Stressor-Resource Matrix Approach
Abstract
To deal with multiple stressors, one can represent stressors as the rows and resources as the columns of a table. An entry in the table represents how closely that stressor is correlated to that resource. Each row can be summed to determine the impact of that stressor across all resources. The stressors with the largest row sums are taken to be the stressors with the greatest overall impact. Each column can also be summed to determine impact across all stressors. The resources with the largest column sums are taken to be resources under the greatest stress.
Method Details
In typical application of the matrix approach, quantitative information is not available and a panel of experts is asked to assess the individual impacts and supply a qualitative value. In the ReVA context, data is available for stressors and resources and it is possible to apply the matrix approach quantitatively.
A correlation matrix is calculated for the entire data set over all watersheds and each row of correlation coefficients is summed. The resultant row sum includes all of the direct and indirect interactions among the variables. Thus, indirect effects with other stressors are included along with the direct effects of stressors on resources.
The correlation analysis involves a large number of interactions and possibly a number of spurious correlations. Small, spurious coefficients might accumulate over the row sum and alter the results. To test the sensitivity of the method, we systematically removed smaller coefficients and redid the row sums. The results indicate that the ranking is insensitive for the top three or four stressors. The explanation is probably that small coefficients are equally likely to be positive or negative and only have a minor influence on the row sum.
The correlation matrix can also be used to indicate the resources experiencing the greatest stress by ranking the column sums. We tested the sensitivity of the rankings by removing small correlation coefficients. Beyond the first two variables, the rankings of the remaining variables change significantly as the smaller coefficients are removed.
Limitations
The technique was originally designed to identify the top few stressors within a site or watershed. The tests performed here reinforce the idea of limiting the results to 2 or 3 stressors and vulnerable assets. Once the analysis gets beyond about 3, the row or column sums tend to converge and the exact ranking of a stressor or asset becomes very sensitive to small changes in the sums.
The primary disadvantage of this approach to integration is the difficulty of interpreting and communicating the results. This approach has been used in the literature to rank direct impacts. In the current analysis, correlations are not direct impacts. Even large negative values are a complex combination of direct and indirect impacts as well as synergistic and cumulative effects. The correlations will be strongly influenced by spatial patterns of co-occurrence. The important point is that the correlations express the resultant of past and present stressors, spatial pattern and synergistic and cumulative effects. Therefore, the results of the correlation analysis will have to be carefully stated with sufficient caveats warning the reader against the natural tendency to interpret the results as direct impacts. In the usual application, the top ranked stressors are identified as the one most in need of immediate managerial action. That conclusion is not necessarily valid in our case, and elimination of the top stressors might well result in little, or long-delayed, responses.
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