Intensity Raster into Kappa

Question

I am writing some code to simulate a forest stand. I have simulated the positions of large and medium sized trees using Spatstats. The next step I want to do is simulate smaller trees. I have been trying to write some code that enables the smaller trees to be located further away from large and medium sized trees.

I can simulate the correct number of smaller trees using a single number kappa for a Thomas clumping model in Spatstat, however this produces clumping close to larger/medium trees. I am struggling to simulate the correct number of smaller trees where the parent points are located in less dense parts of the forest stand.

I have tried using the density function in spatstat on the large and medium sized trees. I then tried inverting the raster so that the areas with less trees have a higher pixel value, but I cant seem to find a way of changing this to a Kappa raster which will give me the correct number of smaller trees to be generated.

The code below gives me a number for the correct number of small trees to be generated

Window size is 100x100m

kappaS<-(Number_Small_Trees_to_be_Generated)/(mean(muS)*winarea)

Small.Trees1<-rThomas(kappa=kappaS,
                      scale=sigmaM,
                  mu=muS,
                  win=Window222)

I'm hoping to find a way of producing a kappa raster that simulates the correct number of points where the parent points are more likley to be produce in less dense areas of the stand.

Many thanks for any help!

Answer 1

I recommend that you read Section 12.3.4 "Inhomogeneous cluster models" in the spatstat book Spatial Point Patterns: Methodology and Applications with R. Unfortunately this is not one of the free sample chapters, so you have to hope that your local library has the book. (Disclaimer: I'm a coauthor.)

In that section it is explained how the intensity of your suggested process is a complicated expression (convolution), and it is not easy to control how many points will be generated. Mathematically it is much easier to handle an inhomogeneous offspring process (i.e. letting mu be spatially varying). This means that you get parents everywhere, but they generate offspring depending on the location, so in areas with many adult/medium trees few offspring are generated whereas many are generated in empty areas. The details are in the book. Good luck!