Optimal Conservation Outcomes Require Both Restoration and Protection — TEI-tagged view

Hugh P. PossinghampersName, Michael BodepersName, Carissa J. KleinpersName (2015date). “Optimal Conservation Outcomes Require Both Restoration and Protection.” PLOS Biologytitle·j.

Object of study — the relative long-term conservation outcomes of protecting intact habitat and restoring degraded habitat

Research question — when should limited conservation budgets prioritise habitat restorationterm, habitat protectionterm, or a timed sequence of the two

Contribution — a unified dynamic landscape theory and rule of thumb comparing restorationterm and protectionterm across biodiversity and ecosystem-service objectives

Full text — tagged

Optimal Conservation Outcomes Require Both Restorationterm and Protectionterm Abstract Conservation outcomes are principally achieved through the protection of intact habitatterm or the restoration of degraded habitatterm. Restorationterm is generally considered a lower priority action than protectionterm because protectionterm is thought to provide superior outcomes, at lower costs, without the time delay required for restorationterm. Yet while it is broadly accepted that protected intact habitat safeguards more biodiversity and generates greater ecosystem services per unit area than restored habitat, conservation lacks a theory that can coherently compare the relative outcomes of the two actions. We use a dynamic landscape modelterm to integrate these two actions into a unified conservation theory of protection and restorationterm. Using nonlinear benefit functionsterm, we show that both actions are crucial components of a conservation strategy that seeks to optimise either biodiversity conservationterm or ecosystem services provision. In contrast to conservation orthodoxy, in some circumstances, restorationterm should be strongly preferred to protectionterm. The relative priority of protectionterm and restorationterm depends on their costs and also on the different time lags that are inherent to both protectionterm and restorationterm. We derive a simple and easy-to-interpret heuristic that integrates these factors into a single equation that applies equally to biodiversity conservationterm and ecosystem service objectives. We use two examples to illustrate the theory: bird conservation in tropical rainforests and coastal defenceterm provided by mangrove forests.

Introduction Habitat conservation is central to biodiversity conservationterm. Habitat can be conserved by either protecting it if it remains intact or by restoring it once it has been degraded. Conservation organisations often pursue both restorationterm and protectionterm simultaneously, and management guidelines advocate the use of both actions [ 1 , 2 ]. However, the orthodox position is that managers should “protect first, restore second” where possible, and the priority of protectionterm has been argued in the scientific literature [ 3 – 7 ] and management guidelines internationally [ 8 – 10 ], for both biodiversity conservationterm and ecosystem service provisionterm. This prioritisation of investment in protectionterm over restorationterm is justified with reference to the relative costs, expected benefits, and timescales of the two actions [ 3 – 12 ]. While restorationterm can improve a site’s ecological condition, restored habitat will often take decades to regain the majority of its biodiversity and ecosystem attributes [ 3 , 13 ].

Despite this prevailing wisdom, recent experiments have revealed that the disparity between restorationterm and protectionterm is smaller than expected, and strongly context dependent. The majority of many ecosystem features, particularly certain ecosystem services, can be provided by restored habitat [ 3 ], sometimes within a surprisingly short timeframe [ 14 , 15 ]. Moreover, ongoing technological advances [ 16 ] mean that the cost of this restorationterm can be low enough to generate a net social benefit [ 11 , 17 ]. At the same time, conservation theory has highlighted disadvantages to habitat protectionterm that parallel problems identified for restorationterm. Protected areas also suffer from poor implementation and management and do not guarantee the conservation of intact habitat, species assemblages, or ecosystem services [ 18 , 19 ]. Dynamic landscape modelsterm further illustrate how the benefits of protectionterm are also subject to time delays, since protectionterm does not create new habitat, but only reduces the likelihood of future habitat lossterm [ 20 ]. Moreover, in highly degraded landscapes that leave many species with non-viable populations (i.e., extinction debtsterm [ 21 ]), habitat protectionterm will only have a secondary effect on biodiversity loss rates. Restorationterm is the only in situ conservation interventionterm that can actively reduce an extinction debtterm·def [ 22 , 23 ].

The relative priority of protectionterm and restorationterm can only be coherently assessed by a conservation resource allocation theory that incorporates both actions and that quantifies both their costs and benefits in a comparable manner. In particular, this theory must be temporally explicit, since both the benefits of the two actions accrue at different rates. In this paper, we incorporate restorationterm and protectionterm into a shared dynamic landscape modelterm [ 20 ] that explicitly includes restoration ratesterm, dynamic species loss (i.e., extinction debtsterm), and ecosystem service provisionterm (see Materials and Methods ). To contrast the performance of habitat protectionterm and restorationterm, we apply this unified theory to two divergent examples: ecosystem service provisionterm in the Coral Triangle and biodiversity conservationterm in the Atlantic forests.

Results Example 1: Coastal Defenceterm in the Coral Triangle Intact mangrove ecosystemsterm help defend coastal communitiesterm from storm surges and floodsterm [ 24 , 25 ], events that are increasing in frequency and intensity as the climate changes [ 26 ]. In Southeast Asia, the impact of frequent extreme weather events on coastal communitiesterm is pronounced due to vulnerable infrastructure and high rates of mangrove deforestation [ 27 ]. We focused on the northern tip of Borneo (Sabah, Malaysia), where over 38,000 people live on the coast. Approximately 78% of mangrove forests remain from an original 535 km 2 , after more than 30 years of losing 0.5%–0.8% annually to other uses (e.gterm·var., urban development and aquaculture) [ 27 ]. The Sabah Forestry Department is charged with both the protectionterm and restorationterm of mangrove forests, two actions that gained popularity across Southeast Asia after the 2004 Indian Ocean tsunami, but they lack a decision framework for deciding which action is best to implement [ 28 ].

Barbier et al. [ 25 ] calculated that coastal defenceterm benefits accrue as a nonlinear function of the area of surrounding intact mangrove habitat: where P ( t )term·var is the area of protected mangrove forestterm, F ( t )term·var is the area of unprotected but intact mangrove forestterm, and k = 2.1x10 –3 ( S1 Text ). Eq (1) measures ecosystem service provisionterm by the proportional reduction in damage caused by a lower wave height in areas sheltered by mangrove forests. In this example, over the course of a 30-year project starting in 2006, managers must choose to share an annual conservation budget equivalent to US$15 million between the protectionterm of intact mangrove forests, the restorationterm (and subsequent protectionterm) of degraded mangrove habitat, or a combination of both actions. Their aim is to maximize the total coastal defenceterm provided to communities by mangrove forests over the project lifetime: where rterm·var is the economic discount rate. We assume that restored mangrove forests do not contribute to coastal defenceterm until restorationterm is complete (see S1 Text for parameterisation details).

To maximise coastal defenceterm, the model predicts that northern Sabah managers should prioritise the restorationterm of cleared or degraded mangrove habitat over the protectionterm of intact forests ( Fig. 1A and Fig. 2A ). The optimal allocation schedule suggests that restorationterm should be an absolute priority (i.e., all available funds should be directed towards restorationterm), even though the optimisation method allows managers to allocate part of their funds to both actions (e.gterm·var., 95% to restorationterm and 5% to protectionterm). Restorationterm results in a smaller amount of protected forestterm than protectionterm ( Fig. 1B ), both because restorationterm is significantly more expensive, and because restored habitat only becomes intact and protectedterm after a substantial time lag. Nevertheless, restorationterm provides the local community with more coastal defenceterm because it results in less degraded land and more intact forestterm (protected and unprotected; Fig. 2A ). The optimal allocation therefore assigns a higher priority to restorationterm.

Allocation schedules for mangrove ecosystem service provisionterm. Proportion of landscape in each land state over a 30-year mangrove conservation project in Sabah. Results show (A) the optimal allocation decision to only restore, and (Bterm·var) the standard approach of pursuing protectionterm while intact habitat remains unprotected. Prioritising restorationterm results in fewer protected areas (green) and a greater amount of unprotected intact habitat (grey), but has greater success limiting the amount of degraded land (red), therefore maximising the provision of ecosystem services (see Fig. 2A ). The data used in this figure is given in S1 Data , and the Matlab code that generated it can be found in S2 Text .

Performance of alternative allocation schedules. The conservation outcomes delivered by different allocation schedules, both measured relative to a null model of no management investment. (A) Annual provision of additional ecosystem services from mangrove conservation in Sabah under the optimal allocation (restoration-only, blue line), and the standard, protection-only approach (green line). Performance is measured relative to the amount of coastal defenceterm that would be expected in the absence of management intervention. (Bterm·var) Extinctions averted by the optimal allocation schedule, which switches from protectionterm to restorationterm after 20 years (dashed black line). Results are also shown for the standard, protection-only approach (green line), and a restoration-only approach (blue line). The number of observed extinctions is reported in comparison to the number of extinctions we would expect in the absence of management intervention. The data used in this figure is given in S2 Data , and the Matlab code that generated it can be found in S2 Text and S3 Text .

Example 2: Biodiversity Conservationterm in Paraguay’s Atlantic Forests Paraguay contains some of the last remnants of South America’s high-latitude tropical rainforests, which remained predominantly intact into the 1970s [ 29 ]. Given the extraordinary endemic bird species richness (148 species) and high levels of habitat lossterm (>90%) in this ecoregion, the small number of extinctions to date indicates the presence of a substantial extinction debtterm·def [ 30 ]. Managers want to minimise the number of bird extinctions by either restoring and then protecting cleared or degraded habitat, by protecting the last remaining stands of intact rainforest, or by a combination of the two [ 31 ]. The species–area relationshipterm relates the equilibrium species richnessterm to the area of intact habitatterm, regardless of its protectionterm status: where αterm·var represents regional species richness and zterm·var is a constant. We make the conservative assumption that restored habitat does not mitigate the extinction debtterm·def until restorationterm is complete, and we estimate the recovery rate using long-term surveys of species richness following forest clearance (although the complete recovery of population abundances will take longer than the return of species; S1 Text ). Species extinctions often lag significantly behind habitat lossterm, but debt “relaxation” can be averted if degraded habitat is quickly restored. The rate of species extinctionterm is modelled as proportional to the size of the species debtterm, calculated as the difference between extant species richness and the number of species that would be supported by the current habitat distribution at equilibriumterm [ 32 ]: where θterm·var is the rate of extinction debtterm·def relaxation. The managers’ objective is to minimize the total number of extinctions during a T year conservation project: We calculated a retrospective optimal management strategyterm for protectionterm and restorationterm between 1970–2013 ( Fig. 3 ; see S1 Text for parameterisation details), assuming an ongoing annual budget equivalent to US$100 million (2014). The results show that, in the Atlantic Forests, restorationterm and protectionterm would have achieved broadly comparable outcomes ( Fig. 2B ). However, to optimally reduce species extinctions over the time period, managers should have pursued habitat protectionterm for the first 20 years and then switched their efforts entirely towards restorationterm ( Fig. 3A ). It is not optimal to fund both actions simultaneously, at any point in time.

Allocation schedules for rainforest biodiversity conservationterm. Proportion of landscape in each land state through time over 43 years of rainforest conservation in Paraguay’s Atlantic Forest (1970–2013). Results show (A) the optimal allocation schedule of protectionterm for 20 years, followed by 23 years of restorationterm, and (Bterm·var) the standard approach of protectionterm while intact habitat remains unprotected. An early switch from protectionterm to restorationterm results in fewer protected areas (green) and more unprotected habitat (grey), but less degraded land (red). The result is fewer species extinctions (see Fig. 2B ). The data used in this figure is given in S3 Data , and the Matlab code that generated it can be found in S3 Text .

Rates of habitat degradation in Paraguay’s Atlantic Forests were so rapid that neither action would have had a large impact on the size of the extinction debtterm·def. Nevertheless, an initial focus on protectionterm would have quickly reduced the amount of habitat that was unprotectedterm, and that therefore could be degraded. Once this was achieved, a switch to restorationterm would have allowed managers to address the extinction debtterm·def directly, by converting degraded land back into intact habitat.

Rule of Thumb We identified the best allocation schedules using optimal control theoryterm, but the relative benefits of protectionterm and reservation can often be better understood and implemented using myopic heuristicsterm [ 20 ]. Both biodiversity and ecosystem service objectives are advanced by an increase in the total amount of intact habitatterm (protected and unprotected). The act of protectionterm increases intact habitat indirectly by reducing the amount of unprotected habitat available for degradation, while restorationterm converts degraded land to protected intact habitat, after a time delay. A linearisation of the state equations ( Eq 7 ; Materials and Methods ) indicates that protectionterm should be a higher conservation priority if half the ratio of the restorationterm and habitat lossterm rates is less than the ratio of their costs (see S1 Text for derivation): Roughly speaking, restorationterm is favoured if its relatively higher costs ( c Rterm·var / c Pterm·var ) are outweighed by its more rapid reduction of degraded land relative to protectionterm ( gterm·var /2 δterm·var ). In agreement with our optimal control solutions ( Fig. 1 and Fig. 3 ), Eq (6) predicts that restorationterm should be strongly favoured over protectionterm in mangrove forests ( gterm·var /2 δterm·var = 13.1; c Rterm·var / c Pterm·var = 3.0). In contrast, protectionterm should be considered a slightly higher priority than restorationterm in the Atlantic Forests ( gterm·var /2 δterm·var = 1.1; c Rterm·var / c Pterm·var = 1.6; see S1 Text for parameter values).

This simple rule of thumb holds true for both ecosystem service provisionterm and biodiversity conservationterm objectives. The right-hand side of this condition is familiar—relative costs of actionterm are consistently identified as important elements of prioritisation [ 33 – 35 ]. However, the left-hand side highlights another important factor in conservation planning: the timescales over which interventions yield benefitsterm. An interpretation of this temporal ratio is that restorationterm will become a higher priority when habitat quickly regains its pristine qualities; protectionterm should be preferred when the restoration rateterm is slow or when the rate of land degradationterm is rapid. This rule can be readily modified to include the probability that restorationterm and protectionterm will be unsuccessful; the results of this modification indicate that including failure ratesterm are equivalent to increases in the costs of the respective actionterm ( S1 Text ). For example, if the probability of restorationterm being successful was only 50%, then that is equivalent to a doubling of the cost of restorationterm.

Discussion Constrained by limited budgets, conservation organisations and governments must always choose between restorationterm and protectionterm. Our framework provides a coherent framework that can help resolve longstanding uncertainties about the relative priority of these two fundamental actions. The results and implications are much more complex than simply “protect first, restore second.” In both of our examples, the long-term objectives will be best achieved if priority is given to restorationterm at some point in the project, despite its higher cost, and despite a substantial delay before restored habitat can contribute to project objectives.

As well as demonstrating the benefits of restorationterm, our results indicate that the optimal solution is always to spend all available resources on either restorationterm or protectionterm, never both. While the option of splitting the budget between the two actions was available to our optimisation method, it was never optimal to fund both actions simultaneously. This type of either-or solutionterm—known as bang-bang controlterm—is often sensitive to model assumptions about homogeneity, uncertainty, and linearity. Our model makes all of these assumptions. The model in Eq (7) considers only the overall landscape scale and contains no fine-resolution ecological or economic variationterm, with all land incurring the same restorationterm or protectionterm costs. In reality, conservation costs (and benefits) vary dramatically between locations and projects [ 36 ]. We assume that the rates of land loss and restorationterm are known and deterministic, but land degradation is a stochastic process, and depends on highly uncertain factors, as do both restorationterm success and protected area performance. Finally, the management control terms in Eq (7) are linear in the control variable u ( t )term·var (e.gterm·var., uB / c Pterm·var ), while in reality, expenditure generally achieves diminishing marginal returnsterm [ 37 ]. Relaxing any of these assumptions will tend to smooth the abrupt switch between restorationterm and protectionterm—that is, will create a more continuous transition period during which both actions are funded simultaneously.

Our objective functions (Eqs 2 and 5 ) aim to maximise unidimensional descriptions of biodiversity conservationterm (the number of bird species) and ecosystem service provisionterm (the amount of coastal protectionterm). For individual ecosystem services like coastal protectionterm or carbon sequestration, this is a reasonable formulation of conservation objectives. However, many conservation agencies carry out projects that aim to deliver multiple benefitsterm simultaneously, and almost all conservation actions will inevitably provide benefits to more than one ecosystem service or measure of biodiversity. It is possible, for example, to imagine a conservation project that pursues both our stated objectives—coastal protectionterm and species conservation—simultaneously. While it is possible to aggregate the provision of multiple benefitsterm into unidimensional quantities by calculating the monetary value of different ecosystem services [ 25 ] or by assigning relative weightings to different species [ 38 ], this is not always appropriate or desirable. The process of aggregation will also be further complicated by the divergent values of multiple stakeholders [ 39 ]. In such situations, optimisation may not be as useful as an exploration of how restorationterm and protectionterm affect trade-offs between objectivesterm and conflict between stakeholders.

Our broad, qualitative conclusion—that protectionterm should not always be prioritised over restorationterm—is robust to the parameterisation of our two examples and to the structure of the restorationterm process ( S1 Text ). However, both restorationterm and protectionterm are more complicated and nuanced than any of the abstracted models we apply here. Recent meta-analyses of terrestrial and aquatic restorationterm projects show that even successful restorationterm projects are unable to recover reference-level biodiversity and ecosystem servicesterm (they achieved an average of 80%–86% of reference sites, although technological improvements continue to improve these outcomes [ 3 , 16 ]). Moreover, these benefits accrue to different ecosystem features at varying timescales, and may take decades to be realised, particularly for the restorationterm of biodiversity [ 40 , 41 ]. Alternate versions of the landscape model can incorporate incomplete restorationterm (one alternative formulation is given in the S1 Text ), but at the cost of increased complexity and greater information requirements. Protectionterm is also rarely perfectly effective, both because effectively managed protected areas cannot halt all degrading activities [ 18 ] and because many protected areas are poorly managed [ 42 ]. Furthermore, decisions to restore or protect are influenced by a variety of important factors not considered here, including the feasibility of actions in a given place, which is influenced by operational (e.gterm·var., technical success), legal (e.gterm·var., land tenure), political (e.gterm·var., political will), and social constraints (e.gterm·var., the willingness of landowners). In particular, our nonspatial model omits the constraints placed on managers by spatial conservation objectives. For example, if managers want to connect particular areas or reduce fragmentation in a landscape, restorationterm will be the only suitable action. Despite these omissions, we believe that simple, general theoryterm can still provide useful insights into a problem.

By providing a unified, dynamic framework within which to compare their long-term outcomes, our theory provides evidence and rationale for pursuing restorationterm alongside protectionterm—even in preference to protectionterm—under the right circumstances. An explicit theoretical framework also helps to highlight relationships that determine the priority of the two actions: the relative costs of restorationterm and protectionterm, and the rate at which restored habitat approaches the benefits of intact habitat relative to the habitat conversion rate. Our two examples illustrate this general theory and demonstrate the unexpected potential for restorationterm to parallel or precede protectionterm. However, the approach and simple rule of thumb should be seen as informative, not prescriptive.

Materials and Methods Our framework is not intended to inform precisely where protectionterm and restorationterm should occur at a fine scaleterm within a landscape, but to offer insights into the allocation of a limited conservation budget at a meso-scaleterm (e.gterm·var., bioregional or catchment conservation initiatives). The model is nonspatial, assuming that the conservation state of the landscape can be described by the aggregate proportions of the land in different states (e.gterm·var., the proportion protected, degraded, etc.). Actual decisions about precisely where to act are inherently spatial and should be informed using spatial zoning toolsterm that optimize for multiple conservation actions [ 43 ].

Dynamic Conservation Landscape Model The decision about whether to restore or protect is underpinned by a basic dynamic landscape modelterm. Each small area of land at time t is classified as being in one of four states: intact and unprotectedterm, F ( t )term·var; intact and protectedterm, P ( t )term·var; degraded or clearedterm, C ( t ); or undergoing restorationterm, Rterm·var ( t ). We describe the total amount of land in each state as a proportion of the landscape, and the model ensures that F ( t )term·var + P ( t )term·var + C ( t ) + Rterm·var ( t ) = 1 at all times.

In our model, transitions of land between the four states are driven by two actions and two processes. The two actions, protectionterm and restorationterm, are entirely determined by the managers. At each point in time across a T -year project, managers can allocate a varying proportion (0≤ u ( t )term·var≤1) of a fixed annual budget ( Bterm·var ) to protectionterm, and the remainder 1— u ( t )term·var to restorationterm. We note that this choice of u ( t )term·var allows managers to simultaneously fund both actions—that is, to allocate a proportion of their resources to protectionterm, and the remainder to restorationterm (e.gterm·var., if u ( t )term·var = 0.1, managers spend 10% of their budget on protectionterm and 90% on restorationterm). Managers cannot directly alter the two processes. The first process is land degradation, in which we assume that unprotected land is being degraded at proportional rate δterm·var [ 20 , 44 , 45 ]. That is, landscapes with large amounts of intact, unprotected habitatterm will experience large absolute rates of habitat lossterm. Managers can therefore reduce habitat lossterm by decreasing the amount of unprotected habitat through protectionterm, but they cannot directly affect the loss rate δterm·var . We note that alternative models of land degradation (e.gterm·var., constant rates) could also be used. The second process is restorationterm. We assume that restoration actionsterm, once undertaken, do not create intact habitat immediately. Once managers spend resources by purchasing degraded land and undertaking restoration actionsterm, the land undergoing restorationterm, Rterm·var ( t ), only regains its intact qualitiesterm at a proportional rate gterm·var . We note that this is a continuous model of restorationterm, rather than a time-lag model, but show in the S1 Text that this simplification does not qualitatively alter our conclusions.

By combining these actions and processes, the rate of change of each land state becomes: The variables c Pterm·var and c Rterm·var denote the costs of protectionterm and restorationterm respectively. Because habitat must be purchased before it is restored, c Rterm·var is generally larger than c Pterm·var . However, if land has been abandoned, or if the primary value of land comes from the intact habitat itself (e.gterm·var., timber), then purchasing degraded land for restorationterm may be cheaper than purchasing intact habitat for protectionterm. The protectionterm or restorationterm of a land parcel both require ongoing management, and we therefore assume that these two cost parametersterm measure the endowed costterm of undertaking both actions until the end of the project. That is, c Pterm·var is equal to the initial purchase price of the land, plus the time discounted cost of all future actions required to effectively manage the protected area. Likewise, c Rterm·var is the sum of the land purchase price, the time discounted cost of the initial intensive restoration actionsterm, and then the time discounted cost of ensuring that the restorationterm and subsequent protectionterm are effective. The entirety of these endowed coststerm must be paid in the year that a given parcel of land is restored or protected. The dynamics described by Eq (7) are illustrated in Fig. 4 .

Dynamics of the unified restorationterm and protectionterm model. Schematic representation of the landscape dynamics described by Eq (7) . Arrows show the direction of state changes between the four land states, with the mathematical terms indicating the magnitude of the flux. For example, the blue arrow extending from restoring land (Rterm·var) to degraded land (C) indicates that the process of restorationterm moves land from the “degraded” state to the “restoring” state.

Identifying the optimal management scheduleterm is equivalent to determining the specific control functionterm u ( t )term·var that maximises the objective function. There are clearly a very large number of candidate control functions, but fortunately the optimal function can be identified by applying Pontryagin’s maximum principle [ 46 , 47 ] to the system dynamics in Eq (3) , and each problem’s objective function (Eq 1 – 2 ). The details of this analysis are shown in the S1 Text . We note that it is not essential to understand the specifics of this optimisation method since alternative methods could equally be used to solve for the optimal solution, notably stochastic dynamic programming [ 20 ].

Supporting Information (CSV) Click here for additional data file.

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Arrows show the direction of state changes between the four land states. Flux rates correspond to processes contained in Eq. (S1) of S1 Text .

(TIF) Click here for additional data file.

Best-fit constant proportional loss rate model (i.e., exponential decline in unprotected intact habitat) is shown with the grey line. The underlying data in this figure is given in S4 Data .

(TIF) Click here for additional data file.

Best-fit asymptotic exponential recovery trajectories to each dataset are shown with correspondingly coloured lines. The underlying data in this figure was sourced from Aide et al. [ 31 ] and is given in S5 Data .

(TIF) Click here for additional data file.

Results are shown for three different values of gterm·var , the rate of restorationterm. These are (A) the nominal estimate, gterm·var* = 0.21; (Bterm·var) 75% of the nominal value, gterm·var = 0.16; and (C) 50% of the nominal value, gterm·var = 0.10. Optimal schedules are very similar, and in all cases give priority to restorationterm. Faster restoration ratesterm simply mean that less habitat remains in the restoring state at any given time. The data used in this figure is given in S6 Data , and the Matlab code that generated it can be found in S2 Text .

(TIF) Click here for additional data file.

Results are shown for three different values of gterm·var , the rate of restorationterm. These are (A) the nominal estimate, gterm·var* = 0.089; (Bterm·var) 80% of the nominal value, gterm·var = 0.071; and (C) 120% of the nominal value, gterm·var = 0.107. The optimal schedules are qualitatively similar, beginning with protectionterm, then switching resources to restorationterm after years have elapsed. However, for lower values of gterm·var , managers should spend more time protecting intact habitat before they shift across to restoring degraded habitat. The data used in this figure is given in S7 Data , and the Matlab code that generated it can be found in S3 Text .

(TIF) Click here for additional data file.

Resources are invested in restorationterm for approximately 13 years, after which time they are shifted across to protectionterm for the remainder of the project duration. As with the continuous-restoration model, the schedule initially prioritises restorationterm. However, allocations differ in the latter years of the project, where optimisation of the fixed-delay model begins to protect land. This difference is partly due to the fact that any restorationterm in the last 14.5 years (the time lag of restorationterm) will produce no benefits since it will not be complete before the end of the project timeline. The data used in this figure is given in S8 Data , and the Matlab code that generated it can be found in S2 Text .

(TIF) Click here for additional data file.

Resources are initially invested in protectionterm for 15 years, before switching to restorationterm for another period of approximately 15 years. Resources are finally allocated back to protectionterm for the final 12 years of the project. This spending pattern begins with the same sequence of allocations as the continuous-restoration model (i.e., protect-then-restore), before changing in the final years to prioritise protectionterm. This difference reflects the fact that restorationterm undertaken in the final years of the project will be incomplete (and therefore of no value) when the project ends. The data used in this figure is given in S9 Data , and the Matlab code that generated it can be found in S3 Text .

(TIF) Click here for additional data file.

(A) When managers preferentially restore and protect less expensive land (i.e., mangrove habitat that is not suitable for aquaculture), and protectionterm costs are therefore reduced by 25% from its nominal value. This also reduces the cost of restorationterm, since it also requires the purchase of land. (Bterm·var) When managers preferentially restore abandoned land, there is therefore no opportunity cost for restorationterm (only the cost of the restoration actionterm). This reduces the cost of restorationterm but leaves the cost of protectionterm unchanged. Neither alternate assumption changes the qualitative conclusions of our analysis. The data used in this figure is given in S10 Data , and the Matlab code that generated it can be found in S2 Text .

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The data in this figure was sourced from the supplementary information in Barbier et al. [ 25 ], and is given in S11 Data .

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Acknowledgments This paper has benefited from past work and discussions with S. Polasky, S. Andelman, D. Lindenmayer, M. Burgman, D. Tyre, Bterm·var. Wintle, K. Wilson, M. McCarthy, Rterm·var. Jumin, C. Baker, and Rterm·var. Pressey.

Data Availability All relevant data are within the paper and its Supporting Information files.

Funding Statement HPP, MB, and CJK were funded by the Australian Research Council ( http://www.arc.gov.au/ ). MB was funded by a DECRA Fellowship; CJK was funded by an Australian Research Council Postdoctoral Fellowship; HPP was funded by an ARC Laureate Fellowship. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

References Associated Data Supplementary Materials (CSV) Click here for additional data file.

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Arrows show the direction of state changes between the four land states. Flux rates correspond to processes contained in Eq. (S1) of S1 Text .

(TIF) Click here for additional data file.

Best-fit constant proportional loss rate model (i.e., exponential decline in unprotected intact habitat) is shown with the grey line. The underlying data in this figure is given in S4 Data .

(TIF) Click here for additional data file.

Best-fit asymptotic exponential recovery trajectories to each dataset are shown with correspondingly coloured lines. The underlying data in this figure was sourced from Aide et al. [ 31 ] and is given in S5 Data .

(TIF) Click here for additional data file.

Results are shown for three different values of gterm·var , the rate of restorationterm. These are (A) the nominal estimate, gterm·var* = 0.21; (Bterm·var) 75% of the nominal value, gterm·var = 0.16; and (C) 50% of the nominal value, gterm·var = 0.10. Optimal schedules are very similar, and in all cases give priority to restorationterm. Faster restoration ratesterm simply mean that less habitat remains in the restoring state at any given time. The data used in this figure is given in S6 Data , and the Matlab code that generated it can be found in S2 Text .

(TIF) Click here for additional data file.

Results are shown for three different values of gterm·var , the rate of restorationterm. These are (A) the nominal estimate, gterm·var* = 0.089; (Bterm·var) 80% of the nominal value, gterm·var = 0.071; and (C) 120% of the nominal value, gterm·var = 0.107. The optimal schedules are qualitatively similar, beginning with protectionterm, then switching resources to restorationterm after years have elapsed. However, for lower values of gterm·var , managers should spend more time protecting intact habitat before they shift across to restoring degraded habitat. The data used in this figure is given in S7 Data , and the Matlab code that generated it can be found in S3 Text .

(TIF) Click here for additional data file.

Resources are invested in restorationterm for approximately 13 years, after which time they are shifted across to protectionterm for the remainder of the project duration. As with the continuous-restoration model, the schedule initially prioritises restorationterm. However, allocations differ in the latter years of the project, where optimisation of the fixed-delay model begins to protect land. This difference is partly due to the fact that any restorationterm in the last 14.5 years (the time lag of restorationterm) will produce no benefits since it will not be complete before the end of the project timeline. The data used in this figure is given in S8 Data , and the Matlab code that generated it can be found in S2 Text .

(TIF) Click here for additional data file.

Resources are initially invested in protectionterm for 15 years, before switching to restorationterm for another period of approximately 15 years. Resources are finally allocated back to protectionterm for the final 12 years of the project. This spending pattern begins with the same sequence of allocations as the continuous-restoration model (i.e., protect-then-restore), before changing in the final years to prioritise protectionterm. This difference reflects the fact that restorationterm undertaken in the final years of the project will be incomplete (and therefore of no value) when the project ends. The data used in this figure is given in S9 Data , and the Matlab code that generated it can be found in S3 Text .

(TIF) Click here for additional data file.

(A) When managers preferentially restore and protect less expensive land (i.e., mangrove habitat that is not suitable for aquaculture), and protectionterm costs are therefore reduced by 25% from its nominal value. This also reduces the cost of restorationterm, since it also requires the purchase of land. (Bterm·var) When managers preferentially restore abandoned land, there is therefore no opportunity cost for restorationterm (only the cost of the restoration actionterm). This reduces the cost of restorationterm but leaves the cost of protectionterm unchanged. Neither alternate assumption changes the qualitative conclusions of our analysis. The data used in this figure is given in S10 Data , and the Matlab code that generated it can be found in S2 Text .

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The data in this figure was sourced from the supplementary information in Barbier et al. [ 25 ], and is given in S11 Data .

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Data Availability Statement All relevant data are within the paper and its Supporting Information files.