Appendix A. Example with fictitious data to illustrate the process from survey-type data to a transition matrix for a single grid cell. Let us assume a grid cell (100 m2) at time t with three states (S1=40 m2, S2=55 m2, S3=5 m2) and at t +1 with four states (S1=30 m2, S2=50 m2, S3=15 m2, S4=5 m2).
TABLE A1. Contingency table for a single grid cell based on formulas 4–5.
to state |
||||||||||
S1 |
S2 |
S3 |
S4 |
∑ (t) |
||||||
from state |
S1 |
30 |
0 |
6.67 |
3.33 |
40 |
|
|||
S2 |
0 |
50 |
3.33 |
1.67 |
55 |
|||||
S3 |
0 |
0 |
5 |
0 |
5 |
|||||
S4 |
0 |
0 |
0 |
0 |
0 |
|
||||
∑ (t+1) |
30 |
50 |
15 |
5 |
110 |
|||||
TABLE A2. Transition matrix P for a single grid cell (formula 6).
to state |
||||||
S1 |
S2 |
S3 |
S4 |
∑ |
||
from state |
S1 |
0.75 |
0.00 |
0.17 |
0.08 |
1.00 |
S2 |
0.00 |
0.91 |
0.06 |
0.03 |
1.00 |
|
S3 |
0.00 |
0.00 |
1.00 |
0.00 |
1.00 |
|
S4 |
0.00 |
0.00 |
0.00 |
0.00 |
0.00 |
|