# Michaelis Menton with negative growth - height onlyThis behavior uses a modified Michaelis-Menton function to do height growth. You can optionally add autocorrelation and a degree of stochasticity to the growth. ### Parameters for this behaviorParameter name | Description |
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Michaelis-Menton Neg Growth - Alpha | Alpha parameter. | Michaelis-Menton Neg Growth - Beta | Beta parameter. Cannot be equal to zero. | Michaelis-Menton Neg Growth - Gamma | Gamma parameter. | Michaelis-Menton Neg Growth - Phi | Phi parameter. | Michaelis-Menton Neg Growth - Growth Standard Deviation | Standard deviation of growth stochasticity, cm / yr. Use zero if growth should have no stochasticity. | Michaelis-Menton Neg Growth - Autocorrelation Prob (0-1) | Probability of autocorrelation from year to year, as a value from 0 to 1. Use 0 if there should be no autocorrelation. |
### How it worksThe amount of height growth is calculated as: where: *Y* is the amount of height growth for one year, in cm*GLI* is the light level*α * is the **Michaelis-Menton Neg Growth - Alpha** parameter*β * is the **Michaelis-Menton Neg Growth - Beta** parameter*γ * is the **Michaelis-Menton Neg Growth - Gamma** parameter*φ * is the **Michaelis-Menton Neg Growth - Phi** parameter*H* is the tree's height in cm
Optionally, the value of *Y* can be randomized by adding to it a stochastic factor *SF*, which is a random draw on a normal distribution with mean zero and standard deviation set using the **Michaelis-Menton Neg Growth - Growth Standard Deviation** parameter. *SF* can be positive or negative and is in units of centimeters of height growth. If you do not want to add *SF*, set the value of this parameter to zero. If you are using the stochastic factor *SF*, you can also introduce autocorrelation in the growth stochasticity. Each year, for each tree, a random number is compared to the value in the **Michaelis-Menton Neg Growth - Autocorrelation Prob (0-1)** parameter for that tree's species to determine if the stochastic factor will be autocorrelated for that year. If it is autocorrelated, the previous year's stochastic factor *SF* is added to *Y* to determine height growth. If it is not autocorrelated, a new value for *SF* is drawn. If you do not wish to use autocorrelation, set the value of the autocorrelation parameter to zero. Autocorrelation is ignored if there is no growth stochasticity. If the timestep is more than one year long, growth is recalculated for each year of the timestep, increasing the height each time. Stochasticity and autocorrelation are also evaluated on a yearly basis. ### How to apply itThis 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 a diameter growth behavior applied. |