生物集団の格子模型(基研短期研究会「格子理論の進展-素粒子から生物まで-」,研究会報告)

Abstract

Lattice model is useful for studying population dynamics with spatial structure. Here I review two types of applications of the lattice model; one is for disease propagation in dynamical epidemiology, and the other is for "wave regeneration" in forest dynamics. In the former application each lattice site is assumed to have one of 2 or 3 states at each time, and the ultimate stationary state is studied in 1- and 2-dimension. Although few rigorous estimates can be made, approximations are required for the entire analysis. A new approximation method called modified decoupling approximation (MDA) is tested by computer simulation. In the latter application each site is characterized by the height of the tree. The feature for actual wave regeneration seems to be reproduced by two-dimensional lattice model. Quantitative predictions are derived with which ecological field data can be compared.