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Welcome to the second installment in the video series of how to use, and to interpret the
PontiusMatrix version 41, made by Graduate Students at Clark University. In this video,
we cover Transition Level Intensity Analysis. Specifically, we describe how the Pontius
Matrix evaluates transitions to Category 1 and from Category 1.
Transition Level Intensity Analysis examines the transitions from one category at the initial
time to a different category at the final time. Given the gain of a particular category,
we compare the output from these two equations. The first equation is the observed transition
intensity, which is the size of the transition to a gaining category divided by the size
of the losing category at the initial time. If the first category were to gain with uniform
intensity across the entire area, then the second equation would be the transition intensity
that we would observe. Transition Level Intensity Analysis compares the observed intensity to
the uniform intensity, for each transition of a gaining category. If the observed transition
intensity is greater than the uniform intensity, then we say that the gaining category targets
the losing category. If the observed transition intensity is less than the uniform intensity,
then we say that the gaining category avoids the losing category.
For a case study, we examine land cover change in Kalimantan, Indonesia. The map in the upper
left shows the location of the study site. Maps A and B show land cover for the years
2000 and 2004 respectively. Maps C and D show the losing and gaining categories respectively,
with persistence in gray. This video focuses on the dynamics of the first category, which
here is Forest. Map D shows Forest gain in green, while map C shows the corresponding
losing categories in red for Bare and yellow for Grass. Map C shows Forest loss in green,
while map D shows the corresponding gaining categories in red for Bare and yellow for
Grass. The contingency table in the upper right shows the percent of the spatial extent
for the three categories: forest, bare, and grass. The first column shows that Forest
persistence accounts for 77% of the spatial extent, the transition from Bare to Forest
accounts for 4%, and the transition from Forest to Grass accounts for 1%. Thus the first column
shows the gains of Forest, whereas the first row shows the losses of Forest. The first
row shows that the transition from Forest to Bare accounts for 6%, and the transition
from Forest to Grass accounts for 4% of the spatial extent. Now that we understand our
raw data, let us see what Intensity Analysis can teach us.
Here we see the figure that the Pontius Matrix 41 Excel file produces on its Transition Intensity
sheet. The figure shows the transition intensities for the gains by category 1, in this case,
Forest. The observed intensity is the size of the transition from the losing category
to forest, divided by the size of the losing category at the initial time.
The contingency table shows the values used to calculate the observed transition intensity
from Bare to Forest. And these values calculate the observed transition
intensity from grass to forest. The uniform line is size of the gain of forest
divided by the size of non-forest at the initial time. In the Pontius Matrix 41 Excel file,
the Uniform line must be moved by the user. The observed intensity for the transition
from Bare to Forest is less than the uniform intensity, therefore we conclude that the
gain of Forest avoids Bare. The observed intensity for the transition from Grass to Forest is
greater than the uniform intensity, therefore we conclude that the gain of forest targets
Grass. These results are intuitive, because they show that Forest grows more intensively
on places that are Grass than on places that are Bare. The results also explain the initially
counter intuitive result that the transition from Bare to Forest is larger than the transition
from Grass to Forest. Intensity Analysis reveals that the reason is that the size of Bare is
larger than the size of Grass at the initial time.
Here is the figure from Uniform Gain Figure Sheet of the Pontius Matrix 41 file. There
are two bars for each gaining category, both of which show the size of the transition from
category 1 to the gaining category. The green bars are the observed transition sizes.
This is the observed transition size from Forest to Bare.
This is the observed transition size from Forest to Grass.
If the gain of the gaining category were uniform, then the size of the transition from Forest
to the gaining category would be the red bar. This uniform transition is calculated using
the category’s overall gain, times the initial size of forest, divided by area that is not
the gaining category at the initial time. The values in red show the entries used to
compute the size of the uniform transition from Forest to Bare.
And here, the values in red show the entries used to compute the size of the uniform transition
from Forest to Grass. Results show that the observed bars are less than the uniform bars
for both Bare and Grass. This means that both Bare and Grass gained less intensively from
forest than they did across the entire study area. In other words, when Bare and Grass
gain, they both avoid forest.
This video and the Pontius Matrix shows the dynamics of only the first category in the
contingency table. If you want to analyze all categories simultaneously, then please
use the Intensity Analysis 03 Excel file created by Aldwaik, which contains a computer program
to perform the calculations quickly. Obtain the file is at the link in the video description.
The software reads the category names, the time points, and the contingency table, then
produces output for every category.
If you have used Intensity Analysis before, you might notice that this video does not
use the part of Intensity Analysis that analyses transitions given a category’s loss, for
reasons explained in Pontius et al (2013). The reason is that the calculations for the
transition intensities given a category’s loss use the sizes of the categories at the
final time, but the transitions influence the sizes of the categories at the final time,
thus the results are not clearly interpretable. This video shows how to analyze transitions
due to the loss of a category in a manner is interpretable.
This concludes our video concerning how to use the Pontius Matrix 41. To learn more about
the Pontius Matrix or to download the excel program please visit the link in the description.
There you will find further videos and publications as well. Thank you for watching! We encourage
you to continue with our video series and watch video 3 “How to interpret the intensity
of quantity, exchange and shift difference.