A continuous time branching-diffusion process model is presented to describe the development of spatial distributional patterns of a biological population. In the model each unit moves independently following diffusion processes on a plane, and multiplies or goes extinct at random times. Standard methods for measuring the degree of aggregation used in field ecology are applied to this model population. Kuno's CAindex using quadrat sampling is calculated, and the dependence of the index on time, quadrat size, initial density, and diffusion and branching rules, is discussed. Pielou's α index based on distance measurement is evaluated by the solution of a nonlinear partial differential equation. Both methods show that continuous-time branching-diffusion processes produce a contagious spatial pattern; as in a discrete-time model studied by Iwasa and Teramoto (1977).
All Science Journal Classification (ASJC) codes
- Modelling and Simulation
- Agricultural and Biological Sciences (miscellaneous)
- Applied Mathematics