Population dynamics of size-structured populations
- Centre for Mathematics in Industry, Massey University at Albany, Private Bag 102-904, Auckland, New Zealand
Many population cohorts are structured by different attributes: space and age are the most common of these. For many applications this structure is just as important as the temporal evolution with discrete or continuous time. For these applications modellers have to cope with this greatly increased complexity and cannot afford to neglect it. Different modellers proceed in a variety of ways to suit the circumstances and tools available. Nigel Barlow introduced me (in 1988) to the idea of using a limited number of spatial or age compartments, each of which was structurally uniform with well-defined interactive links between compartments. His view, if I interpret it correctly, was that this enabled us to avoid the technically difficult partial differential equation analysis. Of course, there are a wide variety of opinions about this, but I have recently used this approach in an analysis of a plankton– nutrient model, where Nigel was clearly right. We would have never succeeded in using the lovely path- following (in parameter space) computer algorithms had we not adopted Nigel’s approach. This paper addresses a situation where compartments were not, in fact, sufficient: where the population is structured by size or DNA content. Data sets of plant-root-cells, plankton, muscle cells, and cancer cells, often show a steady (in time) size distribution that appears asymptotically and structurally stable. (“Steady-size” means it is constant in shape as time changes.) About the same time as Nigel and I began (in Palmerston North around 1988) looking at a spatially compartmentalised model for tuberculosis in possums, another biologist, Dr Paul Gandar, asked whether we could explain this with a relatively simple model which, when validated and embedded in the cell physiological context, could have the capability of making robust predictions.