Ecosystem Synthesis: Finding Key Linkages between Stock Indices and Multivariate Ecosystem Trends

Summary

The goal of this analysis is to start exploring potential links between stock indices and ecosystem components. One approach is to find similarities between time series of ecosystem indicators and stock indices. This is not an easy task as there are many (!) indicators available, and an attempt to include all time series will result in a large number of pairwise correlations and plots, difficult to interpret (e.g. http://rpubs.com/gomezcatalina/data).

The first step is therefore to reduce the number of indicators that synthesize the Scotian Shelf ecosystem to a more manageable number, without loosing too much information. Using the conceptual model in Figure 1, we identified four main ecosystem components:

• Human components represented by 9 fishing pressure indicators (1970 - 2015, Bundy et al. In Press)
• Biotic components represented by 20 upper trophic level indicators (1970 - 2015, Bundy et al. In Press, and den Heyer)
• Biotic components represented by 13 lower trophic level indicators (1999 to 2015, Johnson et al. 2017)
• Physical components represented by 6 indicators (Hebert et al. 2015)

The ecosystem synthesis consisted in extracting the main trends of each one of the ecosystem components using a Min/max Autocorrelation Factor Analysis (MAFA). MAFA is a type of Principal Component Analysis for time series that identifies and extracts main common trends from multiple time series. MAFA resulted in 12 multivariate trends that synthesize the entire system, instead of the 48 trends summarized in Figure 1. Results of this analysis are presented below. For more information about data used in this analysis please see http://rpubs.com/gomezcatalina/data. For more information about MAFA, please see Chapter 17 in Zuur et al. 2007.

Figure 1. Conceptual model of the Scotian Shelf Bioregion showing the 48 indicators gathered for this exercise

Once the ecosystem was summarized, the next step consisted in exploring the relationship between the main multivariate trends and several stock indices. As a starting point, a Hierarchical Cluster Analysis was conducted, with results displayed as a dendrogram: the greater the distance and the height of their branches in the dendrograms, the greater the difference between the time series. This document only presents results of this analysis, and the goal at the meeting is to discuss these results.

Ecosystem synthesis using a multi-variate approach

Three primary MAFA trends were derived from each component of the Scotian Shelf Bioregion. Figures below show results of this analysis: left panels are the MAFA trends underlying the indicators, and right panels represent indicators that are responsible for these signals (i.e. canonical correlations). Positive and strong correlations show indicators that follow the MAFA trends closely, and vice versa.

Physical components

Human components: Fishing Pressure

Biotic components: upper trophic levels

Biotic components: lower trophic levels

Multivariate Ecosystem Synthesis and Links to Stock Indices

The following section presents a series of dendrograms of multivariate trends synthesizing the Scotian Shelf (i.e. multivariate ecosystem trends) in relation to stock indices. This with the goal of exploring potential linkages between stock indices and multivariate ecosystem trends. The indicators are joined together in a hierarchical fashion from the closest, that is most similar, to the furthest apart, that is the most different. In general, the closer a stock index is to a multivariate trend, and the lower the height of the branches (y-axis), the stronger the potential linkage. Note that all dendrograms are based on results from Hierarchical Cluster Analysis using the Euclidean distance and complete agglomeration method. To assess the uncertainty, and to evaluate how strongly the clusters were supported by data, Approximately Unbiased (AU) p-values were calculated via multiscale bootstrap resampling (10,000 replications) (Suzuki and Shimodaira 2013). Clusters of similar indicators and AU p-values ≥ 95 are highlighted by green rectangles.

Note that linkages between the ecosystem and stock indices are explored in this example with cluster analysis, but other analysis can be incorporated into this approach such as the ones used in the summaries exploring stocks in an ecosystem context e.g. http://rpubs.com/gomezcatalina/Halibut_1999to2015. Also note that in this analysis we included the inverse of the multivariate trends labeled as .1 (e.g. PhysicalCompMAFA1_s is the MAFA trend presented above, and PhysicalCompMAFA1_s.1 is the inverse of this trend).

Multivariate ecosystem trends and biomass stock indices (full time series: 1970 - 2015)

Multivariate ecosystem trends and biomass stock indices (short time series: 1999 - 2015)

Multivariate ecosystem trends and condition and recruitment indices (full time series: 1970 - 2015)

Multivariate ecosystem trends and condition and recruitment indices (full time series: 1999 - 2015)