Ecological examples and applications
There are many examples of successful application of rigorous mathematical results to understanding and prediction of invasive species spread, e.g., see Skellam (1951), Lubina and Levin (1988), Okubo et al. (1989), Andow et al. (1990), Lewis and Kareiva (1993), Shigesada et al. (1995), Owen and Lewis (2001), and also Shigesada and Kawasaki (1997) and the references therein. In most cases, comparison between theory and data is based, directly or indirectly, on the equation for the minimum speed of the population front of the invasive species with logistic growth, i.e., c = 2
√ Dα (see Sections 2.1 and
7.1). Apparently, application of diﬀusion-reaction equations to biological invasion is not exhausted by this relatively simple case. A question of particular importance is what factors can possibly modify the front speed: either speeding up or slowing down, or even blocking/reversing species invasion. A few such factors have been addressed above by means of exactly solvable models; see Sections 4.1, 4.2 and 6.1. In this chapter, we are going to confront the mathematical results with some relevant ecological data in order to verify the theoretical predictions and to further check the models’ capacities.