Understanding Random Spatial Processes

Steve Henderson


 


Independent Random Process

 

This first scatter plot is an example of an independent random process, also known as complete spatial randomness.  This process is characterized by points which are equally likely to occur in any area and whose points are not affected in any way by the location of other points.  The example plot below shows no signs of a preference for various locations on the grid and there is no significant clustering of points.

 

Random

 

However, since this is a random process, given enough iterations, you will find occasions when the points seem to leave large bare areas such as the one below…

 

Random with Empty Spaces

 

…or cluster together by chance.

 

Random Clustering

 





Inhomogeneous Poisson Process

 

This Inhomogeneous Poisson scatter plot illustrates the effects of an underlying first order process on an otherwise random scatter plot.  The weighting factors in the spreadsheet table make it more likely that a point will occur in the top right hand side of the scatter plot as seen in the example below.

 

Inhmg Pos

 

This simulates to first order processes where the characteristics of the location increase the likelihood of an event occurring in them, such as the likelihood of a plant to be found in certain soil types which are favorable for their growth.  Other than the preference for the squares on the upper right, clustering only occurs by random chance as seen in the plot below.

 

Inhmg Pos w/Clustering

 




Interaction Effects

 
The interaction effects scatter plot simulates a second order process, where the proximity of other events increase the likelihood of an event occurring nearby, such as the spread of communicable diseases.   The interaction effects scatter plots do not show a preference for any particular area of the plot, but have a strong tendency to cluster.

 

Interaction

 

As the XY-diff component, which controls how far away a new event is placed from a previous event, is increased, the clusters begin to spread out, such as this example with the XY-diff set to 4.

 

XY-diff=4

 

As the XY-diff increases to 9, the plot starts to look like a random scatter plot because the points are beginning to spread over the entire range of the plot.  This would indicate that weak second- order processes may be indistinguishable from random processes.

 

XY diff = 9