Bifurcation analysis of individual-based models in population dynamics

• I develop a rigorous method for bifurcation analysis of IBMs.
• The approach is demonstrated for a simple IBM of a two-strain infection.
• The two-strain infection model can be completely understood from the steady states of the one-strain model.
• Bifurcation analysis gives insight into fundamental mechanisms of population dynamics by facilitating model comparison.
• Comparison of IBM with population-based ODE model shows that both models make similar predictions.

Individual-based models (IBMs) enable us to investigate the effects of inter-individual differences within a population much more easily than traditional modelling approaches based on differential equations. However, the greater flexibility of IBMs makes it difficult to systematically analyse the parameter dependency of the model behaviour so that an IBM may be hard to interpret. In this article, bifurcation analysis techniques for investigating models based on ordinary differential equations (ODE) are transferred to IBMs. For this purpose, we infer stationary solutions of the IBM from the asymptotic dynamics. The stability of these stationary solutions can then be studied depending on model parameters. As shown previously for ODE models (Siekmann et al., 2010 and Siekmann, 2013), stationary solutions SiS can be used as bifurcation parameters which allows us to predict survival or extinction of populations by simple algebraic relationships. This is demonstrated with the example of a simple two-strain infection IBM. Moreover, analysing model behaviour based on stationary solutions provides a unified representation of different models that allows us to rigorously compare IBMs with other modelling frameworks like, for example, ODE models. A comparison of the IBM to a population-based ODE model of a two-strain infection leads to similar predictions although both models were built with very different modelling approaches.