Velocity of Spatial Population Expansion

摘要

The paper considers the velocity with which an invading population spreads over space. After a brief discussion about diffusion models, on the basis of which some terminology and intuition is developed, a much more general model is introduced. It will be seen that the asymptotic velocity of population expansion can be calculated if information is available on the net-reproduction and the (normalized) reproduction-and-dispersal kernel. The authors conjecture that the asymptotic velocity of population expansion of the linear model equals that of its non-linear modifications in a wide variety of cases. By means of numerical examples they study the effect of the net-reproduction and the shape of the reproduction-and-dispersal kernel on the velocity of population expansion. The fact that the reproduction-and-dispersal kernel is difficult to measure in full, leads them to derive approximation formulas in terms of easily measurable parameters. The relation between the velocity of population expansion as calculated from the general model and that from the widely used Fisher/Skellam model is discussed. As a final step, they show that the model can quantitatively predict observed velocities of population expansion.