## 5 Dynamic Prey-Predator Spatial Model via African Buffalo Optimization
### Season Definition
#### 5.3.2 Migration
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**ID** & **ID-S** & **ID-SS** & **Name-SS** & **ID-M** & **N-Prey** & **N-Predator** \\ \hline
1 & 1 & 1 & Intraspecific Competition & - & 673 & 5 \\
3 & 1 & 3 & Migration & 2 & 673 & 5 \\
5 & 1 & 5 & Migration & 4 & 673 & 5 \\
6 & 1 & 6 & Migration & 5 & 673 & 5 \\
7 & 1 & 7 & Reproduction of Predators & - & 673 & 1109 \\
8 & 1 & 8 & Death of Predators & - & 673 & 638 \\
9 & 1 & 9 & Predation & - & 379 & 638 \\
10 & 1 & 10 & Reproduction of Preys & - & 794 & 638 \\
11 & 50 & 1 & Intraspecific Competition & - & 457 & 1243 \\
12 & 50 & 2 & Migration & 1 & 457 & 1243 \\
13 & 50 & 3 & Migration & 2 & 457 & 1243 \\
14 & 50 & 4 & Migration & 3 & 457 & 1243 \\
15 & 50 & 5 & Migration & 4 & 457 & 1243 \\
16 & 50 & 6 & Migration & 5 & 457 & 1243 \\
17 & 50 & 7 & Reproduction of Predators & - & 457 & 1714 \\
18 & 50 & 8 & Death of Predators & - & 457 & 1243 \\
19 & 50 & 9 & Predation & - & 455 & 1243 \\
20 & 50 & 10 & Reproduction of Preys & - & 505 & 1243 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Simulation carried out without using agents—Case E. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**ID** & **ID-S** & **ID-SS** & **Name-SS** & **ID-M** & **N-Prey** & **N-Predator** \\ \hline
1 & 1 & 1 & Intraspecific Competition & - & 672 & 5 \\
3 & 1 & 3 & Migration & 2 & 672 & 5 \\
5 & 1 & 5 & Migration & 4 & 672 & 5 \\
6 & 1 & 6 & Migration & 5 & 672 & 5 \\
7 & 1 & 7 & Reproduction of Predators & - & 672 & 13 \\
8 & 1 & 8 & Death of Predators & - & 672 & 8 \\
9 & 1 & 9 & Predation & - & 668 & 8 \\
10 & 1 & 10 & Reproduction of Preys & - & 1483 & 8 \\
11 & 50 & 1 & Intraspecific Competition & - & 1291 & 874 \\
12 & 50 & 2 & Migration & 1 & 1291 & 874 \\
13 & 50 & 3 & Migration & 2 & 1291 & 874 \\
14 & 50 & 4 & Migration & 3 & 1291 & 874 \\
15 & 50 & 5 & Migration & 4 & 1291 & 874 \\
16 & 50 & 6 & Migration & 5 & 1291 & 874 \\
17 & 50 & 7 & Reproduction of Predators & - & 1291 & 1402 \\
18 & 50 & 8 & Death of Predators & - & 1291 & 871 \\
19 & 50 & 9 & Predation & - & 875 & 871 \\
20 & 50 & 10 & Reproduction of Preys & - & 1492 & 871 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Simulation performed using agents—Case A. According to the results in Tables 9-13, we can extract the following final results from the populations:

* For the parameters \(lp1\) and \(lp2\) equal to 1, the number of final prey was 1492 and the number of predators was 871 (see Table 9). * For the parameters \(lp1\) and \(lp2\) equal to 2, the number of final prey was 1489 and the number of predators was 878 (see Table 10). * For the parameters \(lp1\) and \(lp2\) equal to 3, the number of final prey was 1491 and the number of predators was 876 (see Table 11). * For the parameters \(lp1\) and \(lp2\) equal to 4, the number of final prey was 1494 and the number of predators was 876 (see Table 12). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**ID** & **ID-S** & **ID-SS** & **Name-SS** & **ID-M** & **N-Prey** & **N-Predator** \\ \hline
1 & 1 & 1 & Intraspecific Competition & - & 669 & 5 \\
3 & 1 & 3 & Migration & 2 & 669 & 5 \\
5 & 1 & 5 & Migration & 4 & 669 & 5 \\
6 & 1 & 6 & Migration & 5 & 669 & 5 \\
7 & 1 & 7 & Reproduction of Predators & - & 669 & 15 \\
8 & 1 & 8 & Death of Predators & - & 669 & 8 \\
9 & 1 & 9 & Predation & - & 666 & 8 \\
10 & 1 & 10 & Reproduction of Preys & - & 1483 & 8 \\
11 & 50 & 1 & Intraspecific Competition & - & 1294 & 874 \\
12 & 50 & 2 & Migration & 1 & 1294 & 874 \\
13 & 50 & 3 & Migration & 2 & 1294 & 874 \\
14 & 50 & 4 & Migration & 3 & 1294 & 874 \\
15 & 50 & 5 & Migration & 4 & 1294 & 874 \\
16 & 50 & 6 & Migration & 5 & 1294 & 874 \\
17 & 50 & 7 & Reproduction of Predators & - & 1294 & 1409 \\
18 & 50 & 8 & Death of Predators & - & 1294 & 878 \\
19 & 50 & 9 & Predation & - & 869 & 878 \\
20 & 50 & 10 & Reproduction of Preys & - & 1489 & 878 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Simulation performed using agents—Case B.