Mathematical and Computational Challenges in Population Biology and Ecosystem Science

Mathematical and computational approaches to biological questions, a marginal activity a short time ago, are now recognized as providing some of the most powerful tools in learning about Nature, guiding empirical work and providing a framework for synthesis and analysis (1,2). In some areas of biology, such as molecular biology, the advent has been recent but dramatic, for example as an adjunct to the analysis of nucleic acid sequences or the structural analysis of macromolecules. In population biology, in contrast, the marriage between mathematical and empirical approaches has a century-long history, rich in tradition and in the insights it has provided. Statistics and stochastic processes, for example, derive their origins from biological questions, as in Galton's invention of the method of genetic correlations and Fisher's creation of the analysis of variance to study problems in agriculture (1). Branching processes were developed to describe genealogical histories; and even such classical subjects as dynamical systems theory have been enriched by contract with problems in population biology (see for example 3,4).