State space displacement analysis of the response of aquatic ecosystems to phenolic toxicants

The state of an ecosystem at any time t may be characterized by a multidimensional state vector x(t). Changes in state are represented by the trajectory traced out by x(t) over time. The effects of toxicant stress are summarized by the displacement of a perturbed state vector, x_p(t), relative to an appropriate control, x_c(t). Within a multivariate statistical framework, the response of an ecosystem to perturbation is conveniently quantified by the distance separating x_p(t) from x_c(t) as measured by a P C Mahalanobis metric. Use of the Mahalanobis metric requires that the covariance matrix associated with the control state vector be estimated.

State space displacement analysis was applied to data on the response of aquatic microcosms and outdoor ponds to alkylphenols. Dose-response relationships were derived using calculated state space separations as integrated measures of the ecological effects of toxicant exposure. Inspection of the data also revealed that the covariance structure varied both with time and with toxicant exposure, suggesting that analysis of such changes might be a useful tool for probing control mechanisms underlying ecosystem dynamics.

State space displacement analysis was further investigated in the context of an ecological simulation model. Replicate state space trajectories, incorporating both natural variability (random initial conditions and stochastic forcings) and measurement error, were produced using Monte Carlo techniques. It was demonstrated that although quantitative estimates of state space separation vary with the estimated covariance matrix, qualitative features of the dose-response relationships are relatively robust to variation in the covariance estimates. Furthermore, the state space methodology was demonstrated to have high statistical power: effects at the lowest simulated dose could readily be detected with as few as one or two Monte Carlo replicates per treatment.

Finally, the problem of selecting a small set of diagnostic variables which reflect ecosystem state was examined. The adequacy of diagnostic variables as predictors of ecological risk is a function of the probabilities of the associated type I and type II statistical errors. A cost-benefit approach for choosing an optimal balance between these error rates was developed.