Inference for Mechanistic Models: Case Studies in Ecology
Mechanistic mathematical models are important tools for understanding the processes that shape ecological systems. Models have been used to describe life cycles of individuals, population dynamics, behavior, and more. However, in order for these models to reach their full potential as both tools for understanding and for prediction we must be able to link modeled quantities to data and infer model parameters.
However, general methods of parameter inference for many of these models are not available, and we must think carefully about how to link sophisticated models with robust inferential techniques. Here I discuss three examples of ecological models of these types. First is a model of the temperature dependence of malaria transmission, which shows the power of even simple models combined with data. The second example uses an example of an individual-based model (IBM) developed to describe the spread of Chytridiomycosis in a population of frogs.
This case study shows how one can perform inference for IBMs that exhibit certain characteristics with a traditional likelihood-based approach. Third, I present a bioenergetic model of individual growth and reproduction in a dynamic environment. This example highlights how input mis-specification can affect inference, and the consequences for prediction in novel environments.