How healthy is the human-ocean system?

Halpern et al (2012 An index to assess the health and benefits of the global ocean Nature 488 11397) propose a detailed measure of the state of the human-ocean system against ten societal goals. They devote less attention to the normative foundation of the index, which is crucial for assessing the overall health of the human-ocean system, notably when it comes to aggregation of potentially conflicting goals. Social choice theory provides several possible functional forms for assessing the compound change in various goals. The one chosen by Halpern et al, the arithmetical mean, is not only a specific but also an extreme case. It implicitly allows for unlimited substitution. A one-unit reduction in one goal can be fully offset by a one-unit increase in another with the same weighting factor. For that reason, the current index satisfies an extremely weak sustainability concept. We show that the results in Halpern et al are not robust when one adopts a strong sustainability concept. The overall health score of the ocean decreases, the ranking of the various coastal states changes substantially, and the assessment of sustainable development needs to be partially reversed.


Introduction
The ocean with its various services and resources is essential for human wealth and development-providing humanity with food, materials, essential substances, energy, and recreational opportunities. However, the free access to, and availability of, ocean resources and services has exerted major pressures on the health of the ocean, including overfishing, thoughtless pollution, or alterations to coastal zones that often cause the degradation of marine ecosystems (coral reefs, mangroves, etc), to name just a few (Visbeck et al 2014). Despite these threats, approaches to achieving more sustainable utilization of ocean resources and services are still rare, and a comprehensive understanding and assessment of the various oceanic factors influencing human wealth has not been established. Against this background, the development of an ocean-health index by Halpern et al (2012) and its subsequent annual updating is an important step towards a sustainable development strategy for the ocean. Halpern et al (2012) define ten ocean-related societal goals to represent the ecological, social, and economic benefits of the ocean and calculate the ocean-health index at the global and local level by taking the weighted arithmetical average score of these goals. The values associated with the goals reflect not only information about the present state but also contain projections of future states derived from the assessment of the pressures on, and the resilience of, the human-ocean system. Accordingly, the values also enable us to derive information on the sustainability of human-ocean system developments. In addition, a first estimate about trends is now possible, as the scores have meanwhile been updated for the year 2013.
However, even though Halpern et al carry out a sensitivity analysis with respect to the weighting of the various goals and the discounting of future states, they leave out the sensitivity of the result to the way in which conflicting goals are aggregated. Implicitly they consider a rather extreme 'normative frame', that of unlimited substitution possibilities among the various goals. Here, we show i) that their aggregation approach should only be considered one possibility among many in assessing the human-ocean system and ii) that assuming less optimistic substitution possibilities-which seems more appropriate when assessing the sustainability of complex human-ecological systems with possible irreversible degradations-has significant implications for the overall ocean health score, the ranking of countries, and the assessment of sustainable development.
A requirement for sustainable development is that the composite endowment with environmental assets does not decrease (e.g., Pearce 1993, Arrow 2003, Dasgupta 2009). However, aggregating environmental assets requires attention to the substitution potential among them-which may be limited for ecological or technical reasons or because social preferences only allow substitution to a limited extent (e.g., Bartelmus 1989, Daly 1991, Victor 1991. Varying degrees in substitution potential are reflected by the distinction between strong and weak sustainability. The concept of strong sustainability requires keeping all assets above critical levels to maintain sustainable development because it does not allow for substitution between them. The concept of weak sustainability, by contrast, allows for unlimited substitution and requires that the aggregate of the various assets (valued with their respective shadow prices) does not decline (e.g., Pearce et al 1989, Daly and Cobb 1989, Hartwick 1990, Hamilton 1994. Obviously, there exists a broad spectrum between these two extremes, and the appropriate level of substitution potential can be expected to differ dependent on the characteristics of the underlying assets to be assessed (e.g., Bateman et al 2011). However, facing complex ecologicalhuman interactions like the human-ocean system, limited substitution possibilities satisfying a rather strong sustainability concept seem to be better suited to accounting adequately for the influence of the various stocks on wealth (e.g., Dasgupta and Heal 1979, Pearce et al 1989, Ekins et al 2003, Ayres 2007, Visbeck et al 2014. We employ results from social choice theory to show that, based on the underlying assumptions in Halpern et al (2012), a meaningful aggregation of the individual goal scores can be obtained by applying a generalized mean. Accordingly, there is a full family of specific functional forms for the ocean-health index depending on the specification of a parameter that characterizes the substitution possibilities. Following the literature on natural resource and ecosystem assessment, we assume limited substitution possibilities for the various goals reflecting the state of the human-ocean system. Decreasing the substitution parameter lowers the overall index from 65 to 52 in 2012 and 2013 because it reduces the potential for offsetting poorer performances in certain goals by better performances in other goals. The implications of a decreased substitution parameter become more striking when we turn to the assessment of individual countries. Countries with an unbalanced performance across the goals significantly deteriorate in the ranking compared to countries with a balanced performance. For example, Russia and Greenland fall in the ranking for 2013 by about 107 and 118 places (out of 220) respectively, while Indonesia and Peru improve by about 78 and 88 places respectively. This effect also becomes significant in assessing the sustainability of current development by comparing the scores between 2012 and 2013. For 29 out of 220 countries, the ocean-health index increases if we assume unlimited substitution possibilities but decreases if we assume limited substitution possibilities. By contrast, there are 21 countries whose score deteriorates under a concept of weak sustainability (unlimited substitution possibilities) but improves under a concept of strong sustainability. Hence we conclude that appropriate ocean management and governance requires thoughtful attention to the method used for data aggregation and the value of the parameter quantifying substitution possibilities among the various goals if we are to obtain a meaningful and appropriate assessment of the state of the human-ocean system.

Methods
The ten ocean-related societal goals of the ocean health index are 1) 'Artisanal Fishing Opportunities', 2) 'Biodiversity' ('Species' and 'Habitats'), 3) 'Coastal Protection', 4) 'Carbon Storage', 5) 'Clean Waters', 6) 'Food Provision' ('Wild Caught Fisheries' and 'Mariculture'), 7) 'Coastal Liveli-hoods&Economics' ('Livelihoods' and 'Economics'), 8) 'Natural Products', 9) 'Sense of Place' ('Iconic Species' and 'Lasting Special Places'), and 10) 'Tourism&Recreation' (Halpern et al 2012). Certain goals are aggregates of subgoals indicated by the terms in the parenthesis above. The goals and subgoals reflect the present and future state, the latter being derived from the assessment of the pressures on, and the resilience of, the specific goal. The ocean-health index is obtained by aggregating the various goals and is calculated at global and local level. Its first release in 2012 provided a ranking of 171 coastal states and regions based on the condition of their marine ecosystems in their EEZs. The index is updated annually, and at present information on ocean health for the year 2013 is already available on the ocean-health index website 4 . The updated ocean-health index for 2012 and 2013 ranks a total of 220 countries/islands compared to 171 countries/regions in Halpern et al. This is due to the fact that previously aggregated regions (like, say, the USA Pacific Uninhabited Territories) have now been evaluated and assessed separately.
In compiling an index, I , like the ocean-health index, a major challenge is the aggregation of different goals reflecting issues as different as oceanic carbon uptake and the number of jobs in the fishery sector. Generally, achieving a meaningful aggregation of such ratio-scale but non-comparable goals would require applying a (weighted) geometric mean (e.g., Ebert and Welsch, 2004). However, such an index would (a) only allow for an ordinal and not a cardinal comparison of the coastal zones and (b) preclude investigation of different levels for the substitution possibilities.
Consequently, Halpern et al assume the existence of goal-specific scaling factors to obtain fully comparable ratio-scale indicators or goals. The scaling factors are obtained by the potential goal-specific best value, thus producing individual goals ranging between 0 and 1 that are then rescaled in terms of the ratio-scale property to be in the range between 0 and 100. According to social choice theory, meaningful aggregation for N ratio-scaled indicators or goals I i is obtained by applying generalized means (Blackorby and Donaldson, 1982): . The parameter σ quantifies the elasticity of substitution between the different indicators for generating ocean health (Solow 1956, Arrow et al 1961, Armington 1969. Thus the ratio-scale fully comparable goals allow for a full class of specific functional forms for the index dependent on σ , which we denote by σ I ( ) because we do not consider any variation in the weights or the individual indicators. Halpern et al have chosen the extreme case of unlimited substitution,  σ → , which results in the arithmetical weighted mean For this specification of σ , the distribution of scores over the different indicators only has any bearing on the value of the ocean-health index to the extent that the constant weighing factors may differ.
Considering limited substitution possibilities instead, and hence subscribing to a concept of relatively strong sustainability, requires choosing a value for σ below 1 (e.g., Gerlagh and van der Zwaan 2002, Heal 2009, Bateman et al 2011, Traeger 2013). More specifically, Sterner and Persson (2008) suggest using σ = 0.5 in their study of the human-climate system. Instead of choosing a specific value for σ , we assume σ to be uniformly distributed between 0 and 1 and perform a Monte Carlo simulation ( = n 10 000) to recalculate the ocean-health index for 2012 and 2013 based on the equallyweighted individual goal scores obtained from the oceanhealth website. The simulation results are not only used to derive the average score but also to calculate a ranking for each simulation and obtain average ranking information. Coastal states with one or more zero scores in an individual goal obtain an index value of zero for σ ⩽ 1 (22 and 21 countries in 2012 and 2013 respectively). Accordingly, all these countries were ranked last. To obtain further ranking information for these countries, we performed stepwise exclusion of those goals with a zero score. Accordingly, complete rankings for 220 countries have now been obtained. To further test the sensitivity of the results to the strong sustainability assumption, we repeated the entire calculation with σ assumed to be exponentially distributed with mean 0.5 so that substitution elasticities above 1 are also considered in the Monte Carlo simulation. The comparison of changes in ocean-health scores between 2012 and 2013 for the different specifications makes for further insights about the sensitivity of sustainable development to the substitution possibilities.

Results
Under a concept of weak sustainability (unlimited substitution possibilities,  σ → ) as assumed by Halpern et al, the index value for both 2012 and 2013 is 65 (with the best possible value being 100). If instead of this we apply a concept of strong sustainability with σ uniformly distributed between 0 and 1, the index values decrease to 52.14 (±8.26) and 51.99 (±8.17) in 2013 and 2012 respectively. The figures in parentheses show the standard deviation. The reduction in the index value is a necessary result of reducing the substitution possibilities because low substitution possibilities imply an unambiguously lower absolute score than with unlimited substitution possibilities, except for the special case of an equal (weighted) score in each goal. The concept of strong sustainability, corresponding to low substitution possibilities, imposes greater restrictions on the potential to compensate for poor performance in certain goals and therefore gives more weight to low-performing goals. Accordingly, assuming σ to be distributed exponentially with mean 0.5 and hence allowing for substitution elasticities above 1 results in a less extreme reduction of ocean-health scores, i.e. 57.92 (±8.07) and 57.70 (±7.98) for 2013 and 2012 respectively.
The implications of differences in substitution possibilities become especially important when comparing the performance of various countries or when assessing development over time. Figure 1 shows the rankings of the 220 countries for  σ → and σ~( ) U 0,1 in 2013, where the error bars indicate the standard deviation obtained from the sensitivity analysis. Without any effect from varying the substitution parameter, data points for all countries would be on the 45°l ine. The figure reveals, however, that the distribution of scores across goals significantly changes the ranking. Above the 45°line are those countries with a rather unbalanced performance and therefore with lower rankings under limited substitution possibilities than under perfect substitution possibilities, and vice versa for countries below the 45°line. Figures A1 and A2 in the appendix show the results for the first 50 countries in 2013 in more detail (A1) and the ranking comparison for 2012 (A2). Table A1 in the appendix provides index and ranking information for 2013 for all countries and islands and the change in the index between 2012 and 2013 resulting from the different specification for the substitution possibilities 5 .
The sensitivity of the ocean-health index to substitution possibilities is particularly apparent for countries with rather uneven ocean-health characteristics. Figure 2 shows the ocean-health index in dependence on substitution elasticity for five selected countries/islands. While both the Amsterdam and Saint Paul's Islands and Ile Europe have low to zero scores for σ < 1, they improve their score significantly when substitution elasticity increases beyond 1. For high substitution elasticities they obtain a larger index value than New Zealand, Thailand, and the Falkland Islands, whose individual goal scores add up to less but are more evenly distributed among the goals. Despite the very poor performance of the Amsterdam and Saint Paul's Islands in 'Food Production' (with a value of 2) and of Ile Europa in the individual goal 'Sense of Place' (with a value of 0) in 2013, a concept of weak sustainability would cause their humanocean system to be assessed as healthier than, for example, that of the Falkland Islands, which perform much better in their lowest individual goal score ('Food Production', with a value of 34).
Consequently, accounting for the influence of the substitution possibilities is important when assessing sustainable development. Figure 3 shows the change in the overall oceanhealth index between 2012 and 2013, again for weak sustainability (σ → ∞) and strong sustainability (σ ∼ U(0,1)). Of specific interest are those countries in the second and fourth quadrant in figure 2. The former shows those countries that have developed unsustainably in accordance with the concept

Discussion and conclusion
The specification of the substitution possibilities cannot be derived from scientific research alone, but requires a normative foundation. Nevertheless, when dealing with such a variety of goals, all of which are essential for human wellbeing, the substitution possibilities should not be considered unlimited. Certainly, the goals defined by Halpern et al (2012) are interlinked by various biological relationships that reduce the probability of situations where certain goals deteriorate without affecting the health of other goals. However, these relationships are not fully understood, and the substantial score-spreads across goals among the countries indicate that various developments are not properly captured by biological relationships. Accordingly, we propose an alternative specification with substitution elasticity below 1 to allow for some degree of substitution but with a significant influence on the overall score by the least-performing goal.
Even though this approach satisfies a stronger sustainability concept, it is somewhat restrictive as it does not distinguish the substitution possibilities among the various goals. By contrast, it avoids any attempt to distinguish between the various goals to emphasize the importance of aggregation from a methodical perspective. However, there may be better substitution possibilities, for example, between goals like 'Coastal Livelihoods&Economics' and 'Tourism&Recreation' than between those goals and such an essential goal as 'Biodiversity'. We can deal with these varying degrees of substitution potential or individual goal significance by using a nested index or by introducing safeminimum standards respectively. In its existing form, the ocean-health index already entails goals that summarize different sub-goals, here again, however, with unlimited substitution possibilities. In general, applying a nested index with various levels allows for consideration of different substitution possibilities at different levels by, for example, first aggregating capital stocks or goals with better substitution possibilities (Dovern et al 2014). Furthermore, safe-minimum standards for ecosystem services can be sustained by avoiding potential critical zones for the state of these ecosystems (Ciriacy-Wantrup 1952). Such minimum standards can easily be introduced by defining lower bounds for certain goals. The individual goal score would drop to zero if the goal falls short of this bound, and the overall score will also drop to zero if substitution elasticities are assumed to be below 1 (Heal 2009), albeit without dominating the index score if the state is still in good condition, which would in turn result from significantly increasing the weight of the goal. The work by Halpern et al represents a seminal contribution to better understanding and management of the human-ocean system. However, precautionary and sustainable ocean governance makes it essential to properly account for the social evaluation of ocean benefits and for the various risks and uncertainties involved in our interaction with the ocean. Policy assessment and advice based on an index with unlimited substitution possibilities could result in (a) certifying a healthy human-ocean system for countries that in reality neglect important aspects of ocean health and (b) identifying development trajectories as sustainable although this is actually not the case. For that reason, we argue that significant attention should be devoted to the proper aggregation of data in assessing the health of the ocean.    Table A1. Ocean-health index, ranking, and change for the various specifications of substitution elasticity.

Ocean-Health Index 2013
Ocean Health Ranking 2013 Change in OH Index 2013-2012