Bad Year:
\(N^{{}^{\prime}}=\par
\begin{bmatrix}\left(1-d_{1\ }\left(1-c\right)\right)\left(S_{1}-\left(1-\left(\frac{1}{f}\right)\right)v\right)&((1-\mu)d_{2}S_{2})(1-c)\\
(\left(1-\mu\right)d_{1}\left(S_{1}-\left(1-\left(\frac{1}{f}\right)\right)v\right))(1-c)&\left(1-d_{2}\left(1-c\right)\right)S_{2}\\
\end{bmatrix}N\) (3)
This model contains two variables for dispersal,\(d_{1}\ \text{and}\ d_{2}\). This is to allow for the dispersal rates
between to the two sub-habitats to be altered independently. The model
was run for 1000 iterations in R, and the fitness (Q ) of the two
sub-habitats was calculated at the end (4). Fitness was determined by
the average growth rate of the population which was calculated by the
change in population size divided by the number of simulations run.
\(Q=\ \frac{\Delta N_{x}}{\Delta t_{x}}\) (4)
The log of the average growth rate \(\operatorname{(log}Q)\) was then
calculated. \(\operatorname{(log}Q)\) was then compared at different
dispersal rates (d1 and d2), and the
relationship between the two investigated. For a detailed description of
the model see the supplementary material.