Modeling spatiotemporal dynamics of vole populations in Europe and America.
The mathematical models proposed and studied in the present paper provide a unified framework to understand complex dynamical patterns in vole populations in Europe and North America. We have extended the well-known model provided by Hanski and Turchin by incorporating the diffusion term and spatial heterogeneity and performed several mathematical and numerical analyses to explore the dynamics in space and time of the model. These models successfully predicted the observed rodent dynamics in these regions. An attempt has been made to bridge the gap between the field and theoretical studies carried out by Turchin and Hanski (1997) and Turchin and Ellner (2000). Simulation experiments, mainly two-dimensional parameter scans, show the importance of spatial heterogeneity in order to understand the poorly understood fluctuations in population densities of voles in Fennoscandia and Northern America. This study shed new light upon the dynamics of voles in these regions. The nonlinear analysis of vole data suggests that the dynamical shift is from stability to chaos. Diffusion driven model systems predict a new type of dynamics not yet observed in the field studies of vole populations carried out so far. This has been termed as chaotic in time and regular in space (CTRS). We observed CTRS dynamics in several simulation experiments. This directs us to expect that dynamics of this animal would be de-correlated in time and simultaneously mass extinctions might be possible at many spatial locations.
Department of Applied Mathematics, Indian School of Mines, Dhanbad, Jharkhand-826 004, India. ranjit_ism@yahoo.com
Ranjit Kumar
RK
Upadhyay
Nitu
N
Kumari
Vikas
V
Rai
D000818:Animals; D003411:Arvicolinae / Q000254:growth & development*; D003198:Computer Simulation; D005060:Europe; D008954:Models, Biological; D009656:North America; D009716:Numerical Analysis, Computer-Assisted; D011156:Population Density; D011157:Population Dynamics; D011235:Predatory Behavior; D012621:Seasons