3.2.2. Calculation of the Land Evolution

The degree of evolution in each tenure category will be assessed by calculating the rate of evolution *E* (*i*, *k*) in the area of land use as follows [70].

$$E\ (i,k) = \frac{Sk - Si}{Si} \times 100\tag{2}$$

(*Si*) the area of a land-use category of the year *i* and (*Sk*) the area of a land-use category of year *k*, with *k* > *i*. *E* (*i*, *k*) will be equal to: If *E* (*i*, *k*) = 0, it is concluded that this land use category is stable, if *E* (*i*, *k*) < 0, it is concluded that there is a regression of this category, and if *E* (*i*, *k*) > 0, there is an extension or evolution of this category.

#### 3.2.3. Analysis of Agricultural Land Transition

To visualize the land cover transition, we merged the layers using the intersection tool in the ArcGIS platform. Then, we used the equation below to show the different transitions between the spatial data and used the pivot table function in Excel to produce statistics according to a couple of classes. Initially, the results of the four components studied showed fourteen different land-use change classes. Since not all land-use change classes have the same degree of importance, those representing the main changes were kept and the others were unified. For example, when we considered the relationship between grassland and permanent wetland, we obtained two different couple of classes change: grassland to permanent wetland and permanent wetland to grassland. Accordingly, the difference in change between these two couple of classes is maintained. In addition, we opted for this methodology to highlight the most important or the dominate transition between couple classes. This operation allowed us to keep the four most representatives, land-use change classes.

$$\mathbf{T} = \text{Layer}\,\mathbf{A} \,\, + \, \left( - \right) \, + \, \text{layer}\,\mathbf{B} \tag{3}$$

Layer A = corresponds to the year of beginning, Layer B = corresponds to the year of arrival,T=result of the transformation. (This method is used by GIS and RS solutions).
