Partial differential equation models of diffusion and advection are fundamental to understanding population behavior and interactions in space, but can be difficult to analyze when space is heterogeneous. As a proxy for partial differential equation models, and to provide some insight into a few questions regarding growth and movement patterns of a single population and two competing populations, a simple three-patch system is used. For a single population it is shown that diffusion rates occur for which the total biomass supported on a heterogeneous landscape exceeds total carrying capacity, confirming previous studies of partial differential equations and other models. It is also shown that the total population supported can increase indefinitely as the sharpness of the heterogeneity increases. For two competing species, it is shown that adding advection to a reaction-diffusion system can potentially reverse the general rule that the species with smaller diffusion rates always wins, or lead to coexistence. Competitive dominance is also favored for the species for which the sharpness of spatial heterogeneity in growth rate is greater. The results are consistent with analyses of partial differential equations, but the patch approach has some advantages in being more intuitively understandable.
|Original language||English (US)|
|Number of pages||18|
|Journal||Discrete and Continuous Dynamical Systems - Series B|
|State||Published - Dec 1 2014|
- Discrete spatial model
- Inhomogeneous environment