Review of Quantitative Analysis of Movement

Intro:

By adding a new dimension to traditional models of the dynamics of populations, the author presents a quantitative analysis of movement at two scales: temporal and spatial. "To add a spatial dimension, one needs to take only two logical steps: (1) redefine population density as a function of both time and space, and (2) replace the system of ordinary differential equations with a partial differential equation system. The spatial model has all the same growth, death, and interaction terms, but in addition there are diffusion terms that redistribute the population in space without changing total population num- bers" (p 45). Turchin describes a natural spatial ex- tension of the Lotka-Volterra model by adopting a d- behaviorally-based diffusion model as an idealized A. continuum representation of an inherently discrete world. He derives the concentration-dependent, ecological Fokker-Planck diffusion equation for the uncorrelated random walk in a heterogeneous environment to contrast with the spatially-dependent, ed. physical Fickian diffusion that ultimately leads to a ge linear density gradient....