Estimating ecosystem risks using cross-validated multiple regression and cross-validated holographic neural networks

Ecological risk analysis is becoming increasingly important to environmenta l decision-making, The goal of ecological risk analysis is to quantify the distribution of possible ecological effects arising from ecosystem exposure to one or more stressors (risk factors). Here we introduce two methods, cr oss-validated multiple regression (MR) and cross-validated holographic neur al networks (HNN), which can be used to infer stress-response relationships from a sample of ecosystems (e.g. lakes, forests, wetlands) for which data on both stressors (S) and measurement endpoints (responses, R) have been c ollected. These inferred relationships can then be used to generate the pro bability distribution of ecological effects phi (R; S) given exposure to a certain level of stress. We illustrate these two methods by quantifying the risks to wetland herptile (reptile and amphibian) species richness posed b y forest cover removal and road construction on adjacent lands, using a sam ple of wetlands from southeastern Ontario. Our results indicate that both M R and HNN predict that the probability of a loss in herptile richness and t he expected magnitude of the loss increases as road density increases and f orest cover decreases, i.e. risk increases. On the other hand, both the mea n and variance of phi, as calculated by HNN, exceed that calculated by MR, with the difference between the two declining as anthropogenic disturbance on adjacent lands increases. Thus, while there is qualitative agreement bet ween the two methods, the risk, as predicted by MR, exceeds that predicted by HNN: the expected loss in herptile richness is greater and the uncertain ty associated with this prediction is smaller. (C) 1999 Elsevier Science B. V. All rights reserved.