State Space of Ecosystems

Apparently as an independent development, A.R. Johnson (1988a) proposed the idea of using a multivariate approach to the analysis of multispecies toxicity tests. This state space analysis is based upon the common representation of complex and dynamic systems as an n-dimensional vector. In other words, the 

In the n-dimensional hypervolume that describes the placement and trajectory of the ecosystem, it is possible to compare the positions of systems at a specified time. This displacement can be measured by computing the distance from the systems, and this displacement vector can be regarded as the displacement of these systems in space. The displacement vectors can be easily calculated and compared. Using the data generated by Giddings et al. (1980) in a series of classic experiments comparing results of the impacts of synthetic oil on aquarium and small-pond multispecies systems, Johnson was able to plot dose-response curves using the mean separation of the replicate systems. These plots are very reminiscent of dose-response curves from typical acute and chronic toxicity tests. 

One of the difficulties in the past of using multivariate methodologies such as those proposed by A. Johnson and Kersting was the computational effort required. Computational requirements are not the limiting factor that they may have once been, even for large datasets. 

The major difficulty with the methods detailed above is the reliance on conventional metric statistics. Vector distances in an n-dimensional space including 

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