Invasion waves are a fundamental building block of theoretical ecology. In this study we aim to take the first steps to link propagation failure and fast acceleration of traveling waves to critical transitions (or tipping points). The approach is based upon a detailed numerical study of various versions of the Fisher-Kolmogorov-Petrovskii-Piscounov (FKPP) equation. The main motivation of this work is to contribute to the following question: how much information do statistics, collected by a stationary observer, contain about the speed and bifurcations of traveling waves? We suggest warning signs based upon closeness to carrying capacity, second-order moments and transients of localized initial invasions.
- Pub Date:
- December 2012
- Quantitative Biology - Populations and Evolution;
- Mathematics - Dynamical Systems;
- Mathematics - Probability;
- Nonlinear Sciences - Pattern Formation and Solitons
- 14 pages, 8 figures