Abstract: Many species show considerable variation in behaviour among individuals. We show that some behaviours are largely deterministic and predictable with mathematical models. We propose a general differential equation model of behaviour in field populations and use the methodology to explain and predict the dynamics of sleep and colony attendance in seabirds as a function of environmental factors. Our model explained over half the variability in the data to which it was fitted, and it predicted the dynamics of an independent data set. Differential equation models may provide new approaches to the study of behaviour in animals and humans.