The following is a little excerpt from a paper that I’m writing on the role of food web models (focusing on mine) in the developing field of conservation paleobiology.
A scientific model is a set of formal statements which are hypothesized to represent or explain some aspect of the natural world. The natural world is complex, and models are necessarily simplifications to some degree. They often reflect educated guesses of the relationship, or nature of a relationship between known processes or observed phenomena. Models do, however, allow us to make predictions about the natural world. Furthermore, models allow us to explore hypothetical possibilities, even when our data are insufficient or incomplete. Conservation paleobiology is concerned with the application of paleontological ideas and data to conservation biology, that is, understanding the circumstances under which species are threatened with extinction, become extinct, or survive those circumstances. These are the concerns that our models must address, and to be of use to conservation biology, they must make predictions of future biodiversity events on the basis of the fossil record.
Scientific models need not be mathematical, but in this paper I will focus on mathematical models for two reasons. First, the paper is intended to be instructive about the creation and use of models in conservation paleobiology. Almost any such model must be expected to contain statements of ecology and paleoecology, and mathematical modeling in ecology has matured into a rich and useful discipline. Therefore, “model” in this paper will always refer to a mathematical formulation. Second, when formulated mathematically, a model gives us much freedom to question our hypotheses and explore implications and consequences outside the bounds of empirical observations. This is particularly useful when data are unknown or incomplete, or the hypothesis itself is incomplete. Mathematical modeling should not be taken, however, as an exclusive alternative to empiricism. The two approaches to science are complementary: a Platonic approach that presumes the existence of fundamental truths, and the Aristotelian approach rooted in empirical observation. If there is any order in Nature, and scientific experience tells us that there is, then our models can be based on our understanding of fundamental principles, and should be expected to be congruent with empirical data to the extent that the model reflects the entirety of the processes producing the data. Incongruence will often require a reformulation of the model, or even revision of the principles themselves, a task made easier and more precise when the model has been stated and communicated mathematically. Alternatively, one should also always bear in mind the division between data and interpretation. While data perhaps seldom lie, scientific theories are based on histories of important misinterpretation, and there are numerous examples of models that predicted as yet unobserved data or phenomena, while being at odds with interpretations of existing data.