Definitions.

In the NI framework, a biodiversity indicator is defined as [15]:

“A natural variable related to any aspect of biodiversity, supposed to respond to environmental modification and representative for a delimited area. It is a variable for which a value in a reference state can be estimated. The set of indicators should cover as homogeneously as possible all aspects of biodiversity, and any addition of a new indicator should result in the addition of information.”

Thus, a biodiversity indicator might refer to the density, abundance or distribution of a population of a single species, a taxonomic, functional or genetic diversity metric, a demographic or behavioural parameter, or any other natural parameter fitting the definition. Several indicator-based assessments of biodiversity or an ecosystem state emphasize the requirement for using a large number of indicators to ensure broad coverage of many aspects of ecosystems and biodiversity, i.e., structural, functional, and taxonomic levels [16], as well as providing a way to monitor different environmental pressure or the provision of ecosystem services [13], [17]–[21]. Designing a perfect set of biodiversity indicators might take decades [22]. Therefore, we adopted a pragmatic approach to building a set of biodiversity indicators that aggregated most of the knowledge available from the ERN [14].

The use of reference states in the NI framework responds to both theoretical and pragmatic needs. References provide a context for the interpretation of each observed indicator value, allowing all observed indicator values to be comparable on the same scale [11], [23]. A reference state has been defined as follows [15]:

“The reference state, for each biodiversity indicator, is supposed to reflect an ecologically sustainable state for this indicator. The reference value, i.e., the numerical value of the indicator in the reference state, is a value that minimizes the probability of extinction of this indicator (or of the species or community to which it is related), maximizes at least one measurable aspect of biodiversity of the natural system to which it is related, and does not threaten any measurable aspect of biodiversity in this or any other natural system.”

Thus, a “measurable aspect of biodiversity” refers to a biodiversity metric at a specified scale [24]–[26]. In practice, the expected value of an indicator in a reference state is used to scale the observed (or estimated) value of each indicator, thereby ensuring that all scaled indicator values are directly comparable. Scaling is a means of measuring the difference between the observed variable and the reference state.

The observed and reference states of a given indicator can be estimated from data, either by model prediction or by expert judgment. As in other approaches to biodiversity assessment [11], expert-based judgments allow the assembly of the maximum volume of information. A reference state can be defined specifically for each indicator, according to the current state of knowledge for each indicator and ecosystem. Indicators do not need to share the same reference state, provided reference states fit the definition above.

Natural systems are composed of a mosaic of ecosystems, and it is crucial that they are distinguished explicitly. Within the NI framework, natural systems are termed “major ecosystems” and are categorized into a set of nine broad natural system types, i.e., mountain, forest, open lowland, freshwater, mires and wetland, coast pelagic, coast bottom, ocean pelagic, and ocean bottom (see Table S1 for definitions). Most ecosystems fall into these broad categories, but other categories, e.g., desert and ice cover, or subdivisions, e.g., different types of forests, can be added as local conditions demand.

The design of spatial and temporal units must fit with the resolution of the available information and with the objectives of knowledge synthesis and management, which may vary among countries and regions. Our case study section details how appropriate units were specified for the implementation of the NI in Norway.

Nature Index calculation.

The observed values, or “states”, of indicator i belonging to major ecosystem j in spatial unit k at date t are denoted by . The corresponding values for the reference states are denoted by . The same reference state for a given indicator can be applied to any date t. Both and are non-negative values.

The estimate of the observed state for an indicator is assumed to be randomly drawn from a statistical distribution L, with two parameters a and b:(1)Three forms of uncertainty can be considered in the NI framework: numerical uncertainty, data source uncertainty, and uncertainty because of lack of knowledge. Numerical uncertainty refers to uncertainty about the observed value of each indicator, which includes natural variability and observation uncertainty. Numerical uncertainty is taken into account when estimating . Monte-Carlo simulations can be implemented to obtain replications of the data collection process, which are denoted by . Estimating the set and implementing a simulation protocol to emulate authentically the data collection process is necessary to obtain a suitable measurement of numerical uncertainty. The case study section details how these problems were solved during the implementation of the NI for Norway.

Uncertainty because of the data source can be quantified by comparing the number of monitoring-based or model-based estimates with the number of expert-based estimates. This allows an assessment of deficiencies in the monitoring data set produced by the ERN.

In some cases, knowledge is so sparse that even expert-based judgments cannot be obtained. The number of documented indicators per spatial unit k provides a means of quantifying this lack of knowledge, which corresponds to the third level of uncertainty.

Each indicator can be expressed using a specific measurement unit, e.g., density, abundance, or species richness. Units must be scaled prior to averaging across spatial units or major ecosystems. Simulated indicator values are scaled using their respective reference state value . This gives a dimensionless quantity ranging from 0 to 1, where 0 is a completely degraded situation and 1 is an optimal situation for biodiversity, which corresponds to the chosen reference state.

Three simple scaling models were used to account for different ways of interpreting an observed indicator value relative to the expected value in a reference state (Figure 1).

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Figure 1. Examples of the use of scaling models.

Scaled value when the observed value of a hypothetical indicator ranged between 0 and 150 and when the value in a reference state was 50.

https://doi.org/10.1371/journal.pone.0018930.g001

The “optimal” model (Figure 1a) is defined as:(2)where is the set of scaled simulated indicator values, i.e., a set of dimensionless values expressing the deviation of the observed indicator value from the reference state. The optimal scaling model implicitly assumes that any departure from the reference state results in a degradation of the state of the major ecosystem related to the indicator. This is useful for indicators such as the moose, Alces alces, which might experience a strong decline because of hunting but whose large populations have on the other side a detrimental effect on the vegetation because of an unsustainable grazing pressure [27], [28].

We use the “minimal” scaling model (Figure 1b) when the reference state refers to a low, precautionary level, as found in marine management of small pelagic fish [29]:(3)When scaling the indicator for the minimal model, we assume that a deteriorated state for the indicator corresponds to a decrease below the reference level, and that any value above this reference level corresponds to an optimal situation.

We use the “maximal” scaling model (Figure 1c) when the reference state refers to a maximal value above which detrimental effects on ecosystems are observed, such as a maximal limit for the density of a proliferating species, or community, of phytoplankton or jelly-fish:(4)Once the set of scaled indicators is calculated, it can be averaged across any of its axes i, j, k, or t, or any combination of axes. For example, an averaged value for all indicators, all spatial units, and all major ecosystems over time can be expressed as:(5)where is a documented value for the indicator i in ecosystem j in spatial unit k and date t, and otherwise. corresponds to a set of n simulated values, at date t. The final NI value can be expressed as the median of the simulated values, together with 95% confidence intervals around the median expressed as 2.5% and 97.5% quantiles. The set of simulated NI values allows for statistical testing by calculating p-values; for example, when comparing the index for two dates t₁ and t₂, .

Definition of weights.

In previous implementations, no particular weights were applied to any of the i, j, or k axes. All calculations were made under a “complete equivalence” assumption, i.e., no locality, no major ecosystem, and no indicator was considered more important than another. This assumption is clearly open to criticism. If all components of biodiversity were equally studied, all indicators could be documented at all dates and spatial locations and, if all spatial locations were equally representative, there would be no need for weights. However, no matter how much care is taken when building the indicator set, discrepancies are likely to occur because not all taxa, functional groups, or geographical areas can be studied to the same degree [14], [20], [30]. Taxa such as fish, birds, and mammals are better documented than others, either because they attract more public interest or because study models are readily accessible. These potential discrepancies between spatial units or indicator representativeness meant it was necessary to introduce weights [14]. Weights can be defined across the indicator axis i, the major ecosystem axis j, and the spatial unit axis k. Introducing any set of weights W_ijkt within the NI formula is straightforward:(6)where the condition for any date t, and if indicator i has not been documented for the major ecosystem j in spatial unit k on date t.

The following rules for weights definition have been implemented in Norway. They have been designed to be readily transferrable to other countries with different data availability.

Our approach addresses the following heterogeneities: indicators specific to a given major ecosystem versus indicators representative of several major ecosystems; indicators belonging to different taxonomic, trophic, or functional groups; well-documented indicators identified by the ERN as strongly representative of any aspect of biodiversity; and spatial units of different size. The following four sequential steps are used to control for these potential heterogeneities (Figure 2).

1. At the finest level (Figure 2a), indicators for a group in a major ecosystem j with spatial unit k should be weighted according to their specific relationship to the major ecosystem using a relative measure of how this indicator relates to each ecosystem. For example, an indicator exclusively representative of forest, such as moose, Alces alces, receives a basic weight of 1 in a forest, but 0 in other major ecosystems. In contrast, the willow ptarmigan, Lagopus lagopus, is a representative of mountains and forests, where it receives a weight of 0.7 for mountains and 0.3 for forests.
2. At the level of a major ecosystem j within a spatial unit k (Figure 2b), some indicators can be considered as particularly important indicators because their values strongly correlate with the state of the ecosystem. The contribution of these “extra-representative” indicators is set at a maximum of 50% of the NI value per spatial unit to ensure that they contribute significantly to the NI value but to prevent them from overwhelming information from other indicators. The following criteria were applied to the selection of extra-representative indicators: (i) they are representative of many species, (ii) they are representative of a large area encompassing several spatial units, and (iii) they are documented by data that allow estimation of the indicator for multiple dates and for the reference state. The other indicators should be weighted such that different groups contribute equally to the NI value, when the NI is calculated for each spatial unit of a major ecosystem (Figure 2b). In our example, the groups are trophic groups. The definition of groups may depend on the knowledge available from the ERN.
3. At the spatial unit k level (Figure 2c), all major ecosystems j assumed to be present in a spatial unit are given equal weights. We assume that each major ecosystem holds a unique spectrum of biodiversity, which prevents them from being ranked against each other. Weights must be calculated to ensure equivalence. In contrast to the BII, this rule ensures that the NI is robust against change in land use [31]. If any major ecosystem is destroyed, the NI value will decrease until the same major ecosystem is restored.
4. To aggregate across several spatial units (Figure 2d), weights should be allocated according to the area of the spatial unit k to ensure that any set of NI values averaged over several spatial units is representative of the total area. In our example (Figure 2), the spatial units were municipalities that differed in area.

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Figure 2. Simplified example of the Nature Index calculation process, including the weights used.

For the sake of simplicity, the numbers of functional groups and major ecosystems have been slightly reduced relative to the Norwegian application.

https://doi.org/10.1371/journal.pone.0018930.g002

The rules for calculating the weights are based on three criteria: (i) some indicators are known to be of higher importance to biodiversity, (ii) indicators can be classified into groups of equal importance in a major ecosystem, and (iii) no major ecosystem is more important than another.

Presentation of results.

NI results can be presented at several aggregated levels and the choice of resolution depends on the underlying question addressed. Presenting the NI as a single value averaged over the axes i, j, and k, may not be the best way to illustrate and synthesize results. Apart from communication purposes, the usefulness of such a global measure is of limited use in environmental management, where sub-indexes may be more relevant. Maps for a specific major ecosystem on a given date, or trends for a given major ecosystem over a specific area, are much easier to interpret and of greater utility to environmental management. Global maps showing average NI values for several major ecosystems may be useful for communicating to the public.

The flexible design of the NI framework lends itself easily to the development of sub-indexes (thematic indexes) that focus on given trophic, taxonomic, or threatened species groups in a specific region or on biodiversity pressures associated with a particular environmental problem. Weights attached to thematic indexes can be binary, in order to reflect the selection of the indicators, major ecosystems, and localities that are relevant to a given theme.

Spatiotemporal resolution of the Nature Index for Norway.

Data were collected in Norway for four years (1950, 1990, 2000, and 2010) using 430 Norwegian municipalities as spatial units (see Text S1 for more details on the practical implementation). Four large regions were applied to open oceans outside coastal waters: Skagerrak, North Sea, Norwegian Sea, and Barents Sea. We chose the year 1950 as our starting point, because data prior to that date were considered unreliable and we wanted to measure the biodiversity impact of strong economic growth during the post-war period. Intervals of 10 years since 1990 were selected to make a trade-off between the expected sensitivity of the index, the amount and quality of older data, and the amount of work required.

The selection of indicators.

The task of identifying biodiversity indicators involved a succession of meetings, which were organized according to major ecosystems; experts selected indicators based on the NI definition and any additional criteria specifically required for the Norwegian implementation of the NI [32]. Experts were required to report several items of information related to each biodiversity indicator (detailed in [15]), including broad ecological characteristics of the indicator, information on conservation or management interest, and other factors affecting weighting and sub-indexing. The whole indicator set is available as an Excel table (Table S2). Information concerning the specificity of indicators to major ecosystems can be found in Table S2, columns P to X. Following discussions with the ecological reference group, weights were considered for eight groups (Table S2, column AH): primary producer generalist, primary producer specialist, decomposer of organic matter, primary consumer and filter feeder, intermediate predator specialist, intermediate predator generalist, top predator specialist, and top predator generalist. The distinction between generalist and specialist was made by each expert.

Data collection.

Data collection began in late June 2009 and was completed in September 2010, before publication of the first version of the NI. Data were assembled via a website connected to an SQL database, which was hosted by the Norwegian Institute for Nature Research (NINA). A demonstration version of this website can be found at http://naturindeks.nina.no (optimized for Microsoft Internet Explorer). The “Veiledning” section of the website opens the manual used to guide experts through the process of data preparation and data entry. Experts used the website to enter the observed value for each indicator, by municipality and by date. Experts also entered the value of the reference state for each indicator in each municipality.

Operational definitions (Table S3) were provided to help experts estimate reference states. All these definitions conformed to a general template. Experts could enter “monitoring based estimates”, “model-based estimates”, or “expert judgments” for their data [11], [33], [34]. A specific field kept track of data sources. Experts chose the scaling model for their indicators (Table S2, column AW).

Experts had to provide lower (25%) and upper (75%) quartiles for each observed indicator value as a measure of numerical uncertainty, as suggested by [33]. Experts could explicitly report a complete lack of knowledge instead of reporting a value for each estimate, i.e., a combination of indicator, spatial unit, and date. When no data were entered, we assumed that the indicator was absent and that nothing was reported.

Geographical information system analyses were used to calculate total municipality area and the area of each major ecosystem within each municipality. GIS calculations were based on the major ecosystem definitions in Table S1, Norwegian digital topographic maps (scale 1∶50,000), and vegetation maps [35]. These calculations were used to identify municipalities with and without mountainous areas and to standardize the presentation of the NI results to match those found with the NCI [10], [12].

Estimating numerical uncertainty.

We used three values to estimate the statistical distribution for each set L_ijkt: the mean observed value of the indicator, and the associated lower and upper quartiles. The process of estimating the statistical distribution using this limited amount of information was very simple. Several statistical distributions were tested, depending on whether the indicator was a continuous or a discrete variable. We calculated the following criterion C for a given two parameters statistical distribution L(a,b):(7)where m refers to the difference between the observed mean estimate of the indicator and the mathematical expectation of the random variable following the distribution L(a,b). The terms q_l and q_u refer to the differences between the estimated lower and upper quartiles of the indicator and the lower and upper quartiles of the distribution L(a,b). For each observed indicator value , we retained the set L(a,b) that minimized C. We tested the following statistical distributions: for continuous variables, we tested truncated-normal, Gumbel, log-normal, Weibull, and gamma distributions; and for discrete variables, we tested Poisson, zero-inflated Poisson, and negative binomial distributions. Once the set L_ijkt was identified, 999 simulated data sets were computed. These simulations mimicked the way data had been entered by the expert. In some cases, the same data were duplicated for several localities. The same simulated data vector was also duplicated for localities where data had been duplicated.

Presentation of Nature Index results for Norway.

In the Norwegian case study, NI results were communicated as maps specific to each major ecosystem (steps a and b, Figure 2) and as trends averaged over the whole country (steps a, b, and then d, Figure 2), with confidence intervals. For mountain ecosystems, the NI calculation was restricted to municipalities where mountains comprised at least 20% of the municipality area. The remaining major terrestrial ecosystems were assumed to occur everywhere in Norway.

The mean number of indicators documented per municipality was calculated for each data source type (data, model, or expert), date, and major ecosystem to illustrate gaps in the data and to detect uncertainty because of data sources.

Some additional analyses were implemented and they are provided as supporting material. They concern the effect of our weighting system on the NI values (Text S2) and a convenient method for communicating NI results to the public, i.e., maps with averages across all indicators per municipality and major ecosystem (Text S3). The ability of the NI framework to focus on topics of environmental concern was demonstrated through four thematic indexes, i.e., top predators, freshwater acidification, environmental quality in the Oslo fjord, and trophic groups in pelagic ecosystems (Text S4).

Statistical and programming tools.

The code used to calculate the NI is available as supporting information (File S1). Data processing and computations were performed using R 2.11.1 freeware [36]. The R code provided in File S1 shows functions used in statistical fitting, data simulation, NI computation, thematic index computation, mapping, and estimation of confidence intervals. The data set collected for mountains is provided as an example. The code in File S1 allows the user to make more specific plots than the ones we present, e.g., maps for each separate indicator (code S1, “NI commands.R” file, section 7.2), comparisons of interpolated and non-interpolated maps (section 7.5), or maps comparing changes over time with their associated p-values (section 7.7).