MATHEMATICAL AND COMPUTATIONAL CHALLENGES IN POPULATION BIOLOGY AND ECOSYSTEMS SCIENCE

Mathematical and computational approaches provide powerful tools in th e study of problems in population biology and ecosystems science. The subject has a rich history intertwined with the development oi statist ics and dynamical systems theory, but recent analytical advances, coup led with the enhanced potential of high-speed computation, have opened up new vistas and presented new challenges. Key challenges involve wa ys to deal with the collective dynamics of heterogeneous ensembles oi individuals, and to scale from small spatial regions to large ones. Th e central issues-understanding how detail at one scale makes its signa ture felt at other scales, and how to relate phenomena across scales-c ut across scientific disciplines and go to the heart of algorithmic de velopment of approaches to high-speed computation. Examples are given from ecology, genetics, epidemiology, and immunology.