Quasi-one-dimensional waves in rodent populations in heterogeneous habitats: A consequence of elevational gradients on spatio-temporal dynamics

Abstract

Wave propagation can be clearly discerned in data collected on mouse populations in the Cibola National Forest (New Mexico, USA) related to seasonal changes. During an exploration of the construction of a methodology for investigations of the spread of the Hantavirus epidemic in mice we have built a system of interacting reaction diffusion equations of the Fisher–Kolmogorov– Petrovskii–Piskunov type. Although that approach has met with clear success recently in explaining Hantavirus refugia and other spatiotemporal correlations, we have discovered that certain observed features of the wave propagation observed in the data we mention are impossible to explain unless modifications are made. However, we have found that it is possible to provide a tentative explanation/ description of the observations on the basis of an assumed Allee effect proposed to exist in the dynamics. Such incorporation of the Allee effect has been found useful in several of our recent investigations both of population dynamics and pattern formation and appears to be natural to the observed system. We report on our investigation of the observations with our extended theory