Myriam Elizabeth Saavedra López - Repositorio Digital USFQ ...

the null hypothesis cannot be completely accepted for the Second Moment Characteristics and it is
necessary therefore to explore Fit Models for Block I.
4.3.5 Fit models for block I
According to Cressie, Baddeley et al, Illian et al and Schabenberger et al, if the null hypothesis of the
CSR test is rejected, then the spatial point patterns should have a clustering or regularly tendency or
both. Different authors have developed different models to fit the distribution of the data set being
studied. Some of these models are Inhomogeneous Points Process, Cox Process (cluster), Poisson
Cluster Process and Simple Inhibition Process (regular).
Spatial points from Block I have a CSR distribution under the First Moment Characteristics (inten-
sity), but the average intensity is 0.33 points per hectare, and accordingly the interaction between
points should not exist. However, when you apply the methods (Function K) under the Second
Moment Characteristics, the null hypothesis is rejected because there is a clustering tendency when
the interaction circle radiuses increase. This ‘controversial’ behaviour of Block I suggests, that one
should ignore the potential new models and find the factors that are affecting the uniform Poisson
distribution of these spatial points. In another words, in this case, the Fit-Model was using methods
where if the null hypothesis is not rejected, the observations show a CSR distribution. Looking at
Block I, (see Figure 7) it is possible to make the following observations:
• In the center-west part of the block there is the biggest concentration of the quadrats (one
hectare) with points.
• In the northern part of the block there are more quadrats without points and there are two
points with distances of contact to other points, greater than 300 meters.
• In the southeastern part, around the edge, there are no quadrats with points.
• In the northwestern corner, there are quadrats without points that extend 400 meters from the
last point to northwestern tip of the block.
• Around the eastern edge there are no quadrats with points.
With these observations and knowledge of the study area forests, such as the distribution patterns of
swamp and ‘terra firma’ forests and the tendency for commercial value trees not to be found right
on the edge where swamp forests meet terra firma forests, it is possible to suggest that the empty
space around the border can be a factor as to why the null hypothesis (spatial points are under
CSR distribution) was rejected when Second Moment Characteristic was used. To demonstrate this
assumption two Fit methods were used: The Cuts Method and The Exclusion-Edge Methods.
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