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

Ecological risk analysis is becoming increasingly important to environmental 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, cross-validated multiple regression (MR) and cross-validated holographic neural 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 collected. These inferred relationships can then be used to generate the probability distribution of ecological effects φ (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 by forest cover removal and road construction on adjacent lands, using a sample of wetlands from southeastern Ontario. Our results indicate that both MR and HNN predict that the probability of a loss in herptile richness and the expected magnitude of the loss increases as road density increases and forest cover decreases, i.e. risk increases. On the other hand, both the mean and variance of φ, 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 between the two methods, the risk, as predicted by MR, exceeds that predicted by HNN: the expected loss in herptile richness is greater and the uncertainty associated with this prediction is smaller.