Nonlinearity and Biology

In this chapter we discuss the origin and role of nonlinearities in some classes of biological models. We describe underlying biological mechanisms that generate nonlinearities and how they have been modeled in subfields, such as ecology and epidemiology. We present examples of recent models to highlight the importance of indirect effects and the emergence of alternative stable states, and trade offs. At the same time, we emphasize recent developments and unresolved challenges in biological modeling, such as data-theory coupling, parameter estimation and the generalization of results from low- to high-dimensional systems. We finish with recent examples of mathematical models of the glucose-insulin regulatory system, cancer treatment, limb development and pattern formation, and DNA.