We can then relate the change in fitness (w ) over management time (t ), via substituting (3) into (4) and solving for the differential with respect to t :
\begin{equation} \frac{\text{dw}}{\text{dt}}=\ \frac{c\bullet e^{2(km)}}{{(1-e^{m\left(t-25\right)})}^{2}}\nonumber \\ \end{equation}
Given (3), the maximum rate of environmental change occurs at , settingt = 25 and z at its initial mean value (z = 0), we can solve for the maximum demographic pressure exerted on our population:
\begin{equation} \left.\ \frac{\text{dw}}{\text{dt}}\right|_{\begin{matrix}t=25\\ z=0\\ \end{matrix}}=\frac{-kce^{-mt-k^{2}}}{4}\nonumber \\ \end{equation}
It is clear that this maximum pressure can be modified by changing either the absolute magnitude of shift (c ) or the flattening constant, m . By changing either c or m we can explore varying demographic pressures; we have chosen to explore a range of m in what follows.