3.1. The SE approach’s potential responses

Oceanic islands are often characterized by remarkable coadaptation among resident species due to strong isolation effects on evolutionary histories (Carlquist Reference Carlquist1974). So, the SE theory seems well disposed to offer a meaningful functional description of A–B–C, especially Millstein (Reference Millstein2020) modified account since it integrates Thompson (Reference Thompson2005) Geographic Mosaic Theory of Coevolution (GMTC). The GMTC explains the coadaptation that emerges between proximate populations over evolutionary timescales. Populations that happen to coexist in the same geographical area jury-rig their ecological interactions to produce SE functions. But how might the SE theory fit T’s arrival into its functional description of A–B–C?

Established island populations sometimes lose their ability to compete against conspecifics if they are highly isolated. Wilson (Reference Wilson1961) taxon cycle concept describes the general replacement procedure. His work on Melanesian ants revealed that established island populations thrived for several generations but were outcompeted as soon as a novel competitor arrived on the island.Footnote ³ However, it is not necessarily the case that T replaces A, B, or C. Instead, i₁ might be within T’s seasonal migratory range when i₁’s productivity supports more populations (MacArthur Reference MacArthur1969). If so, T’s seasonal arrival could affect the coadaptation dynamics of A–B–C, albeit to a lesser degree.

In a taxon cycle scenario, T probably does not possess an SE function with respect to A–B–C since T lacks a historical connection to the evolutionary process that generated the SE functions possessed by A, B, and C. But the substitutability of T for the replaced population raises a question in regard to the status of the other populations that remain on i₁. Does the loss of their evolutionary partner affect their SE functions? The question challenges the SE theory’s commitment to the idea that coadaptation is a communal process. It seems incorrect to revise the SE functions ascribed to the remaining populations even though one member is lost from the original functional description. The evolutionary processes remain operative as long as the populations continue to interact.

The seasonal migration scenario is a different story. It might be said that T possesses an SE function of increased flight duration (Amundson and Lauder Reference Amundson and Lauder1994). Specific morphological traits aside, greater vagility is an evolutionary trait that increases T’s ecological fitness (Holt Reference Holt, Robert and Schluter1993). But this interpretation is vulnerable to the liberality criterion. T possesses its SE function irrespective of A–B–C. T’s SE function operates over a spatial scale larger than i₁. Hence, T’s SE function is not exclusive to A–B–C. The scalar incompatibility, in turn, exacerbates the problem. If T belongs to the SE theory’s functional description of A–B–C, then where is the precise stopping point? Why not include the populations that T interacts with on other islands, like i₂? In most cases the SE theorist makes a thoughtful decision about the appropriate stopping point (in space and time). But such decisions defy the liberality criterion to pursue a better understanding of the complex phenomenon as defined by the SE theorist’s research aims.

3.2. The SC approach’s potential responses

The SC account requires a designated systemic capacity before it is testable. The hypothetical case was inspired by Diamond (Reference Diamond, Martin and Jared1975) research on assembly rules for bird guilds located in the South Pacific. Diamond’s study discovered evidence for MacArthur (Reference MacArthur1972) concept of diffuse competition (i.e., the systematic exclusion of outside competitors by the established members of a community due to their combined niche structure).Footnote ⁴ So, let A–B–C represent a configuration on i₁ that possesses the systemic capacity of competitive exclusion through diffuse competition. A–B–C’s capacity to exclude species is diminished after a disturbance as the alteration to i₁’s environmental conditions (e.g., habitat loss, reduction in resources, etc.) stresses the ecological interactions that hold A–B–C together. T’s invasion of i₁ is highly probable at this time, and the configuration on i₁ transforms into A–B–C–T. A–B–C–T possesses the capacity to resist invaders due to its greater niche saturation. Simultaneously, T returns the environmental conditions on i₁ to their pre-disturbance state via subsidy effects, like seed dispersal (Cumming and Norberg Reference Cumming, Norberg, Norberg and Graeme2008). A, B, and C eventually reestablish ecological interactions strong enough to exclude T. All things considered, is it the case that T possesses an SC function with respect to A–B–C’s systemic capacity to enact competitive exclusion?

I envision four ways for an SC theorist to respond. The first is to deny that T possesses an SC function given that the systemic capacity of A–B–C tends to exclude T when it is at full strength. Ulanowicz (Reference Ulanowicz1997) ascendency model posits a similar claim. An ecosystem may support certain species early in its development because the ecological interactions are weak, but all ecosystems tend towards a state of maximum organization. A teleological perspective, like Ulanowicz (Reference Ulanowicz1990), could claim that any species filtered out during an ecosystem’s ontogenesis does not belong to the ecosystem proper. In truth, this is an underdeveloped area of the ecological function discussion. It is not clear if some threshold separates functions from nonfunctions. Implementation of an expected threshold is prudent since no functional description fully exhausts the causal complexity of a natural system (Wimsatt Reference Wimsatt1972). However, such a practice is antithetical to the liberality criterion because elements of the ecosystem that are known to possess an SC function (to some degree) are intentionally omitted from the functional description.

A second way that an SC theorist could respond to the hypothetical case is to emphasize the dispositional nature of SC functions. Perhaps T only possesses an SC function in relation to A–B–C if the interactions between A, B, and C are weakened by an exogeneous disturbance. Prima facie, this looks like a safe bet since the definition of SC function refers to dispositions. A–B–C is the appropriate functional description under ideal conditions, but explanations require flexibility to safeguard consistency when confronted with nonideal cases. But reference to dispositions becomes pernicious if the boundaries of the ecological unit are not well defined (as in the hypothetical case). Species exist all over the planet that, if introduced, would possess an SC function with respect to A–B–C. Despite the fact that T is more proximate and, as a result, more likely to interact with A–B–C, it would be impossible to establish criteria for dispositional SC functions that do not beg the question, why these conditions? Thus, the introduction of dispositional SC functions engenders more conceptual inconsistencies that contravene the liberality criterion.

Third, an SC theorist could accept that T possesses an SC function. As I previously stated, Odenbaugh (Reference Odenbaugh and Hazzlett2010, Reference Odenbaugh2019) argues for the SC theory given its ability to incorporate various abiotic elements, like lightning strikes and volcanic eruptions, into functional descriptions of systemic capacities, like nitrogen fixation. Similarly, moderate disturbances (e.g., hurricanes) are regularly incorporated into island dynamics. Patch dynamics theory (Pickett and White Reference Pickett and White1985), hierarchy theory (O’Neill et al. Reference O’Neill, DeAngelis, Waide and Allen1986), and resilience theory (Scheffer Reference Scheffer2009) all support this interpretation. So, it appears reasonable to attribute an SC function to T if the abiotic elements that prompt T’s dispersal from i₂ are part of the functional description, too. But this interpretation is also imperfect. Two different systemic capacities are conflated. The original systemic capacity was competitive exclusion via diffuse competition, which belongs solely to the ecological interactions between A, B, and C. If the disturbance is incorporated into the functional description, then the systemic capacity is more akin to adaptive capacity, a property associated with resilience (Sundstrom et al. Reference Sundstrom, Allen, Angeler, Lance, Craig and Garmestani2022). Competitive exclusion is strongest during the conservation phase of an ecosystem’s adaptive cycle—a period marked by low adaptability and low resilience due to the increased rigidity of the internal interactions—but T arrives during earlier post-disturbance phases when ecological interactions are weak (Holling and Gunderson Reference Holling, Gunderson, Lance and Holling2002).Footnote ⁵ Consequently, it is more accurate to say that T possesses a PE function as opposed to an SC function.

The simplest solution, though, is to ignore the liberality criterion. The flexibility of the SC theory to accommodate diverse research interests is a distinct virtue that Odenbaugh (Reference Odenbaugh and Hazzlett2010, Reference Odenbaugh2019) rightfully emphasizes. Nothing prevents a qualified functional description of A–B–C where an SC function is attributed to T under specific contexts. However, the practice would certainly defy the liberality criterion. The ecological dynamics are not discrete enough to meet the expectations placed on functional descriptions by the liberality criterion. Ultimately, I argue that a functional description should be evaluated based on its explanatory advantages rather than its adherence to the liberality criterion. And the SC theory clearly provides a number of explanatory advantages.

3.3. The OT approach’s potential responses

The hypothetical case tests the OT theory’s logical commitment to system closure. On the OT theory, A, B, and C possess OT functions due to each’s ability to circulate structure-inducing resources (e.g., biomass) in an autocatalytic way that promotes A–B–C’s self-maintenance as an integrated unit. Ulanowicz (Reference Ulanowicz1986, Reference Ulanowicz1997) ascendency model is a network analysis approach that is highly compatible with the OT theory on this point. The ascendency model utilizes information theory to calculate ecosystem connectedness. With the additional quantitative dimension (i.e., information theory), a functional description of A–B–C as a collection of OT functions appears practical, scientifically informative, and reasonable as long as A–B–C forms a closed causal loop. But no perfectly homeostatic systems exist in nature, and Nunes-Neto et al. (Reference Nunes-Neto, Moreno and El-Hani2014) admit as much. An ecosystem closed at one scale is open at the one above (Wiens Reference Wiens1989; Holt Reference Holt, Gary, Mary and Gary2004). So, how does the OT theory accommodate T’s arrival on i₁?

The solution is for the OT theory to revise its idealization of a causal loop. The movements of energy and matter that increase system connectedness do not form a deterministic pattern. The movements from one compartment (e.g., A, B, and C) to another within the network are probabilistic. Organizational structure emerges when the probabilities of interactions all near 1 (i.e., certain). Plenty of errancy exists throughout a network, though. Errancy, or overhead, is essential to organizational integrity because it prevents the overconnectedness that induces system fragility (Ulanowciz Reference Ulanowicz1997). In terms of the hypothetical case, an OT theorist could claim that T possesses an OT function once it establishes probabilistic relations with other compartments that promote the ecosystem’s self-maintenance to an appreciable degree (figure 2). What probability value constitutes an appreciable degree is a matter of debate, but the logical consistency of the OT theory is preserved and the liberality criterion is seemingly satisfied.

Figure 2.

Hypothetical organization diagrams of A–B–C at t1 (prior to T’s arrival) and A–B–C–T at t2 (after T’s arrival). From Ulanowicz’s (1997) ascendency model, arrows represent the flows of information between compartments. Information quantifies flows of structure-inducing energy or matter. Values correspond to probabilities between 0 and 1. Dashed arrows represent errancies (i.e., overhead). Ulanowicz’s (1995, 653) simplest example is the Cone Spring ecosystem, which includes compartments for plants, detritus, bacteria, detritovores, and carnivores.

Although the proposed solution seems plausible enough, it is inadequate. Two populations of T must first be distinguished to clarify the inadequacy. Let T₁ represent the population of T that immigrates to i₁, and let T₂ represent the population of T that remains on i₂. Some vagile species, like T, have a high enough dispersal rate to overcome a high extinction rate. The result is a peculiar situation where a species’ fundamental niche is smaller than its realized niche (Pulliam Reference Pulliam1988). In effect, the species contributes to the organization of the ecosystem without reciprocal flows that embed it into the system’s self-maintaining web of interactions (figure 3). In ecological terms, T₂ is a source population that sustains a sink population, T₁ (Whittaker Reference Whittaker1998). Therefore, the conditions that define OT functions are faced with a choice between two unattractive options. Either T₂ does not possess an OT function since it lacks the trademark closure that is central to the OT theory, which appears dubious if the organizational integrity of A–B–C exhibits some dependency on the inputs from T₂. Or T₂ does possess an OT function, and the notion of system closure needs revision as it is scaled up to the level of ecosystems (Lean Reference Lean2021).

Figure 3.

A diagram that represents the organizational structure between the two islands, i1 and i2. D and E are species that belong to the D–T–E ecosystem on i2. T1 and T2 indicate the populations that are located on i1 and i2 respectively. Ulanowicz (1986) suggests a similar approach to handle spatial heterogeneity in an earlier formulation of the ascendency model.

Nunes-Neto et al. opt for the second of the two options, but their revisions are insufficient to satisfy the liberality criterion. They apply hierarchy theory to refine their conception of a closure of constraints. The logic of their account relies on Simon (Reference Simon1962) characterization of systems as nearly decomposable organizational structures. Put simply, the interactions between system parts produce emergent organizational structure (i.e., the whole is greater than the sum of the parts). But the organizational structure never achieves homeostasis. Instead, a hierarchy of loosely coupled systems regulates the organizational structure of systems through cross-scalar constraints (Simon Reference Simon and Howard1973). Nunes-Neto et al. argue (sensu Pattee Reference Pattee and Robert1972) that systems are embedded in a control hierarchy that coordinates flows of energy and matter towards perpetual self-maintenance. Lower-level agents restrict the behaviors of higher-level organizational structures, and vice versa. Therefore, T appears to constitute a constraint that entangles two levels. One level is A–B–C on i₁, and the other level is the i₁–i₂ configuration (i.e., the combination of species that belong to both i₁ and i₂ and that form a self-maintaining causal loop). So, neither T₁ nor T₂ technically possess an OT function with respect to A–B–C. Only the metapopulation T properly possesses an OT function in the context of a multi-level hierarchy of constraints.Footnote ⁶

The hierarchical construal of system closure is vulnerable to at least two criticisms. First, hierarchy theory is fundamentally incompatible with the liberality criterion. The liberality criterion is a matter of metaphysical precision, and hierarchy theory is conceived as an epistemological tool to simplify complexity (Allen and Starr Reference Allen and Starr1982; O’Neill et al. Reference O’Neill, DeAngelis, Waide and Allen1986; Allen and Hoekstra Reference Allen and Hoekstra1992; cf. Salthe Reference Salthe1985).Footnote ⁷ Organizational structure is not neatly differentiated into discrete levels (Potochnik Reference Potochnik, Brooks, DiFrisco and Wimsatt2021). Second, the hierarchical construal is committed to the unintuitive idea that a member of T₂ possesses an OT function in relation to A–B–C even though it never disperses to i₁. The idea is equally problematic if the analysis focuses on the members of T₁. Some members of T₁ will not contribute to the self-maintenance of A–B–C in the same manner or to the same degree. So, do all members of T₁ have to be divided into individual compartments to avert the misattribution of OT functions? If so, that would be an impractical workaround just to satisfy the liberality criterion.

3.4. The PE Approach’s Potential Responses

Dussault and Bouchard (Reference Dussault and Bouchard2017) posit the PE theory as an intermediate account that avoids the excessive liberality of the SC theory and the excessive restrictiveness of the OT theory. As previously shown, one of the SC theory’s responses recommends a view that is compatible with the PE theory, and the OT theory fails to include ecological agents that originate from outside an ecosystem’s set boundaries. But does the PE theory successfully describe the hypothetical case? I argue that the PE theory is a strong candidate, but it succumbs to the liberality criterion, too.

Since the PE theory’s principles are derived from Holling (Reference Holling1973, Reference Holling and Peter1996) original resilience concept, let A–B–C represent a self-organizing ecosystem with high ecological resilience (i.e., an ability to absorb exogenous disturbances to remain within the same qualitatively distinct stability regime). If A–B–C possesses strong internal feedback dynamics, then T’s arrival will likely have a negligible effect on the dominant processes. Walker (Reference Walker1995) refers to species like T as passengers that are entrained by the dominant processes enacted by drivers (i.e., A, B, and C). The passenger–driver designation effectively differentiates T’s weaker PE function from the stronger PE functions that hold A, B, and C together. Then, T’s functional group and functional response roles can be added as supplemental details to the more definitive functional description of A–B–C.

The PE theory also provides even greater ontogenetic precision in response to the hypothetical case. If T arrives after a stochastic dispersal event, then it probably possesses a minor PE function as a passenger species with respect to A–B–C. T would contribute only slightly to A–B–C’s persistence. But if the arrival of T to i₁ coincides with a moderate disturbance, then T’s PE function is likely more noteworthy. Vagile species perform PE functions as mobile links to promote ecosystem recovery. Mobile links make ecological contributions as resources linkers (e.g., nutrient transportation), genetic linkers (e.g., seed dispersion), and process linkers (e.g., trophic interaction; Nyström and Folke Reference Nystrӧm and Folke2001; Lundberg and Moberg Reference Lundberg and Moberg2003). The significance of mobile links reaches its peak during the reorganization and exploitation phases of the adaptive cycle. As the ecosystem progresses towards the conservation phase, dominant processes reemerge (Clark Reference Clark2024). Resilience theorists associate the PE functions that are performed by mobile links with spatial resilience rather than the traditional interpretation of ecological resilience that primarily concerns internal self-organizing feedbacks (Cumming Reference Cumming2011). Thus, the PE theory seems to outperform the alternative frameworks in its ability to situate T’s PE function within the ontogenetic narrative of A–B–C.

Despite the PE theory’s superior ability to differentiate T’s PE function, its response to the hypothetical case remains deficient. Dussault and Bouchard’s account overlooks two important details about resilience. First, most PE functions are context sensitive. Obviously, a species can perform more than one PE function at a time, but the significance of each PE function will often vary from ecosystem to ecosystem. For example, B’s critical PE function in A–B–C might be being prey, whereas its critical PE function in B–D–E (on another island) is being a grazer, especially if the two ecosystems are located in zones with characteristically different stability regimes (e.g., grassland versus montane forest). Does B possess the whole assortment of its PE functions at all locations, or only the ones relevant to the ecosystem under consideration? Even though the species is the same, the functional description fails to satisfy the liberality criterion if it includes more PE functions than actually exist in a given context.

Morrow (Reference Morrow2023) counterfactual account offers a way to respond to this first issue. On this view, B possesses a PE function insofar as it would perform the same PE function regardless of the current stability regime of the ecosystem under consideration. In response to the hypothetical case, T possesses a PE function as long as T performs the same PE function (to some degree) in deserts, forests, tundra, and so on. Morrow’s counterfactual account prevents an explosion of PE functions, but, at the same time, it invites a similar T₁–T₂ problem as before. T₁’s most critical PE function with respect to A–B–C is being a post-disturbance mobile link. But the mobile link PE function does not apply to all members of T₂. Some members of T₂ never disperse after a disturbance, yet all members of T₁ originate from the T₂ population. Moreover, several generations might pass between moderate disturbance events (Holling Reference Holling2001). So, it is unclear if T₂ rightfully belongs to the functional description of A–B–C.

The second neglected detail concerns adaptive capacity. An ecosystem that lacks sufficient adaptive capacity is liable to undergo transformation from one stability regime to another after a moderate disturbance (Allen and Holling Reference Allen and Holling2010). If an ecosystem possesses sufficient adaptive capacity, then it innovates via processes of internal reorganization to remain in the same stability regime (Sundstrom et al. Reference Sundstrom, Allen, Angeler, Lance, Craig and Garmestani2022). Innovation complicates the attribution of PE functions because the ecosystem persists but some of its component populations, which possess PE functions, are replaced. Imagine that T develops a PE function to replace B in A–B–C. The PE theory assigns PE functions relative to the persistent ecosystem, so A–B–C and A–T–C are virtually functional equivalents as long as the dominant causal processes have not collapsed and restructured. How does the PE theory explain B’s possession of a PE function prior to T’s arrival and its lack of a PE function after its replacement if the ecosystem never switches stability regimes? Does B somehow belong to the functional description of A–T–C? Although this line of questioning appears troublesome for the PE theory, it is only troublesome if the liberality criterion serves as the chief measure of the PE theory’s adequacy.