Explain Historical Example of connecting models and data?
An excellent instance of a program that links theory and data is collaborative work on the population dynamics of flour beetles, Tribolium, in laboratory microcosms (Costantino et al. 1997, Dennis et al. 2001). In this work, a model for the population dynamics of flour beetles that was developed relies upon reproduction by adults and cannibalism on immature stages. Careful studies including the model, controlled laboratory population experiments, and statistical methods identified many nonlinear phenomena in population data, including equilibria, cycles, multiple attractors, resonance, transitions among dynamic regimes (bifurcations), basins of attraction, saddle influences, and stable and unstable manifolds. A particular result of the model is that chaos takes part over a range of cannibalism rates, with less exotic dynamics taking place at low and high cannibalism levels. By performing experiments manipulating cannibalism over its whole range, Costantino et al. (1997) witnessed the predicted degeneration of simple dynamics into chaos and the consequent recovery. This provides the strongest type of evidence for the existence of chaos in ecological systems, because it shows the direct correspondence among model and real dynamics over a range of dynamical patterns. This example as well illustrates how experimental problems can generate novel theoretical advances, since it required new methods for fitting nonlinear models to stochastic data sets.