# Ecorisk

## Outline

- Introduction {#intro}
  - Overview risk assessments {#ra_over}
  - Aim of the package {#aim}
  - Brief summary of package and workflow {#summary}
- How to do a risk assessment {#risk-intro}
  - Scoping {#scoping}
  - Preparation {#prep}
  - Scoring {#scoring}
  - Analysis {#analysis}
- The ecorisk package theory {#ecorisk}
  - Risk assessment analysis {#ra-analyis}
    - Expert based semiquantitative pathway {#analysis_score}
    - Modelling quantitative pathway {#analysis_model}
    - Vulnerability {#vulnerability}
    - Status assessment {#status}
    - Risk {#risk}
    - Aggregation {#aggregation}
  - What to do now? Plotting! {#aftermath}
- Ecorisk tutorial
  - Background
  - Data preparation
  - Analysis
  - Results
- Contact
- References {#references}

# Introduction

ecorisk is a package for risk assessment analysis in marine sciences, but can also be applied to terrestrial ecosystems. Risk assessments are an integral part of integrated ecosystem assessments, which are used within ecosystem based management (Levin et al. 2014). The implementation of risk assessments to support ecosystem based management faces a number of challenges, this includes for example

- The assessment on an ecosystem level heavily relies on data driven modeling approaches e.g.(Fu et al. 2018). Those data driven quantitative approaches are not suitable for information limited systems.
- To better support ecosystem based management risk assessments should be able to assess various indicator types, not only single species, but also integrated food web indicators. Other challenges to make risk assessments ready for ecosystem based management have been identified by (Clark et al. 2022).

To better support application of risk assessments in ecosystem based management this package implements a modular framework, where single indicator and pressure combinations are semiquantitatively or quantitatively evaluated and thereafter aggregated to compound risks as well as an ecosystem risk score. The highlights of this framework include:

1. risk assessments from single indicator pressure combination up to an ecosystem scale
2. integration of different knowledge types and thus more flexibility
3. assessment of integrated management indicators
4. explicit uncertainty assessment

First this vignette will give you a short introduction of common risk assessment methods and the terminology used within this package. You will find this together with a short workflow description in the first chapter. The second chapter covers the risk assessment procedure. The implementation and detailed description of the usage of the ecorisk functions will be given in chapter 3 and chapter 4.

## Overview risk assessments

Risk assessments are well known in various scientific fields. This package focuses on marine science (but this does not exclude the application in another context). Within this field, risk assessment methods are commonly divided into qualitative, semiquantitative and quantitative approaches. Additionally risk assessments are classified according to their level of complexity (based on (Holsman et al. 2017)):

Level 1: effects of one pressure on one indicator

Level 2: effects of multiple pressures on one indicator

Level 3: effects of multiple pressures on multiple indicators

Level 3 can be considered as ecosystem level, if the effects of the pressures on the indicators are aggregated and not considered individually. Table 1 gives an overview of applied risk assessment methods assigned to the associated data level and complexity.

Table 1: Overview of different risk assessment methods with papers applying those. Some methods have been applied at different data and complexity levels and are therefore mentioned more often.

Data / Complexity level | qualitative | semiquantitative | quantitative antitative
--- | --- | --- | ---
Level 1 | Likelihood- Consequence approach (W. J. Fletcher 2005) | Productivity - Susceptibility approach (Patrick et al. 2010; Stobutzki, Miller, and Brewer 2001) | Dose-response assessments (Fahd, Veitch, and Khan 2019; Håkanson 1980; Kramer et al. 2011; Long et al. 1995)
Level 2 | Qualitative network model (Giakoumi et al. 2015) | Qualitative network model (Altman et al. 2011; Cook, Fletcher, and Kelble 2014; Reum et al. 2015) Vulnerability analysis (Allison et al. 2009; Cinner et al. 2012; Cinner et al. 2013; Gaichas, Link, and Hare 2014; Graham et al. 2011; Hare et al. 2016) ODEMM framework (Knights et al. 2015) | Ecosystem modelling * (Fu et al. 2018)
Level 3 | Qualitative network model (Altman et al. 2011; P. J. Fletcher et al. 2014) Vulnerability analysis (Gaichas, Link, and Hare 2014) ODEMM framework (Knights et al. 2015) |  | Ecosystem modelling * (Fu et al. 2018)

* ecosystem approaches are marked with a *

The central question of each risk assessment is:

What is the risk that given the effect of the pressure x on the indicator y, y will reach or remain in an undesirable status?

To evaluate this question various methods have been developed (Fernandes, Vieira da Silva, and Frazão Santos 2022). An often used approach is to assess the exposure of the pressure and the sensitivity of the indicator, but several synonyms are used, thus complicating comparability of the methods. In addition to these two axes some methods assess a third axis: the adaptive capacity or resilience of the indicator. All three compartments are then combined to the vulnerability or in some methods to the risk. Within this framework exposure, sensitivity and adaptive capacity form together the vulnerability. Since the central question includes the current status of the indicator, this has to be included in the risk assessment. (Those methods that do not require status assessment can still use the output values of the vulnerability function of this package and treat them as output of the risk assessment ). In the end risk (or vulnerability) scores help to identify, understand and prioritize the risks resulting from different pressures (International Organization for Standardization 2009).

## Aim of the package

With this package we want to facilitate application of risk assessments in information rich and limited situations. We want to encourage users to incorporate different knowledge types, to widen the evidence base. For this purpose ecorisk combines semiquantitative scoring approaches with time series based modelling in one assessment. The framework is build in a modular and flexible manner, covering all complexity levels (see chapter Overview risk assessments). With ecorisk individual species can be used as indicators as well as integrated biodiversity, food web or life-history indices, for example the HELCOM zooplankton mean size indicator (HELCOM, n.d.) or the OSPAR large fish index (Lynam, C.P. and Piet, G.J. 2023). The framework allows to assess long term pressures as well as short term extreme events, while explicitly accounting for the associated uncertainty. The package is generalistic in terms of the considered spatial and temporal scale and can be applied to a wide range of ecosystems. To enhance communication to a broader public ecorisk provides different plotting functions, which can be customized later on. In the next subchapter you get a brief overview of the ecorisk package and its workflow. If you directly want to learn how you can perform a risk assessment go to chapter 2 and chapter 3. For example application of the ecorisk functions go to chapter 4.

## Brief summary of package and workflow

The ecorisk package supports the ecorisk framework (Gutte et al., in prep) by providing tools for analysis, assessment and communication. The workflow starts with two pathways, which are later on combined to one. One pathway provides functions for expert scoring approaches, the other for risk assessments based on time series data. Both pathways analyse the two vulnerability components exposure and sensitivity for each indicator ~ pressure combination. The adaptive capacity can be analysed within the expert scoring pathway. Both pathways optionally assess the associated uncertainty of of each component. After assessment of exposure and sensitivity the package continues within one joint pathway by combining the vulnerability components, assessing the status of each indicator, followed by the calculation of the risk from vulnerability and status. Now the risk scores from each indicator ~ pressure combination can be aggregated to higher complexity levels up to the (eco-)system risk score, which can be plotted thereafter. The next chapters describe in detail how such a risk assessment can be conducted (chapter 2) and the usage of the individual functions (chapter 3).

# How to do a risk assessment

To conduct a risk assessment it is useful to split the process into several parts (Hare et al. 2016):

1. a scoping phase
2. preparation phase
3. scoring phase
4. analysis phase

In the following the four phases are explained in the ecorisk context.

## Scoping

In the first phase the risk question(s) should be clearly defined. The risk question should also define all relevant spatial and temporal scales. Based on these definitions representative indicators and pressures are chosen for the assessment. Once the selection has been conducted all available data (literature or time series data in the ecorisk context) will be gathered.

## Preparation

The preparation depends on the data level of the assessment. For semiquantitative expert scoring it is useful to prepare factsheets about the indicators and the influence of the pressures on them. Scoring guidelines should clearly define each score the experts can give and a scoring template supports an easier analysis of the given scores. For the quantitative time series approach all data must be aggregated to yearly values, e.g. yearly mean temperature or maximum chlorophyll-a concentrations in spring.

## Scoring

In the semiquantitative pathway experts will score the risk components exposure, sensitivity and optionally the adaptive capacity. For a better compatibility with the quantitative pathway the following scoring scheme is suggested.

- Exposure (E) 1 - 5 (low to high impact)

- Sensitivity (S) -5 - 5 (high negative impact - high positive impact, a 0 means no influence)

- Adaptive capacity (AC) -1 - 1 (no adaptive capacity to good adaptive capacity)

- For all scorings it is recommended to score the associated uncertainty on a scale from 1 to 3 (low to high).

The individual expert scorings will be aggregated using the ecorisk functions for the semiquantitative pathway.

The status can be assessed by the experts too or based on thresholds from the literature (e.g. HELCOM indicator status reports, IUCN red list entries).

For the quantitative pathway the prepared time series are analysed with the ecorisk functions. These will score the exposure, sensitivity and status of the indicator based on the dynamics of the time series. Ecorisk automatically evaluates the uncertainty associated with the exposure and sensitivity scores.

## Analysis

The scores from the previous step will be now combined. First vulnerability (V) is calculated as follows: \(V = (-S + AC) - E\)

or if sensitivity was scored to be positive:

\(V = (S + AC) + E\)

The vulnerability scores are afterwards combined with the status to derive the final risk scores. The risk scores can the be combined to higher complexity level, i.e. cumulative effects of the pressures, cumulative impacts on the indicators and ecosystem risk scores.

# The ecorisk package theory

The ecorisk package supports the ecorisk framework (Gutte et al., in prep.). It provides functions for the semiquantitative expert scoring and a time series based quantitative approach. Ecorisk supports the integration of different knowledge types, iterative risk assessment processes and the analysis of integrated indicators. The ecorisk workflow is split at the beginning into two pathways (Figure 1), depending on the data input. In each pathway individual indicator pressure combinations are analysed for their risk. The pathways are combined again for the assessment of vulnerability and risk.

{width=“600”, height = “800”}

## Risk assessment analysis

For the risk assessment with the ecorisk package the user should have conducted an expert scoring exercise or prepared time series to analyse. Example data sets can be found in the ecorisk package. Templates for exposure and a sensitivity and adaptive capacity scoring can be created using the functions `create_template_exposure()` and `crt_sensitivity()`. The output can be saved as csv or excel file. After they have been filled out by the experts, they can directly be anayzed further with the ecorisk workflow.

### Expert based semiquantitative pathway

The expert scorings are analysed with the functions `calc_exposure()` and `calc_sensitivity()`. Both aggregate the scores given by the individual expert. In case several traits have been assessed for the indicators sensitivity, the function will calculate an aggregated sensitivity score, but will keep the trait-based scores, thus the vulnerability can be calculated first per trait and only afterwards be aggregated.

### Modelling quantitative pathway

To calculate an exposure score the function `model_exposure()` analyses the time series of the pressure. The user has to provide a base line to which the assessment time frame should be compared. The function evaluates

1. how much the conditions of the pressure in the assessment time frame differ compared to the baseline measured in standard deviations,

2. how often a significant deviation (> 1 standard deviation) from the baseline can be observed in the assessment time frame and

3. how the future trend of the pressure will likely be based on a linear model.

The function gives for each compartment a score from 1 - 5 (low to high) and the future direction of the pressure (increase or decrease). A spatial scale can not be evaluated by this function, but the user can provide a score.
The function `model_sensitivity()` evaluates the indicators sensitivity towards the pressure based on the relationship of the indicator and pressure time series. The relationship will be analysed using a generalized additive model. It is tested whether the relationship is significant, if so the strength of the relationship (\(R^2\)) is used to set a score from 1 - 5 (low to high). In case the relationship is non-linear (edf > 1), the sensitivity score will be increased by 1. Whether the relationship between indicator and pressure in the assessment time frame is positive or negative is evaluated using the slope of a linear model. The uncertainty is scored from 1 - 3 (low to high) based on the relation of the confidence intervals of the GAM to the overall range of the input data.

### Vulnerability

The `vulnerability()` function uses the scores from the semiquantitative and the quantitative pathway and combines for each indicator ~ pressure combination the exposure and sensitivity scores. For the semiquantitative pathway the following equations are applied (assuming that the experts assessed the ongoing dynamics of pressure and indicator, meaning a negative expert sensitivity score is negative due to the pressure dynamics, e.g. the temperature increases which is bad for the indicator and thus the indicator gets a negative sensitivity score):

\(V = (-S + AC) - E\) \(V = (S + AC) + E\)

In the modelling pathway the direction of the vulnerability depends on the directions supplied by the model_exposure and model_sensitivity functions. If both have the same direction a positive effect is assumed, if they have different direction the vulnerability score will be negative, sensitivity and exposure are again summed up to derive the vulnerability score.

### Status assessment

The function `status()` compares the conditions of the indicator in the assessment time frame to the baseline conditions. The status can be either good or undesired, depending on whether the indicator stays within the predefined thresholds or not. The user can parameterize whether the indicator should be in similar conditions as during the baseline or outside of these conditions. The user can also use semiquantitative data to assess the status by themselves.

### Risk

The final risk score will be calculated by the function `risk()`. It combines the vulnerability and the status scores to a risk score per indicator ~ pressure combination.

### Aggregation

The risk scores from all indicator pressure combinations are aggregated to

1. multi pressure risk scores (all pressures affecting one indicator)

2. multi indicator risk scores (all indicators affected by one pressure) and

3. a system risk based on all multi pressure risk scores

using the function `aggregate_risk()`. If the user has the scores from several experts it is recommended to run the analysis for the scores of each expert individually and aggregate the risk scores and aggregated risk scores from all experts afterwards. This also allows to assess variance between experts.

## What to do now? Plotting!

The results of the risk assessment can be analysed using the two ecorisk plotting functions `plot_radar()` and `plot_heatmap()`. The first one shows per indicator the multi pressure risk and the individual risk scores, deriving the multi pressure risk score. The heatmap plot gives an overview over all assessment results. In the bottom right corner it provides the system risk, the map shows the risks for each indicator pressure combination and to the left and at the bottom the multi pressure / multi indicator risks are displayed. Both plotting functions can show the associated uncertainty.

# Ecorisk tutorial

## Background

Let’s suppose we want to conduct a risk assessment for a fictional marine ecosystem. We want to investigate whether the system is at risk of being in an undesired state due to 5 ongoing pressures:

- Temperature increase due to climate change
- Salinity decrease due to climate change
- a decreasing nutrient input after a phase of eutrophication
- oxygen depletion
- fishing pressure

To best represent our ecosystem we choose state indicators from different trophic levels: phytoplankton, zooplankton, two fish species (herring and cod), and seabirds. For some of these we have more or less detailed expert knowledge and for some of them we have time series representing this state indicator. Thus we decide on the following assessment scheme using both the expert scoring and the modelling pathway of ecorisk:

Expert scoring pathway | Modelling pathway
--- | ---
Trait | General | Model
Cod | Phytoplankton | Cod spawning stock biomass
Herring | Seabirds | Zooplankton mean size

For the two fish species enough knowledge is available for a detail expert scoring using species traits. Phytoplankton and seabirds are larger species groups, a scoring on a trait basis would be very difficult, therefore the experts will give here only one general score for sensitivity and adaptive capacity of these two groups. The time series we want to use for the modeling approach are i) spawning stock biomass of the cod stock as indicator for the health of the species and ii) zooplankton mean size which represents the status of the zooplankton group and gives an indication about the status of the food web. The pressures will be assessed using both pathways.

## Data preparation

First step is to create the scoring tables, which will be filled out by our experts. With the functions `create_template_exposure()` and `crt_sensitivity()`, we can automatically create tables for further usage in the ecorisk workflow. The functions need the names of the pressures and for sensitivity also the names of the indicators. For exposure we want to investigate 4 components:

- the magnitude of change,

- the future trend,

- the frequency of the change and

- the spatial coverage of the change in the ecosystem.

To define vulnerability the experts should score the sensitivity and the adaptive capacity. They should differentiate between two types of effect: direct effects only and the combination of direct and indirect effects. Indirect effects occur for example due to food web interactions. If possible the experts will score four individual species traits:

- Feeding

- Behaviour

- Reproduction

- Habitat

otherwise they will give general sensitivity and adaptive capacity scores. Both the exposure and the sensitivity scoring include an uncertainty assessment. As a second step we rename the variables in our scoring templates.

    exposure_scoring <- create_template_exposure(
      pressures = c("temperature", "salinity", "oxygen", "nutrient", "fishing"),
      n_components = 4,
      mode_uncertainty = "component"
    )
    names(exposure_scoring)
    #> [1] "pressure"                "component_1"
    #> [3] "component_2"             "component_3"
    #> [5] "component_4"             "uncertainty_component_1"
    #> [7] "uncertainty_component_2" "uncertainty_component_3"
    #> [9] "uncertainty_component_4"
    # Rename exposure components
    names(exposure_scoring)[2:9] <- c("magnitude", "frequency", "trend", "spatial",
                                      "uncertainty_magnitude", "uncertainty_frequency",
                                      "uncertainty_trend", "uncertainty_spatial")

    sensitivity_scoring <- create_template_sensitivity(
      indicators = c("phytoplankton", "herring", "cod", "seabirds"),
      pressures = c("temperature", "salinity", "oxygen", "nutrient", "fishing"),
      type = c("direct", "direct_indirect"),
      n_sensitivity_traits = 5,
      mode_adaptive_capacity = "trait",
      mode_uncertainty = "trait"
    )
    names(sensitivity_scoring)
    #>  [1] "indicator"                "pressure"
    #>  [3] "type"                     "sens_trait_1"
    #>  [5] "sens_trait_2"             "sens_trait_3"
    #>  [7] "sens_trait_4"             "sens_trait_5"
    #>  [9] "ac_trait_1"               "ac_trait_2"
    #> [11] "ac_trait_3"               "ac_trait_4"
    #> [13] "ac_trait_5"               "uncertainty_sens_trait_1"
    #> [15] "uncertainty_sens_trait_2" "uncertainty_sens_trait_3"
    #> [17] "uncertainty_sens_trait_4" "uncertainty_sens_trait_5"
    #> [19] "uncertainty_ac_trait_1"   "uncertainty_ac_trait_2"
    #> [21] "uncertainty_ac_trait_3"   "uncertainty_ac_trait_4"
    #> [23] "uncertainty_ac_trait_5"

    # Replaice the generic traits names ('...trait_1', '...trait_2') with
    # the actual trait names
    names(sensitivity_scoring) <- names(sensitivity_scoring) |>
      stringr::str_replace("trait_1$", "feeding") |>
      stringr::str_replace("trait_2$", "behaviour") |>
      stringr::str_replace("trait_3$", "reproduction") |>
      stringr::str_replace("trait_4$", "habitat") |>
      stringr::str_replace("trait_5$", "general")

The experts have filled out the scoring tables in a joint exercise, thus we do not have to aggregate the individual expert scores. If individual expert scores are given, it is recommended to follow the work flow until the risk calculation and aggregation of risk scores is completed and then aggregate these scores across all experts. This allows for more precise and detailed results, as differences in the results between experts can be evaluated.

    exposure_scoring <- ex_expert_exposure
    head(exposure_scoring)
    #>      pressure magnitude frequency trend spatial uncertainty_magnitude
    #> 1 temperature         1         1     4       5                     1
    #> 2    salinity         1         4     1       3                     2
    #> 3      oxygen         1         1     1       2                     2
    #> 4    nutrient         2         2     3       2                     1
    #> 5     fishing         5         4     5       2                     3
    #>   uncertainty_frequency uncertainty_trend uncertainty_spatial
    #> 1                     1                 3                   3
    #> 2                     2                 2                   2
    #> 3                     2                 3                   3
    #> 4                     2                 2                   3
    #> 5                     1                 2                   1
    sensitivity_scoring <- ex_expert_sensitivity
    head(sensitivity_scoring)
    #>       indicator    pressure            type sens_feeding sens_behaviour
    #> 1 phytoplankton temperature          direct           NA             NA
    #> 2 phytoplankton    salinity          direct           NA             NA
    #> 3 phytoplankton      oxygen          direct           NA             NA
    #> 4 phytoplankton    nutrient          direct           NA             NA
    #> 5 phytoplankton     fishing          direct           NA             NA
    #> 6 phytoplankton temperature direct_indirect           NA             NA
    #>   sens_reproduction sens_habitat sens_general ac_feeding ac_behaviour
    #> 1                NA           NA           -3         NA           NA
    #> 2                NA           NA            0         NA           NA
    #> 3                NA           NA           -2         NA           NA
    #> 4                NA           NA           -3         NA           NA
    #> 5                NA           NA            0         NA           NA
    #> 6                NA           NA           -4         NA           NA
    #>   ac_reproduction ac_habitat ac_general uncertainty_sens_feeding
    #> 1              NA         NA          1                       NA
    #> 2              NA         NA          1                       NA
    #> 3              NA         NA          1                       NA
    #> 4              NA         NA          1                       NA
    #> 5              NA         NA          0                       NA
    #> 6              NA         NA          1                       NA
    #>   uncertainty_sens_behaviour uncertainty_sens_reproduction
    #> 1                         NA                            NA
    #> 2                         NA                            NA
    #> 3                         NA                            NA
    #> 4                         NA                            NA
    #> 5                         NA                            NA
    #> 6                         NA                            NA
    #>   uncertainty_sens_habitat uncertainty_sens_general uncertainty_ac_feeding
    #> 1                       NA                        1                     NA
    #> 2                       NA                        2                     NA
    #> 3                       NA                        2                     NA
    #> 4                       NA                        2                     NA
    #> 5                       NA                        1                     NA
    #> 6                       NA                        1                     NA
    #>   uncertainty_ac_behaviour uncertainty_ac_reproduction uncertainty_ac_habitat
    #> 1                       NA                          NA                     NA
    #> 2                       NA                          NA                     NA
    #> 3                       NA                          NA                     NA
    #> 4                       NA                          NA                     NA
    #> 5                       NA                          NA                     NA
    #> 6                       NA                          NA                     NA
    #>   uncertainty_ac_general
    #> 1                      1
    #> 2                      2
    #> 3                      2
    #> 4                      2
    #> 5                      1
    #> 6                      1

The experts followed this scoring scheme:

- Exposure 1- 5 (low to high)

- Sensitivity -5 - 5 (high negative to high positive influence)

- Adaptive capacity -1 - 1 (low to high)

- Uncertainty 1 - 3 (low to high)

For more information about this scheme see also section 2.3. Scoring. This scoring scheme aligns with the results of the modelling pathway.

To prepare the modelling pathway we load our time series data. The data includes indicator variables for our five pressures and two state indicators (cod and zooplankton). The data covers a time frame from 1984 to 2016. The data was created based on trends of similar indicators from the Baltic Sea. There is another example data set with data from the North Sea.

    ts_pressures <- pressure_ts_baltic
    head(ts_pressures)
    #>   year nitrogen phosphorous surf_temp_sum bot_temp_ann surf_sal_sum bot_sal_ann
    #> 1 1984 20.75630   0.5909141      14.64714     4.626137     6.177466    8.831664
    #> 2 1985 20.69365   0.5167932      12.24114     4.049684     6.206347    8.715647
    #> 3 1986 21.00117   0.5564102      12.24247     4.047897     6.228291    8.144442
    #> 4 1987 21.12562   0.4828138      10.25126     3.915981     5.984160    8.349860
    #> 5 1988 19.33260   0.5308540      13.96107     4.418284     5.909042    8.166351
    #> 6 1989 20.88782   0.5963618      13.65516     4.942516     5.875959    7.925876
    #>   bot_oxy_ann fishing_cod
    #> 1    4.298515   0.7798201
    #> 2    4.325501   0.7705255
    #> 3    4.598441   0.9276049
    #> 4    4.310448   0.8718370
    #> 5    4.096484   0.8253639
    #> 6    4.248611   0.9619950
    ts_indicators <- indicator_ts_baltic
    head(ts_indicators)
    #>   year zooplankton_mean_size eastern_baltic_cod
    #> 1 1984              24.46262           662.0919
    #> 2 1985              11.72344           548.5772
    #> 3 1986              13.71266           402.0580
    #> 4 1987              15.14893           322.6262
    #> 5 1988              24.91170           301.2875
    #> 6 1989              11.86890           241.8906

## Analysis

Now we will calculate exposure and sensitivity scores in both pathways. We start with the expert scoring pathway using the functions `calc_exposure()` and `calc_sensitivity()`. They calculate from the exposure components and sensitivity trait scores general scores using an aggregation method selected by the user. We will use the arithmetic mean to aggregate component and trait scores. Other options are median, minimum or maximum.

    exp_expert <- calc_exposure(
      pressures = exposure_scoring$pressure,
      components = exposure_scoring[ ,2:5],
      uncertainty = exposure_scoring[ ,6:9],
      method = "mean"
    )
    head(exp_expert)
    #>      pressure exposure uncertainty
    #> 1 temperature     2.75        2.00
    #> 2    salinity     2.25        2.00
    #> 3      oxygen     1.25        2.50
    #> 4    nutrient     2.25        2.00
    #> 5     fishing     4.00        1.75

    sens_ac_expert <- calc_sensitivity(
      indicators = sensitivity_scoring$indicator,
      pressures = sensitivity_scoring$pressure,
      type = sensitivity_scoring$type,
      sensitivity_traits = sensitivity_scoring[ ,4:8],
      adaptive_capacities = sensitivity_scoring[ ,9:13],
      uncertainty_sens = sensitivity_scoring[ ,14:18],
      uncertainty_ac = sensitivity_scoring[ ,19:23],
      method = "mean"
    )
    head(sens_ac_expert)
    #>       indicator    pressure            type pathway sensitivity
    #> 1 phytoplankton temperature          direct  expert          -3
    #> 2 phytoplankton    salinity          direct  expert           0
    #> 3 phytoplankton      oxygen          direct  expert          -2
    #> 4 phytoplankton    nutrient          direct  expert          -3
    #> 5 phytoplankton     fishing          direct  expert           0
    #> 6 phytoplankton temperature direct_indirect  expert          -4
    #>   adaptive_capacity uncertainty_sens uncertainty_ac sens_original.sens_feeding
    #> 1                 1                1              1                         NA
    #> 2                 1                2              2                         NA
    #> 3                 1                2              2                         NA
    #> 4                 1                2              2                         NA
    #> 5                 0                1              1                         NA
    #> 6                 1                1              1                         NA
    #>   sens_original.sens_behaviour sens_original.sens_reproduction
    #> 1                           NA                              NA
    #> 2                           NA                              NA
    #> 3                           NA                              NA
    #> 4                           NA                              NA
    #> 5                           NA                              NA
    #> 6                           NA                              NA
    #>   sens_original.sens_habitat sens_original.sens_general ac_original.ac_feeding
    #> 1                         NA                         -3                     NA
    #> 2                         NA                          0                     NA
    #> 3                         NA                         -2                     NA
    #> 4                         NA                         -3                     NA
    #> 5                         NA                          0                     NA
    #> 6                         NA                         -4                     NA
    #>   ac_original.ac_behaviour ac_original.ac_reproduction ac_original.ac_habitat
    #> 1                       NA                          NA                     NA
    #> 2                       NA                          NA                     NA
    #> 3                       NA                          NA                     NA
    #> 4                       NA                          NA                     NA
    #> 5                       NA                          NA                     NA
    #> 6                       NA                          NA                     NA
    #>   ac_original.ac_general
    #> 1                      1
    #> 2                      1
    #> 3                      1
    #> 4                      1
    #> 5                      0
    #> 6                      1

Both data sets now contain the aggregated expert scores. The sensitivity dataset also contains the initial expert scores, thus we can still calculate vulnerability for each trait individually, which will lead to more precise results. Additionally the last column gives information about the pathway of the scores to compare later on the results from both pathways.

In the modelling pathway we use the functions `model_exposure()` and `model_sensitivity()`. To assess exposure based on a time series we have to define a period where baseline conditions are assumed, the baseline conditions are then compared to the conditions in the assessment time period. In this tutorial the baseline is set to the first 10 years of the time series and the assessment time period are the last 5 years of the time series. Since baseline conditions are considered as “good” for our ecosystem all pressures should return to baseline conditions, we specify this with the argument trend. The spatial scale cannot be assessed with temporal data only, thus we have to specify the scores. We use here the same value for the spatial component that the experts gave for the pressures in the expert scoring.

    exposure_model <- model_exposure(
      pressure_time_series = ts_pressures,
      base_years = c(start = 1984, end = 1993),
      current_years = c(start = 2007, end = 2016),
      trend = "return",
      spatial = c(2, 2, 5, 5, 3, 3, 2, 2)
    )
    #> Registered S3 method overwritten by 'quantmod':
    #>   method            from
    #>   as.zoo.data.frame zoo
    exposure_model
    #>        pressure exposure uncertainty comp_magnitude comp_frequency comp_trend
    #> 1      nitrogen     3.25           2              3              5          3
    #> 2   phosphorous     2.00           2              1              2          3
    #> 3 surf_temp_sum     3.25           2              2              3          3
    #> 4  bot_temp_ann     3.50           2              2              4          3
    #> 5  surf_sal_sum     3.25           2              2              5          3
    #> 6   bot_sal_ann     2.75           3              1              3          4
    #> 7   bot_oxy_ann     3.00           2              2              5          3
    #> 8   fishing_cod     3.25           3              3              5          3
    #>   comp_direction comp_spatial uncertainty_arima uncertainty_gam mean_baseline
    #> 1       increase            2                 2               3    19.8141436
    #> 2       increase            2                 2               2     0.5734645
    #> 3       increase            5                 2               2    13.2227690
    #> 4       increase            5                 2               2     4.7876146
    #> 5       decrease            3                 2               2     5.9609406
    #> 6       decrease            3                 3               3     8.2235847
    #> 7       decrease            2                 2               2     4.4527522
    #> 8       decrease            2                 3               3     0.8957243
    #>   mean_current standard_deviation_baseline slope_linear_model
    #> 1   22.4085515                  1.27462524         0.13135681
    #> 2    0.6287693                  0.07808664         0.15626299
    #> 3   14.7021123                  1.33356555         0.20863265
    #> 4    6.1324167                  0.72058273         0.02144553
    #> 5    5.6123374                  0.18378270        -0.12287663
    #> 6    7.9426842                  0.33153236        -0.30833474
    #> 7    4.0093738                  0.26302107        -0.15798683
    #> 8    0.4765706                  0.20083878        -0.13339762
    #>   p_value_linear_model
    #> 1         2.550606e-01
    #> 2         1.672706e-01
    #> 3         5.010921e-02
    #> 4         8.585639e-01
    #> 5         2.897796e-01
    #> 6         7.878018e-05
    #> 7         1.619831e-01
    #> 8         2.470676e-01

The output gives us the aggregated exposure score, which is the arithmetic mean of all exposure components. These are the same components that have been evaluated by our experts. The `model_exposure()` function does not evaluate the associated uncertainty.

We should check for all pressures if the direction is capturing the correct dynamics and not only a short term fluctuation.

To assess sensitivity with time series data we also have to specify the assessment time period to determine if the pressure has in the assessment time period a negative or positive influence on the state indicator. The influence is determined using a simple linear model, so we can simply check if the direction was correctly determined using a simple plot. First we set up a data frame specifying for each indicator pressure combination the assessment time period.

    sens_ac_model <- model_sensitivity(
      indicator_time_series = ts_indicators,
      pressure_time_series = pressure_ts_baltic,
      current_years = c(start = 2010, end = 2016)
    )
    sens_ac_model
    #>                indicator      pressure            type pathway sensitivity
    #> 1  zooplankton_mean_size      nitrogen direct_indirect   model           3
    #> 2  zooplankton_mean_size   phosphorous direct_indirect   model           0
    #> 3  zooplankton_mean_size surf_temp_sum direct_indirect   model           0
    #> 4  zooplankton_mean_size  bot_temp_ann direct_indirect   model           0
    #> 5  zooplankton_mean_size  surf_sal_sum direct_indirect   model          -1
    #> 6  zooplankton_mean_size   bot_sal_ann direct_indirect   model          -1
    #> 7  zooplankton_mean_size   bot_oxy_ann direct_indirect   model           0
    #> 8  zooplankton_mean_size   fishing_cod direct_indirect   model           0
    #> 9     eastern_baltic_cod      nitrogen direct_indirect   model          -1
    #> 10    eastern_baltic_cod   phosphorous direct_indirect   model           0
    #> 11    eastern_baltic_cod surf_temp_sum direct_indirect   model          -1
    #> 12    eastern_baltic_cod  bot_temp_ann direct_indirect   model          -3
    #> 13    eastern_baltic_cod  surf_sal_sum direct_indirect   model           3
    #> 14    eastern_baltic_cod   bot_sal_ann direct_indirect   model           0
    #> 15    eastern_baltic_cod   bot_oxy_ann direct_indirect   model           1
    #> 16    eastern_baltic_cod   fishing_cod direct_indirect   model          -1
    #>    adaptive_capacity uncertainty_sens uncertainty_ac          r_sq      p_value
    #> 1                  0                2             NA  0.2431778963 0.0172601903
    #> 2                  0                1             NA -0.0002984071 0.3273367464
    #> 3                  0                1             NA -0.0178499546 0.5125884857
    #> 4                  0                1             NA  0.0294320635 0.1703455137
    #> 5                  0                2             NA  0.1005289236 0.0403973732
    #> 6                  0                2             NA  0.1673089042 0.0706193795
    #> 7                  0                1             NA -0.0286932790 0.7452975202
    #> 8                  0                2             NA -0.0301214578 0.8015015038
    #> 9                  0                2             NA -0.0218030319 0.7902502903
    #> 10                 0                1             NA  0.0401034383 0.1364793690
    #> 11                 0                1             NA  0.0987273652 0.0418798313
    #> 12                 0                1             NA  0.3762302850 0.0009652114
    #> 13                 0                2             NA  0.7424928607 0.0000000000
    #> 14                 0                2             NA  0.0584726393 0.0938685078
    #> 15                 0                1             NA  0.1832875957 0.0517027687
    #> 16                 0                2             NA  0.0100039535 0.5556690537
    #>         edf uncertainty_gam uncertainty_arima
    #> 1  2.847710               2                 2
    #> 2  1.000000               1                 2
    #> 3  1.000000               1                 2
    #> 4  1.000000               1                 2
    #> 5  1.000000               2                 2
    #> 6  2.192887               2                 2
    #> 7  1.000000               1                 2
    #> 8  1.000000               2                 2
    #> 9  1.126509               2                 2
    #> 10 1.000000               1                 2
    #> 11 1.000000               1                 2
    #> 12 2.054487               1                 2
    #> 13 2.320244               2                 2
    #> 14 1.000000               2                 2
    #> 15 2.094211               1                 2
    #> 16 1.621876               2                 2

The output of the function contains for each indicator and pressure combination the type of effect, the sensitivity score, the uncertainty associated with the uncertainty scoring and the model parameters that are used for the sensitivity scoring. The function evaluates sensitivity using a generalized additive model, if it is significant the \(R^2\) value is used to set a score between 1 and 5. For non-significant models the score is set to 0. The edf score evaluates non-linearity of the relationships, as these are more risky, the sensitivity will be increased for edf scores >1, but maximum to 5.

Lets continue by calculating the vulnerability for both pathways with the function `vulnerability()`. The vulnerability function combines exposure, sensitivity and adaptive capacity into the vulnerability score. For negative sensitivity score the following function applies:

\(V = (S + AC) - E\) and for positive scores:

\(V = (S + AC) + E\),

where V = vulnerability, S = sensitivity, AC = adaptive capacity and E = exposure. For trait based scoring this will be done for each trait individually. The vulnerabilities of each trait will then be aggregated, we can decide with the parameter method_v if we want to use an arithmetic mean, median, minimum or maximum for the aggregation, same applies for aggregation of trait based uncertainty scores.

    vuln_experts <- vulnerability(
      exposure_results = exp_expert,
      sensitivity_results = sens_ac_expert,
      method_vulnerability = "mean",
      method_uncertainty = "mean"
    )

    vuln_model <- vulnerability(
      exposure_results = exposure_model,
      sensitivity_results = sens_ac_model,
      method_vulnerability = "mean",
      method_uncertainty = "mean"
    )

    head(vuln_experts)
    #>       indicator    pressure            type pathway vulnerability uncertainty
    #> 1 phytoplankton temperature          direct  expert         -4.75    1.333333
    #> 2 phytoplankton    salinity          direct  expert          0.00    2.000000
    #> 3 phytoplankton      oxygen          direct  expert         -2.25    2.166667
    #> 4 phytoplankton    nutrient          direct  expert         -4.25    2.000000
    #> 5 phytoplankton     fishing          direct  expert          0.00    1.250000
    #> 6 phytoplankton temperature direct_indirect  expert         -5.75    1.333333
    head(vuln_model)
    #>               indicator      pressure            type pathway vulnerability
    #> 1 zooplankton_mean_size      nitrogen direct_indirect   model          6.25
    #> 2 zooplankton_mean_size   phosphorous direct_indirect   model          0.00
    #> 3 zooplankton_mean_size surf_temp_sum direct_indirect   model          0.00
    #> 4 zooplankton_mean_size  bot_temp_ann direct_indirect   model          0.00
    #> 5 zooplankton_mean_size  surf_sal_sum direct_indirect   model          4.25
    #> 6 zooplankton_mean_size   bot_sal_ann direct_indirect   model          3.75
    #>   uncertainty
    #> 1         2.0
    #> 2         1.5
    #> 3         1.5
    #> 4         1.5
    #> 5         2.0
    #> 6         2.5

The output of the vulnerability gives us for each indicator pressure type combination the vulnerability score with its associated uncertainty and the pathway with which the vulnerability has been determined.

To calculate the risk we need to know whether the indicator is currently in a good or undesired state, since the risk to be in an undesired state is higher if the indicator is already in it. Status can be determined by the experts or using the time series of the indicator. Our experts have assessed that phytoplankton and seabirds are currently in a good state, but herring and cod unfortunately not. An undesired state gets a score of -1 and a good state of +1.

    status_experts <- data.frame(
      indicator = c("phytoplankton", "herring", "cod", "seabirds"),
      status = c("good", "undesired", "undesired", "good"),
      score = c(1, -1, -1, 1)
    )
    status_experts
    #>       indicator    status score
    #> 1 phytoplankton      good     1
    #> 2       herring undesired    -1
    #> 3           cod undesired    -1
    #> 4      seabirds      good     1

In the modelling pathway the function `status()` evaluates indicator status based on time series. To assess the status we have to set baseline conditions where the indicator is assumed to be in a good status and our assessment time frame for which the status shall be evaluated (similar to the `model_exposure()`) function. Additionally we can set a range around the baseline mean which is considered as good status. We can specify whether it is undesired if the indicator is in the assessment time period below or above this range using the arguments `sign` and `condition`. For our status assessment we assume good baseline conditions in the first ten years as the mean ± 1 standard deviation. Undesired status is defined as being below 1 standard deviation so we set sign = “-” and condition = “<”.

    status_model <- status(
      indicator_time_series = ts_indicators,
      base_years = c(start = 1984, end = 1993),
      current_years = c(start = 2012, end = 2016),
      sign = "-",
      condition = "<"
    )
    status_model
    #>               indicator    status score
    #> 1 zooplankton_mean_size undesired    -1
    #> 2    eastern_baltic_cod undesired    -1

Both of our indicators are in the assessment time period in an undesired status.

Now we combine vulnerability and status to the final risk scores. Both pathways use the function `risk()`.

    risk_expert <- risk(
      vulnerability = vuln_experts,
      status = status_experts
    )
    risk_model <- risk(
      vulnerability = vuln_model,
      status = status_model
    )

    head(risk_expert)
    #>       indicator    pressure            type pathway vulnerability status  risk
    #> 1 phytoplankton temperature          direct  expert         -4.75   good -3.75
    #> 2 phytoplankton    salinity          direct  expert          0.00   good  0.00
    #> 3 phytoplankton      oxygen          direct  expert         -2.25   good -1.25
    #> 4 phytoplankton    nutrient          direct  expert         -4.25   good -3.25
    #> 5 phytoplankton     fishing          direct  expert          0.00   good  0.00
    #> 6 phytoplankton temperature direct_indirect  expert         -5.75   good -4.75
    #>   uncertainty
    #> 1    1.333333
    #> 2    2.000000
    #> 3    2.166667
    #> 4    2.000000
    #> 5    1.250000
    #> 6    1.333333
    head(risk_model)
    #>               indicator      pressure            type pathway vulnerability
    #> 1 zooplankton_mean_size      nitrogen direct_indirect   model          6.25
    #> 2 zooplankton_mean_size   phosphorous direct_indirect   model          0.00
    #> 3 zooplankton_mean_size surf_temp_sum direct_indirect   model          0.00
    #> 4 zooplankton_mean_size  bot_temp_ann direct_indirect   model          0.00
    #> 5 zooplankton_mean_size  surf_sal_sum direct_indirect   model          4.25
    #> 6 zooplankton_mean_size   bot_sal_ann direct_indirect   model          3.75
    #>      status risk uncertainty
    #> 1 undesired 5.25         2.0
    #> 2 undesired 0.00         1.5
    #> 3 undesired 0.00         1.5
    #> 4 undesired 0.00         1.5
    #> 5 undesired 3.25         2.0
    #> 6 undesired 2.75         2.5

The output of the risk function gives us per indicator - pressure - type combination the risk, calculated from vulnerability and status, as well as the uncertainty associated with the risk evaluation. Before we combine both data frames we will rename the pressure variables of the model based risk assessment to align with the names of the expert based assessment. This is necessary to correctly aggregate the risk values per pressure to multi pressure risk scores. Furthermore we will select for each pressure, which has more than one variable one of them. We follow here a precautionary approach thus we will select the one posing the highest risk.

    risk_model <- risk_model[c(1, 3, 5, 7, 8, 9, 12, 14:16), ]
    risk_model$pressure <- c(
      "nutrient", "temperature", "salinity", "oxygen", "fishing",   # for zooplankton
      "nutrient", "temperature", "salinity", "oxygen", "fishing")   # for cod

Now we combine both risk assessment data sets and aggregate them to get multi pressure, multi indicator and ecosystem risk scores. The aggregated score will automatically be calculated per pathway, type, pathway and type, and without accounting for type or pathway.

    risks <- rbind(risk_expert, risk_model)

    aggregated_risk <- aggregate_risk(
      risk_results = risks,
      method = "mean"
    )

    aggregated_risk$multi_indicator_risk
    #>       pressure            type  pathway      risk uncertainty
    #> 5      fishing          direct   expert -5.062500    1.416667
    #> 10     fishing direct_indirect   expert -6.250000    1.416667
    #> 15     fishing direct_indirect    model  1.625000    2.500000
    #> 20     fishing          direct combined -5.062500    1.416667
    #> 25     fishing direct_indirect combined -3.625000    1.777778
    #> 30     fishing        combined   expert -5.656250    1.416667
    #> 35     fishing        combined    model  1.625000    2.500000
    #> 40     fishing        combined combined -4.200000    1.633333
    #> 4     nutrient          direct   expert -1.250000    2.083333
    #> 9     nutrient direct_indirect   expert -2.140625    2.083333
    #> 11    nutrient direct_indirect    model  0.000000    2.000000
    #> 19    nutrient          direct combined -1.250000    2.083333
    #> 24    nutrient direct_indirect combined -1.427083    2.055556
    #> 29    nutrient        combined   expert -1.695312    2.083333
    #> 31    nutrient        combined    model  0.000000    2.000000
    #> 39    nutrient        combined combined -1.356250    2.066667
    #> 3       oxygen          direct   expert -2.468750    2.250000
    #> 8       oxygen direct_indirect   expert -4.187500    2.250000
    #> 14      oxygen direct_indirect    model -2.500000    1.500000
    #> 18      oxygen          direct combined -2.468750    2.250000
    #> 23      oxygen direct_indirect combined -3.625000    2.000000
    #> 28      oxygen        combined   expert -3.328125    2.250000
    #> 34      oxygen        combined    model -2.500000    1.500000
    #> 38      oxygen        combined combined -3.162500    2.100000
    #> 2     salinity          direct   expert -1.812500    1.750000
    #> 7     salinity direct_indirect   expert -3.734375    1.750000
    #> 13    salinity direct_indirect    model  1.625000    2.250000
    #> 17    salinity          direct combined -1.812500    1.750000
    #> 22    salinity direct_indirect combined -1.947917    1.916667
    #> 27    salinity        combined   expert -2.773438    1.750000
    #> 33    salinity        combined    model  1.625000    2.250000
    #> 37    salinity        combined combined -1.893750    1.850000
    #> 1  temperature          direct   expert -4.281250    1.416667
    #> 6  temperature direct_indirect   expert -6.750000    1.416667
    #> 12 temperature direct_indirect    model -3.750000    1.500000
    #> 16 temperature          direct combined -4.281250    1.416667
    #> 21 temperature direct_indirect combined -5.750000    1.444444
    #> 26 temperature        combined   expert -5.515625    1.416667
    #> 32 temperature        combined    model -3.750000    1.500000
    #> 36 temperature        combined combined -5.162500    1.433333
    aggregated_risk$multi_pressure_risk
    #>                indicator            type  pathway     risk uncertainty
    #> 3                    cod          direct   expert -5.03750    1.616667
    #> 7                    cod direct_indirect   expert -7.20000    1.616667
    #> 13                   cod          direct combined -5.03750    1.616667
    #> 17                   cod direct_indirect combined -7.20000    1.616667
    #> 23                   cod        combined   expert -6.11875    1.616667
    #> 29                   cod        combined combined -6.11875    1.616667
    #> 10    eastern_baltic_cod direct_indirect    model -2.90000    2.000000
    #> 20    eastern_baltic_cod direct_indirect combined -2.90000    2.000000
    #> 26    eastern_baltic_cod        combined    model -2.90000    2.000000
    #> 32    eastern_baltic_cod        combined combined -2.90000    2.000000
    #> 2                herring          direct   expert -3.26250    1.616667
    #> 6                herring direct_indirect   expert -4.50000    1.616667
    #> 12               herring          direct combined -3.26250    1.616667
    #> 16               herring direct_indirect combined -4.50000    1.616667
    #> 22               herring        combined   expert -3.88125    1.616667
    #> 28               herring        combined combined -3.88125    1.616667
    #> 1          phytoplankton          direct   expert -1.65000    1.750000
    #> 5          phytoplankton direct_indirect   expert -2.25000    1.750000
    #> 11         phytoplankton          direct combined -1.65000    1.750000
    #> 15         phytoplankton direct_indirect combined -2.25000    1.750000
    #> 21         phytoplankton        combined   expert -1.95000    1.750000
    #> 27         phytoplankton        combined combined -1.95000    1.750000
    #> 4               seabirds          direct   expert -1.95000    2.150000
    #> 8               seabirds direct_indirect   expert -4.50000    2.150000
    #> 14              seabirds          direct combined -1.95000    2.150000
    #> 18              seabirds direct_indirect combined -4.50000    2.150000
    #> 24              seabirds        combined   expert -3.22500    2.150000
    #> 30              seabirds        combined combined -3.22500    2.150000
    #> 9  zooplankton_mean_size direct_indirect    model  1.70000    1.900000
    #> 19 zooplankton_mean_size direct_indirect combined  1.70000    1.900000
    #> 25 zooplankton_mean_size        combined    model  1.70000    1.900000
    #> 31 zooplankton_mean_size        combined combined  1.70000    1.900000

The aggregated risk scores are in three lists:

- One with all risks aggregated per pressure,

- one aggregated per indicator and

- one with the ecosystem risk, which is an aggregation of all multi pressure risk scores.

In all lists the scores are first aggregated per type and pathway, then per type regardless of the pathway, then per pathway regardless of the type and as last regardless of the type and pathway.

## Results

To get an easier overview of the results and help with the interpretation ecorisk provides two plotting functions `plot_radar()` and `plot_heatmap()`.

The first one creates for each indicator a radar plot with the risk scores per pressure and type. In the centre it shows the aggregated multi-pressure risk, we have to select which we want to use. This plot helps to identify per indicator the most influencing pressures and compare results from different types. If uncertainty has been assessed this will be displayed as a ring around the radar plot. In this example we will the use the aggregated score of direct and indirect effects, regardless of the pathway. Theses are assumed to better reflect reality compared to direct effects only.

    p_radar <- plot_radar(
      risk_scores = risks,
      aggregated_scores = aggregated_risk,
      type = "direct_indirect",
      pathway = "combined"
    )

    p_radar[[1]]

    p_radar[[2]]

    p_radar[[3]]

    p_radar[[4]]

    p_radar[[5]]

    p_radar[[6]]

All of the indicators have a negative multi-pressure score. The indicators assessed with the expert scoring pathway show a higher risk due to the combined direct and indirect effects compared to direct effects only. The uncertainty is generally lower in the modelling pathway. Comparing the modelling and expert pathway for cod it is noticeable that both have a similar multi-pressure score but the individual risk scores are quiet different: The experts assessed fishing as the most influencing pressure, whereas in the modelling pathway salinity is considered as the pressure with the highest impact. To directly compare modelling and expert pathway for cod we can correlate them in a plot:

    temp <- risks[c(26:30, 45:49), c(1, 2, 7)]
    temp <- temp |>
      tidyr::pivot_wider(names_from = indicator, values_from = risk)

    ggplot2::ggplot(dat = temp,
        ggplot2::aes(x = cod, y = eastern_baltic_cod, colour = pressure)) +
      ggplot2::geom_point() +
      ggplot2::geom_abline(slope = 1, intercept = 0) +
      ggplot2::xlim(-10, 10) +
      ggplot2::ylim(-10,10) +
      ggplot2::labs(x = "Expert-based pathway", y = "Modelling-based pathway") +
      ggplot2::theme_minimal()
    #> Warning: Removed 1 row containing missing values or values outside the scale range
    #> (`geom_point()`).

We can see that the risk scores for nutrients, oxygen and temperature are quiet similar for both pathways. But the values for salinity indicate no risk in the modelling pathway. This might be due to a salinity time series that does not catch the ongoing dynamics, and thus resulting in a non significant relationship between pressure and indicator. The scores for fishing have even opposing directions, this could be due to a different understanding of fishing and the future developments: In the modelling pathway it has been shown that fishing is decreasing, which will be positive for the indicators, thus in the future it will have a positive effect. But the expert probably assumed that fishing will always have negative effects, without considering the positive development of the decreasing fishing pressure. This is a linguistic uncertainty, which should have been discussed in the planning and scoping phase of the assessment, to ensure that all have a common understanding. Nevertheless we should reiterate with our experts as well as check if the `model_sensitivity()` and `model_exposure()` function have correctly determined the effect direction.

The function `plot_heatmap()` creates for each assessment type a heatmap of all pressure indicator combinations, optionally with the associated uncertainty. The aggregated multi-pressure and indicator scores are shown at the bottom and to the left of the heatmap as well as the system risk score at the bottom right. For the aggregated scores we have to choose which one we want to use as we already did for the `plot_radar()` function. This function gives an complete overview of the system dynamics allowing to easily compare ecosystems and determine by which indicators and pressures ecosystem risk is driven.

    p_heat <- plot_heatmap(
      risk_scores = risks,
      aggregated_scores = aggregated_risk,
      uncertainty = TRUE
    )

    p_heat[[1]]

    p_heat[[2]]

The first heatmap includes only direct effects, thus this heatmap is a bit smaller as we did not assess for all indicators direct effects only. The multi pressure and indicator scores are the aggregated direct scores for all assessed pathways. The grey frame around the heatmap tiles show the uncertainty associated with the score. We can see with this heatmap that cod is the indicator most at risk, this risk is due to high effects of fishing and temperature. The least at risk indicators are phytoplankton and seabirds. Both are not affected by several of the pressures, but still seabirds are at a medium to high risk due to fishing. The second heatmap shows the direct and indirect effects including also the indicator which were assessed with the modelling pathway. Again the cod indicator is most at risk, followed by the modelled cod indicator, herring and seabirds. The pressures with the highest negative impact are temperature and fishing. Zooplankton is an example for an indicator which will likely thrive under the pressures. It is still worthwhile to include such indicators in a risk assessment as these positive changes in one indicator can have negative effects for the entire system, thus every change can bear a risk for the system. Overall the system is a bit more at risk considering the combination of direct and indirect effects compared to direct effects only.

What can we do now with the results of our risk assessment? Here are some examples:

- We can inform the management by prioritizing which pressures pose the highest risk and which indicators are most at risk.
- We can use the information to guide research: did any effect come by surprise (especially from the modelling pathway)? Which risks are associated with high uncertainties?
- If we are interested in non - linear effects and how indicators and pressures interact with each other we could use our results as a basis for a network analysis and develop questions based on the risk assessment output or select specific indicator and pressure combinations that we want to further investigate with a more quantitative analysis.

# Contact

If you have issues with the package or questions please send an e-mail to: helene.gutte@uni-hamburg.de

# References

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