The role of interactions in hypothesis testing of ecological scenarios with process models

Hypothesis testing is widely employed for comparing the effect of treatments in field and laboratory experiments. Although comparison of scenarios through process models is also an important aspect in ecological simulation, studies conducted in that area usually do not account for the uncertainty (estimation error) associated with the simulation results. This paper proposes an approach for testing hypotheses through process models accounting for estimation error in values of treatment entities (model factors that characterize the treatments or scenarios) and external entities (remaining model factors) that interact with treatment entities. External entities, as represented by the model, may in turn be thought of as a characterization of the environment in which the simulation experiment is conducted. This approach is a generalization of a previous work developed under the assumption that no external entity interacts with treatment entities. This method focuses on differences between predictions obtained from the treatments, rather than on absolute values predicted for each treatment. Fitting low-order orthogonal polynomials is suggested as a means to identify entity interactions in process models. An example is conducted to indirectly test the effect of tree spacing (through its inverse effect on wood density in some species) on the growth of a forest stand. Specifically, we employed a forest growth process model to test whether the growth of basal area is affected by different wood densities resulting from two initial spacings (3 and 6 m) in a red pine ( Pinus resinosa Ait.) stand growing in the Great Lakes region of North America from ages 36 to 60 years. Results of the effect of spacing on wood density were in turn obtained from a field study. The importance of accounting for uncertainty in interacting external entities became evident as the variance of the mean difference between predicted treatment means was six times larger when that source of uncertainty was accounted for. Although basal area for the wider spacing was significantly larger in both tests, the power of the tests was affected considerably by the different levels of uncertainty resulting from these two approaches.