Eulerian techniques for individual-based models with additive components

Individual-based models appeal to marine ecologists because of the emphasis on the individual as the fundamental ecological unit, but their analysis often includes computationally demanding statistical analysis of stochastic Lagrangian simulations. This paper shows that certain individual-based models, those based on Markov additive processes, lend themselves to a simplified Eulerian analysis where low-order statistics can be computed exactly with relatively modest effort. We illustrate the framework with a hypothetical example from larval transport and growth, where the approach leads to partial differential equations for the mean and variance of larval length, as a function of position and time. We discuss the general applicability of the framework, and the merits of an Eulerian analysis versus individual-based simulation.