Browsed relative growth behavior

This behavior simulates herbivory by allowing trees to grow at different rates when browsed versus unbrowsed.

Parameters for this behavior

Parameter name	Description
Asymptotic Diameter Growth (A)	Asymptote of the Michaelis-Menton growth function at high light - function term A below.
Slope of Growth Response (S)	Slope of the Michaelis-Menton growth function at zero light - function term S below.
Relative Michaelis-Menton Growth - Diameter Exponent	The exponent to be used with diameter when calculating relative growth.
Browsed Asymptotic Diameter Growth (A)	Asymptote of the Michaelis-Menton growth function at high light when a plant has been browsed.
Browsed Slope of Growth Response (S)	Slope of the Michaelis-Menton growth function at zero light when a plant has been browsed.
Browsed Diameter Exponent	The diameter exponent for growth when a plant has been browsed.

How it works

Trees grow according to the relative growth version of the Michaelis-Menton function. The same function is used for both browsed and unbrowsed trees, but the parameters are different. The function is:

where:

Y is the amount of annual relative growth
A is the Asymptotic Diameter Growth (A) or Browsed Asymptotic Diameter Growth (A) parameter
S is the Slope of Growth Response (S) or Browsed Slope of Growth Response (S) parameter
GLI is the global light index, calculated by a light behavior

Growth is compounded over multiple timesteps with the equation:

G = ((Y + 1)^T - 1) * diam ^X

where:

G is the amount of diameter growth for the timestep, in cm
diam is the diameter of the tree in cm (at 10 cm height if seedling or sapling, or DBH if adult)
T is the number of years per timestep
X is the Relative Michaelis-Menton Growth - Diameter Exponent or Browsed Diameter Exponent parameter

Whether or not a tree is browsed is determined by the Random browse behavior.

How to apply it

This behavior can be applied to seedlings, saplings, and adults of any species. Any tree species/type combination to which it is applied must also have a light behavior and the Random browse behavior applied. You can use either the diam with auto height or diam only version.