Estudios Realizados en Chile

The relative cell frequencies of persistence, gains and losses for each landcover class during the study period were thus derived from the change/no change maps together with the modified VLC maps. These data were used to populate the transition matrix of landcover change from 1965 to 2009, following the structure of Figure 3.2 (Pontius et al 2004). The rows show the relative cell frequencies (%) of the landcover classes at time =1 and the

columns show this information for the landcover classes at time=2. The entry in the (i)th row and the (j)th column shows the proportion of landcover class i at time=1 in landcover class j at time=2 (P_ij). The total at the end of ith row, in the Total time=1 column shows the

proportion of the landscape in class i at time =1 (P_i+). The total at the bottom of the jth column, in the Total time=2 row shows the proportion of the landscape in class j at time= 2 (P_+j). The column at the end of the table shows the pattern of losses for landcover class i between timer =1 and 2, that is it shows loss of class i to the other landcover classes (column j ) as a proportion of the total landscape. Conversely the bottom row shows the gains in landcover class j at time=2, from all other classes at time =1, as a proportion of the total landscape.

Persistence values (Pij, i=j) for each landcover class run along the diagonal and are highlighted in gray and bold type. The second value is the proportion of the landscape that would have been expected in that landcover class if transitions were occurring as a result of random process rather than systematic change (Equation 3). This value is calculated by holding the persistence of the landcover class i constant and redistributing the observed losses amongst the other classes relative to their proportion on the landscape. The logic being that landcover classes will exhibit random transitions due to chance and perhaps error in direct relation to the proportion of the landscape they cover

Lij = (Pi+ - Pii)

(

) ^[

Lij=expected proportion of landcover i ( in the total landscape area) if losses to landcover j are from random process

100 Pi+ =total % area (as a proportion of total landscape area) in landcover i at time=1

Pii = persistence of landcover i

P+j = total % area of landcover i at time =2

The third value in circular parentheses is the actual proportion of that landcover class on the landscape (the first value) minus the expected value (Figure 3.2, Equation 4). This gives the residual proportion of the landscape that has undergone transition once random processes are taken into account.

Observed – Expected = Pij - Lij [Equation 4]

Pij= Observed proportion

Lij= Expected proportion (Equation 3)

The number in the final row of each class cell in Figure 3.2 is used to identify systematic transitions. This is calculated by dividing the difference value (row 3) by the expected value (Figure 3.2, Equation 5), giving a ratio of the magnitude of the difference between the observed and expected value, relative to the size of the expected value. This ratio is analogous to the Chi-square ratios and the magnitude of the ratio describes the relative strength of the signal indicating systematic transition. If the observed changes are occurring by random chance then the value of this row will be zero or very close to zero.

Ratio = (Pij-Lij/Lij) [Equation 5]

Pij= Observed proportion

Lij= Expected proportion (Equation 3)

101 Figure 3.3.2 The structure of the landcover transition matrix used to identify and quantify change processes between two maps at different points in time; adapted from Pontius et al (2004).

Time 2

Time 1 LANDCOVER 1 LANDCOVER 2 LANDCOVER 3 Total_time=1 Gross Loss

Interpretation of the transition matrices followed the method put forward by Pontius et al (2004). Entries on the diagonal indicate the proportion of the landscape that shows persistence of that particular landcover class. Off-diagonal entries indicate transition from class i to class j. The matrices were used to quantify the landcover characteristics in each time interval in terms of net change per category as well as gains, losses and swap amongst categories. Following Pontius et al (2004) the off-diagonal values in the transition matrices were used to identify which landcover conversions were more the result of systematic process rather than random chance or methodological error. This method was also applied by

Schulze et al (2010) analysing landcover change patterns in Chile.

The method to interpret the transition matrix figures follows Pontius et al (2004) closely.

This method identifies systematic landcover change processes and also the magnitude of the

102 observed changes relative to all other transitions occurring on the landscape at that time. If number in round parentheses is positive then that class lost more to whatever class in column j than by random chance/error. If the difference in parentheses is negative then the category in column j gained less, or alternatively, the category in that row i lost less to the category in that column j than would have been expected by a process of random chance or error. The fourth number in each cell is the ratio of the actual number minus the observed proportion divided by the expected proportion of change and is analogous with the basis of Chi-square tests (Pontius et al 2004). The magnitude of this number indicates the difference between the observed value and the expected value, relative to the expected value. This value is used to identify systematic landcover transitions rather than changes occurring randomly. If the processes of observed loss are random then the differences shown in the transition matrices will be zero or very close to zero. These figures indicate the main

processes through which landcover is occurring in both village landscapes (Question 4, page 86). Furthermore they indicate how they will most likely develop in the future, if the

overarching socio-economic conditions remain true (Question 5, page 86).

103

3.3 Results