Mathematical Biology: SCCC411B Spring 1997 -- Miller / Wethey
Department of Biological Sciences and Department of Mathematics
University of South Carolina

Project Report

Huffaker, R., T. LoFaro and K. Cooper 1996. Small mammal dispersion.

Report by Katherine Coykendall, and Robbie Young

The following two equations are describing two populations of beavers subjected to different environmental factors. Population x is controlled by trapping whereas population y is not. The model allows for migration between the two populations. The dimensionless equations for the "trapped" population (x') and the uncontrolled population (y') are evaluated and used to find the nullclines.



diff(x(t),t)=x*(1-x)-m*(x-y)-p*x;
diff(y(t),t)=r*y*(1-y)+k*m*(x-y);

The following graph shows the two nullclines with the parameters stated in the paper. The non-dimensional parameters in parentheses were used because x' and y' are dimensionless equations. This illustrates the response of the system to varying initial conditions. According to the paper, there is a "zero dispersion line" where the populations' numbers are equal and, hence, no migration occurs.




Up until now, the per capita annual trapping rate (px) has been assumed to be zero. The next model assumes a 100% trapping rate for beavers in population x. Notice p is equal to P/Rx where P is equal to 1. Here again are new nullclines taking into account positive trapping rates.