Puerto Rico semi-stochastic - diam only

This behavior combines a deterministic growth function for small trees with completely stochastic growth for larger trees. It's meant to be used when a species uses a height growth behavior as the primary growth method.

Parameters for this behavior

Parameter name	Description
PR - "a" Parameter for Deterministic Growth	"a" parameter used to calculate deterministic growth when a tree is below the stochastic height threshold.
PR - "b" Parameter for Deterministic Growth	"b" parameter used to calculate deterministic growth when a tree is below the stochastic height threshold.
PR - Height Threshold for Stochastic Growth (m)	The tree height threshold, in meters, between deterministic and stochastic growth.
PR - Mean DBH (cm) for Stochastic Growth	The mean for DBH values, in cm, when a tree uses stochastic growth. This is the mean of the DBH value, NOT the amount of growth.
PR - DBH Standard Deviation for Stochastic Growth	Standard deviation for DBH values when a tree uses stochastic growth. This is the standard deviation of the DBH value, NOT the amount of growth.

How it works

The divide between the two growth functions is defined in the PR - Height Threshold for Stochastic Growth (m) parameter. Trees shorter than this use the following function:

Y = (A * exp(-B * Height)) - Diam

where:

Y = diameter growth for the timestep, in cm
a = PR - "a" Parameter for Deterministic Growth parameter
b = PR - "b" Parameter for Deterministic Growth parameter
Height = tree height in cm AFTER height growth in the current timestep
diam = diameter of the tree at which to apply growth (before growth), in cm

Above the height cutoff, trees are assigned random diameters drawn from a normal distribution. The normal distribution is defined by the PR - Mean DBH (cm) for Stochastic Growth and PR - DBH Standard Deviation for Stochastic Growth parameters, and represents the distribution of DBH values, NOT growth values. The amount of growth for a tree is Y = D' - D, where Y is the amount of growth, D' is the new diameter chosen from the normal distribution, and D is the previous diameter. This means that growth can be negative. The effect is to create a tree population with normally-distributed diameters, where any individual tree may jump from place to place within the distribution.

How to apply it

This function can be applied to seedlings, saplings, or adults of any species. Any tree using this behavior must also use a height-only growth behavior.