Growth behaviors
In this document:
How growth is applied
Growth parameters
Absolute growth behaviors
--Absolute growth limited to radial increment behavior - diam with auto height
--Absolute growth limited to radial increment behavior - diam only
--Absolute growth limited to basal area increment behavior - diam with auto height
--Absolute growth limited to basal area increment behavior - diam only
--Non-limited absolute growth behavior - diam with auto height
--Non-limited absolute growth behavior - diam only
Allometric diameter growth - diam only
Allometric height growth
Basal area NCI growth - diam with auto height
Basal area NCI growth - diam only
Constant basal area growth behavior - diam with auto height
Browsed relative growth behavior - diam with auto height
Browsed relative growth behavior - diam only
Constant basal area growth behavior - diam only
Constant radial growth behavior - diam with auto height
Constant radial growth behavior - diam only
Double resource relative growth - diam with auto height
Double resource relative growth - diam only
Lagged post harvest growth - diam with auto height
Lagged post harvest growth - diam only
Linear growth - height only
Linear growth - diam with auto height
Linear growth - diam only
Linear bi-level growth - diam with auto height
Linear bi-level growth - diam only
Linear growth w/ exponential shade reduction - height only
Linear growth w/ exponential shade reduction - diam with auto height
Linear growth w/ exponential shade reduction - diam only
Logistic growth - height only
Logistic growth - diam with auto height
Logistic growth - diam only
Logistic growth w/ size dependent asymptote - height only
Logistic growth w/ size dependent asymptote - diam with auto height
Logistic growth w/ size dependent asymptote - diam only
Lognormal bi-level growth - height only
Lognormal with exponential shade reduction - height only
Lognormal with exponential shade reduction - diam with auto height
Lognormal with exponential shade reduction - diam only
Michaelis Menton with negative growth - height only
Michaelis Menton with photoinhibition - height only
NCI growth behavior - diam with auto height
NCI growth behavior - diam only
Power growth - height only
Puerto Rico semi-stochastic - diam only
Puerto Rico storm bi-level growth - diam with auto height
Relative growth behaviors
--Relative growth limited to radial increment behavior - diam with auto height
--Relative growth limited to radial increment behavior - diam only
--Relative growth limited to basal area increment behavior - diam with auto height
--Relative growth limited to basal area increment behavior - diam only
--Non-limited relative growth behavior - diam with auto height
--Non-limited relative growth behavior - diam only
--Relative growth - height only
Stochastic gap growth
Growth behaviors increase the size of a tree. A tree has two basic size dimensions: diameter and height. A growth behavior can increase tree size using one of three methods.
In the first method, the behavior calculates an amount of diameter increase, and then adds this amount to the tree's diameter. The tree's new height is calculated from the new diameter using the appropriate allometry equation. This is the way that growth has been applied in all previous versions of SORTIE, and is the method you should choose if you are in doubt about which one you want. Behaviors using this method have the tag "diam with auto height" in their name.
In the second method, the behavior calculates an amount of diameter increase, and then adds this amount to the tree's diameter. The height is not allowed to change. The rationale behind this is that tree diameter and height are not always strictly coupled by the allometry equations; sometimes, diameter and height should be allowed to vary independently. If you use a growth behavior of this type, it is required that you pair it with a separate behavior incrementing height. Behaviors using this method have the tag "diam only" in their name.
In the third method, the behavior calculates an amount of height increase, and then adds this amount to the tree's height. The diameter is not allowed to change. The rationale is the same as that for the second method. If you use a growth behavior of this type, it is required that you pair it with a separate behavior incrementing diameter. Behaviors using this method have the tag "height only" in their name.
Growth behaviors using the second and third method must work together in pairs. Behaviors using the first method work alone. If you pair a behavior using method one with a behavior using method three, the height-incrementing behavior will be ignored.
When incrementing a tree's diameter with new growth, seedlings and saplings have the amount of growth increase applied to their diameter at 10 cm. Adults have the amount applied to their DBH. For more on tree types and their measurements, see the trees topic. For more on tree size relationships, including how trees transition between life history stages, see the allometry topic.
Note: All behaviors convert growth to diameter growth in cm for internal consistency. The equations below reflect this. Some behaviors may take parameters in mm, or for radial growth. Take careful note of your behavior's parameters.
It is important to be careful when mixing different growth methods for different life history stages of a tree species. For instance: if tree seedlings or saplings get separate diameter and height increments, then their diameters and heights will be "uncoupled." This means that you cannot use one of the size dimensions to predict the other through an allometric equation. Trees with the same diameter will have different heights, and vice versa. Say that you do not have data on separate diameter and height growth for adults, so you assign the adults to a behavior that increments diameter and then automatically updates height according to the allometry equations. You are likely to notice strange results for new adult trees. You will lose the variability in height/diameter ratio that was developed. Suddenly, all trees with the same diameter will have the same height again, and vice versa. This means that individuals may suddenly jump in height, or even shrink.
The "Allometric height growth" and "allometric diameter growth" behaviors were developed to help bridge this gap. When used with a behavior that only increments diameter or height, they will preserve height or diameter differences that have developed across individuals in a species.
- Adult Constant Area Growth in sq. cm/yr The constant amount of basal area by which to increase a tree's basal area. Used in basal-area-increment-limited behaviors and constant basal area growth behaviors.
- Adult Constant Radial Growth in mm/yr The constant value by which to increase a tree's radius at breast height. Used in radial-increment-limited-growth behaviors and constant radial increment behaviors.
- Asymptotic Diameter Growth (A) Asymptote of the Michaelis-Menton growth function at high light in absolute and relative growth behaviors - A in the equations below. Used in absolute and relative growth behaviors.
- Asymptotic Height Growth (A) Asymptote of the Michaelis-Menton growth function at high light - A in the equations below. Used in the Relative growth - height only behavior.
- Basal Area NCI - BA Divisor The value by which to divide neighbor basal area. Used in the Basal area NCI growth behaviors.
- Basal Area NCI - Use Only Larger Neighbors Whether to use all neighbors larger than the minimum DBH (false) or only neighbors larger than the target tree (true). Used in the Basal area NCI growth behaviors.
- Browsed Asymptotic Diameter Growth (A) Asymptote of the Michaelis-Menton growth function at high light when a plant has been browsed. Used by the Browsed relative growth behavior - diam with auto height and Browsed relative growth behavior - diam only behaviors.
- Browsed Slope of Growth Response (S) Slope of the Michaelis-Menton growth function at zero light when a plant has been browsed. Used by the Browsed relative growth behavior - diam with auto height and Browsed relative growth behavior - diam only behaviors.
- Browsed Diameter Exponent The diameter exponent for growth when a plant has been browsed. Used by the Browsed relative growth behavior - diam with auto height and Browsed relative growth behavior - diam only behaviors.
- Double resource - Influence of Resource (C) The parameter governing the influence of the second resource on the double-resource Michaelis-Menton equation. Used by the Double resource relative growth - diam with auto height and Double resource relative growth - diam only behaviors.
- Include Snags in NCI Calculations Whether or not to include snags when finding competitive neighbors for NCI. Used in the NCI growth behavior - diam with auto height and NCI growth behavior - diam only behaviors.
- Length of Current Release Factor Controls the magnitude of the effects of release. Used in absolute growth behaviors.
- Length of Last Suppression Factor Controls the magnitude of the effects of suppression. Used in absolute growth behaviors.
- Linear Bi-Level - Intercept for High-Light Growth (a) The intercept of the linear growth function used in high-light conditions. Used in the Linear bi-level growth - diam with auto height and Linear bi-level growth - diam only behaviors.
- Linear Bi-Level - Intercept for Low-Light Growth (a) The intercept of the linear growth function used in low-light conditions. Used in the Linear bi-level growth - diam with auto height and Linear bi-level growth - diam only behaviors.
- Linear Bi-Level - Slope for High-Light Growth (b) The slope of the linear growth function used in high-light conditions. Used in the Linear bi-level growth - diam with auto height and Linear bi-level growth - diam only behaviors.
- Linear Bi-Level - Slope for Low-Light Growth (b) The slope of the linear growth function used in low-light conditions. Used in the Linear bi-level growth - diam with auto height and Linear bi-level growth - diam only behaviors.
- Linear Bi-Level - Threshold for High-Light Growth (0 - 100) The threshold between low-light and high-light parameters, as a value between 0 and 100. Used in the Linear bi-level growth - diam with auto height and Linear bi-level growth - diam only behaviors.
- Logistic - Asymptotic Diam Growth - Full Light in mm/yr (a) Asymptotic annual growth at full light, in mm/yr. Used by the Logistic growth - diam with auto height and Logistic growth - diam only behaviors.
- Logistic - Asymptotic Height Growth - Full Light in cm/yr (a) Asymptotic annual growth at full light, in cm/yr. Used by the Logistic growth - height only behavior.
- Logistic - Diam Shape Param 1 (b) Shape parameter 1. Used by the Logistic growth - diam with auto height and Logistic growth - diam only behaviors.
- Logistic - Diam Shape Param 2 (c) Shape parameter 2. Used by the Logistic growth - diam with auto height and Logistic growth - diam only behaviors.
- Logistic - Height Shape Param 1 (b) Shape parameter 1. Used by the Logistic growth - height only behavior.
- Logistic - Height Shape Param 2 (c) Shape parameter 2. Used by the Logistic growth - height only behavior.
- Lognormal Bi-Level - Max Growth in High Light (m) The maximum height growth, in meters, under high-light conditions. Used by the Lognormal bi-level growth - height only behavior.
- Lognormal Bi-Level - Max Growth in Low Light (m) The maximum height growth, in meters, under low-light conditions. Used by the Lognormal bi-level growth - height only behavior.
- Lognormal Bi-Level - X0 for High-Light Growth The X0 parameter to use under high-light growth conditions. Used by the Lognormal bi-level growth - height only behavior.
- Lognormal Bi-Level - X0 for Low-Light Growth The X0 parameter to use under low-light growth conditions. Used by the Lognormal bi-level growth - height only behavior.
- Lognormal Bi-Level - Xb for High-Light Growth The Xb parameter to use under high-light growth conditions. Used by the Lognormal bi-level growth - height only behavior.
- Lognormal Bi-Level - Xb for Low-Light Growth The Xb parameter to use under low-light growth conditions. Used by the Lognormal bi-level growth - height only behavior.
- Lognormal Bi-Level - Threshold for High-Light Growth (0 - 100) Used by the Lognormal bi-level growth - height only behavior.
- Lognormal - Diam Effect of Shade (c) Effect of shade. Used by the Lognormal with exponential shade reduction - diam with auto height and Lognormal with exponential shade reduction - diam only behaviors.
- Lognormal - Diam Growth Increment at Diam 36, in mm/yr (a) Annual growth increment at diameter 36, in mm/yr. Used by the Lognormal with exponential shade reduction - diam with auto height and Lognormal with exponential shade reduction - diam only behaviors.
- Lognormal - Diam Shape Parameter (b) Shape parameter. Used by the Lognormal with exponential shade reduction - diam with auto height and Lognormal with exponential shade reduction - diam only behaviors.
- Lognormal - Height Effect of Shade (c) Effect of shade. Used by the Lognormal with exponential shade reduction - height only behavior.
- Lognormal - Height Growth Increment at Diam 36, in cm/yr (a) Annual growth increment at diameter 36, in cm/yr. Used by the Lognormal with exponential shade reduction - height only behavior.
- Lognormal - Height Shape Parameter (b) Shape parameter. Used by the Lognormal with exponential shade reduction - height only behavior.
- Michaelis-Menton with Negative Growth - Alpha Alpha parameter. Used by the Michaelis Menton with negative growth - height only behavior.
- Michaelis-Menton with Negative Growth - Beta Beta parameter. Cannot be equal to zero. Used by the Michaelis Menton with negative growth - height only behavior.
- Michaelis-Menton with Negative Growth - Gamma Gamma parameter. Used by the Michaelis Menton with negative growth - height only behavior.
- Michaelis-Menton with Negative Growth - Phi Phi parameter. Used by the Michaelis Menton with negative growth - height only behavior.
- Michaelis-Menton with Photoinhibition - Alpha Alpha parameter. Used by the Michaelis Menton with photoinhibition - height only behavior.
- Michaelis-Menton with Photoinhibition - Beta Beta parameter. Cannot be equal to zero. Used by the Michaelis Menton with photoinhibition - height only behavior.
- Michaelis-Menton with Photoinhibition - D D parameter. Used by the Michaelis Menton with photoinhibition - height only behavior.
- Michaelis-Menton with Photoinhibition - Phi Phi parameter. Used by the Michaelis Menton with photoinhibition - height only behavior.
- Mortality Threshold for Suppression Defines the growth rate for suppressed status in terms of tree mortality. The value is expressed as the proportion of trees which die at the growth rate which defines suppressed status, expressed as a fraction between 0 and 1. For instance, if this value is 0.1, the growth
rate for suppressed status is one at which 10% of trees die with that growth. Used in absolute growth behaviors.
- NCI Alpha NCI function exponent. Used in the NCI growth behavior - diam with auto height and NCI growth behavior - diam only behaviors.
- NCI Beta NCI function exponent. Used in the NCI growth behavior - diam with auto height and NCI growth behavior - diam only behaviors.
- NCI Crowding Effect Slope (C) The slope of the curve for the crowding effect equation. Used in the NCI growth behavior - diam with auto height and NCI growth behavior - diam only behaviors.
- NCI Crowding Effect Steepness (D) The steepness of the curve for the crowding effect equation. Used in the NCI growth behavior - diam with auto height and NCI growth behavior - diam only behaviors.
- NCI Damage Effect - Complete Storm Damage (0-1) The fraction by which a tree's growth rate is reduced when it has sustained complete storm damage. Set this to 1 if you are not including storms in your run. Used in the NCI growth behavior - diam with auto height and NCI growth behavior - diam only behaviors.
- NCI Damage Effect - Medium Storm Damage (0-1) The fraction by which a tree's growth rate is reduced when it has sustained medium storm damage. Set this to 1 if you are not including storms in your run. Used in the NCI growth behavior - diam with auto height and NCI growth behavior - diam only behaviors.
- Species i NCI lambda neighbors The competitive effect of neighbors of species i on the target tree species's growth, between 0 and 1. Used in the NCI growth behavior - diam with auto height and NCI growth behavior - diam only behaviors.
- NCI Maximum Crowding Distance, in meters The maximum distance, in m, at which a neighboring tree has competitive effects on a target tree. Used in the NCI growth behavior - diam with auto height and NCI growth behavior - diam only behaviors.
- NCI Maximum Potential Growth, cm/yr Maximum potential diameter growth for a tree, in cm/yr. Used in the NCI growth behavior - diam with auto height and NCI growth behavior - diam only behaviors.
- NCI Minimum Neighbor DBH, in cm The minimum DBH for trees of that species to compete as neighbors. Used for all species, not just those using NCI growth. Used in the NCI growth behavior - diam with auto height and NCI growth behavior - diam only behaviors.
- NCI DBH Divisor (q) The value by which neighbor DBHs are divided when calculating NCI. This can be used to make units adjustments. Used in the NCI growth behavior - diam with auto height and NCI growth behavior - diam only behaviors.
- NCI Neighbor Storm Damage (eta) - Complete (0-1) The fraction to which a neighbor's competitive effect is reduced when the neighbor has sustained complete storm damage. Set this to 1 if you are not including storms in your run. Used in the NCI growth behavior - diam with auto height and NCI growth behavior - diam only behaviors.
- NCI Neighbor Storm Damage (eta) - Medium (0-1) The fraction to which a neighbor's competitive effect is reduced when the neighbor has sustained medium storm damage. Set this to 1 if you are not including storms in your run. Used in the NCI growth behavior - diam with auto height and NCI growth behavior - diam only behaviors.
- NCI Shading Effect Coefficient (m) The coefficient in the shading effect equation. Set this value to 0 if you do not wish to use shading. Used in the NCI growth behavior - diam with auto height and NCI growth behavior - diam only behaviors.
- NCI Shading Effect Exponent (n) The exponent in the shading effect equation. If you set the NCI Shading Effect Coefficient (m) parameter to 0, this value is ignored. Used in the NCI growth behavior - diam with auto height and NCI growth behavior - diam only behaviors.
- NCI Size Effect Mode, in cm (X0) The mode of the size effect curve. Used in the NCI growth behavior - diam with auto height and NCI growth behavior - diam only behaviors.
- NCI Size Effect Variance, in cm (Xb) The variance of the size effect curve. Used in the NCI growth behavior - diam with auto height and NCI growth behavior - diam only behaviors.
- NCI Size Sensitivity to NCI (gamma) The sensitivity of a tree's growth rate to its DBH. Set this to 0 to remove the DBH term altogether. Used in the NCI growth behavior - diam with auto height and NCI growth behavior - diam only behaviors.
- Post Harvest Growth - DBH Growth Effect The effect of DBH on growth. Used in the Lagged post harvest growth - diam with auto height and Lagged post harvest growth - diam only behaviors.
- Post Harvest Growth - DBH NCI Effect The effect of DBH on the neighborhood competition index. Used in the Lagged post harvest growth - diam with auto height and Lagged post harvest growth - diam only behaviors.
- Post Harvest Growth - Max Growth Constant Maximum annual radial growth, in mm. Used in the Lagged post harvest growth - diam with auto height and Lagged post harvest growth - diam only behaviors.
- Post Harvest Growth - NCI Constant A constant adjusting the effects of NCI. Used in the Lagged post harvest growth - diam with auto height and Lagged post harvest growth - diam only behaviors.
- Post Harvest Growth - NCI Distance (m) The maximum distance at which neighboring trees can have competitive effects. Used in the Lagged post harvest growth - diam with auto height and Lagged post harvest growth - diam only behaviors.
- Post Harvest Growth - Time Since Harvest Rate Param A parameter controlling the rate at which the actual growth approaches the potential growth after a harvest. Used in the Lagged post harvest growth - diam with auto height and Lagged post harvest growth - diam only behaviors.
- PR - "a" Parameter for Deterministic Growth "a" parameter used to calculate deterministic growth when a tree is below the stochastic height threshold. Used in the Puerto Rico semi-stochastic - diam only behavior.
- PR - "b" Parameter for Deterministic Growth "b" parameter used to calculate deterministic growth when a tree is below the stochastic height threshold. Used in the Puerto Rico semi-stochastic - diam only behavior.
- 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. Used in the Puerto Rico semi-stochastic - diam only behavior.
- PR - Height Threshold for Stochastic Growth (m) The tree height threshold, in meters, between deterministic and stochastic growth. Used in the Puerto Rico semi-stochastic - diam only behavior.
- 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. Used in the Puerto Rico semi-stochastic - diam only behavior.
- PR Storm Bi-Level - Threshold for High-Light Growth (0 - 100) The threshold between low-light and high-light equations, as a value between 0 and 100. Used in the Puerto Rico storm bi-level growth - diam with auto height behavior.
- PR Storm Bi-Level - High-Light "a" The "a" value in the high-light growth function. Used in the Puerto Rico storm bi-level growth - diam with auto height behavior.
- PR Storm Bi-Level - High-Light "b" The "b" value in the high-light growth function. Used in the Puerto Rico storm bi-level growth - diam with auto height behavior.
- PR Storm Bi-Level - Intercept for Low-Light Growth (a) The intercept of the linear growth function used in low-light conditions. Used in the Puerto Rico storm bi-level growth - diam with auto height behavior.
- PR Storm Bi-Level - Slope for Low-Light Growth (b) The slope of the linear growth function used in high-light conditions. Used in the Puerto Rico storm bi-level growth - diam with auto height behavior.
- Relative Michaelis-Menton Growth - Diameter Exponent The exponent to be used with diameter when calculating relative growth. Used in the Relative growth behaviors.
- Relative Michaelis-Menton Growth - Height Exponent The exponent to be used with height when calculating relative growth. Used in the Relative growth - height only behavior.
- Shaded Linear - Diam Intercept in mm/yr (a) Intercept of the size dependent growth potential, in mm/yr. Used by the Linear growth w/ exponential shade reduction - diam with auto height and Linear growth w/ exponential shade reduction - diam only behaviors.
- Shaded Linear - Diam Shade Exponent (c) Effect of shading. Used by the Linear growth w/ exponential shade reduction - diam with auto height and Linear growth w/ exponential shade reduction - diam only behaviors.
- Shaded Linear - Diam Slope (b) Slope of the size dependent annual growth potential. Used by the Linear growth w/ exponential shade reduction - diam with auto height and Linear growth w/ exponential shade reduction - diam only behaviors.
- Shaded Linear - Height Intercept in cm/yr (a) Intercept of the size dependent growth potential, in cm/yr. Used by the Linear growth w/ exponential shade reduction - height only behavior.
- Shaded Linear - Height Shade Exponent (c) Effect of shading. Used by the Linear growth w/ exponential shade reduction - height only behavior.
- Shaded Linear - Height Slope (b) Slope of the size dependent annual growth potential. Used by the Linear growth w/ exponential shade reduction - height only behavior.
- Simple Linear - Diam Intercept in mm/yr (a) Intercept of the linear growth function, or growth at no light, in mm/yr. Used by the Linear growth - diam with auto height and Linear growth - diam only behaviors.
- Simple Linear - Diam Slope (b) Slope of the linear growth function. Used by the Linear growth - diam with auto height and Linear growth - diam only behaviors.
- Simple Linear - Height Intercept in cm/yr (a) Intercept of the linear growth function, or growth at no light, in cm/yr. Used by the Linear growth - height only behavior.
- Simple Linear - Height Slope (b) Slope of the linear growth function. Used by the Linear growth - height only behavior.
- Size Dep. Logistic - Diam Intercept (a) Intercept of the size dependent annual growth potential. Used by the Logistic growth w/ size dependent asymptote - diam only and Logistic growth w/ size dependent asymptote - diam with auto height behaviors.
- Size Dep. Logistic - Diam Shape Param 1 (c) Shape parameter 1 for shade reduction of annual growth. Used by the Logistic growth w/ size dependent asymptote - diam only and Logistic growth w/ size dependent asymptote - diam with auto height behaviors.
- Size Dep. Logistic - Diam Shape Param 2 (d) Shape parameter 2 for shade reduction of annual growth. Used by the Logistic growth w/ size dependent asymptote - height only and Logistic growth w/ size dependent asymptote - diam with auto height behaviors.
- Size Dep. Logistic - Diam Slope (b) Slope of the size dependent annual growth potential. Used by the Logistic growth w/ size dependent asymptote - diam only and Logistic growth w/ size dependent asymptote - diam with auto height behaviors.
- Size Dep. Logistic - Height Intercept (a) Intercept of the size dependent annual growth potential. Used by the Logistic growth w/ size dependent asymptote - height only behavior.
- Size Dep. Logistic - Height Shape Param 1 (c) Shape parameter 1 for shade reduction of annual growth. Used by the Logistic growth w/ size dependent asymptote - height only behavior.
- Size Dep. Logistic - Height Shape Param 2 (d) Shape parameter 2 for shade reduction of annual growth. Used by the Logistic growth w/ size dependent asymptote - height only behavior.
- Size Dep. Logistic - Height Slope (b) Slope of the size dependent annual growth potential. Used by the Logistic growth w/ size dependent asymptote - height only behavior.
- Slope of Growth Response (S) Slope of the Michaelis-Menton growth function at zero light for relative and absolute growth behaviors - S in the equations below. Used in absolute and growth behaviors.
- Slope of Height Growth Response (S) Slope of the Michaelis-Menton growth function at zero light - S in the equations below. Used in the Relative growth - height only behavior.
- Years Exceeding Threshold Before a Tree is Suppressed The number of years for which a tree's growth must be below the defined suppression threshold before it is considered to be suppressed. Used in absolute growth behaviors.
Relative growth behaviors
Several behaviors apply a relative growth version of the Michaelis-Menton function. Relative growth is calculated with the equation:
where:
- Y is the amount of annual relative growth
- A is the Asymptotic Diameter Growth (A) or Asymptotic Height Growth (A) parameter
- S is the Slope of Growth Response (S) or Slope of Height Growth Response (S) parameter
- GLI is the global light index, calculated by a light behavior
Diameter 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 parameter
Relative height growth is calculated slightly differently. The details are discussed in the section for the Relative growth - height only behavior below. Relative growth is discussed in Pacala et al 1996.
Relative growth limited to radial increment - diam with auto height
How it works
This behavior calculates an amount of diameter growth according to the relative growth equation. Growth is limited to a maximum of the constant radial growth increment for the species of tree to which it is being applied. The increment is calculated as described in the "Constant radial growth" behavior. Tree height is allowed to update automatically according to the allometry equations. Note that the increment parameter specifies radial growth; the behavior makes all necessary conversions.
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 applied.
Behavior reference string: relradial
Relative growth limited to radial increment - diam only
How it works
This behavior calculates an amount of diameter growth according to the relative growth equation. Growth is limited to a maximum of the constant radial growth increment for the species of tree to which it is being applied. The increment is calculated as described in the "Constant radial growth" behavior. Note that the increment parameter specifies radial growth; the behavior makes all necessary conversions.
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 a height-incrementing growth behavior applied.
Behavior reference string: relradial diam only
Relative growth limited to basal area increment - diam with auto height
How it works
This behavior calculates an amount of diameter growth according to the relative growth equation. Growth is limited to a maximum of a constant basal area increment. The amount of diameter increase is calculated by dividing the annual basal area increment of the tree's species by the diameter of the tree. The increment is calculated as described in the "Constant basal area growth" behavior. Tree height is allowed to update automatically according to the allometry equations.
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 applied.
Behavior reference string: relba
Relative growth limited to basal area increment - diam only
How it works
This behavior calculates an amount of diameter growth according to the relative growth equation. Growth is limited to a maximum of a constant basal area increment. The amount of diameter increase is calculated by dividing the annual basal area increment of the tree's species by the diameter of the tree. The increment is calculated as described in the "Constant basal area growth" 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 a height-incrementing growth behavior applied.
Behavior reference string: relba diam only
Non-limited relative growth - diam with auto height
How it works
The amount of increase returned by the relative growth equation is applied to the tree. Tree height is allowed to update automatically according to the allometry equations.
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 applied.
Behavior reference string: relunlim
Non-limited relative growth - diam only
How it works
The amount of increase returned by the relative growth equation is applied to the tree.
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 a height-incrementing growth behavior applied.
Behavior reference string: relunlim diam only
Relative growth - height only
This behavior uses the Michaelis-Menton function to do height growth.
How it works
After the Michaelis-Menton function is used to calculate Y as described in the section above, the amount of height growth is calculated as:
G = Y * Height X
where:
- G is the amount of height growth for one year, in cm
- Height is the height of the tree in cm
- X is the Relative Michaelis-Menton Growth - Height Exponent parameter
If the timestep is more than one year long, growth is recalculated for each year of the timestep, increasing the height each time.
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 a diameter growth behavior applied.
Behavior reference string: relative michaelis-menton height growth
Allometric diameter and height growth
How it works
These behaviors are designed to be secondary growth behaviors. If you have a behavior that primarily updates one tree dimension (diameter or height), one of these behaviors can be used on the other dimension to ensure even growth. These behaviors calculate a growth amount based on the allometry equations. The amount of growth is:
Y = f(Xt+1) - f(Xt)
where Y is the amount of growth calculated by this behavior, f(X) is the allometry equation relating diameter and height, X t is the other tree dimension (either height or diameter) before the primary growth is applied, and X t+1 is the other tree dimension after primary growth is applied. The allometric diameter growth behavior can be paired with any height-only growth behavior, and the allometric height growth behavior can be paired with any diam-only growth behavior.
How to apply it
These behaviors 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 growth behavior applied that grows the opposite tree dimension.
Behavior reference string: diameter incrementer and height incrementer
Double resource relative growth - diam with auto height
This behavior uses a double Michaelis-Menton function to calculate relative growth based on two resources: light and a second resource. The identity of the second resource is unimportant and could be anything, from exchangeable calcium levels to soil moisture. Relative growth is calculated with the equation:
where:
- Y is the amount of annual relative growth
- A is the Asymptotic Diameter Growth (A) parameter
- S is the Slope of Growth Response (S) parameter
- C is the Double resource - Influence of Resource (C) parameter, in units appropriate to the value of R
- R is the amount of the second resource, in units appropriate to the value of C
- 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
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
Note that setting the C parameter in the equation above to 0 eliminates the second resource and makes this equivalent to the "Non-limited relative growth" behavior.
How it works
The amount of the second resource is captured in a grid object called Resource. Currently it is up to you to enter a map of the values for this resource grid; for instructions on how to do this, see the Grid Setup Window topic. This behavior does not in any way alter the values in this grid.
Once growth has been calculated and applied to the tree's diameter, tree height is allowed to update automatically according to the allometry equations.
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 applied. You must also enter a map of second resource values into the Resource grid.
Behavior reference string: Double resource relative growth - diam with auto height
Double resource relative growth - diam only
How it works
This behavior calculates growth exactly like the "Double resource relative growth - diam with auto height" behavior. Height is updated separately using another 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 a height-incrementing growth behavior applied. You must also enter a map of second resource values into the Resource grid.
Behavior reference string: Double resource relative growth - diam only
Absolute growth behaviors
Several behaviors apply an absolute growth version of the Michaelis-Menton function. Absolute growth is calculated with the equation:
where
- Y = log10(radial growth + 1)
- SF is the suppression factor
- A is the Asymptotic Diameter Growth (A) parameter
- S is the Slope of Growth Response (S) parameter
- GLI is the global light index, calculated by a light behavior
Amount of diameter growth per timestep is calculated as
growth = (((10Y - 1) * 2 )/ 10) * T
where T is the number of years per timestep.
The absolute growth behaviors also take into account suppression status. A tree is considered suppressed if its growth rate for the previous timestep falls below a certain threshold. That threshold is the rate of growth at which X% of juveniles die, where X is a user-settable parameter. The threshold is calculated for each species by solving the BC mortality equation for G (growth), where m is the threshold growth rate.
A tree's suppression state is a multiplicative factor in its growth rate. If a tree is not suppressed, the suppression factor in the growth equation is set to 1 (no effect on growth). If the tree is suppressed, the suppression factor is calculated as follows:
SF = e((g*YLR) - (d*YLS))
where:
- SF is the suppression factor
- g is the Length of Current Release Factor parameter
- YLR is the length of the last (or current) period of release,
in years
- d is the Length of Last Suppression Factor parameter
- YLS is the length of the last (or current) period of
suppression, in years
Details of this model are published in Wright et al 2000.
Absolute growth limited to radial increment - diam with auto height
How it works
This behavior calculates an amount of diameter growth according to the absolute growth equation. Growth is limited to a maximum of the constant radial increment for the species of tree to which it is being applied. The increment is calculated as described in the "Constant radial growth" behavior. Tree height is allowed to update automatically according to the allometry equations. Note that the increment parameter specifies radial growth; the behavior makes all necessary conversions.
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 applied.
Behavior reference string: absradial
Absolute growth limited to radial increment - diam only
How it works
This behavior calculates an amount of diameter growth according to the absolute growth equation. Growth is limited to a maximum of the constant radial increment for the species of tree to which it is being applied. The increment is calculated as described in the "Constant radial growth" behavior. Note that the increment parameter specifies radial growth; the behavior makes all necessary conversions.
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 a height-incrementing growth behavior applied.
Behavior reference string: absradial diam only
Absolute growth limited to basal area increment - diam with auto height
How it works
This behavior calculates an amount of diameter growth according to the absolute growth equation. Growth is limited to a maximum of a constant basal area increment. The amount of diameter increase is calculated by dividing the annual basal area increment of the tree's species by the diameter of the tree. The increment is calculated as described in the "Constant basal area growth" behavior. Tree height is allowed to update automatically according to the allometry equations.
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 applied.
Behavior reference string: absba
Absolute growth limited to basal area increment - diam only
How it works
This behavior calculates an amount of diameter growth according to the absolute growth equation. Growth is limited to a maximum of a constant basal area increment. The amount of diameter increase is calculated by dividing the annual basal area increment of the tree's species by the diameter of the tree. The increment is calculated as described in the "Constant basal area growth" 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 a height-incrementing growth behavior applied.
Behavior reference string: absba diam only
Non-limited absolute growth - diam with auto height
How it works
The amount of diameter increase returned by the absolute growth equation is applied to the tree. Tree height is allowed to update automatically according to the allometry equations.
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 applied.
Behavior reference string: absunlim
Non-limited absolute growth - diam only
How it works
The amount of diameter increase returned by the absolute growth equation is applied to the tree.
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 a height-incrementing growth behavior applied.
Behavior reference string: absunlim diam only
Constant basal area growth - diam with auto height
How it works
The amount of diameter increase is calculated from a constant basal area increment. The increase is calculated as follows:
Y = (g / diam) * 100 * T
where
- Y is the amount of diameter increase, in cm
- g is the Adult Constant Area Growth in sq. cm/yr parameter
- diam is the tree's diameter, in cm
- T is the number of years per timestep
Tree height is allowed to update automatically according to the allometry equations.
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 applied.
Behavior reference string: constbagrowth
Constant basal area growth - diam only
How it works
The amount of diameter increase is calculated from a constant basal area increment. The increase is calculated as follows:
Y = (g / diam) * 100 * T
where
- Y is the amount of diameter increase, in cm
- g is the Adult Constant Area Growth in sq. cm/yr parameter
- diam is the tree's diameter, in cm
- T is the number of years per timestep
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 a height-incrementing growth behavior applied.
Behavior reference string: constbagrowth diam only
Constant radial growth - diam with auto height
How it works
The amount of diameter increase is calculated from the constant radial increment. The increase is calculated as follows:
Y = (g4 / 10) * 2 * T
where
- Y is the amount of diameter growth, in cm, to add to the tree
- g4 is the Adult Constant Radial Growth in mm/yr parameter
- T is the number of years per timestep
Tree height is allowed to update automatically according to the allometry equations. Note that the increment parameter specifies radial growth; the behavior makes all necessary conversions to diameter growth.
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 applied.
Behavior reference string: constradialgrowth
Constant radial growth - diam only
How it works
The amount of diameter increase is calculated from the constant radial increment. The increase is calculated as follows:
Y = (g4 / 10) * 2 * T
where
- Y is the amount of diameter growth, in cm, to add to the tree
- g4 is the Adult Constant Radial Growth in mm/yr parameter
- T is the number of years per timestep
Note that the increment parameter specifies radial growth; the behavior makes all necessary conversions to diameter growth.
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 a height-incrementing growth behavior applied.
Behavior reference string: constradialgrowth diam only
NCI growth - diam with auto height
This behavior uses the effects of neighbor competitiveness to influence growth rates ("NCI" stands for neighborhood competition index). A tree's maximum potential growth rate is reduced due to competitiveness and several other possible factors. You can use certain parameter values to turn these influences on and off to reflect the conditions appropriate for your run.
How it works
For a tree, the amount of growth per year is calculated as:
Growth = Max Growth * Size Effect * Shading Effect * Crowding Effect * Damage Effect
Max Growth is the maximum diameter growth the tree can attain, in cm/yr, entered in the NCI Maximum Potential Growth, cm/yr parameter. Size Effect, Shading Effect, Crowding Effect, and Damage Effect are all optional factors which act to reduce the maximum growth rate and will vary depending on the conditions a tree is in. Each of these effects is a value between 0 and 1.
Size Effect is calculated as:
where:
- DBH is of the target tree, in cm
- X0 is the NCI Size Effect Mode, in cm (X0) parameter
- Xb is the NCI Size Effect Variance, in cm (Xb)
Shading Effect is calculated as:
where:
- m is the NCI Shading Effect Coefficient (m) parameter
- n is the NCI Shading Effect Exponent (n) parameter
- S is the amount of shade cast by neighbors, from 0 (no shade) to 1 (full shade). This value should come from the Sail light behavior.
This effect is not required. To omit the Shading Effect, set the NCI Shading Effect Coefficient (m) parameter to 0.
Crowding Effect is calculated as:
where:
- C is the NCI Crowding Effect Slope (C) parameter
- DBH is of the target tree, in cm
- γ is the NCI Size Sensitivity to NCI (gamma) parameter for the target tree's species
- D is the NCI Crowding Effect Steepness (D) parameter
- NCI is this tree's NCI value (equation below)
The NCI value sums up the competitive effect of all neighbors with a DBH at least that of the NCI Minimum Neighbor DBH, in cm parameter, out to a maximum distance set in the NCI Max Radius of Crowding Neighbors, in m parameter. The competitiveness of a neighbor increases with the neighbor's size and decreases with distance and storm damage to the neighbor (optional). The neighbor's species also matters; the effect depends on the relationship between the target species and the neighbor species. Seedlings never compete. You set whether or not snags compete in the Include Snags in NCI Calculations parameter.
The crowding effect is optional. You can omit it by setting either the NCI Crowding Effect Slope (C) or NCI Max Radius of Crowding Neighbors, in m parameters to 0.
NCI is calculated as:
where:
- the calculation sums over j = 1...S species and k = 1...N neighbors of each species of at least a DBH of NCI Minimum Neighbor DBH, in cm, out to a distance of NCI Max Radius of Crowding Neighbors, in m
- ηk is the storm damage parameter of the kth neighbor, depending on the damage status (optional). If the neighbor is undamaged, the value is 1. If the neighbor has medium damage, the value is the NCI Neighbor Storm Damage (eta) - Medium (0-1) parameter for the target species. If the neighbor has complete damage, the value is the NCI Neighbor Storm Damage (eta) - Complete (0-1) parameter for the target species. To omit the storm damage term, set all values for the above two parameters to 1.
- α is the NCI Alpha parameter for the target tree's species
- β is the NCI Beta parameter for the target tree's species
- DBHjk is the DBH of the kth neighbor, in cm
- q is the NCI DBH Divisor (q) parameter. Set this to a value greater than 1 to rescale the competitive effects of neighbors
- λik is the Species j NCI Lambda parameter for the target species relative to the kth neighbor's species
- distanceik is distance from target to neighbor, in m
The value of Damage Effect is optional. If you elect not to use storms in your run, set all values in the NCI Damage Effect - Medium Storm Damage (0-1) and NCI Damage Effect - Complete Storm Damage (0-1) parameters to 1. If you are using storms, then the value of Damage Effect depends on the tree's damage category. If the tree is undamaged, Damage Effect equals 1. If the tree has medium storm damage, the value is the NCI Damage Effect - Medium Storm Damage (0-1) parameter. If the tree has complete storm damage, the value is the NCI Damage Effect - Complete Storm Damage (0-1) parameter.
The amount of growth is in cm/year. For multi-year timesteps, the behavior will calculate total growth with a loop. Each loop iteration will increment DBH for one year. For each year, any portion of the growth equation with DBH as a term is recalculated with the previous year's updated DBH value.
The final total growth amount is added to the tree's DBH. Height is calculated according to the appropriate allometric equation.
How to apply it
This behavior can be applied to saplings and adults of any species. It cannot be applied to seedlings.
If the Shading Effect term is activated in the growth equation, then the trees to which this behavior is applied must also have a light behavior applied - the Sail light behavior is the one designed to work with the NCI behavior. The use of any other light behavior is at your own risk.
If any storm damage parameters are set to anything other than 1, it is recommended (but not required) that you have the Storm damage applier behavior applied.
Behavior reference string: ncigrowth
NCI growth - diam only
This behavior works exactly like the "NCI growth - diam with auto height" behavior to calculate an amount of diameter increase.
How to apply it
This behavior can be applied to saplings and adults of any species. It cannot be applied to seedlings.
If the Shading Effect term is activated in the growth equation, then the trees to which this behavior is applied must also have a light behavior applied - the Sail light behavior is the one designed to work with the NCI behavior. The use of any other light behavior is at your own risk.
If any storm damage parameters are set to anything other than 1, it is recommended (but not required) that you have the Storm damage applier behavior applied.
Behavior reference string: ncigrowth diam only
Basal area NCI growth - diam with auto height
This behavior uses the effects of neighbor competitiveness to influence growth rates ("NCI" stands for neighborhood competition index). In this case, the NCI is based on the basal area of neighboring trees. A tree's maximum potential growth rate is reduced due to competitiveness and several other possible factors.
How it works
For a tree, the amount of growth per year is calculated as:
Growth = Max Growth * Size Effect * Crowding Effect
Max Growth is the maximum diameter growth the tree can attain, in cm/yr, entered in the NCI Maximum Potential Growth, cm/yr parameter. Size Effect and Crowding Effect are factors which act to reduce the maximum growth rate and will vary depending on the conditions a tree is in. Each of these effects is a value between 0 and 1.
Size Effect is calculated as:
where:
- DBH is of the target tree, in cm
- X0 is the NCI Size Effect Mode, in cm (X0) parameter
- Xb is the NCI Size Effect Variance, in cm (Xb)
Crowding Effect is calculated as:
CE = exp(-C * (DBH γ * BAn / BADiv) D)
where:
- C is the NCI Crowding Effect Slope (C) parameter
- DBH is of the target tree, in cm
- γ is the NCI Size Sensitivity to NCI (gamma) parameter for the target tree's species
- D is the NCI Crowding Effect Steepness (D) parameter
- BAn is the sum of the basal areas, in square cm, of eligible neighbors
- BADiv is the Basal Area NCI - BA Divisor parameter
When calculating BAn, this behavior uses neighbors of all species out to the distance set in the NCI Max Radius of Crowding Neighbors, in m parameter. The neighbors must have a DBH larger than the values set in the NCI Minimum Neighbor DBH, in cm parameter. If the Basal Area NCI - Use Only Larger Neighbors parameter is set to true, they must also have a DBH larger than the target tree's DBH. Seedlings and snags never contribute to BAn.
The amount of growth is in cm/year. For multi-year timesteps, the behavior will calculate total growth with a loop. Each loop iteration will increment DBH for one year. For each year, any portion of the growth equation with DBH as a term is recalculated with the previous year's updated DBH value.
The final total growth amount is added to the tree's DBH. Height is calculated according to the appropriate allometric equation.
How to apply it
This behavior can be applied to saplings and adults of any species. It cannot be applied to seedlings.
Behavior reference string: ncibagrowth
Basal area NCI growth - diam only
This behavior works exactly like the "Basal area NCI growth - diam with auto height" behavior to calculate an amount of diameter increase.
How to apply it
This behavior can be applied to saplings and adults of any species. It cannot be applied to seedlings.
Behavior reference string: ncibagrowth diam only
Linear growth - height only
How it works
This behavior calculates an amount of height growth as:
Y = (a + (b * GLI)) * T
where
- Y = amount of height increase, in cm
- a = Simple Linear - Height Intercept in cm/yr (a) parameter
- b = Simple Linear - Height Slope (b) parameter
- GLI = global light index, as a percentage between 0 and 100, calculated by a light behavior
- T = number of years per timestep
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 a diameter-only growth behavior applied.
Behavior reference string: simple linear growth height only
Linear growth - diam with auto height
How it works
This behavior calculates an amount of diameter growth as:
Y = (a + (b * GLI)) * T
where
- Y = amount of diameter increase, in mm
- a = Simple Linear - Diam Intercept in mm/yr (a) parameter
- b = Simple Linear - Diam Slope (b) parameter
- GLI = global light index, as a percentage between 0 and 100, calculated by a light behavior
- T = number of years per timestep
After applying the amount of diameter increase, tree height is allowed to update automatically according to the allometry equations.
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 applied.
Behavior reference string: simple linear growth
Linear growth - diam only
How it works
This behavior calculates an amount of diameter growth as:
Y = (a + (b * GLI)) * T
where
- Y = amount of diameter increase, in mm
- a = Simple Linear - Diam Intercept in mm/yr (a) parameter
- b = Simple Linear - Diam Slope (b) parameter
- GLI = global light index, as a percentage between 0 and 100, calculated by a light behavior
- T = number of years per timestep
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 a height-only growth behavior applied.
Behavior reference string: simple linear growth diam only
Linear growth w/ exponential shade reduction - height only
How it works
This behavior calculates an amount of height growth as:
Y = (a + (b * diam)) * (GLI/100)c * T
where
- Y = amount of height increase, in cm
- a = Shaded Linear - Height Intercept in cm/yr (a) parameter
- b = Shaded Linear - Height Slope (b) parameter
- c = Shaded Linear - Height Shade Exponent (c) parameter
- diam = diameter (diameter at 10 cm for seedlings and saplings, DBH for adults)
- GLI = global light index, as a percentage between 0 and 100, calculated by a light behavior
- T = number of years per timestep
In order to find the total amount of height increase for a timestep, the behavior takes as an input the amount of diameter growth increase. Assume that the number of years per timestep is X. The amount of diameter increase is divided by X. Then the logistic growth equation is calculated X times, with the diameter incremented by the amount of diameter increase per timestep each time. The total height increment is the sum of the X individual height increments.
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 a diameter-only growth behavior applied.
Behavior reference string: shaded linear growth height
Linear growth w/ exponential shade reduction - diam with auto height
How it works
This behavior calculates an amount of diameter growth as:
Y = (a + (b * diam)) * (GLI/100)c * T
where
- Y = amount of diameter increase, in mm
- a = Shaded Linear - Diam Intercept in mm/yr (a) parameter
- b = Shaded Linear - Diam Slope (b) parameter
- c = Shaded Linear - Diam Shade Exponent (c) parameter
- diam = diameter (diameter at 10 cm for seedlings and saplings, DBH for adults)
- GLI = global light index, as a percentage between 0 and 100, calculated by a light behavior
- T = number of years per timestep
After applying the amount of diameter increase, tree height is allowed to update automatically according to the allometry equations.
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 applied.
Behavior reference string: shaded linear growth
Linear growth w/ exponential shade reduction - diam only
How it works
This behavior calculates an amount of diameter growth as:
Y = (a + (b * diam)) * (GLI/100)c * T
where
- Y = amount of diameter increase, in mm
- a = Shaded Linear - Diam Intercept in mm/yr (a) parameter
- b = Shaded Linear - Diam Slope (b) parameter
- c = Shaded Linear - Diam Shade Exponent (c) parameter
- diam = diameter (diameter at 10 cm for seedlings and saplings, DBH for adults)
- GLI = global light index, as a percentage between 0 and 100, calculated by a light behavior
- T = number of years per timestep
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 a height-only growth behavior applied.
Behavior reference string: shaded linear growth diam only
Logistic growth - height only
How it works
The amount of height increase is calculated as:
where
- Y = amount of height increase, in cm
- a = Logistic - Asymptotic Height Growth - Full Light in cm/yr (a)
- b = Logistic - Height Shape Param 1 (b) parameter
- c = Logistic - Height Shape Param 2 (c) parameter
- GLI = global light index, as a percentage between 0 and 100, calculated by a light behavior
- T = number of years per timestep
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 a diameter-only growth behavior applied.
Behavior reference string: logistic growth height only
Logistic growth - diam with auto height
How it works
The amount of diameter increase is calculated as:
where
- Y = amount of diameter increase, in mm
- a = Logistic - Asymptotic Diam Growth - Full Light in mm/yr (a) parameter
- b = Logistic - Diam Shape Param 1 (b) parameter
- c = Logistic - Diam Shape Param 2 (c) parameter
- GLI = global light index, as a percentage between 0 and 100, calculated by a light behavior
- T = number of years per timestep
After applying the amount of diameter increase, tree height is allowed to update automatically according to the allometry equations.
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 applied.
Behavior reference string: logistic growth
Logistic growth - diam only
How it works
The amount of diameter increase is calculated as:
where
- Y = amount of diameter increase, in mm
- a = Logistic - Asymptotic Diam Growth - Full Light in mm/yr (a) parameter
- b = Logistic - Diam Shape Param 1 (b) parameter
- c = Logistic - Diam Shape Param 2 (c) parameter
- GLI = global light index, as a percentage between 0 and 100, calculated by a light behavior
- T = number of years per timestep
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 a height-only growth behavior applied.
Behavior reference string: logistic growth diam only
Logistic growth w/ size dependent asymptote - height only
How it works
This behavior calculates annual height increases as:
where
- Y = amount of height increase, in cm
- a = Size Dep. Logistic - Height Intercept (a) parameter
- b = Size Dep. Logistic - Height Slope (b) parameter
- c = Size Dep. Logistic - Height Shape Param 1 (c) parameter
- d = Size Dep. Logistic - Height Shape Param 2 (d) parameter
- GLI = global light index, as a percentage between 0 and 100, calculated by a light behavior
- diam = diameter (diameter at 10 cm for seedlings and saplings, DBH for adults)
In order to find the total amount of height increase for a timestep, the behavior takes as an input the amount of diameter growth increase. Assume that the number of years per timestep is X. The amount of diameter increase is divided by X. Then the logistic growth equation is calculated X times, with the diameter incremented by the amount of diameter increase per timestep each time. The total height increment is the sum of the X individual height increments.
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 a diameter-only growth behavior applied.
Behavior reference string: size dependent logistic growth height
Logistic growth w/ size dependent asymptote - diam with auto height
How it works
This behavior calculates annual diameter increases as:
where
- Y = amount of diameter increase, in mm
- a = Size Dep. Logistic - Diam Intercept (a) parameter
- b = Size Dep. Logistic - Diam Slope (b) parameter
- c = Size Dep. Logistic - Diam Shape Param 1 (c) parameter
- d = Size Dep. Logistic - Diam Shape Param 2 (d) parameter
- GLI = global light index, as a percentage between 0 and 100, calculated by a light behavior
- diam = diameter (diameter at 10 cm for seedlings and saplings, DBH for adults)
Assume that the number of years per timestep is X. In order to find the total amount of diameter increase for a timestep, the logistic growth equation is calculated X times, with the diameter incremented by the amount of diameter increase for the previous year. The total diameter increment is the sum of the X individual diameter increments. After applying the amount of diameter increase, tree height is allowed to update automatically according to the allometry equations.
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 applied.
Behavior reference string: size dependent logistic growth
Logistic growth w/ size dependent asymptote - diam only
How it works
This behavior calculates annual diameter increases as:
where
- Y = amount of diameter increase, in mm
- a = Size Dep. Logistic - Diam Intercept (a) parameter
- b = Size Dep. Logistic - Diam Slope (b) parameter
- c = Size Dep. Logistic - Diam Shape Param 1 (c) parameter
- d = Size Dep. Logistic - Diam Shape Param 2 (d) parameter
- GLI = global light index, as a percentage between 0 and 100, calculated by a light behavior
- diam = diameter (diameter at 10 cm for seedlings and saplings, DBH for adults)
Assume that the number of years per timestep is X. In order to find the total amount of diameter increase for a timestep, the logistic growth equation is calculated X times, with the diameter incremented by the amount of diameter increase for the previous year. The total diameter increment is the sum of the X individual diameter increments.
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 a height-only growth behavior applied.
Behavior reference string: size dependent logistic growth diam only
Lognormal with exponential shade reduction - height only
How it works
This behavior calculates annual height increases as:
where
- Y = amount of height increase, in cm
- a = Lognormal - Height Growth Increment at Diam 36, in cm/yr (a) parameter
- b = Lognormal - Height Shape Parameter (b) parameter
- c = Lognormal - Height Effect of Shade (c) parameter
- GLI = global light index, as a percentage between 0 and 100, calculated by a light behavior
- diam = diameter (diameter at 10 cm for seedlings and saplings, DBH for adults)
In order to find the total amount of height increase for a timestep, the behavior takes as an input the amount of diameter growth increase. Assume that the number of years per timestep is X. The amount of diameter increase is divided by X. Then the lognormal growth equation is calculated X times, with the diameter incremented by the amount of diameter increase per timestep each time. The total height increment is the sum of the X individual height increments.
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 a diameter-only growth behavior applied.
Behavior reference string: lognormal growth height only
Lognormal with exponential shade reduction - diam with auto height
How it works
This behavior calculates annual height increases as:
where
- Y = amount of height increase, in cm
- a = Lognormal - Diam Growth Increment at Diam 36, in mm/yr (a) parameter
- b = Lognormal - Diam Shape Parameter (b) parameter
- c = Lognormal - Diam Effect of Shade (c) parameter
- GLI = global light index, as a percentage between 0 and 100, calculated by a light behavior
- diam = diameter (diameter at 10 cm for seedlings and saplings, DBH for adults)
Assume that the number of years per timestep is X. In order to find the total amount of diameter increase for a timestep, the lognormal growth equation is calculated X times, with the diameter incremented by the amount of diameter increase for the previous year. The total diameter increment is the sum of the X individual diameter increments. After applying the amount of diameter increase, tree height is allowed to update automatically according to the allometry equations.
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 applied.
Behavior reference string: lognormal growth
Lognormal with exponential shade reduction - diam only
How it works
This behavior calculates annual height increases as:
where
- Y = amount of height increase, in cm
- a = Lognormal - Diam Growth Increment at Diam 36, in mm/yr (a) parameter
- b = Lognormal - Diam Shape Parameter (b) parameter
- c = Lognormal - Diam Effect of Shade (c) parameter
- GLI = global light index, as a percentage between 0 and 100, calculated by a light behavior
- diam = diameter (diameter at 10 cm for seedlings and saplings, DBH for adults)
Assume that the number of years per timestep is X. In order to find the total amount of diameter increase for a timestep, the lognormal growth equation is calculated X times, with the diameter incremented by the amount of diameter increase for the previous year. The total diameter increment is the sum of the X individual diameter increments.
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 a height-only growth behavior applied.
Behavior reference string: lognormal growth diam only
Stochastic Gap Growth
This behavior uses a shortcut for simulating gap dynamics with very competitive conditions. This behavior causes rapid growth in high light, with a unique "winner"; low light produces no growth at all.
How it works
This behavior simulates high growth in gap conditions. It relies on the Gap Light grid created by the Gap Light behavior to tell it where the gaps are. In this grid, each cell is either in gap (with 100% GLI) or not in gap (with 0% GLI). If a cell is in gap, a tree in that cell is randomly chosen out of all the trees to which the behavior applies to be promoted directly to adult tree status (even if it is a seedling). This tree represents the "winner". All other trees in the cell do not grow. In cells that are not in gap, no trees grow.
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 the Gap Light behavior applied.
Behavior reference string: Stochastic Gap Growth
Linear bi-level growth - diam with auto height
This behavior increments growth according to a simple linear equation, with the possibility of two sets of parameters for each species: one for high-light conditions and one for low-light conditions. This can also be used alone without the light levels.
How it works
The equation used by this behavior to increment growth is:
Y = (a + b * diam) * T
where
- Y = amount of diameter growth in cm
- a = growth intercept; in high-light conditions, this is the Linear Bi-Level - Intercept for High-Light Growth (a) parameter; in low-light conditions, this is the Linear Bi-Level - Intercept for Low-Light Growth (a) parameter
- b = growth slope; in high-light conditions, this is the Linear Bi-Level - Slope for High-Light Growth (b) parameter; in low-light conditions, this is the Linear Bi-Level - Slope for Low-Light Growth (b) parameter
- diam = diameter (diameter at 10 cm for seedlings and saplings, DBH for adults)
- T = number of years per timestep
Light levels come from the Storm Light grid produced by the Storm Light behavior. The threshold between the use of high-light and low-light parameters is set in the Linear Bi-Level - Threshold for High-Light Growth (0 - 100) parameter.
This behavior can also be used without Storm Light. In this case, only the low-light growth parameters are used.
How to apply it
This behavior can be applied to seedlings, saplings, and adults of any species. If you wish to use the light-level parameter switch, also use the Storm Light behavior.
Behavior reference string: linear bilevel growth
Linear bi-level growth - diam only
This behavior increments growth according to a simple linear equation, with the possibility of two sets of parameters for each species: one for high-light conditions and one for low-light conditions. This can also be used alone without the light levels.
How it works
The equation used by this behavior to increment growth is:
Y = (a + b * diam) * T
where
- Y = amount of diameter growth in cm
- a = growth intercept; in high-light conditions, this is the Linear Bi-Level - Intercept for High-Light Growth (a) parameter; in low-light conditions, this is the Linear Bi-Level - Intercept for Low-Light Growth (a) parameter
- b = growth slope; in high-light conditions, this is the Linear Bi-Level - Slope for High-Light Growth (b) parameter; in low-light conditions, this is the Linear Bi-Level - Slope for Low-Light Growth (b) parameter
- diam = diameter (diameter at 10 cm for seedlings and saplings, DBH for adults)
- T = number of years per timestep
Light levels come from the Storm Light grid produced by the Storm Light behavior. The threshold between the use of high-light and low-light parameters is set in the Linear Bi-Level - Threshold for High-Light Growth (0 - 100) parameter.
This behavior can also be used without Storm Light. In this case, only the low-light growth parameters are used.
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 height-only growth behavior applied. If you wish to use the light-level parameter switch, also use the Storm Light behavior.
Behavior reference string: linear bilevel growth diam only
Lognormal bi-level growth - height only
This behavior increments growth according to a simple linear equation, with the possibility of two sets of parameters for each species: one for high-light conditions and one for low-light conditions. This can also be used alone without the light levels.
How it works
The equation used by this behavior to increment growth is:
where
- Y - amount of height growth in m
- MG - maximum growth, in meters; in high-light conditions, this is the Lognormal Bi-Level - Max Growth in High Light (m) parameter; in low-light conditions, this is the Lognormal Bi-Level - Max Growth in Low Light (m) parameter
- X0 - in high-light conditions, this is the Lognormal Bi-Level - X0 for High-Light Growth parameter; in low-light conditions, this is the Lognormal Bi-Level - X0 for Low-Light Growth parameter
- Xb - in high-light conditions, this is the Lognormal Bi-Level - Xb for High-Light Growth parameter; in low-light conditions, this is the Lognormal Bi-Level - Xb for Low-Light Growth parameter
- H - tree height in meters
- T - number of years per timestep
Light levels come from the Storm Light grid produced by the Storm Light behavior. The threshold between the use of high-light and low-light parameters is set in the Lognormal Bi-Level - Threshold for High-Light Growth (0 - 100) parameter.
This behavior can also be used without Storm Light. In this case, only the low-light growth parameters are used.
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 diam-only growth behavior applied. If you wish to use the light-level parameter switch, also use the Storm Light behavior.
Behavior reference string: log bilevel growth height only
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.
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.
Behavior reference string: PR semi-stochastic diam only
Puerto Rico storm bi-level growth - diam with auto height
This behavior increments growth according to two possible growth equations, one to be used in low-light conditions and the other to be used in high-light conditions. This behavior was originally created for the Puerto Rico model.
How it works
Light levels come from the Storm Light grid produced by the Storm Light behavior. The threshold between the use of the high-light and low-light functions is set in the PR Storm Bi-Level - Threshold for High-Light Growth (0 - 100) parameter.
The function used in low-light conditions is:
Y = (a + b * diam) * T
where
- Y = amount of diameter growth in cm
- a = PR Storm Bi-Level - Intercept for Low-Light Growth (a) parameter
- b = PR Storm Bi-Level - Slope for Low-Light Growth (b) parameter
- diam = diameter (diameter at 10 cm for seedlings and saplings, DBH for adults)
- T = number of years per timestep
The function used in high-light conditions is:
H = T * a * diam * e(-b * N)
where
- H = amount of height growth, in cm
- a = PR Storm Bi-Level - High-Light "a" parameter
- b = PR Storm Bi-Level - High-Light "b" parameter
- diam = diameter (diameter at 10 cm for seedlings and saplings, DBH for adults)
- N = number of years since the last storm, from the Storm Damage grid produced by the Storm disturbance behavior
- T = number of years per timestep
H is expressed in centimeters of height growth. This is transformed into a number of cm of diameter growth, which is what this behavior passes along. This means that during tree life history stage transitions, the height the tree ends up with is not guaranteed to match the height calculated by the high-light growth function.
How to apply it
This behavior can be applied to seedlings, saplings, and adults of any species. You must also use the Storm disturbance and Storm Light behaviors.
Behavior reference string: PR storm bilevel growth
Browsed relative growth behavior - diam with auto height
This behavior simulates herbivory by allowing trees to grow at different rates when browsed versus unbrowsed.
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.
Behavior reference string: browsed relative growth
Browsed relative growth behavior - diam only
This behavior works exactly like the "Browsed relative growth behavior - diam with auto height" behavior to calculate an amount of diameter growth.
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.
Behavior reference string: browsed relative growth diam only
Michaelis Menton with negative growth - height only
This behavior uses a modified Michaelis-Menton function to do height growth.
How it works
The 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 with Negative Growth - Alpha parameter
- β is the Michaelis-Menton with Negative Growth - Beta parameter
- γ is the Michaelis-Menton with Negative Growth - Gamma parameter
- φ is the Michaelis-Menton with Negative Growth - Phi parameter
- H is the tree's height in cm
If the timestep is more than one year long, growth is recalculated for each year of the timestep, increasing the height each time.
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 a diameter growth behavior applied.
Behavior reference string: Michaelis Menten negative growth height only
Michaelis Menton with photoinhibition - height only
This behavior uses a modified Michaelis-Menton function to do height growth.
How it works
The 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 with Photoinhibition - Alpha parameter
- β is the Michaelis-Menton with Photoinhibition - Beta parameter
- D is the Michaelis-Menton with Photoinhibition - D parameter
- φ is the Michaelis-Menton with Photoinhibition - Phi parameter
- H is the tree's height in cm
If the timestep is more than one year long, growth is recalculated for each year of the timestep, increasing the height each time.
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 a diameter growth behavior applied.
Behavior reference string: Michaelis Menten photoinhibition growth height only
Power growth - height only
This behavior uses a power function to do height growth.
How it works
The amount of height growth is calculated as:
Y = n H φ
where:
- Y is the amount of height growth for one year, in cm
- n is the Power Height Growth - n parameter
- φ is the Power Height Growth - Exp parameter
- H is the tree's height in cm
If the timestep is more than one year long, growth is recalculated for each year of the timestep, increasing the height each time.
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 diameter growth behavior applied.
Behavior reference string: power growth height only
Lagged post harvest growth
This behavior increments growth as a function of DBH and neighboring basal area, and incorporates a lag period after harvesting during which trees acclimate to their post-harvest growing conditions.
How it works
A tree's potential growth is calculated by:
PARG = α * exp(-δ * DBH) * exp(-η BA * exp(-ω * DBH))
where:
- PARG is potential annual radial growth (mm/y)
- DBH is in cm
- BA is the basal area (in sq m) of adult trees within the distance given in the Post Harvest Growth - NCI Distance (m) parameter
- α is the Post Harvest Growth - Max Growth Constant parameter, the maximum radial growth in millimeters per year
- δ is the Post Harvest Growth - DBH Growth Effect parameter
- η is the Post Harvest Growth - NCI Constant parameter
- ω is the Post Harvest Growth - DBH NCI Effect parameter
If no harvest has occurred yet in this run, then the tree's actual growth, ARG, equals PARG. If a harvest has occurred at some point during this run, then ARG is calculated by:
ARG = ARGpre + (PARG - ARGpre) * (1 - exp(-τ * H * t))
where:
- ARG is annual radial growth (mm/y) for the current timestep
- ARGpre is annual radial growth for the last timestep prior to harvest
- H is the number of timesteps since the last harvest
- t is the number of years per timestep
- τ is the Post Harvest Growth - Time Since Harvest Rate Param parameter
Annual radial growth ARG is used to calculate timestep diameter growth using
DG = ARG * t * 2/10
where t is the number of years per timestep.
Model forms are based on those in Thorpe et al. (in review, For. Ecol. Manage.).
How to apply it
This behavior can be applied to saplings and adults of any species.
Behavior reference string: lagged post-harvest growth or lagged post-harvest growth diam only
Last updated: 03-Jun-2009 02:40 PM