Optimal restoration: accounting for space, time and uncertainty

Authors


Correspondence author. E-mail: k.wilson2@uq.edu.au

Summary

1. In general, conservation seeks to prevent further habitat loss but in many cases there is a need to reverse habitat degradation. Restoration of habitat is necessary to achieve biodiversity conservation goals but often it is a costly and time-intensive process. Prioritization of where and when habitat is restored can help to ensure the cost-effective delivery of desired outcomes.

2. We develop a restoration prioritization decision support tool to identify the combination of restoration sites and the schedule for their implementation most likely to deliver the greatest utility for a fixed budget and operational constraints. We use a case study to apply our prioritization approach in order to illustrate the data that can be employed to parameterise the analysis and the outputs that are able to inform restoration planning. We compare restoration schedules under alternative utility functions to demonstrate trade-offs associated with different objectives, assumptions and preferences for particular outcomes.

3. Our prioritization approach is spatially and temporally explicit and accounts for the costs and benefits of restoration, the likelihood of restoration success, the probability of stochastic events, feedbacks, time lags and spatial connectivity.

4. Through collaboration with restoration practitioners we derive quantitative and spatially explicit data on each site requiring restoration. We determine the relative priority for restoring each site and develop a restoration schedule over 20 years.

5. Our results showed that after 20 years a little over a half of the sites requiring restoration are likely be successfully restored, while the total expenditure at our site will be c. US$13·7 million – almost the entire budget of $14 million.

6. Synthesis and applications. Our restoration prioritization approach provides a schedule for where and when restoration should occur, and also provides operational guidance and support for cost-effective restoration planning such as informing the likely total cost of restoration.

Introduction

Ecological restoration is widely regarded as essential for biodiversity conservation, particularly in human-dominated ecosystems (Jordan, Peters & Allen 1988; Young 2000; Carroll et al. 2004). However, restoration is often costly and typically takes many years to deliver desired outcomes. Furthermore, myriad factors influence the decisions of where and when restoration should occur (Hobbs & Kristjanson 2003). It is therefore imperative to ensure the efficient use of available resources through prioritization of management actions.

Cost-effectiveness analysis has been used to prioritize restoration activities within a single site, or for a handful of sites, in a number of cases (Macmillan, Harley & Morisson 1998; Hyman & Leibowitz 2000; Petty & Thorne 2005; Dymond, Ausseil & Overton 2008; Goldstein, Pejchar & Daily 2009). Such analyses typically provide a static evaluation of restoration priorities and as a consequence have not accounted for spatial dependencies between sites and do not deliver a temporal sequencing of restoration. There is, however, a growing body of theory and associated decision support tools for prioritizing conservation investments in the context of spatial and temporal dynamics (Moilanen, Wilson & Possingham 2009; Wilson, Carwardine & Possingham 2009).

Despite over a 1 000 publications in the peer reviewed literature on systematic conservation planning (Moilanen, Possingham & Wilson 2009), only a handful concern the prioritization of restoration (Noss, Nielsen & Vance-Boland 2009). Westphal et al. (2003) linked habitat restoration with the metapopulation dynamics of an endangered bird and this allowed for an optimal temporal sequencing of restoration over a given time horizon. Such detailed analyses are, however, only feasible for well-studied species and finding the optimal spatially and temporally explicit solution is computationally prohibitive for large problems (Crossman & Bryan 2006). More recently, Thomson et al. (2009) used reserve selection software to schedule restoration effort to maximize habitat for 62 species of bird, accounting for species connectivity requirements and time lags in the provision of habitat and resources.

Aside from time lags, a number of additional complexities are important in determining restoration priorities, particularly feedbacks between investments and spatial dependencies between existing habitat and the sites that are restored (Lindenmayer et al. 2002; Suding, Gross & Houseman 2004). As many restoration projects fail to meet their goals (Zedler & Callaway 1999; Wilkins, Keith & Adam 2003; Choi 2004; Zedler 2007), it is also important to account for the likelihood of restoration success and how it ultimately affects restoration costs and decision making (Hobbs & Kristjanson 2003; Bottrill et al. 2008; Hobbs 2009). Typically multiple management goals or preferences also need to be accounted for. Without explicit prioritization, restoration decisions are likely to be made in an ad hoc manner, which may compromise the efficiency with which restoration objectives are achieved. It is clear that the development of a comprehensive restoration prioritization framework and associated decision support tool would represent an important contribution to conservation science and management.

Hobbs (2007) and Beechie, Pess & Roni (2008) provide useful conceptual frameworks for restoration prioritization, specifically outlining key considerations such as setting goals and identifying constraints. We expand upon this and develop a return-on-investment restoration prioritization framework that is spatially and temporally explicit and accounts for the costs and benefits of restoration, likelihood of restoration success, the probability of stochastic events and spatial connectivity. We illustrate its application to restoration planning on the Irvine Ranch Natural Landmark in southern California.

Materials and methods

Study Area

The Irvine Ranch Natural Landmark encompasses wildlands from the Santa Ana Mountains to the coast in southern California (see Fig. S1, Supporting Information). This circa 17 600 ha complex of properties contains some of the largest remaining stands of native vegetation in southern California. Although these wildlands are fully protected, they are under short- and long-term ecological stress from multiple historic and contemporary sources, including grazing, urban fragmentation, invasive species and an increase in fire frequency (O’Leary & Westman 1998; Allen et al. 2000; Keeley 2006). Four native dominant habitat types occur on the Irvine Ranch Natural Landmark: coastal sage scrub (Artemesia californica), perennial native grasslands (Nassella pulchra), chaparral (Adenostoma fasciculatum) and oak-sycamore woodland (Quercus agrifolia) (Sawyer, Wolf & Evens 2009). There are 923 sites requiring restoration on the property, identified by a reserve-wide weed survey, a grassland survey, and an assessment of areas considered to have historically been oak woodland habitat. The total area requiring restoration is 1 353 ha and the sites have a minimum size of 0·5 ha, a maximum size of 28 ha and a median size of 1 ha (see Fig. S2).

Formulating the Restoration Prioritization Problem

The restoration prioritization problem must be in context of an explicitly stated goal and an associated conservation objective, which has an associated measure of performance (Tear et al. 2005). Our goal is to develop and implement a restoration strategy that delivers both site and landscape-level benefits and is financially and logistically feasible. Our objective is to maximize the utility of restoration, given a fixed annual budget constraint over a pre-specified timeframe. Within an optimization framework, we require information on our objective function, the state variables, control variables, costs, benefits, constraints and system dynamics (Wilson, Carwardine & Possingham 2009).

Formally, we represent the state of the landscape at time t with the vector yt, where inline image is the state of each individual site i, where i = 1,…, Ns. If site i is intact yit = 2, if it is being restored yit = 1, and if it is degraded yit = 0. We also define inline image, where zit = 1 if site i is intact and zero otherwise, and therefore represents the set of sites that are fully restored. A variety of restoration actions with different costs, benefits and likelihood of success are usually available. We therefore represent the control variable, the set of actions to be performed, with the vector xt, where inline image is the restoration action selected for site i at time t and Wit, the set of possible restoration actions available for site i at time t. If xit = 0 then no action has been selected for site i at time t. In this case study there is the option of only one possible action, in addition to the option of no action, per site. Accounting for the impacts of uncertainty and environmental stochasticity on the outcomes of restoration action, we define the system dynamics with a set of conditional transition probabilities P. For each state-action pair we define P(yt|yt-1, xt), the probability that the system is in state yt given the initial state yt-1, and restoration actions xt, with yt-1 × xt → P(yt) defined as a probability distribution over yt based on the likelihood of restoration success at each site.

Our objective function is to maximize the expected utility inline image from restoration achieved by being in state yt at the end of the timeframe of interest T, where at each time step the utility is calculated as:

image(eqn 1)

which is the sum of the benefits achieved from being in state yt weighted by the probability of being in each state, and subject to the constraint:

image(eqn 2)

where inline image is the cost of restoration action xit at site i and Bt is the budget constraint (for further information refer to the Supporting Information).

Thus, for each candidate restoration site we need to know the initial state, the restoration actions able to be implemented at each site, requirements for spatial clustering, the cost, likelihood of success and benefits of restoration, and the probability of stochastic events that will influence the restoration outcomes.

We describe below (and in Appendix S1) how this information can be derived using the Irvine Ranch Natural Landmark as a case study.

The Initial State

The state of the system was represented in terms of the current degradation state of each candidate restoration site, classified as follows:

  • 1 Highly degraded: 85–100% non-native species coverage.
  • 2 Partially degraded: 70–85% non-native species coverage.
  • 3 Functionally restored/intact: <70% non-native species coverage.

The degradation state of a site influences its relative restorability and the required restoration action (Suding, Gross & Houseman 2004). The determinants and indicators of site degradation will vary among ecosystems and depend on site and regionally specific threats. In southern California, the coverage of non-native species is considered an informative indicator of degradation as such species are highly competitive and quickly colonize degraded sites (Eliason & Allen 1997; Dyer & Rice 1999; Cox & Allen 2008).

For each candidate restoration site, we determined the desired habitat type based on the site’s known or predicted original habitat type (as deduced from remnant vegetation, soil type, or in the case of oak woodlands, the predicted original extent), and adjacent extant vegetation (Isaac et al. 2007; Irvine Ranch Conservancy 2008).

The Restoration Actions

Generally, more than one type of restoration action is available to be implemented at a site and these actions typically differ in cost, likelihood of success, and benefit/utility (see below), which will probably also depend on the desired habitat type.

Two potential restoration actions were considered on the Irvine Ranch Natural Landmark, although any number of actions could be accounted for within the prioritization framework. The actions we considered were termed ‘full restoration’ and ‘partial restoration’ and the choice of which to implement at each site depends on the initial degradation state and was therefore pre-specified for each site. Full restoration will take a site from a highly degraded to a functionally restored state. This restoration action requires seeding a full quantity of functional species and implementing site preparation and maintenance across an entire site. Partial restoration will take a site from a partially degraded to a functionally restored state. This restoration action requires seeding a partial quantity and complement of species and less site preparation and maintenance. The difference in cost of partial and full restoration depends on the habitat type and slope (see Table S1). While partial restoration requires less seed and maintenance it does require a more customized approach to planning and site preparation, and a more cautious and labour-intensive approach is necessary when utilizing equipment and herbicides around extant patches of vegetation, particularly on steep slopes. We assumed both types of restoration action take 5 years to complete for the coastal sage scrub, native grasslands and chaparral habitat types, and 15 years for the oak woodland habitat. We accounted for these time lags in the prioritization analysis by delaying the transition to a restored state for either 5 or 15 years from the initial year in which restoration was initiated. Thus the benefits of restoration were not realized in the analysis until after the time lag is complete.

Clustering of Restoration

Candidate sites for restoration were grouped into restoration clusters identified as all adjacent sites within the same sub-watershed. There are 101 restoration clusters on the Irvine Ranch Natural Landmark, comprising groups of 1–22 sites that range in size from 1 to 30 ha. Restoration action was implemented at all sites within a restoration cluster, within the constraint of the available budget and limits on the area of land that can be restored in any 1 year (see Constraints below). The identification of restoration clusters was considered important for the Irvine Ranch Natural Landmark to enable implementation logistics to be accounted for, particularly moving equipment between restoration sites in any one season. The relevance of such considerations will vary between landscapes.

The Cost of Restoration

We determined the cost per hectare of restoration for each site as a function of the restoration action, desired habitat type and slope. The base cost per hectare encompassed the initial costs of restoration, including thatch reduction, invasive species control, and seeding and planting (Eliason & Allen 1997; Dyer & Rice 1999; Cox & Allen 2008). The baseline cost was increased on slopes with a steep grade or with difficult access because more expensive, specialized equipment or extensive manual labour would be required. The estimated cost of restoring each site averaged US$11 838 and ranged from US$3 370 to US$201 018 (Table S1 and Fig. S3a). The total cost of restoring all candidate sites, without considering the possibility of restoration failure and ignoring inflation, is c. US$10·93 million. The cost of restoration at a site was independent of restoration undertaken at other sites and the degradation state of surrounding sites, and is assumed to be constant through time.

We also accounted for a start-up cost of US$10 000 included for each year restoration was commenced in a new restoration cluster. This start-up cost accounted for the costs associated with shifting equipment and personnel between sites.

The Likelihood of Restoration Success

The likelihood of restoration success was determined as a probability that restoration action at each site would succeed or fail. If restoration at a site failed, it was returned to the pool of sites for consideration for restoration in the following year and sites that failed in the previous time step were automatically reselected in the next time step. Overall, the number of times that a site could fail in the first year was constrained to two to account for the cumulative benefits associated with previous restoration attempts at a site. Any threshold relevant to the landscape being considered could be specified. Following successful restoration, a site was considered to reach a restored state at the end of the pre-specified time lag.

For the Irvine Ranch Natural Landmark we determined a baseline likelihood of success for each habitat type and restoration action and decreased this baseline if the sites occurred on a steep slope or had a southern aspect. The extent to which the site perimeter is shared with degraded vegetation was also used to modify the likelihood of success (Table S1 and Fig. S3b). The likelihood of success was recalculated at each time step by updating the percentage of each site perimeter shared with intact vegetation to include newly restored sites.

Seasonal conditions are also important in determining the likelihood of restoration success. The baseline likelihood of success is based on good growing conditions, but in southern California a bad growing season due to drought occurs on average every 4 years (therefore the probability that it will be a good growing season in any 1 year is 0·75). We assumed that a bad growing season reduces the likelihood of restoration success in the first year to 0·2 (allowing for minimal levels of survival and seed dormancy rates).

Stochastic Events

Stochastic effects such as fire or flooding can be incorporated into the prioritization analysis as a probability that sites where restoration had been initiated will be degraded. At the Irvine Ranch Natural Landmark, a key ecological dynamic is fire (Allen et al. 2000; Brooks et al. 2004; Suding, Gross & Houseman 2004; Keeley, Baer-Keeley & Fotheringham 2005). The probability of fire was assumed to be spatially homogenous across the Natural Landmark and occurring once every 15 years (an annual probability of 0·06). To account for the extensive nature of most fires, the occurrence of fire was determined at a restoration cluster level. In the occurrence of fire, the likelihood of restoration success was reduced to zero although intact or already restored sites were considered to remain intact. The system dynamics and state transitions assumed for this study region are summarized in Fig. 1.

Figure 1.

 System dynamics indicating possible state transitions, where * denotes, ‘fire, no action or action unsuccessful’.

Constraints

Budget and operational constraints will be specific to particular projects. The constraints to restoration on the Irvine Ranch Natural Landmark reflect a fixed, annual budget and also the area of land that can be restored each year due to operational and seasonal limitations, as is the case in many restoration projects. The projected budget available for restoration at the Irvine Ranch Natural Landmark is c. US$700 000 per annum over 20 years (US$14 million in total, ignoring inflation), although restoration is likely to continue beyond this timeframe. Surplus funds not used in the allocated year, are carried forward in the prioritization analysis for use in the following year. In addition, we constrained the area able to be restored to 80 ha year−1.

Restoration Utility

The utility of restoration can be measured using a variety of socio-economic and ecological parameters. We define the utility of restoration for each dollar invested in terms of contribution towards a set of conservation features j, where = 1,…, Nt. Our objective is to maximize the expected utility inline image from restoration action in system yt where:

image(eqn 3)

and inline image are feature-specific functions transforming representation into a reward relevant to conservation feature j. The overarching framework is therefore based on the principle of complementarity as each function inline image evaluates the value of each feature jointly over all sites (Moilanen, Possingham & Polasky 2009). The weights wj represent the degree to which conservation feature j contributes to the overall restoration utility. This general utility equation can be adapted to incorporate any number of conservation features and functional forms. The final utility inline image for the Irvine Ranch Natural Landmark case was developed as a function of the benefit of the multi-objective benefit from restoration inline image, where:

image(eqn 4)

for inline image the benefit obtained from restoring habitat, inline image from representation of rare and sensitive species, inline image from increasing spatial connectivity, and inline image for representation of features associated with the enhancing resilience of the system to disturbances such as fire and invasive species. In the Irvine Ranch landscape these features include areas located in areas of high risk of fire ignition, in the two climate change corridors that have been identified on the reserve, and in riparian corridors. The form of the utility obtained from restoring habitat in the Irvine Ranch Natural Landmark was then adjusted to a sigmoidal relationship to reflect the assumption that a minimum level of funds will need to be expended to overcome particular biotic and abiotic obstacles to restoration success (Andren 1994; Fahrig 2002; Huggett 2005; Hobbs 2007). We outline the details of the sigmoidal adjustment and forms of the functions for the conservation features in the Appendix S1, where we also describe how they might be adapted for alternative problem formulations.

Aside from calculating utility in ecological terms, utility was also calculated in economic terms – specifically the anticipated reduction in overall cost through restoring particular sites (see below).

Solution Methods

The overall aim is to find a restoration schedule through manipulation of the control variable that has the greatest utility subject to the constraints. The restoration prioritization problem is too large to solve optimally, so a simulated annealing algorithm was implemented to search for near-optimal solutions. We also compared the performance of two ‘rule-of-thumb’ heuristics against the solution from the simulated annealing algorithm (i) ‘maximize marginal return-on-investment’, (ii) ‘minimize future expected cost’ (see Supporting Information for further details).

For the ‘maximize marginal return-on-investment’ heuristic the restoration clusters were scored according to their (utility/expected cost), where the expected cost is the cost divided by the likelihood of success. For the ‘minimize future expected cost’ heuristic, restoration clusters were scored according to their (reduction in future expected cost/expected cost). The potential to reduce the future expected cost was based on the resulting increase in the likelihood of success of neighbouring sites (in different restoration clusters) due to an increase in the perimeter of neighbouring sites that is restored. The restoration clusters were selected iteratively by each heuristic, with the highest scoring cluster selected at each time step for investment until the constraints were met. The scores for each site were updated after each time step as sites were restored and adjustments were made to the likelihood of restoration success of each site.

The choice to implement the rule-of-thumb heuristics instead of only the simulated annealing algorithm was to gain a better insight into the problem dynamics and to deliver a restoration prioritization decision support tool suitable for practical implementation. This was considered more useful for restoration practitioners and more appropriate when operating in a dynamic and long-term implementation environment, during which the system conditions and the problem formulation are likely to change. The rule-of-thumb heuristics have the opportunity to update their site selection schedules based on the impact of stochastic events (such as fire) and restoration failure. In contrast the simulated annealing algorithm delivers a static solution that performs well on average, but is not designed to be reevaluated in subsequent years based on realized outcomes through time and/or alterations to the system conditions. We also implemented a random selection heuristic that selected restoration clusters at each time step at random, until the constraints had been met.

We compared the performance of the two rule-of-thumb heuristics to the simulated annealing and random solutions by recording the average, best, and worst results after 20 years and after 100 000 simulations. We identified the solutions with the greatest mean expected utility score (i.e. a solution that is robust to variation in the likelihood of success outcomes) and we determined the utility scores over the best and worst likelihood of success outcomes.

Sensitivity Analysis

We compared the maximize marginal return-on-investment solutions when each of the rare species, fire ignition risk zones, climate change corridors and riparian corridor preferences were removed separately but the preference for spatial connectivity remained. We also considered the separate removal of each of the four preferences when there was no preference for spatial connectivity (i.e. a total of eight scenarios were considered). In addition we assessed the sensitivity of the prioritization results to changes in the annual constraints. We repeated the analysis with the funding and area constraints set to half and double of the original values and evaluated the impact of these modifications separately and in combination.

Results

Performance of the Solution Methods

By seeking to maximize the marginal return-on-investment using the rule-of-thumb heuristic we obtained restoration schedules that gave the greatest utility score (and greatest score for each of the preferences) on average after 20 years (Fig. 2a). After 40 years each of the heuristics had acquired on average 99% or greater of the total restoration utility (Fig. 2b). The simulated annealing algorithm was optimized over both 20 and 30 year timeframes. After 20 and 30 years the overall utility score from the maximize marginal return-on-investment heuristic was 80% of the 20 year simulated annealing solution and 97% of the 30 year simulated annealing solution respectively (Fig. 3a). The random selection algorithm outperformed the heuristic method that sought to minimize the future expected cost (Fig. 3a). After 40 years there was very little difference in the utility achieved using the different solution methods (including the random allocation approach). The utility score increases through time as sites are restored, as does the level of performance uncertainty due to the possible impacts of the likelihood of success outcomes (Fig. 3b).

Figure 2.

 Comparison of the performance of the restoration schedules when different solution methods are employed. Utility scores are measured after (a) 20 and (b) 40 years.

Figure 3.

 (a) The performance of the rule-of-thumb heuristics compared to the simulated annealing and random selection algorithms. (b) The utility of restoration (using the maximize marginal return-on-investment heuristic) showing mean expected, best and worst case outcomes.

Practical Implications of the Restoration Schedule

Over the 20 year time period (reflecting the current budget timeframe) it is predicted that not all sites will be restored on the Irvine Ranch Natural Landmark. Using the schedule from the maximize marginal return-on-investment heuristic, restoration would be commenced in 725 sites, and on average sites would be chosen 1·4 times for restoration. After 20 years, 555 sites are predicted to be successfully restored [equating to 724 ha, leaving 368 sites (and 629 ha)] still requiring some level of restoration. On average all sites would be successfully initiated after 30 years, with all sites fully restored after 43 years. The total expenditure after 20 years for the sites that are restored would be US$13·7 million. The spatial distribution through time of the sites to be restored based on the recommendations from the maximize marginal return-on-investment heuristic are displayed in Fig. 4.

Figure 4.

 A draft schedule for restoration (a) year 1, (b) year 5, (c) year 10, (d) year 15 and (e) year 20 for the maximize marginal return-on-investment heuristic, using the best solution over each timeframe. The probability of restoration being initiated at each site after 20 years is displayed in (f).

Impact of Preferences and Annual Constraints

We explored the impact of including preferences for particular outcomes by determining the extent to which these preferences (e.g. restoring habitat in climate change corridors) would be achieved incidentally when not explicitly targeted. When preferences for restoring the habitat of rare species, fire ignition risk zones, climate change corridors and riparian corridors were individually removed we find very little difference in the solutions. However, under the scenario when there was also no preference for spatial connectivity between restoration clusters, then removal of each of the individual preferences led to a reduction in the extent to which each of the preferences was achieved (Fig. 5). The preference for spatial connectivity between restoration clusters therefore drove the selection of sites.

Figure 5.

 A comparison of overall utility scores for individual preferences when the preferences are explicitly targeted or ignored in the selection of sites and when spatial connectivity between restoration clusters was not sought. Utility scores are measured after 20 years.

Through the sensitivity analysis of the budget and area constraints, we found that when the levels of annual funding and area able to be restored were varied, the order in which restoration clusters was selected remained the same. When the constraints were doubled from original levels all sites would be fully restored after 31 years. When the levels of the constraints were halved all sites would not be restored within a 50 year timeframe, with only 82·5% of the total utility on average restored by year 50. Individual changes in the level of the constraints (i.e. alteration of the budget available, but not area, or vice versa) did not significantly change the results, and in the case that only one or other of the constraints were increased, there was only marginal increase in the speed with which the utility could be acquired. This indicates that both the budget and area constraints were influential in determining the level of restoration benefit able to be achieved each year.

Discussion

We have shown that the application of a return-on-investment approach to restoration prioritization can provide a comprehensive restoration schedule to inform the selection of sites to restore. Our prioritization approach is based on a clearly formulated problem, with the objective, constraints, and knowledge of the system dynamics outlined a priori. Information on key considerations when planning for restoration were able to be appropriately incorporated: cost, benefits, likelihood of success, spatial considerations, feedbacks, time lags and the probability of stochastic events. The use of a dynamic prioritization framework allowed for updating of restoration priorities during the course of the restoration process based on previous outcomes, which was particularly important to account for the impacts of fire and drought.

We compared the restoration schedules using alternative problem formulations and solution methods. Over the nominal 20 year planning period we found that by maximizing the marginal return-on-investment we can achieve a greater overall utility score. The simulated annealing solution optimized for 20 years revealed that higher returns are able to be achieved at the cost of reduced performance in later years. The simulated annealing solution optimized for 30 years performed best in the long run but poorly during the first 25 years of the restoration process. The minimize future expected cost heuristic provided suboptimal solutions for the majority of the restoration timeframe and was outperformed by the random selection heuristic. The aim of the minimize future expected cost heuristic was to target restoration towards sites that would increase the likelihood of success of neighbouring sites (by increasing the percentage of the perimeter shared with restored sites). The results showed that this heuristic was more successful at targeting such sites compared to the marginal return-on-investment heuristic. Under the minimize future expected cost approach, the likelihood of success was improved at an average of 11 sites over the course of the restoration process, vs. improvements at an average of just two sites under the marginal return-on-investment heuristic. Overall, however, there are a relatively small number of neighbour to neighbour pairs (a total of 57) in different restoration clusters, which along with the time lag that delayed the rate at which benefits from restoration were accrued, limited the impact of such targeting. The small increase in likelihood of success as a result of improvement in the perimeter quality of neighbouring sites (0·05, prior to moderation by fire and drought probabilities) further limited the performance of the minimize future expected cost heuristic for the Irvine Ranch case study. Thus, while the minimize future expected cost heuristic may be appropriate for guiding prioritization in some situations, its performance for this particular case study was limited due to the characteristics of candidate restoration sites.

The implementation of the random selection heuristic provided a system control, facilitating an evaluation of the improvement that our targeted prioritization methods offered over ad hoc selection. We find from our results that the random allocation of restoration effort will achieve a similar overall utility in the long-term to more objective prioritization approaches, particularly the minimize future cost heuristic, but also the maximize marginal return-on-investment heuristic and to a lesser degree the simulated annealing algorithm (Fig. 3a). The random heuristic performed well (within 10% of the maximize marginal return-on-investment heuristic) reflecting key features of this case study: where there is no permanent loss of sites requiring restoration, there is no way to speed the restoration process and the differences between sites are small. The performance of the random heuristic did, however, vary depending on the particular configuration of sites selected. Results from the worst case scenario revealed that its performance was much less robust than the maximize marginal return-on-investment heuristic, underperforming by 20–30% over the first 30 years.

We find that on average after 40 years we maximize the restoration utility, regardless of the solution method employed. This does not imply, however, that all sites will be restored to their full ecological functionality by this time. We anticipate that greater differentiation between the solution methods would be obtained if the measure of restoration performance was adjusted to more closely reflect the ecological functionality of the sites restored and if we accounted for a broader suite of restoration actions that differed in their contribution to restoring this functionality. It is likely that under such circumstances we would see a greater advantage of a strategic approach to restoration prioritization.

A large number of complexities are able to be considered in our prioritization approach, however, in this application a number of simplifications were employed due to the nature of the data available and the preferences of end users. As outlined in Appendix S1 we could modify the analysis to weight each habitat type differently and then target sites for restoration that would contribute the most underrepresented habitat type. We could also relax the assumption that all sites where a rare or sensitive species occurs have equal value, although the data required for this is currently not available for our study region. Similarly, while in this application there was only one choice of restoration action per site, the multi-action variable inline image allows for multiple possible actions at each site. Incorporating multiple possible actions introduces a number of additional complications, for example, dependencies between actions may need to be considered and transition probabilities between states under each of the different actions, or sets of actions, would need to be defined (Fig. 1). The complexity of finding optimal and near-optimal solutions under the multi-action formulation will increase significantly (van Teeffelen & Moilanen 2008; Possingham, Moilanen & Wilson 2009). Further development and testing of algorithms to solve such problems represents an important next step to deliver a comprehensive methodology for determining restoration priorities. Uncertainty in parameters, such as the likelihood of success, could also be represented by use of a distribution of likelihood values inline image, or through implementation of non-probabilistic approaches such as information gap analysis for situations where there is not enough information to define a probability distribution (Ben-Haim 2001).

Our systematic approach also allows for dependencies and the interconnectedness of system components to be revealed. For example, by explicitly accounting for the likelihood of restoration success the importance of factoring contingencies into the overall budget was revealed. We also discovered that the available budget will be likely to fall short of that required to restore all sites. Furthermore, restoration of the sites identified as priorities in the first 5 years will reduce the cost of restoration by an average of US$78 200 compared to if they were commenced in the 20th year. This reduction in overall expected cost is possible because of the cost efficiency and higher likelihood of success of restoration at these sites (the basis on which they were selected), thereby increasing the likelihood of success of other sites and allowing for more efficient use of funds throughout the remaining planning period. Therefore, aside from providing a schedule for where and when restoration should occur, our restoration prioritization approach provides other forms of operational guidance and support.

The benefits of habitat restoration are not constrained to the restored site, as there are both on- and off-site impacts associated with restoration. Spatial dependencies are of particular significance since the speed and likelihood with which the benefits are realized is determined by the interactions between neighbouring sites. Ensuring compactness of restored and intact sites is therefore likely to enhance the likelihood of restoration success. We explicitly sought compact solutions as part of our utility function at both a site level and at the level of restoration clusters. Clustering was also delivered through the specification of the constraints, specifically, that once a restoration cluster was selected all sites belonging to that restoration cluster would be selected for restoration action in that year. The likelihood of success calculations also accounted for neighbourhood effects.

This research has illustrated the value of a clearly stated objective; nonetheless, few published approaches to prioritizing restoration activities require the objective to be explicitly stated (Beechie, Pess & Roni 2008). Working within a basic optimization framework, it was possible to include a considerable degree of problem complexity and we were able to incorporate key information that managers deemed important for restoration. The framework and prioritization approach is widely applicable and the data employed represent key considerations when planning for restoration. Overall, the return-on-investment approach to restoration prioritization helps to structure decisions. The value of a structured prioritization process is revealed both in the information delivered on restoration priorities and in the clarification of objectives, system relationships and operational constraints.

Acknowledgements

This research was supported by Grant #2008-0323 made through the Conservation Opportunity Fund of the Resources Legacy Fund to the Irvine Ranch Conservancy, the Australian Research Council and the Australian Centre for Ecological Risk Analysis; The Nature Conservancy and The Irvine Company for contributing survey data; and April Newlander, Melissa Lippincott and Isaac Ostmann for help in conducting field surveys. We also acknowledge J. Keeley, R. Hobbs, G. Ewan and M. Evans for informative discussions.

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