Uncertainty and spatial linear models for ecological data

Models are not perfect; they do not fit the data exactly and they do not allow exact prediction. Given that models are imperfect, we need to assess the uncertainties in the fits of the models and their ability to predict new outcomes. The goals of building models for scientific problems include (1) understanding and developing appropriate relationships between variables, and (2) predicting variables in the future or at locations where data have not been collected. Ecological models range in complexity from those that are relatively simple (e.g., linear regression) to those that are very complex (e.g., ecosystem models, forest-growth models, and nitrogen-cycling models). In a mathematical model, parameters control the relationships between variables in the model. In this framework of parametric modeling, inference is the process whereby we take output (data) and estimate model parameters, whereas deduction is the process whereby we take a parameterized model and obtain output (data) or deduce properties. We often add random components in both inference and deduction to reflect a model’s lack-of-fit and our uncertainty about predicting outcomes. Complex models in ecology have largely been of the deductive type, where the scientist takes some values of parameters (usually obtained from an independent data source or chosen from a reasonable range of values) and then simulates results based on model relationships. These models may be quite realistic, but the manner in which their parameters are obtained for the simulations is questionable.