Common trends refer to trends that are similar across ecosystem components. Identifying common trends can be useful as a diagnostic tool to reveal past changes and to explore the relationships among biological communities and between these communities and environmental conditions.
Trend estimation and classification analyses (TREC)
For the investigation, trend estimation and classification analyses (TREC) are applied to WGIBAR time series data including 7 abiotic components, 18 biotic components, and 8 human impacts. The estimates obtained by polynomial trend model are shown in Fig. 2.2.1.1. Using trends for 1 and 6, two-category discrimination is applied to roughly classify them as three groups (Fig. 2.2.1.2).
Figure 2.2.1.1. Estimated trend (red) and observation (black). X-axis indicates years (1980-2019) and y-axis indicates standardized values for each dataIn the classified groups, some precise common configurations are still shown, e.g. linear, exponentially or saturation curves in upward. These trends become references to apply more than two-category discrimination. The reference is corresponding to the representative icon figure, which serve general reference for the needs of stakeholders. The details for classified each category and assigned icons are shown in Fig.2.2.1.3.
The ongoing warming were associated with increased trend in water temperature, larger area covered by Atlantic warm water masses and decreased trend ice coverage since 1980s. The warming was also associated with increased macro zooplankton such as krill and jellyfish biomass, increased fish recruitment (age 0) which trigger positive development of fish stocks (cod, haddock and herring).
Figure 2.2.1.2. Dendrogram obtained by 2-category-discriminant analysis procedure (upper panel) and the classified groups (roughly three, upward, flat and downward) (lower table).
Figure 2.2.1.3. The details for classified data in each category.
Warning signal analysis
To investigate whether the most recent observation follow the recent trend or is away from the trend, one (or more) years ahead predictions are calculated. The trend in this case is estimated by stochastic trend model. Stochastic trend model is presented by a class of auto-regressive model and is easily set in state space representation. Kalman filter algorithm is applied to estimate trend component and to calculate the prediction. The trend estimates look more fluctuated rather than estimates by polynomial trend. This is because of that stochastic trend follows the data variation in each time point. We run the algorithm using the data recording until 2016 and calculate the prediction for 2017-2019. In Fig.2.2.2.1, the estimated trend and prediction with the confidence interval are plotted by red line. Real observations for 2017-2019 are plotted by black dots. Existing black dots inside/outside the confidence intervals gives the statistical criteria to know the distance between observation and predicted value by trend model. This may make an assessment whether the observation is a sign and something ‘unusual’ going on the ecosystem that may represent a warning signal.
Figure 2.2.2.1. 3-years-ahead prediction and the confidence intervals (red line) for the trend obtained by the data recording for 1980-2016 (black line). Black dots indicate real observations recording on 2017-2019.
Table 2.2.1.2. Observations for abiotic and biotic variables located outside of or the just border of the confidence intervals for the prediction values in the period 2017-2019, which were calculated by the trend and observation noise using the observations until 2016.