Trade-offs between efficiency, equality and equity in restoration for flood protection

Conservation decision-makers and practitioners increasingly strive for efficient and equitable outcomes for people and nature. However, environmental management programs commonly benefit some groups of people more than others, and very little is known about how efforts to promote equality (i.e. even distributions) and equity (i.e. proportional distributions) trade-off against efficiency (i.e. total net outcome per dollar spent). Based on a case study in the Brigalow Belt Bioregion, Australia, we quantified trade-offs between equality, equity, and efficiency in planning for flood protection. We considered optimal restoration strategies that allocate a fixed budget (a) evenly among beneficiary sectors (i.e. seeking equality among urban residents, rural communities, and the food sector), (b) evenly among local government areas (LGAs) within the Brigalow Belt (i.e. seeking spatial equality), and (c) preferentially to areas of highest socioeconomic disadvantage (i.e. seeking equity). We assessed equality using the Gini coefficient, and equity using an index of socioeconomic disadvantage. At an AUD10M budget, evenly distributing the budget among beneficiary sectors was 80% less efficient than ignoring beneficiary groups, and did not improve equality in the distribution of flood protection among beneficiary sectors. Evenly distributing the budget among LGAs ensured restoration in four areas that were otherwise ignored, with a modest reduction in efficiency (12%–25%). Directing flood protection to areas of highest socioeconomic disadvantage did not result in additional reductions in efficiency, and captured areas of high disadvantage for the rural and urban sectors that were missed otherwise. We show here that different ways of targeting equity and equality lead to quite different trade-offs with efficiency. Our approach can be used to guide transparent negotiations between beneficiaries and other stakeholders involved in a planning process.


Introduction
Urgent action is needed to protect, restore, and sustainably manage ecosystems to secure their benefits to people, commonly known as ecosystem services (box 1) (Chan andSatterfield 2020, Mandle et al 2020). Given limited resources available for management and conservation interventions, finding efficient solutions that achieve the greatest return on investment is crucial (Possingham et al 2001, Moilanen et al 2009, Halpern et al 2013. However, such interventions may not result in a fair distribution of benefits for different groups of people across a planning region (Mandle et al 2015, Grima et al 2019, Gourevitch et al 2020. Furthermore, what is regarded as a 'fair' benefit distribution will vary according to underlying social, economic, and political conditions affecting peoples' opportunities to derive benefits (McDermott et al 2013, Vucetich et al 2018. Thus, there is strong need to develop Box 1. Glossary.

Concept
Definition Beneficiaries People whose well-being is influenced by ecosystem services (Daw et al 2011, Keeler et al 2012. Demand Extent to which an ecosystem service is currently or potentially used, needed, or preferred by people (Villamagna et al 2013, Bagstad et al 2013. Ecosystem Services Biophysical and social conditions and processes by which people, directly or indirectly, obtain benefits from ecosystems that sustain and fulfill human well-being (MEA 2005, Daily 1997). Efficiency Total net outcome per dollar spent (Brown et al 2018, Halpern et al 2013. Equality Even distribution of ecosystem service benefits among beneficiaries (McDermott et al 2013). Equity Distribution of ecosystem service benefits according to different beneficiaries' opportunities to derive benefits (McDermott et al 2013). Fair Distribution of ecosystem service benefits according to well-reasoned application of three principles: equality (all humans are entitled to the same outcomes), need (what is necessary for realizing a healthy, meaningful life), and desert (noun form of deserve-benefit is distributed in proportion to peoples' contributions) (Vucetich et al 2018, McDermott et al 2013, Wagstaff 1994. Flow Biophysical or human capital-driven interactions and processes that connect supply and demand (Fisher et al 2009, Villamagna et al 2013. Optimization problem Mathematical formulation describing the problem of finding the best solution from all feasible solutions (Moilanen et al 2009). Passive restoration Method to assist the natural re-establishment of vegetation utilizing low-cost techniques such as restriction of livestock grazing or vegetation thinning to reduce competition and promote growth (Evans et al 2015). Spatial planning Structured decision analysis approach with a series of stages to meet specific objectives, usually through the prioritization of the most feasible places for conservation investment (Moilanen et al 2009). Supply Ecosystem conditions and processes that contribute to the potential delivery of a particular ecosystem service (Fisher et al 2009, Villamagna et al 2013.
spatial planning solutions that recognize the diversity of ecosystem service beneficiaries in a landscape and their different opportunities to access benefits (Chan andSatterfield 2020, Villarreal-Rosas et al 2020). In equal approaches, benefit is distributed evenly among beneficiaries, while in equitable approaches, benefit is distributed relative to peoples' opportunities to access ecosystem services (Daw et al 2011, McDermott et al 2013. Promoting fairness through equal and equitable planning strategies is likely to result in trade-offs with efficiency (Halpern et al 2013, Klein et al 2015, Brown et al 2018. Investigating these trade-offs is fundamental to guide fair conservation investments. People's opportunities to obtain benefits from ecosystem services are influenced by the physical locations where people demand a service relative to the places where ecosystem services are supplied, and the flow mechanisms that enable the benefits of a service to be utilized by people (Haines-Young andPotschin 2010, Serna-Chavez et al 2014). For example, physical and mental health benefits from outdoor experiences are not distributed evenly across a landscape and, the distance between people's residencies and the location of natural areas affects people's opportunities to benefit from recreation activities in nature (Sonter et al 2016, Martinez-Harms et al 2018. Underlying socioeconomic factors also influence people's ability to reach or benefit from a service, including people's access to ecosystem service substitutes, or their ability to overcome ecosystem service loss (Daw et al 2011, Wilkerson et al 2018, Vallet et al 2019. For example, in the US, Latino and African American residents live in areas with low access to urban green space, where heat island effects are felt more strongly, yet, such minority groups usually have less economic opportunity to pay for air conditioning (Nesbitt et al 2019, Hoffman et al 2020. Addressing inequalities through management or conservation intervention requires developing planning strategies that acknowledge benefit is distributed differently amongst people (Daw et al 2011, Chan and Satterfield 2020, Villarreal-Rosas et al 2020. Yet, to date, most planning approaches for ecosystem services have focused on obtaining total benefit gains (Villarreal-Rosas et al 2020). That is, the sum of all the benefits regardless of to whom those benefits flow or if local benefit decreases occur, which overlooks the variation in the flow of benefits among people (Daw et al 2011, McDermott et al 2013. Some studies have started to explore this issue when planning for ecosystem services. For example, Gourevitch et al (2020) and Li et al (2020) found that floodplain restoration is an economically viable intervention to reduce flood damage, although mitigation of flood risk benefited more the socioeconomically advantaged beneficiary sectors (Gourevitch et al 2020). This suggests that management plans seeking to benefit the most disadvantaged people in society may imply higher management costs, although the extent of such trade-offs has been understudied in the ecosystem services literature.
In this study, we aim to assess how efficiency is affected when promoting equality and equity in spatial planning, and we discuss how this information is useful to advance towards fair management plans for ecosystem services. We use as a case study the provision of flood protection in the Brigalow Belt, Australia. Flood protection is one of the most severely affected ecosystem services from land degradation, increasing the risk to life and property for millions of people globally (Pesaresi et al 2017). In the Brigalow Belt-an area affected by widespread deforestationprevious flood events have caused local damage to housing and infrastructure valued at over AU$5 billion (State of Queensland 2019, Commonwealth of Australia 2020). Programs are available to assist with recovery after floods (Australian Government 2020), yet variation in income, education, employment security, and housing characteristics influence the capacity of rural and urban residents to benefit from these programs (Morrissey andReser 2007, Veitch 2009).
A previous study in the Brigalow Belt identified highly disproportionate declines in flood protection across three beneficiary sectors due to forest loss (namely: urban residents, rural communities, and the food sector) (Villarreal-Rosas et al 2022). Investing in forest restoration constitutes a naturebased alternative to decrease flood risk, and has been shown to be an economically viable solution in other regions (Gourevitch et al 2020, Li et al 2020. Here, we develop different forest restoration investment strategies to address some of the previously identified disparities in the distribution of flood protection from forest cover among beneficiary sectors in the Brigalow Belt. Our three strategies for restoration investment include: promoting equality by (a) evenly distributing monetary resources among beneficiary sectors, or (b) evenly distributing monetary resources among local government areas (LGAs); and (c) promoting equity by giving priority to areas of high socioeconomic disadvantage. In this respect, we ask, to what extent do investment strategies improve equality and equity among beneficiary sectors, compared to a baseline strategy where these are ignored, and how is efficiency (the total flood protection obtained under different planning budgets) affected when promoting equality and equity of investment strategies?

Study area
Forest cover loss reduces the capacity of ecosystems to regulate flood intensity, exacerbating damages to people from flood events (MEA 2005, IPBES 2019). The Brigalow Belt Bioregion (351 500 km 2 ) located within the State of Queensland (figure 1) has had one of the highest deforestation rates in Australia in recent times (Evans 2016). The Brigalow Belt is named after the Aboriginal name for the region's dominant tree species Acacia harpophylla (Ponce Reyes et al 2016, Department of the Environment 2020). Notably, Brigalow trees sprout from the root stock in the soil (suckering) following disturbance (Chandler et al 2007). Despite broad scale clearing of Brigalow forest in some regions, much of the cleared land retains regenerative capacity (Butler 2009, Lucas et al 2014. This is particularly true in areas of extensive grazing, where clearing of regrowth is a common management practice for landholders (Butler 2009, Dwyer et al 2009, Fensham and Guymer 2009). Thus, promoting regrowth of Brigalow forest constitutes an alternative for the restoration and maintenance of ecosystem function (Dwyer et al 2009, Evans et al 2015. Promoting vegetation regrowth is a passive restoration method that requires little intervention, as such, it represents a low cost and highly efficient restoration alternative (Dwyer et al 2009, Evans et al 2015. However, allowing regrowth implies foregone revenue for farmers (Evans et al 2015).

Investment strategies
We first defined an optimization problem to find the best places to invest in passive restoration of Brigalow forest to enhance flood protection for three beneficiary sectors: urban residents, rural communities, and the food sector (box 2). In our optimization problem, enhancing flood protection for each beneficiary sector represented a sub-objective; all sub-objectives were incorporated as an equally weighted sum into the objective function (box 2). We used cadastral lots from the Queensland cadastral dataset (Department of Natural Resources, Mines and Energy 2018) as decision units (with a total of 18 863) where passive restoration was allocated to. Selection of decision units was constrained by budget levels that represented 3%-50% of the total opportunity cost (the cost of grassland turning into Brigalow regrowth) for extensive grazing in the Brigalow Belt ($340 M AUD per annum). We considered this set of predefined budgets to explore changes in the amount of flood protection captured at different expenditures. We then used the restoration opportunities optimization tool (Beatty et al 2018) to solve the optimization problem (table S1 for full details (available online at stacks.iop.org/ ERL/17/014001/mmedia)). Decision units comprised locations where passive restoration is feasible to apply independently of benefits or costs (table S1). We calculated flood protection at the decision unit level, as the marginal reduction value in quickflow production after intervention multiplied by the sum of all downstream demand for flood protection the decision unit had access to. Reductions in quickflow after intervention were estimated using the InVEST 3.5.0 Seasonal Water Yield model (table S1). Demand for flood protection was estimated as the area and number of infrastructure at risk of flooding at the downstream floodplain areas of sub-watersheds identifying each beneficiary sector (table S1). Demand values for each beneficiary sector were aggregated to decision units as the sum of demand of all the sub-watersheds that overlapped with a given decision unit (table S1). Decision units often provided benefit to more than one beneficiary sector. Decision units were associated to LGAs using the 'Local Government Area Boundaries Queensland' dataset (Department of Natural Resources, Mines and Energy 2019).
We developed different investment strategies to solve this optimization problem (i.e. different objective functions, box 2). Our investment strategies aim to address previously identified inequalities in the distribution of flood protection among multiple beneficiaries and LGAs in the Brigalow Belt (Villarreal-Rosas et al 2022). Therefore, our first two investment strategies promoted equality by constraining how restoration resources are allocated among beneficiary sectors or among LGAs (table 1). Then, we accounted for equity in our investment strategies by giving preference to locations of high socioeconomic disadvantage. We also considered a 'baseline' investment strategy for

Box 2. Objective functions and constraints used for each investment strategy.
comparison, which ignored equality and equity (table 1).
In the 'baseline' strategy, the available budget could be used to select decision units anywhere in the Brigalow Belt (box 2). In the 'sectors' strategy the budget was equally divided among each beneficiary sector. In the 'sectors + disadvantage' strategy, the budget is equally divided among each beneficiary sector, but investments were preferentially directed to areas of highest socioeconomic disadvantage. In the 'LGA' strategy, the budget was equally divided between 18 LGAs (6 were excluded as they did not have area available for intervention or infrastructure at risk, see table S1. In the 'LGA + disadvantage' strategy, the budget is equally divided among each LGA, but investments were preferentially directed to areas of highest socioeconomic disadvantage.

Comparing efficiency, equality, and equity among strategies
We compared changes in efficiency, equality and equity between the 'baseline' and the 'sectors' and 'sectors + disadvantage' strategies (table 1(A)); and between the 'baseline' and the 'LGA' and ' LGA + disadvantage' strategies (table 1(B)). We assessed efficiency as the total sum of flood protection benefits (across all decision units selected) at each budget level. We assessed equality using the Gini coefficient because it is a widely used measure of statistical concentration among values of a frequency distribution (Ceriani and Verme 2012). The Gini coefficient is applicable to any size distribution of general data sets, and has been globally used to assess social inequality (Sitthiyot and Holasut 2020). It has also been used to assess the distribution of ecosystem services at different spatial scales (Ceriani and Verme 2012, Li et al 2017, Benra and Nahuelhual 2019, Yang et al 2021. The Gini coefficient does not account for absolute distributions, but this is acceptable given that we use the Gini coefficient as a relative measure of change in the distribution of flood protection (Sitthiyot and Holasut 2020). We calculated the Gini coefficient using the 'gini' function from package REAT, version 3.0.2, R, where values of 0 mean perfect equality while values of 1 perfect inequality.
To assess changes in equality among beneficiary sectors (table 1(A)) the Gini coefficient was calculated based on the sum of flood protection benefits for each beneficiary sector across decision units selected. To assess changes in equality among LGAs (table 1(B)) the Gini coefficient was calculated based on the sum of flood protection benefits for each LGA. Decision units differed in the amount of area available for intervention (table S1), to account for this, we weighted the Gini coefficient considering the total area available for intervention within decision units selected.
We assessed equity by estimating the extent to which areas of highest socioeconomic disadvantage were captured across all strategies using the Index of Relative Socio-Economic Disadvantage (IRSD) (ABS 2018). The IRSD reflects people's access to material and social resources and is based on variables such as income, education, employment, occupation and housing characteristics (ABS 2018). We use the IRSD as a proxy for people's capacity in the region to recover economically and psychologically from the damages of flood events (Morrissey andReser 2007, Veitch 2009).

Impacts on efficiency
All our investment strategies were less efficient at capturing flood protection for all beneficiary sectors than the 'baseline' , where equality and equity were ignored. That is, under the same budget, any other strategy captured less flood protection than the 'baseline' (figure 2). The 'sectors' and 'sectors + disadvantage' strategies represented high losses in efficiency compared to the 'baseline' (figure 2). This is particularly true at the lowest budget levels. For example, at a $10 M budget, the 'sectors' strategy captured almost 80% less flood protection for our three beneficiary sectors than the 'baseline' (figure 2). This is explained by an overall reduction in the number of decision units selected in favor of achieving the allocated expenditure per beneficiary sector. Both the 'LGA' and ' LGA + disadvantage' strategies implied a similar reduction in efficiency compared to the 'baseline' strategy. This was 25% for rural communities and the food sector, while 12% for urban residents at the $10 M budget constraint, at higher expenditures reductions in efficiency reached ∼50% (figure 2).

Impacts on equality among beneficiary sectors
The 'baseline' investment strategy resulted in highly disproportionate distributions of flood protection among beneficiary sectors (figure 3). That is, from the total amount of flood protection captured in the 'baseline' strategy at a $10 M budget, the food sector received almost twice the protection than urban residents received, and around 14 times more than rural communities ( figure 3(a)). The inequality in the distribution of flood protection among beneficiary sectors is also reflected in a Gini coefficient of ∼0.6 obtained in the 'baseline' strategy (figure 3(b)). We found the 'sectors' strategy to be unsuccessful at improving equality among beneficiary sectors compared to the 'baseline' (figure 3). The proportion of flood protection captured from this strategy was very similar to the 'baseline' , that is, highly inequitable and favoring the food sector ( figure 3). Demand for the food sector was widely spread across the landscape, resulting in indirect benefits for this beneficiary sector even when it was not specifically targeted (Villarreal-Rosas et al 2022).
On the other hand, demand by rural communities was more localized (Villarreal-Rosas et al 2022), resulting in a smaller proportion of benefit captured by this sector. This explains why the proportion of flood protection among beneficiaries is almost identical in the 'baseline' , 'sectors' and 'sectors + disadvantage' strategies (figure 3).

Impacts on equality among
LGAs High inequality was found in the distribution of flood protection among LGAs in the 'baseline' strategy, particularly at $10 and $17 M budget constraints, with Gini coefficients of 0.9 and 1 respectively (figure 4). We found the 'LGA' strategy to be successful at improving equality among LGAs compared to the 'baseline' strategy (figure 4). The highest improvement in equality among LGAs was at the $17 M budget (5% of total), with Gini coefficients changing from 1.0 (perfect inequality) to <0.7 between the 'baseline' and ' LGA' strategy ( figure 4). Under the 'LGA' strategy, inequality progressively increased as the budget increased and more area was selected ( figure 4). This is explained by some LGAs having all decision units already selected, while others having additional units available for selection with higher budgets. Irrespective of the strategy, equality among LGAs converge to intermediate Gini coefficients as more area gets selected (as reflected in the $137 and 171 M budget constraints) ( figure 4). This suggests that, as more area is selected, the distribution of flood protection among beneficiary sectors is influenced more by the landscape interactions between supply and demand areas providing flood protection (as found in Villarreal-Rosas et al 2022) than the investment strategy. The high inequality found under the 'baseline' strategy is explained by four LGAs (Charters Towers, Livingstone, Blackall Tambo, Balonne) that did not receive any flood protection benefit at all under the 'baseline' strategy, while the 'LGA' strategy ensured some level of flood protection for all LGAs ( figure 5).

Impacts on equity
The 'baseline' strategy captured areas of similar socioeconomic disadvantage for our three beneficiary sectors, with values ranging between 0.17 and 0.20, from a maximum of 0.30 (indicating higher disadvantage) (figure 6). The 'sectors + disadvantage' strategy captured areas of similar LGA + disadvantage' , the equally allocated budget among LGAs is directed to areas of highest socioeconomic disadvantage.
socioeconomic disadvantage values to the 'baseline' strategy ( figure 6). This indicates that, our investment strategy seeking to improve equity among beneficiary sectors in the Brigalow Belt performs no better than strategies entirely ignoring socioeconomic disadvantage at the 10 M budget constraint (3%). The ' LGA + disadvantage' strategy captured areas of higher socioeconomic disadvantage values for rural communities and urban residents than the 'baseline' strategy at a $10 M budget constraint (figure 6). Higher expenditures in the 'LGA + disadvantage' strategy do not improve equity compared to our other strategies (figure S1). As opposed to the 'sectors + disadvantage' , the 'LGA + disadvantage' strategy was successful at capturing areas of highest disadvantage as it promoted the selection of decision units in each LGA that would otherwise not be selected. The disadvantage values captured for the food sector across all our different strategies did not change much due to a more homogeneous disadvantage index for this beneficiary sector across the Brigalow Belt ( figure 6).

Discussion
We use a spatially explicit prioritization framework to identify how different investment strategies perform at improving equality and equity among beneficiary sectors and LGAs, and the extent to which efficiency is compromised as a result. Management plans incorporating multiple beneficiary sectors imply inherent trade-offs, and systematic prioritization approaches, like the one we apply here, are critical to making such compromises transparent (Halpern et al 2013, Villarreal-Rosas et al 2020. Below we discuss the implications of promoting equality and equity when planning for ecosystem services and indicate aspects to consider in future work to help operationalize fair management plans.

Lessons learnt from our investment strategies
The 'baseline' strategy demonstrated that without consideration of equality or equity in the planning process, flood protection benefits of passive restoration are disproportionally distributed among beneficiary sectors and LGAs. Our investment strategies sought to improve equality and equity by changing how monetary resources available for intervention were allocated. The strategy 'sectors' , aiming at improving equality among beneficiary sectors was unsuccessful; it resulted in large reductions in efficiency and did not improve equality among beneficiary sectors compared to the 'baseline' . Inequalities in the distribution of flood protection among sectors in the context of forest restoration are explained by (a) the specific configuration of demand for the different beneficiary sectors in the Brigalow Belt and (b) the characteristics relevant to the provision of flood protection. Flood protection is considered a nonrival service, whereby the service does not degrade or transform when someone uses or benefits from it (Fisher et al 2009). In our approach, we assume flood protection is a perfectly non-rival service, which means that our decision units were not exclusive to beneficiary sectors, as flood protection provided to one beneficiary sector does not decrease protection to other beneficiary sectors. Given the wide distribution LGAs under different strategies. Investment strategies: 'baseline' , the budget available can be allocated anywhere in the Brigalow Belt; 'sectors' , the budget is equally allocated among beneficiary sector; 'sectors + disadvantage' , the equally allocated budget among beneficiary sectors is directed to areas of highest socioeconomic disadvantage; 'LGA' , the budget is equally allocated among LGAs; 'LGA + disadvantage' , the equally allocated budget among LGAs is directed to areas of highest socioeconomic disadvantage. Strategy 'sectors + disadvantage' is not illustrated as decision units selected were very similar to the 'sectors' strategy.
of demand from the food sector, most decision units that were selected to benefit the urban or rural sector indirectly also benefited the food sector, resulting in unequal distributions of benefit. Applying our 'sectors' strategy to other ecosystem services and planning contexts may return very different results. For instance, provisioning ecosystem services like timber extraction are considered rival (i.e. another person cannot benefit from timber extraction if some else has already benefitted from it) (Fisher et al 2009). In this case, evenly distributing economic resources for reforestation could achieve equal gains in forest cover across different communities (Orsi et al 2011), although people's capacity to obtain profit from timber extraction may differ (Chomba et al 2016). The strategy ' LGA' aimed at improving equality among LGAs was successful; although it represented an increase in costs of up to 25%, it ensured flood protection to all LGAs, including four that would be missed otherwise. This is important because solutions that miss benefit for some locations are less likely to be accepted and implemented successfully (Halpern et al 2013, Klein et al 2015, Kovacs et al 2016, Ali et al 2020. Thus, potential efficiency losses of enhancing equality may be minor if we assume that solutions that ignore equality have a lower probability of implementation success (Halpern et al 2013, Rosenthal et al 2015. In addition, our results show that equality and equity among LGAs does not improve beyond the $10 M budget constraint. Hence, identifying the optimal expenditure required to enhance equality or equity, as we do in this study, can help avoid unnecessary investments. Ensuring benefit is distributed among the different beneficiaries and locations where it is demanded is a policy imperative Figure 6. The Index of socioeconomic disadvantage (max values from decision units selected) captured for each beneficiary sector under different investment strategies at the $10 M budget. Investment strategies: 'baseline' , the budget available can be allocated anywhere in the Brigalow Belt; 'sectors' , the budget is equally allocated among beneficiary sector; 'sectors + disadvantage' , the equally allocated budget among beneficiary sectors is directed to areas of highest socioeconomic disadvantage; 'LGA' , the budget is equally allocated among LGAs; 'LGA + disadvantage' , the equally allocated budget among LGAs is directed to areas of highest socioeconomic disadvantage. (Chan andSatterfield 2020, Mandle et al 2020), and our approach provides a way for practitioners and policy makers to identify efficient solutions that benefit all beneficiaries and locations across a landscape.
There is an ethical imperative in spatial conservation planning for ecosystem services to ensure positive outcomes for the most vulnerable sectors of the population (Daw et al 2011, McDermott et al 2013, Althor et al 2016. In order to address this, we accounted for socioeconomic disadvantage in our investment strategies. That is, we sought to improve equity in our solutions by directing flood protection to areas with less opportunity to overcome damages of flood events. We expected to see a contrasting difference in the decision units selected and higher allocations to socially disadvantaged locations when specifically targeting disadvantage (i.e. 'sectors' vs 'sectors + disadvantage' and 'LGA' vs 'LGA + disadvantage'). However, this was not the case given the narrow range of the socioeconomic disadvantage index in the region (>0-0.3) and a moderate correlation between areas of high demand of flood protection and high disadvantage across the Brigalow Belt (table S2). That is, prioritizing flood protection to areas with high demand (our overarching conservation objective) already captured areas of high disadvantage. Similar results were found in Gourevitch et al (2020), where the economic value of houses subject to flooding was quite homogeneous. Therefore, targeting equity-weighted utility of flood risk reduction only represented small changes in area selection compared to not targeting equityweighted utility (Gourevitch et al 2020). We suspect more contrasting differences between ignoring and accounting for disadvantage may occur in regions where socioeconomic differences across the population are marked (Pedlowski et al 2002, Suwarno et al 2016, Abebe et al 2020.
Despite the narrow changes in decision units selected when targeting disadvantage, our results indicate that investment strategies may require to be specific to a beneficiary sector. For instance, accounting for disadvantage for the food sector may not be necessary as doing so costed more for no equity benefit. This is because demand for flood protection for the food sector was located across highly homogenous socioeconomic areas. Conversely, accounting for disadvantage represented relevant improvements in equity for urban residents and rural communities. Thus, the food sector could be treated separately in the planning process to increase overall efficiency. Other locations of even higher socioeconomic disadvantage for urban residents and rural communities (e.g. Townsville City, the top North LGA, see figure 6) were not captured as no units to apply passive restoration were available that would deliver protection to them (based on the supply-demand configurations for each beneficiary sector at the subwatershed level). Alternative management interventions may be necessary to enhance protection against flood events for those regions. Possible alternatives targeting the demand component include improved zoning regulations, property relocation, or improving emergency responses from people (Gourevitch et al 2020, Villarreal-Rosas et al 2020.

Operationalizing fair management plans
What is regarded as a fair distribution of ecosystem service benefits depends on the sociocultural and economic circumstances that affect beneficiaries in a planning region (McDermott et al 2013, Vucetich et al 2018. Our study highlighted the winners, losers, and costs of alternative strategies promoting equality and equity in the distribution of flood protection in the Brigalow Belt Bioregion. Negotiations would then be required to identify what solutions are acceptable for all beneficiaries, even if that involves unequal distribution of benefits (Vira et al 2012, Kovacs et al 2016. Alternative strategies are available to balance trade-offs among beneficiary sectors (Fu et al 2018. For instance, in compensatory programs, one beneficiary sector provides economic compensation to other sectors in return for applying actions that enhance ecosystem services (Bremer et al 2018. For example, in the Yongding River watershed in China, a fair cost-sharing program for maintaining water quality required downstream beneficiaries in Beijing pay US$6.31 M to upstream provinces (Fu et al 2018). Previous research in the Brigalow Belt has shown the economic feasibility of compensating farmers in return of carbon sequestration (Evans et al 2015). Flood protection services could also be included as part of a Payments for Ecosystem Services scheme, where some of the funds are directed to ensure benefit to rural communities (the beneficiary sector obtaining least flood protection benefit from intervention). Exploring how compensatory schemes could be applied to address disproportionate distribution of flood protection within beneficiary sectors for the Brigalow Belt was beyond the scope of this study. Yet, we provide baseline information to expand on this analysis describing how benefits are distributed across the landscape for different beneficiaries.
Advancing towards fair outcomes in spatial prioritization for ecosystem services requires early engagement with beneficiary sectors and recognition of their socio-cultural and political context (Vira et al 2012, Rosenthal et al 2015, Kovacs et al 2016. For example, in North India, monetary compensations for upstream beneficiaries to protect and sustainably manage forested areas were provided by downstream beneficiaries in return of better water quality and increased protection against flood events (Kovacs et al 2016). However, imbalanced power relations between the rural upstream and wealthier downstream towns created intra-community conflicts in the upstream town, undermining their capacity to build collective institutions fundamental for the long-term existence of the compensatory schemes (Kovacs et al 2016).
These examples indicate the need to explore beyond how benefits are spread in society (as we do in this study) to also consider the underlying socioeconomic conditions that influence the ability of sectors to derive ecosystem services (McDermott et al 2013). For instance, people may have physical access and desired demand for particular ecosystem services, but lack the power or capabilities for deriving benefit (Daw et al 2011, Vira et al 2012, Hanna et al 2020. In our approach, we assessed flood protection at the watershed level, and we then aggregated results at the LGA scale. This was useful to represent areas at which many decisions regarding water management take place in the Brigalow Belt (State of Queensland 2020). Yet, watershed boundaries at which flood protection services are produced and delivered usually expand beyond the limits of LGAs. Thus, future compensatory plans for the Brigalow Belt should consider the degree of collaboration across LGAs and other government levels, as well as an assessment of the power dynamics and hierarchies between beneficiary sectors in the region.
Also of high priority in future studies is to incorporate temporal dynamics affecting distributional outcomes. In our approach, we assume demand and disadvantage factors are static. However, this is unlikely, and accounting for the temporal variability of these factors may drastically affect the distribution of ecosystem services among beneficiaries (Villarreal-Rosas et al 2020). Thus, promoting and assessing fairness in conservation plans also requires comparison of the expected changes in ecosystem service distribution across time, together with an assessment of the changes in the socioeconomic opportunities different people experience.

Concluding remarks
Achieving efficient and fair outcomes from management and conservation interventions targeting ecosystem services is a desirable goal pursued by practitioners and decision-makers, but it involves tradeoffs. Here we have identified the type and extent of trade-offs between efficient, equal, and equitable solutions under a spatially explicit prioritization framework. In the Brigalow Belt, even budget allocations are a poor strategy to promote equal and equitable distributions of flood protection among beneficiaries, but successful at promoting equality and equity among LGAs. These findings were largely determined by the configuration of demand, and patterns of socioeconomic disadvantage specific to the beneficiary sectors we considered. Trade-offs between equity, equality, and efficiency from the application of similar investment strategies are likely to vary depending on the specific ecosystem services, beneficiaries, and planning contexts. Recognition of the potential trade-offs between different beneficiaries caused by management interventions is critical to identify solutions that beneficiaries regard as fair and sustainable.

Data availability statement
The data that support the findings of this study are available upon reasonable request from the authors.