Stochastic formulation of ecological models and their applications

The increasing use of computer simulation by theoretical ecologists started a move away from models formulated at the population level towards individual-based models. However, many of the models studied at the individual level are not analysed mathematically and remain defined in terms of a computer algorithm. This is not surprising, given that they are intrinsically stochastic and require tools and techniques for their study that may be unfamiliar to ecologists. Here, we argue that the construction of ecological models at the individual level and their subsequent analysis is, in many cases, straightforward and leads to important insights. We discuss recent work that highlights the importance of stochastic effects for parameter ranges and systems where it was previously thought that such effects would be negligible.