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

How growth is applied

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.

Growth parameters

Relative growth behaviors

Several behaviors apply a relative growth version of the Michaelis-Menton function. Relative growth is calculated with the equation:


where:

Diameter growth is compounded over multiple timesteps with the equation:

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

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:

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:

Growth is compounded over multiple timesteps with the equation:

G = ((Y + 1)T - 1) * diam
where:

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 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: 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 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

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

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

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:

NCI size effect equation

where:

Shading Effect is calculated as:

NCI shading effect equation

where:

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:

NCI crowding effect equation

where:

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:

NCI equation

where:

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:

NCI size effect equation

where:

Crowding Effect is calculated as:

CE = exp(-C * (DBH γ * BAn / BADiv) D)

where:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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:

Lognormal bi-level equation

where

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:

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

The function used in high-light conditions is:

H = T * a * diam * e(-b * N)

where

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:

Growth is compounded over multiple timesteps with the equation:

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

where:

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:

Michaelis Menton with negative growth equation

where:

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:

Michaelis Menton with photoinhibition growth equation

where:

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:

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:

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:

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