Integrating adaptation pathways and Ostrom’s framework for sustainable governance of social-ecological systems in a changing world

Objective and structure of the article

Building on these theoretical foundations, we aim to integrate Ostrom’s frameworks with mathematical methods to enhance the design of nested DAPP maps and deepen the understanding of complex SES adaptations across multiple levels of organization. The methodology section elaborates on the general formalism, detailing the steps and mathematical links between rule clustering at different levels for the IADF, SESF, CISF, and DAPP.

We apply this method to an agro-ecological landscape characterized by species-rich hedgerow networks that provide a bundle of ES to the local community. Our case study focuses on two archetypal SES—peri-urban and rural—each defined by distinct MCA visions of ES needs. We also account for variations in hedgerow height and plant species richness, which are differentially influenced by human management and climate change, and in turn, affect the dynamic delivery of ES in our model. The resulting DAPP maps highlight the adaptive pathways required to address the challenges of climate change, particularly drought stress, on hedgerow functionality. These maps reveal nested levels of viable adaptation and capture differences in SES archetypes under varying climate stress scenarios.

Finally, we identify key indicators that elucidate the primary drivers influencing DAPP map variations and adaptation outcomes, offering insights into the complex interplay between nested human management, ecosystem functionality, and climate change.

Step 1.1. Definition of the 1^st tier action set

For the 1^st tier, we used the SESF version developed by McGinnis & Ostrom (2014), emphasizing the generalization from users to actors attributes. As such, we defined U as a set of eight possible sub-sets of actions targeting different elements of the SES, such as U = {U_S, U_GS, U_RS, U_RU, U_GS, U_A, U_I, U_O} (see Table 1 for definitions of subsets).

Step 1.2. Definition of the 2^nd tier action set

The 1^st tier action set was then decomposed to emphasize a 2^nd tier of possible action sets. For instance $U_S\in U$ was defined as U_S = {U_S2, U_S3, U_S4, U_S5, U_S6, U_S7, U_S8, U_S9} as per Table 1, emphasizing the possible actions involving various external elements impacting/ed on/by the SES. Some second tier attributes were modified using Vogt et al.’s (2015) SESF version, in order to better integrate ecological and ES attributes as possible targets of adaptation (see Table 1). We particularly transformed its 2^nd tier attribute “externalities to other SES” (O3) into a 3^rd tier action (see step 1.3) to emphasize the role of ecological resource infrastructures and associated species.

Step 1.3. Definition of the 3^rd tier action set

We further introduced a 3^rd tier action subset in anticipation of the integration of the action sets into the CISF (step 2). For instance, we subdivided certain 2^nd tier attributes (see action sets in Table 1: U_S1:U_S3, U_RS4, U_RU1, U_RU3, U_GS2:U_GS10, U_A1:U_A9, U_I2:U_I10, U_O1) into three new 3^rd tier attributes to emphasize the fact that actions can target different roles attributed to actors (A in Table 1), to infrastructures from the resource and governance systems (RS, GS), interactions (I) and outcomes (O). The 3^rd tier action set U emphasized the three following roles:

(i) Resource exploitation role (E) attributed to exploiting actors ( $U_{E:A_2}$), social infrastructures (e.g., norms and social capital, $U_{E:A_6}$), of institutional infrastructures (e.g., rules-in use, strategies: $U_{E:G{S}_1}$ to $U_{E:G{S}_{10}}$) and of physical infrastructures (such as supply chains or exploiting technologies, $U_{E:S_7}$). These attributes involve various social-ecological interactions ( $U_{E:I_1}$ to $U_{E:I_{10}}$) associated with the hedgerows’ resource appropriation, provisioning, production, distribution/supply (chain), transformation, consumption/use and monitoring of own cost-effectiveness. They also involve various resource outcomes ( $U_{E:O_1}$ → $U_{E:O_3}$) in relation with the production of the desired ES. These attributes can all be related with the sustainable dimension of the resource utilization, provided they solely benefit from utilitarian objectives.

(ii) Resource Conservation role (C) (3^rd tier action set noted e.g., $U_{C:A_1}$) is attributed to actors and infrastructures involved in supporting, maintaining, and monitoring resource systems to uphold broader societal and ecological values. The C-role often encompasses resource management driven by intrinsic ethical or aesthetic motivations—such as valuing life for its own sake, preserving cultural heritage, or safeguarding landscape beauty. Additionally, the C-role extends to the management of ES with utilitarian benefits that go beyond the immediate resource owners. These benefits may serve local communities, national interests, or even the global population. Examples include actions to prevent wildfires and landslides that could threaten nearby villages or enhancing carbon sequestration to mitigate global climate change.

(iii) Policy-making role (P) (3^rd tier action set noted e.g., $U_{P:A_2}$) refers first to the role of support for E and/or C roles. It also refers to the role of arbitration and conflict-resolution between E and C roles, when trade-offs emerge between purely utilitarian E values and intrinsic or collective C values. Thirdly, it refers to the role of triggering adaptation actions during the DAPP process, like when changing operational, collective or constitutional arrangements.

It is important to note that SES do not necessarily possess E, C, and/or P role attributes and associated actions. For instance a resource free of humans do not have E, C and P. Furthermore, all the combinations between the three can in theory be found.

Following the same logic of defining these three roles targeted by these actions, we further specified the role that triggers these actions on the targeted role. For instance, the C-role can trigger an action targeting the economic attributes (A₂) of the E-role. Using the SESF logic, this action was encoded as $U_{C\to E:A_2}$.

Step 1.4. Definition of the 4^th tier action set

We then defined a 4^th tier action set, relative to the nested levels of adaptation initiatives operating at different time scales.

Using examples from Ostrom (1990) that were presented in the introduction, we define the adaptation actions at the level of the operational-choice arrangement (U^OCA), of collective-choice arrangement (U^KCA), of constitutional-choice arrangement (U^CCA), meta-constitutional-choice arrangement (U^MCA), etc. These levels are nested and can be attributed to any kind of roles defined in step 1.3 (cf. Table 1 for the sub-set possessing this 4^th tier attribution). For instance, ${\mathit{U}}_{\mathit{C}\to \mathit{E}:{\mathit{A}}_2}^{\mathit{O}\mathit{C}{\mathit{A}}_1\to \mathit{O}\mathit{C}{\mathit{A}}_2}$ means that the adaptation of OCA₁ into OCA₂ consists in changing the action that role C triggers on attributes A₂ of E-role. Using the same logic, we will see in step 2.2 how to define adaptation actions at other upper levels of institutional arrangements (KCA, CCA, MCA, etc.).

Step 2.1. Defining the model used for the CISF

The CISF is flexible and different model implementations can be defined. Here we defined the three interacting compartments RU, PI and PIP has representing the three interacting roles that actors and governance systems’ infrastructures possess (respectively E, C and P), as defined in step 1.3. This way, each role compartment could possess its own model of representation (as defined in Aggarwal & Anderies, 2023), set of actors and infrastructures (like in Pichancourt, 2023, 2024). Furthermore like in Muneepeerakul & Anderies (2020) or Pichancourt (2023, 2024), the same actor and infrastructure can possess multiple roles (E, C and P), whose rate of implication or interaction rate is modeled using any of the following linking action sets U_2a, U_2b, U_3a, U_3b, U_6a, U_6b from Fig. 1. For example, actors and private/shared infrastructures can simultaneously be attributed to (i) a supply chain role in E (e.g., as farmers and intermediary supply chains from farm to fork, forest harvesters with their sawmills and tracks, fishermen from the fleet to the auction house and fish market), (ii) a conservation role in C (e.g., as neighboring group of farmers in partnership with public, private or NGOs conservation agencies), and (iii) a policy or arbitration role of P (e.g., as a board member of a governing body that is buying lands and renting them to farmers, and set specific rules and granting schemes). Using this encoding we attributed multiple actions sets from the SESF to one code of action defined in the CISF (Fig. 1).

Based on this structure (cf. Fig. 1), we then model how the different roles interact with the external context (i.e., associated with action set U_S from Table 1), using any of the set action links U_7d, U_7f, U_7h. For instance, an external NGO can offer three distinct technological training schemes to increase the capacity of action of the three role compartments (i.e., U_S7 from Table 1): one for actors with exploiting roles on how to sustainably exploit their private resource R for private or club ES benefits ( U_7d = U_E:S7); another for actors with broader conservation role on how to collectively monitor or restore the state of R for broader public and common ES outcomes (U_7f = U_C:S7); and a third for actors or infrastructures with broader governing role to establishing DAPP rules at a certain level (U_7h = U_P:S7).

Step 2.2. Define adaptation actions per level of governance arrangement

In step 2.2 we use the CISF to define adaptation actions at different level of governance arrangement (i.e., OCA, KCA, CCA, MCA, etc.). Different CCAs of interest can be defined by specifying the eligibility criteria for certain roles within the CISF. This can be achieved by switching on and off specific roles as needed (see Fig. 2).

For every CCA, adaptation actions at a KCA level are modeled by switching on and of certain interactions between role compartments, leading to different coordination networks and chains of actions between actors and infrastructures, within and between roles (Fig. 3).

Finally, for every KCA, different OCA and their transition can be modeled by changing the acceptable range for the intensity or frequency of operational actions (Fig. 4).

Step 4.1. Definition of the constraint domain of satisfaction for the levels of ES

Based on Eq. (1), we can evaluate the congruence between costs and benefits for all the possible scenarios of CIS arrangements (CCA, KCA and OCA), as specified by Ostrom’s second design principle of good governance (Ostrom, 1990). To achieve this, we must respect the basic condition that the state turnover of R, such that:

(2) $${\displaystyle \frac{dR}{dt}\ge 0\Rightarrow U_{0a}+\left(U_{1a}.U_{5a^{\prime }}+U_{4b}\right)C\ge U_{7b}+U_{1b}.U_{5a}.}$$

From Eq. (2) and Fig. 2, we see that the potential resource turn-over rate (dR/dt) depends on both the intrinsic rate of increase of R (U_0a), and the conservation actions originating from either E through U_1a or from C through U_4b.

Now imagine that the E-state is defined by the level of n ecosystem services ES₁, ES₂,…, ES_n, exploited by E. The state space of R is now defined as $S_R=\left\{E{S}_1,E{S}_2,\dots ,E{S}_i,\dots ,E{S}_n\right\}\in {\mathbb{R}}^{\mathrm{n}}$. Equation (1a) would be thus ${\displaystyle \frac{dR\left(ES\right)}{dt}=\left({\displaystyle \frac{dE{S}_1}{dt},{\displaystyle \frac{dE{S}_2}{dt},\dots {\displaystyle \frac{dE{S}_n}{dt}}}}\right).}$

Population needs would be defined as viable iff the delivery of n ecosystem services (ES⁺) or disservices (ES⁻) respect the following constraints: ES⁺_i ≥ ES⁺_i,min and ES⁻_j ≤ ES⁻_j,max, where ES⁺_i,min and ES⁻_j,max represent the minimal and maximal acceptable value of ES i or j respectively associated with actors’ needs. Together for the n ES, these threshold form a constraint domain K_R, that we refer to as the satisfactory domain of R, such that $K_R=\left\{\left(E{S}_1,E{S}_2,...,E{S}_n\right)\vee E{S}_i^{min}\le E{S}_i\le E{S}_i^{max}\mathrm{\forall }i,K\in S_R\right\}$.

Step 4.2. Definition of the set of viable trajectories of resource that respect K_R

Based on the Eq. (2) and K_R, we now define robustness (or lack thereof) as the subset of the state space for which there is at least one sequence of adaptive governance action $u(.)\in A\left(T\right)fort\in \left[0,T\right]$, starting from the initial state, that robustly keeps the SES’s trajectory within K_R, for any time step t during the time horizon T. As such, and following Aubin, Bayen & Saint-Pierre’s (2011) Viable Control Theory, we state that u(.) is viable (i.e., robust¹ ) and the set of all viable u(.), is called the viability kernel $Via{b}_{K_R}$ defined as:

(3) $$Via{b}_{K_R}\left(T\right)=\left\{R\left(t=0\right)\in K_R:\mathrm{\exists }u(.),suchthat\mathrm{\forall }t\in \left[0,T\right],R\left(t\right)\in K_R\right\}.$$

In the most general case specified after Ostrom (1990), the nested sets of adaptive actions of governance changes are defined for u(t) $\in$ U^OCA $\in$ U^KCA $\in$ U^CCA $\in$ U^MCA… $\in$ U, such that:

(4) $$u(.)=\left(u^{CCA:KCA:OCA}\left(0\right),u^{CCA:KCA:OCA}\left(1\right),...,u^{CCA:KCA:OCA}\left(t\right),...,u^{CCA:KCA:OCA}\left(T\right)\right).$$

In practice, we efficiently compute $Via{b}_{K_R}$ for Eq. (1) representing the dynamics of the SES, using the Saint-Pierre backward algorithm on a discrete grid of the state space (Aubin, Bayen & Saint-Pierre, 2011).

Specification of the application example

The method was applied to a case study involving two SES sites in central France (one peri-urban and one rural), each with distinct visions and needs regarding ES, corresponding to different history and MCA. For each SES, adaptation actions were defined at the CCA and KCA levels, while OCA actions remained fixed for every KCA. Operational actions focused on managing a hedgerow network, with transitions between different hedgerow states defined by height and plant species richness (and the presence/absence of hedgerows). Since these states produced nine ES and were influenced by climate change, we compared DAPP maps across three climate stress levels for two SES.

DAPP maps were organized around nine potential scenarios of nested governance (CCA|KCA), with adaptations considered every five years over a 30-year period. This resulted in 4,782,969 (9⁷) possible governance pathways, each evaluated for viability.

With this approach, we modeled DAPP maps where, for every step, we identifed the type of nested governance arrangement (CCA, KCA and OCA). We then determined what these adaptations assumed in term of changes in the SES structure (through the CISF). We finally checked the underpinning definitions of the SES attributes (using Ostrom’s SESF) that these adaptations implied.

We provide in supplementary files details on how we performed the SESF analysis (S1), gathered ecological data to model the resource dynamics (S2), applied the methodological steps to create DAPP maps (S3) and coded the model into Gnu-Octave (Eaton et al., 2024) to produce the results (S4). The main results are summarized below, with S5 providing supplementary results.

Five-year time-step evaluation of the viability and security of governance pathways

DAPP maps presented in Fig. 5 globally confirm our expectation that keeping the same governance arrangement for 30 years (especially CCA₁, the one most frequently observed in our study site) is not predicted to be viable. They show on the contrary, that multiple adaptations are required, involving sequences of transitions between various combinations of CCA/KCA.

We decomposed the possible 30-year pathways into succession of 5-year pathway segments between two decision steps/nodes. We show that some of these segments are crossed by many unique 30-year pathway options, offering thus a broader range of future adaptation options. The darker segments on Fig. 5 seem less sensitive to an increase in climate stress level (0, 1, 2), but are sensitive to change in the SES context (peri-urban, rural).

The diversity of viable pathway segments and transitions options also changed with the SES type. More specifically, peri-urban SES (Figs. 5A–5C) offered a greater choice of viable pathways than rural SES, especially between viable KCA options within CCA₂,_{3 or 4} options. This pattern was pretty insensitive to the increase in the level of climatic stress. This matched with the greater constrains on the satisfactory space that characterizes rural SES (see Table S2 in Supplemental S2). Accordingly, in rural SES, fewer satisfactory options of KCA transitions per CCA option were predicted (Figs. 5D–5F). There, actors would have to accept more drastic CCA transitions in order to respect the limits of the ES satisfactory domain. This is true in particular with no additional climate stress (Fig. 5D), as actors do have to first transit through CCA-B2. This first transition corresponds to contracting with the state government to become eligible for payments for ecosystem services (PES) (Fig. 4D, see links 2a,b in Fig. 2B). Then, 20 years later, we predict that viability maintenance of the rural SES requires to transform CCA₂|KCA₂ into CCA₄|KCA₈. This transformation is more demanding than from CCA₁ to CCA₂|KCA₂, as it involves the setting of a new P-role for arbitration, collective rules and economic support between C and E (cf. Fig. 1). Unexpectedly, increased drought stress is predicted to diversify the number of KCA options, especially within the CCA₃ option (Figs. 5E, 5F). However this larger choice is expected to come at the expense of the security level for every KCA choice (lighter gray shade), making those KCA transitions riskier.

The most secured 30-year viable decision pathways

We then selected the top 10% most secured options of viable 30-years adaptation pathways within the ES satisfactory domain out of the options in Fig. 6. This selection reduced in some cases drastically the number of viable pathways. For instance, for peri-urban SES, this subset of pathways requires transit as fast as possible toward a combination of CCA₄|KCA₉ when climate stress level is the lowest (Fig. 6A, option of arrangement CCA₄|KCA₉: see Table S1 in Supplemental S2 for details); or to transit through CCA₄|KCA₈ when climate stress level is the greatest (Fig. 6C, option D.1). Such drastic transformations are predicted to have large benefits, as they lead to a state where all the other governance pathway options become viable by 2040–2050. Interestingly, at climate stress level 1 (Fig. 6B), there is still a great diversity of highly secured viable pathways that sustain the required levels for all ES to be viable.

Similarly, in the rural SES, the most secured pathways lead a reduction in the transition time to CCA₂|KCA₃ for climate stress level 0 (Fig. 6D) or toward CCA₃|KCA₅ for climate stress level 2 (Fig. 6F). Subsequently, securing adaptation are achieved by further shortening the time required to transition to CCA₄|KCA₉ (Figs. 5D, 5F).

The model unexpectedly predicts that actors from the two SES will have a larger range of secured options at different time scales under climate stress level 1, as opposed to under milder or harsher conditions (Figs. 6B, 6E). This appears particularly true for peri-urban SES (Fig. 6E).

Switching pathways to prioritize different ES and resolve actor conflicts

Optimal DAPP maps (Fig. 7) were derived from Fig. 6, and showed viable adaptation pathways that maximize one ES⁺ at a time (or minimize one ES⁻). For example, in peri-urban SES with minimal level of climate stress (Fig. 7A), we predict that transiting directly to CCA₄|KCA₉ (as Fig. 6A would suggest to do to be more secured) will minimize the costs of maintenance but without maximizing the other ES⁺ (or minimizing the other ES⁻). The target of minimizing environmental hazards rather requires to delay the transition to CCA₃|KCA₇ (i.e., by creating a C-role) then the arrangement CCA₂|KCA₃ (i.e., contracting for PES). Maximizing all the other ES⁺ would require to transit first through the arrangement CCA₃|KCA₇, and then either CCA₂|KCA₃ or CCA₄|KCA₈.

These results highlighted how the choices of pathways optimizing one ES⁺/ES⁻ can impact other ES level through trade-off effects (Fig. 8). For instance, the pathway that maximizes pollination as priority objective (i.e., through pathway CCA₁|KCA_1(2020) → CCA₃|KCA_{7(2020–2030)} → CCA₂|KCA_{3(2030–2040)} → CCA₄|KCA_{8(2040–2050)} in Fig. 7A), is expected to produce positive, thus synergistic, effects by reducing environmental hazards (brown line) and maximizing fruit production (Fig. 8A). This pathway is also predicted to have negative impacts on wood biomass production (green line), sunlight protection (blue line) and landscape aesthetics (orange line). Consequently, new winners and losers relative to the ES are expected to emerge with changing pathways and thus according to the ES⁺ or ES⁻ that are prioritized. Conversely, if actors seek to minimize the ES⁻ “cost of maintenance” (Fig. 7F), then the most optimal adaptation pathway involves the following transition: CCA₁|KCA_1(2020) → CCA₄|KCA_{9(2020–2040)} → CCA₁|KCA_{1(2040–2050)} (Fig. 7A). This should result in a continual parallel decline of all the other ES⁺ and ES⁻ over the next 30 years (Fig. 8F), alleviating the risks of ES trade-offs.

Sensitivity of DAPPs to changes in climate stress, SES and hedgerow types

Set of viability solutions according to the proportions of hedgerow types

We represented the viability kernel in the hedgerow state-space (Fig. 9) and examined how its size and shape—proxies for the number and types of adaptation pathways—were influenced by the proportion of different hedgerow types: species-poor hedgerows (PH) vs species-rich hedgerows (RH), and tall hedgerows (TH) vs short hedgerows (SH).

We found that its shape and size were bound by minimal and maximal proportions of every hedgerow type, but that the proportions differed with climatic stress levels and SES types. For peri-urban SES, viable pathways were found under greater climatic stress, with a large range of proportions of RH, but a narrower one for PH (Fig. 9). By contrast in rural SES, greater climatic stress levels fit with viable pathways with much narrower ranges of proportion of both PH and RH. Patterns were somehow similar when considering species diversity to describe hedgerow types (Fig. S9 in Supplemental S5).

Overall, as climate stress increases, maintaining large diversity of viable pathway options should require relatively more RH than PH (Fig. 9) and more TH than SH (Fig. S9), regardless of the type of SES. If the state of the hedgerows remain constant (blue dots close to the threshold in Figs. 9 and S9), then greater climate change would put both SES types in an unsecured state, reducing drastically the number of possible adaptive actions, and increasing the risk of being trapped into a non-viable state (Figs. 9C, 9F and S9C, S9F).

Expected security gains per ES from switching hedgerow management targets

ES⁺ and ES⁻ depended for a large part on the hedgerow species richness and height (see model in Table S2). We analyzed retrospectively whether switching actions from one hedgerow type to another may lead to more or less security gains, expressed as a distance to the limits of the ES satisfactory domain K_r (within $Via{b}_{K_R}$) for every ES⁺ and ES⁻, following methodological step 6. This was done for both the viable and non-viable adaptation pathways. We then analyzed whether the results contrasted when changing SES type and climatic stress level. The analysis revealed three consistent patterns of ES security shared between the two SES types (Figs. 10 and S10).

Viable pathways (green violins) that increased relatively more the proportion of RH than PH (Fig. 10) were likely to build greater security in the viable ES⁺ provisioning (for pollination, fruit production, biomass production and sunlight protection). Conversely, viable pathways that increased relatively more the proportion of PH than RH (Fig. 10) were also likely to build greater security for keeping ES⁻ (i.e., maintenance costs, environmental hazards) within the satisfactory threshold. In the absence of additional climate stress, we found only limited contrasts between viable and non-viable pathways (Figs. 10A, 10D and S10A, S10D). Increasing climate stress levels was predicted to amplify existing patterns of ES security, by pushing for even more RH for ES⁺ and even more PH for ES⁻.

Similar pattern of viability was observed for ES⁺ security when increasing TH over SH and for ES⁻ when increasing SH over TH (see Fig. S10 in Supplemental S5). This pattern of priorities between hedgerow types was consistent across climate stress levels 0 and 1, but reversed at climate stress level 2 (see e.g., Fig. S10C for environmental hazards).

In the particular case of landscape aesthetics, ES security gains were not impacted by changing hedgerow types, as it was defined as the Shannon index of the diversity of all hedgerows, and was thus insensitive to changing any one type of hedgerow (see Table S2).

DAPP maps enriches our predictions of potential adaptation options

Previous studies on the use of DAPP maps highlighted the importance of integrating detailed information on the SES context of adaptation (e.g., Stanton & Roelich, 2021). However, these studies also indicate that guidelines for organizing this information in a way that reflects the hierarchical nature of SES management.

Our goal was to demonstrate how to construct information-rich nested DAPP maps using Ostrom’s (1990) governance theory. We had two complementary objectives. The primary was practical: to design effective decision-support tools. The second was theoretical: to question whether and how the nature of abstract structures—such as nested adaptive institutional arrangements—could explain changes that manifest in the state, structure and dynamics of empirical phenomena, such as biodiversity, ecological infrastructures (hedgerows) and the delivery of ecosystem services to a diversity of actors.

To achieve this, we developed a method grounded in Ostrom’s main frameworks (i.e., IADF, SESF and CISF). Using these, we mathematically derived a social-ecologically rich set of adaptation actions and predictive, viable DAPP maps. We applied this method to analyze the long-term sustainable provision of ES produced by hedgerows in two SES, under climate change.

The results emphasized the influence of the SES type (rural vs per-urban) and climate stress levels (three drought levels) on possible pathways of nested governance adaptation supporting ES provisioning. We found that a wide diversity of possible nested arrangements and transitions between them were viable (among the ~5 million possible pathways), highlighting the great flexibility for diverse actors to meet their needs.

This nested DAPP approach demonstrates strong potential for tackling unique and complex SES adaptation challenges, while maintaining a sufficiently generic framework. We discuss the strengths and limitations of this method in the context of our case study.

Nested structure of DAPP maps enables more incremental adaptation options

Previous DAPP approaches, applied on complex SES involving biodiversity and ES, were defined at distinct levels of governance (e.g., Colloff et al., 2016; Lavorel et al., 2019, 2020; Bruley et al., 2021; Bergeret & Lavorel, 2022). The added-value of our integrated method was to show how to generate nested DAPP maps between these levels, involving adaptation actions between OCAs, within and between different KCAs, CCAs, for two SES characterized by different MCAs.

In the archetypical SES we presented, most actors who possessed hedgerows primarily used the nested governance structure CCA₁|KCA₁ (with a fixed OCA detailed in Supplemental S2). Our results indicate that this polycentric arrangement may not be sustainable in the long term, especially if climate change impacts hedgerows that are tall and biodiverse.

For rural actors, the most secured nested arrangement to stay in a viable pathway (Fig. 5) would be to transform CCA₁|KCA₁ into the most complex and polycentric CCA₄|KCA₈ (see Fig. 2 and further details in Table S1 from Supplemental S2). Even if we predict a permitted delay of few decades for this transition, in practice a direct CCA_{1 → 4} transformation should be very costly (for economic, technical, social or even cultural reasons). It could be anticipated from the required substantial disparities between CCA₁ and CCA₄ in collaboration skills, mutual trust, and the willingness to delegate power and roles among E, C, and P roles (Ostrom, 1990; Ban et al., 2015; Anderies, Barreteau & Brady, 2019). Changing KCA or even OCA would thus require less drastic investments for adaptation than changing CCA, and thus are expected to be adapted more regularly. This was confirmed by the semi-structured interview of actors in our study site (Supplemental S1). But we lacked sufficient data to evaluate the specific costs involved in the transition between different CCA and KCA.

Factoring in these costs may yield nested DAPP maps that better align to the need for more incremental transition pathways, similar to what we predicted in the peri-urban DAPP maps. For example, transitioning through CCA_{1 → 2} or CCA_{1 → 3} first, rather than directly from CCA_{1 → 4}.

The method produced complex tipping points in adaptation pathways

The DAPP framework was initially designed with questions of systemic robustness in mind (Haasnoot et al., 2013; Haasnoot, Warren & Kwakkel, 2019), but not for a great number of nested actions and levels of systemic robustness and spillovers.

Here, we compared the effects of actions on emerging DAPP responses between two SES (peri-urban and rural), whose differences primarily rested on the constraints of ES levels for actors’ satisfaction and the impact of climate change on hedgerows between climate stress levels. All other factors were kept the same because the data we gathered and analyzed through the SESF did not provide enough evidence to detect significant differences between the two SES (see Supplemental S1).

Remarkably, by simply adjusting ES needs to the SES context and the climate stress impacts on hedgerows, we observed the emergence of entirely distinct DAPP maps. These maps had different patterns of transition pathways (Figs. 5–7) and of associated trade-offs and synergies among ES resource users (Fig. 8). The complexity of the patterns was akin to the systemic nature of the CISF representation, as expected by Anderies (2015). DAPP maps also emerged different patterns of viable (robust) pathways (Fig. 5). We also demonstrated how the adaptation choices involved changes in the relative proportion of species-rich/poor and short/tall hedgerows (Figs. 9, 10, S9, S10).

Some of these results were particularly unexpected. For instance, a slight shift in ES preferences between rural and peri-urban SES led to even more pronounced differences in diversity and priorities of pathway options and ES dynamics. Additionally, compared to the rural SES, the best options for securing the viability of peri-urban SES involved a swifter transition to the more intricate CCA₄, with joint arrangements between private, community, and public sectors (see Table S1 for details). Another intriguing finding was the fact that moderate climate stress (level 1) diversified adaptation options, while severe stress (level 2) significantly limited them.

These emerging patterns of diversification or simplification of pathway options, along with others detailed in Supplementary Results S5, remain not fully understood, even though our analyses in Figs. 10 and S10 provided some insights into the key hedgerow types and ES influencing these changes. This highlights the need for further analyses on how changes in actions, hedgerows, and ES production affect pathway diversification.

Perspectives for using this approach for more complex SES

In our study, we considered seven ES as (in)tangible resource units, flowing from the R compartment to the exploitation role compartment E (through action set U_1b in Fig. 1). Following the Millennium Ecosystem Assessment (MEA) (2005), these ES represent mostly provisioning ES (wood, fruits, etc.) and cultural ES (landscape aesthetics). However following the MEA, two other ES categories are worth considering, namely supporting and regulating ES. More recently, Colloff et al. (2016) developed the concept of ‘adaptation services,’ which refers to specific types of supporting or regulating services that enhance the resilience of social systems by providing climate-related benefits, such as protection, resilience, or enabling adaptive options.

The CISF is valuable because it streamlines the modeling of ES from interconnected ecological infrastructures, while also highlighting how the chain of ES and infrastructures can resemble collective-choice arrangements (KCA), a concept emphasized by researchers like La Notte et al. (2017) and Lavorel et al. (2019). For example hedgerows, as semi-natural infrastructures provide supporting ES like pollination and pest control (akin to action set U_4a), which enhance crop growth (U_0a), and regulating ES such as water flow management (U_5a). If biodiversity in hedgerows or grasslands adjusts to climate change, their effects could impact the C, R, and E states, similar to a KCA. The same approach can be used to enrich DAPP studies, like those presented by Lavorel et al. (2019). For instance in their article, grasslands can be described as having a C-role through the control of erosion on adjacent fields (i.e. using action set U_5a). Similarly carbon storage, fodder resilience, and services like aesthetics and shade can be defined using different action sets (U_0a, U_4a, U_1b, U_6b). Lastly, services like connectivity and transformability are connected to the R and C-role compartments, and transformability can be modeled as the acceptable range of structural, compositional or entropic² changes in R or C tolerated by other roles.

Together these examples suggest that the CISF (and thus by association the SESF through Fig. 1) could flexibly be used to model potentially very complex KCA, and by extension DAPP problems, involving complex networks of roles attributed to ecological infrastructures, species, actors and ES (cf. Vogt et al., 2015; Partelow & Winkler, 2016; Rova & Pranovi, 2017).