Stochasticity, pattern formation and the emergence of distinct species

Alan McKane, University of Manchester

We review the mathematical formalism underlying the modelling of stochasticity in biological and chemical systems. Beginning with a description of the system in terms of its basic constituents, we derive the mesoscopic equations governing the dynamics which generalise the more familiar macroscopic equations. We illustrate their use in a number of areas, especially in cases where the multiplicative nature of the noise plays an important role. We end by showing that stochastic effects can lead to the spontaneous formation of species in models of competing organisms, and speculate on the implications of this result.