Modeling Populations of Flour Beetles

Mathematical models can be used to describe and predict the complex dynamics of biological phenomena such as animal populations. There is a trade-off between the amount of mathematical and biological complexity one can include in a model; fewer simplifications lead to a more biologically accurate model, but may come at the cost of adding dimensions or parameters. This increases the difficulty of mathematical analysis and may render some analyses intractable. A critical part of evaluating a mathematical model is connecting it with data. Data is used to give numerical values to a model’s parameters and to judge the adequacy of the model to describe the dynamics of a population. Once parameter values are obtained, the parameterized model can be applied to additional data to test its predictive power. Computer simulations and mathematical analysis can be used to investigate the dynamics of the model and interesting dynamics found may suggest future experiments that could further validate the model.