chapter  2
30 Pages

Spatio-Temporal Modelling — with a View to Biological Growth

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Appendix A: Conditional densities and conditional intensities . . . . . . . . . . . . 71 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

2.1 Introduction

Modelling of biological growth patterns is a field of mathematical biology that has attracted much attention in recent years, see e.g. Chaplain et al. (1999) and Capasso et al. (2002). The biological systems modelled are diverse and comprise growth of plant populations, year rings of trees, capillary networks, bacteria colonies, and tumours. This chapter deals with spatio-temporal models for such random growing objects, using spatio-temporal point processes or the theory of Le´vy bases. For both types of models, the Poisson process will play a key role, either as a reference process or more directly in the model construction.