Physics – Condensed Matter – Statistical Mechanics
Scientific paper
1999-02-15
Physics
Condensed Matter
Statistical Mechanics
19 pages, with 10 ps-figured included
Scientific paper
We study a plant population model introduced recently by J. Wallinga [OIKOS {\bf 74}, 377 (1995)]. It is similar to the contact process (`simple epidemic', `directed percolation'), but instead of using an infection or recovery rate as control parameter, the population size is controlled directly and globally by removing excess plants. We show that the model is very closely related to directed percolation (DP). Anomalous scaling laws appear in the limit of large populations, small densities, and long times. These laws, associated critical exponents, and even some non-universal parameters, can be related to those of DP. As in invasion percolation and in other models where the r\^oles of control and order parameters are interchanged, the critical value $p_c$ of the wetting probability $p$ is obtained in the scaling limit as singular point in the distribution of infection rates. We show that a mean field type approximation leads to a model studied by Y.C. Zhang et al. [J. Stat. Phys. {\bf 58}, 849 (1990)]. Finally, we verify the claim of Wallinga that family extinction in a marginally surviving population is governed by DP scaling laws, and speculate on applications to human mitochondrial DNA.
Broeker Hans-Martin
Grassberger Peter
No associations
LandOfFree
SOC in a population model with global control does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with SOC in a population model with global control, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and SOC in a population model with global control will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-572352