit, and the cultural-practice subunit—and is used as a metric for biocultural diversity. The complete unit of the QCU is referred to and described by its QCU profile [17].

**Figure 2.** A QCU population. A hypothetical collection of Quantum Co-evolution Units (QCUs) represented, within a social-ecological system, showing proportionality and frequency of various QCUs in relation to one another. The QCU population of a social-ecological system could be sampled over various points in time. Changes could be observed and further quantified. Such changes could include the adoption of new QCUs into the profile, deletion of QCUs from the population, and changes in individual QCU frequency within the population [17].

#### *1.3. The Hawaiian Social-Ecological System*

The evolution of social-ecological systems in Hawai'i is uniquely understandable, in part, because the relatively late human colonization allows for tracing the entirety of human history. As such, Hawai'i has been described as a model for the study of social-ecological systems [17,19].

Archaeological evidence indicates settlement no later than 1000 years ago [20], although use of oral history sources indicates initial voyages to the Hawaiian islands may have happened centuries prior [21–24]. In the pre-contact era—prior to contact with Europeans in 1778—the social-ecological system in Hawai'i was intensively managed to maximize resource abundance by attaining a stable state known in Hawaiian as "*'aina momona ¯* ". *'Aina momona ¯* is descriptive of a stable state that can exist in alternative forms in Hawai'i, and is associated with both flooded-field and rain-fed agriculture [25]. This is a stable state that was brought about via a regime shift (originally from an ecosystem into a social-ecological system that maximized ecosystem services). The social-ecological system in the Hawaiian archipelago associated with the pre-contact era will henceforth be referred to as the "Hawaiian social-ecological system", which is identified by the similarity of linked human-ecological units—being the foundational culture, the available plant species, and the cultural uses of those plants—that existed in the Hawaiian ecoregion in the pre-contact era.

Alternative states of *'aina momona ¯* existed in the Hawaiian social-ecological system, and while they had similar functional components with one another, they differed in structure across different regions of the archipelago. As has been described for ecological subsystems [26], it appears that the structures of these alternative regime states were shaped around different keystone components of the same system. Observations about differing structures of alternative regime states associated with either flooded-field or rain-fed agriculture [27] may be related to this phenomenon [28].

The structure of the Hawaiian social-ecological system has been in decline since the 19th century [29]. Gaining an understanding of the biocultural elements, and identifying them as either keystone or redundant components could be beneficial to efforts aimed at restoring the structure, function, and resilience of that system. We utilize theoretical foundations and logical assumptions to explore the the relative importance of biocultural elements in Hawaiian agricultural traditions—a core foundation within the pre-contact social-ecological system in Hawai'i.

#### **2. Theoretical Foundations**

#### *2.1. The Keystone Concept as Relates to System Structure and Function*

Paine [30] first described ecological 'keystone species', as occurring in a situation where patterns of distribution and density of species within an ecological subsystem are disproportionately affected by the activities of a single species. It has since become a major concept within the discipline, but has fueled decades of debate on definitions [31]. Ultimately, this debate stems from disagreements about how to quantify a metaphor. Is the concept of 'keystone' a biological reality, or is it a simple metaphor to understand a complex system? This paper argues the former, and following systems theory [32], asserts that the keystone concept holds true within social-ecological systems. This paper further asserts that it is possible to quantitatively determine a keystone component by assessing functional groups of biocultural elements within a system, and then analyzing the associated diversity within those functional groups.

The disproportionate influence of keystone species suggests there is no functional redundant within the system (Figure 3). If the keystone is removed, then a relatively large number of secondary extinctions would occur [33,34] and the system would reorganize itself with a different structure and function. This process is referred to as a regime shift [35]. Thus, keystone components play a major role in the structure and function of systems.

**Figure 3.** The keystone metaphor. The keystone is the component of a structure that is irreplaceable. Without the keystone, a structure could be reassembled, but could never be the same as if the keystone were present and functioning in its role.

#### *2.2. The Social-Ecological Keystone Concept*

The keystone concept of has been applied to various cultural interactions with the biological world [10–12]. Garibaldi and Turner [11] define *cultural* keystone *species* as "the culturally salient *species* that shape in a major way the cultural identity of a people". *Cultural* keystone *practices*, described by Brosi et al. [12], are *traditions* that are so intrinsic to the culture that, if they were to disappear, the culture would be irreversibly altered. Thus, the usage of the keystone concept by researchers working within the social-ecological system paradigm is not new. However, this paper contends that a "social-ecological keystone" is actually a specific biocultural element (i.e., relationship); further, that social-ecological keystones can be quantitatively determined utilizing the theoretical concepts previously established by Winter and McClatchey [16,17].

A relevant concept here is 'functional group'. In ecological subsystems, functional groups are used to lump together species with similar roles—such as top predator, generalist pollinator, nitrogen fixer, and so on. In social-ecological systems, members of functional groups would be biocultural relationships—such as applying herbal medicine, imbibing fermented sugars, weaving baskets, farming complex carbohydrates, and so on. This paper, therefore, refers to "biocultural functional groups", and has identified the QCU as a unit of measure for the biocultural elements within them.

Based in part on Davic's [31] definition of keystone species, this paper submits that a social-ecological keystone is a strongly interacting biocultural element within its functional group, whose top-down effect on biocultural diversity is large relative to all elements within the system. Biocultural elements, and therefore social-ecological keystones, are neither individual taxa nor individual practices, but rather the linked taxa-practice unit. If a social-ecological keystone is severely disabled (or goes extinct), then there would be no substitute without seriously compromising the structure and function of the system—possibly inducing a regime shift. Correspondingly, if a social-ecological keystone were to go extinct it would cause a cascading effect of secondary extinctions of biocultural elements, and subsequently affect the structure of both the ecological and social subsystems. The theories and methods explored in this manuscript could be used to document and understand such processes.

#### *2.3. The Influence of Crop Diversity and Cropping Systems on the Structure of the Hawaiian Social-Ecological System*

Functional groups associated with agriculture often determine the structure and function of social-ecological systems managed by agrarian societies because agriculture often dictates the form and hierarchy of the social subsystem, and is the foundation of the economy and politics within the social subsystem [36], which subsequently influences the management of the ecological subsystem. The central role of agriculture in cultural development, political complexity, material economy, and social norms of the Hawaiian social-ecological system has been well explored (see Lincoln and Vitousek [37] for a broad overview and detailed reference list). Based on these concepts, this paper holds the assumption that agriculture is a key biocultural functional group within social-ecological systems managed by agrarian societies.

Hawaiian agriculture manifested in highly diverse forms in the Hawaiian social-ecological system. The most salient division often used in anthropological discussion is the difference between wet (flooded-field, irrigated) and dry (rain-fed) agriculture [38,39]. The state environmental factors that drove the opportunities and constraints of agricultural development are highly organized, but not evenly distributed, in the Hawaiian archipelago. The distribution of geological age and rainfall, which subsequently drive soil fertility and land topography, created a spectrum of agricultural opportunties that spanned almost exclusively rain-fed opportunities on the young island of Hawai'i, to almost exclusively flooded-field opporunities on the oldest of the high islands, Kaua'i [27]. These agricultural forms had different requirements (e.g., levels of organization, infrastructural investment) and offered different effects (e.g., levels of resilience, economic surplus).

In brief, flooded-field agriculture was investment intensive, but low maintainenance while offering low vulnerability to both natural and social perturbances. Consequently, flooded-field

agriculture supported socio-political systems on Kaua'i with more diversified social roles and stronger political stability. Conversely, the more labor intensive and vulnerable dryland agricultural systems of Hawai'i Island manifested socio-political systems that were more volatile, saw frequent regime shifts between political leaders, and spawned predatory political ambitions [28]. This implies the existence of "alternative regime states" within the same social-ecological system—a more resilient one built around flooded-field systems of agriculture, and a more vulnerable one built around rain-fed systems of agriculture. These alternative regime states existed even though they are based on the same biocultural elements in the same social-ecological system. The manifestations of the economy and the political systems differed due, at least in part, to the relative and absolute areas of the agricultural systems.

#### *2.4. Social-Ecological System Resilience and the Role of Redundant Components*

Resilience [40,41] is a measure of a system's relative ability to absorb disturbance without changing into a different state (i.e., regime shift), such as a different biological community with different ecosystem services [35]. Biological diversity has been shown to be a key factor in the resilience of ecological subsystems [8,42] because it helps to maintain desired states of dynamic regimes in the face of uncertainty and surprise, and also plays a major role in renewing and reorganizing those systems after disturbance [35]. Maintaining such desired states of dynamic regimes (i.e., "stable states") is more specifically dependent on "response diversity", which is the diversity of responses to environmental change among species that contribute to the same function in the system [43]. Therefore, the more nuanced value of diversity is the increased redundancy within functional groups [44]. Such 'functional diversity' refers to the number of species that perform the same function; if a member of a functional group were to be lost (either temporarily or permanently) via a disturbance event, then its function could be replaced by another species. Ecological systems with high response diversity increase the likelihood for reorganization and renewal into a desired state after disturbance [43]; and are, therefore, more resilient. If a set of functionally redundant species does not exhibit any response diversity, then they do not contribute to system resilience [35]. A loss of biodiversity—more importantly a loss of functional diversity and response diversity—is a major contributing factor in regime shifts [35,45]. In the context of ecological subsystems, regime shifts imply a shift in services which that subsystem provides to the socio-cultural subsystem, and are largely irreversible [35].

Throughout this paper we use the term, 'redundant component' to classify a biocultural element of a functional group that could be substituted if removed—that is, a component that is not a keystone. In accordance with systems theory [32], maintaining resilience in social-ecological systems relies on the management of biocultural diversity, including the seemingly redundant components of these systems. Such "social-ecological redundants" contrary to keystones, may not contribute significantly to the structure and function of social-ecological systems individually, however, if they represent response diversity, then such components may contribute significantly to the resilience of social-ecological systems.

We use the QCU (Figure 1) as a unit of measure to quantitatively classify redundant components of social-ecological systems within biocultural functional groups. This paper contends that biocultural functional redundancy exists in instances where a subunit of the QCU (either biological taxa or sociocultural practice) lost via a disturbance or other event can be easily transferred to other corresponding subunits which would ensure the persistence of that biocultural functional group. For example, using the biocultural functional group of "weaving a plant-based fiber", a culture may have five taxa which it uses to weave. If one of the five taxa were to go extinct, the sociocultural practice could continue because of the functional redundancy that exists in that biocultural functional group.

#### *2.5. Theoretical Assumptions*

This manuscript builds off of four theoretical assumptions in regards to the keystone concept:


#### **3. Testing the Keystone Theory in Social-Ecological Systems**

#### *The Hawaiian Social-Ecological System as a Model*

There are countless social-ecological systems that could be chosen from around the world to model the theories explored in this paper, but in order to test the conceptual validity of these theories a model social-ecological system is ideal. High islands are excellent examples to discuss system function becuase they are big enough to possess all the biological, ecological, chemical, and physical processes needed for complete system study, yet small enough that the complexity of such systems is perceivable [46,47]. Kirch [19] outlines how both the social and ecological factors of Hawai'i, in particular, lend themselves to serving as a model system for biocultural understanding. State factors influencing ecology are either held constant (e.g., parent material, biota) or are extremely broad yet well organized (e.g., climate, age, topography). Simultaneously, social factors lend themselves to study due to the short timeframe of human colonization, the extreme isolation, and the high level of socio-political complexity achieved.

To exemplify the theories expressed above, we focus on the Hawaiian social-ecological system. At the point of contact with Europeans in 1778, this highly modified system was being managed to maintain a human population on the order of 300,000–800,000 people [48,49]. Furthermore, anthropological discussion has argued that Hawai'i developed high levels of socio-political heirarchy manifested in complex systems of land tenure, resource mangement, and taxation, describing Hawai'i as one of nine civilizations to have independently developed into a state system [50]. The Hawaiian archipelago, therefore, represents an island-bound and intensively managed social-ecological system, with a population size and social structure that makes it comparable to the contemporary period.

#### **4. Methodology**

As this is an examination of the structure and function of a system which existed in the past, historical records and archaeological evidence were used to supplement actual observations. The methods described below were used to quantify biocultural diversity, identify key functional groups within systems, as well as quantitatively classify keystone components and redundant components that constitute these functional groups.

#### *4.1. Quantification of Biocultural Diversity*

This research considers a unit of biocultural diversity—referred to as the Quantum Co-evolutionary Unit (QCU)—as any one of the human needs, as described by Max-Neef et al. [51,52], which has a satisfier that comes from within the realm of biodiversity. QCUs were generally assessed from the standpoint of viewing them as components within functional groups that are embedded in the entire system, rather than as individual components standing alone within the context of the entire system.

#### *4.2. Assessing Biocultural Functional Groups in Social-Ecological Systems*

It is the assumption of this paper that within an agrarian society—such as that associated with the Hawaiian social-ecological system—social-ecological keystones can found within the biocultural functional groups associated with agriculture. Biocultural functional groups were identified by reviewing the seminal literature on ancient agricultural and associated practices [53–59]. From this literature review, commonly occurring categories of agricultural function clearly stood out and were identified to be used to define the biocultural fuctional groups. This literature, while select, forms the broad basis for vast majority of subsequent publications in traditional Hawaiian agriculture.

Once the biocultural functional groups associated with agriculture were determined, their components were then quantified to classify them as a keystone component or a redundant component within each respective functional group. As we attempt to examine a time period in the past, data from historical records and publications were used. Handy et al. [54] is a comprehensively researched tome on ancient Hawaiian agriculture that was produced by the B.P. Bishop Museum in collaboration with anthropologists and a highly-respected, well-published, native-speaking Hawaiian ethnographer; it is widely considered the authoritative volume regarding Hawaiian agriculture. For the purposes of this research, the number of written lines dedicated to each biocultural relationship was used as a proxy for the relative importance of that element (see Table S1). Other sources of knowledge in this area exist [53–59], but those works were not systematically approached from the standpoint of plant-based biocultural relationships as was the work of Handy et al. [54]. The number of lines, therefore, provides the numerical quantification of each element subsequently used to calculate the indexes as described below. While this is an ad hoc approach utilizing only a single, albeit substantial, volume on Hawaiian agriculture, we employ this method to demonstrate the application of the QCU concept in a meaningful way and to provide a starting point from which more intesive analyses can be done in the future.

#### *4.3. Quantitatively Classifying Keystone and Redundant Components*

As a means to quantify the relative contribution of elements within functional groups, Davic [31] suggests a variety of community indices could be applied, and uses the dominance index (DI) [60] to determine importance of individual elements within a group:

$$DI\_{BP} = (n\_{\text{max}}/N)$$

where *nmax* represents the number of individuals of the most abundant element, and *N* is the total number of individuals within the functional group as a whole. In cases where more than one potential keystone is identified within a functional group Davic [31] advocates the community dominance index (CDI) of McNaughton [61]:

$$CDI = (n\_1 + n\_2/)N$$

such that *n*<sup>1</sup> and *n*<sup>2</sup> represent the frequency of the two most abundant species within a functional group. Other ecological measures of dominance may also provide quantitative insights to the relative importance of individual elements to a group. Commonly applied in the field of ecology is the Simpson Domination Index [62]:

$$DI\_S = \sum (m\_i/N)^2$$

where *ni* is the population of each species, and *N* is the total population. The Simpson method gives greater consideration to diversity within a system; in contrast the Berger-Parker approach [60] does not account for the number of species, but only the total population of the system. However, the Simpson method falls short in that it can only be applied to characterize groups and not individual elements. Our analysis, therefore, applied the Simpson method to the functional groups to provide a more conservative assessment of domination within each group. We then applied the Berger-Parker equation [60] to quantify each species' dominance within the functional groups. Because we applied these indexes to both the groups and their elements, we refer to *domination of* to characterize the inequality within a group, and to *dominance by* to describe the contribution of individual elements to a group. For the purposes of this paper, we have determined that a value of >0.5 for either DIBP or CDI calculations would result in a classification of a biocultural element as a social-ecological keystone, and a value of <0.5 would result in a classification of a biocultural element as a social-ecological redundant.

#### **5. Results**

A review of the literature regarding Hawaiian agricultural practices [53–59] yielded three classes of crop systems and eighteen biocultural functional groups that span a range of functions, incuding food production, material resource production, and spiritual/religious practice. Dominance *by* and domination *of* three sets of cropping systems (Tables 1 and 2) and the eighteen biocultural functional groups (Table 3) was calculated.

**Table 1.** Dominance Index (DI) as calculated for each of the systems of growing crops in the Hawaiian social-ecological system, as documented by Handy et al. [54].


**Table 2.** Dominance of crops within three major classes of agricultural systems that existed within the Hawaiian social-ecological system.


**Table 3.** The eighteen biocultural functional groups that embody Hawaiian agriculture traditions as identified in the Handy et al. [54] tome on the topic, dominance index (DI) for each, and associated crop species.



**Table 3.** *Cont.*

#### **6. Analysis**

In examining the dominance of cropping system forms of Hawaiian agriculture (Table 1), 'rain-fed' was the dominant crop system (0.44), followed by agroforestry (0.29), and then flooded-field systems (0.27). However, the split was relatively level, and the Simpson Domination Index (DIS) for Hawaiian Cropping Systems based on these relative abundances yields a moderate value of 0.35. This indicates that a severe loss of any one of the three systems would substantially impact Hawaiian agriculture. Conversely, the domination of each the three cropping systems by their crop components varied significantly, indicating wildly different levels of reliance on critical species. The agroforestry systems, with a very low value of 0.11, could easily absorb the loss of any species, including its dominant species. At the opposite end of the spectrum, flooded-field agriculture with an extremely high value of 0.73 would likely catastrophically fail if its most abundant species were to be removed. Rain-fed agriculture, with a more moderate value of 0.26, would likely struggle but adapt to a removal of the dominant species.

Examining the dominance of crops within these agricultural systems, *kalo* (taro, *Colocasia esculenta*) cultivation was either dominant or co-dominant in all three systems (Table 2). Within flooded-field agriculture *kalo* was highly dominant (DIBP = 0.85), a value that classifies it as a keystone component. Within rain-fed systems *kalo* cultivation was only slightly more dominant (0.352) than *'uala* (sweet potato, *Ipomoea batatas*) cultivation (0.349), indicating clear co-dominance. The CDI value of 0.7 classifies the cultivation of these species as a keystone component, which indicates that rain-fed cultivation would likely collapse without either of the two co-dominant species. Within agroforestry systems *kalo* cultivation was also co-dominant (0.18) with *kukui* cultivation (0.19), and was the dominant among non-canopy species. The moderate CDI value of 0.37 suggests that cultivation of either does not play a keystone role, suggesting that agroforestry systems would adapt to the loss of either or both of the co-dominant species.

In examining the eighteen biocultural functional groups (Table 3), cultivating a complex carbohydrate as a food source displayed the highest level of dominance. Other important functional groups (>5% DIBP) include religious and ceremonial associations, wood, famine food, thatching, and medicinal uses. *Kalo* again demonstrates significant importance: it is the dominant species of the dominant functional group, in 43% of the important functional groups, and in 33% of all functional groups. Furthermore, it contributes to more functional groups (61%) than any other species.

An additional finding indicates a relationship between dominance *of* functional groups within Hawaiian social-ecological system, and how dominated *by* their species assemblage those functional groups are (Figure 4). This was a highly significant relationship (r2 0.39, *p* 0.006) described by a log-log function (log(y) = 4.09 − 0.39 × log(x); var(x) = 28.4; var(y) = 903.6; cov[x, y] = −0.5056). Although perhaps intuitive, this indicates that functional groups that make less significant contributions to the social-ecological system are more likely to rely on a smaller assemblage of species. This relationship is important because it indicates that essential functions of a biocultural system will tend to not develop an overly dominant species, likely resulting in increased resilience within the social-ecological system due to functional and responce diversity. In the case of Hawai'i, the most dominant functional group—cultivation of complex carbohydrates—has a relatively high DIS value, indicating a higher reliance on *kalo* than might be expected for such an important function.

**Figure 4.** As importance of function groups pertaining to agriculture within the Hawaiian social-ecological systems decreases, the Domination Index within that group tends to increase along a log-log relationship. This indicates the less significant a functional group is, the more heavily it can rely on a smaller species assemblage.

#### **7. Discussion**
