Mortality behaviors
In this document:
Mortality parameters
GMF Mortality behavior
BC Mortality behavior
Adult Self Thinning behavior
Juvenile Self Thinning behavior
Senescence behavior
Adult Stochastic Mortality behavior
Juvenile Stochastic Mortality behavior
Weibull Snag Mortality behavior
NCI Mortality behavior
Growth and Resource-Based mortality
Competition Mortality
Density Self-Thinning mortality
Logistic Bi-Level Mortality
Stochastic Bi-Level Mortality
Height-GLI Weibull Mortality
The mortality behaviors cause tree death due to natural life cycle causes and competition. Tree death due to disturbance is covered by other behaviors.
Mortality behaviors do not actually remove dead trees from memory. They set a flag which marks trees as dead. This is because some other behaviors, such as the Substrate group, have specific interest in dead trees. Dead trees are eventually removed from memory by the Dead tree remover behavior. It is important to include this behavior in your run to avoid incorrect results in behaviors that use dead trees and unacceptably slow model run times.
Mortality parameters
- Adult Background Mortality Rate The proportion of trees that die each year, as a value between 0 and 1. Used by the Adult stochastic mortality behavior.
- Adult Self-Thinning Intercept Intercept of the adult self-thinning linear function. Used by the Adult self-thinning behavior.
- Adult Self-Thinning Slope Slope of the adult self-thinning linear function. Used by the Adult self-thinning behavior.
- Competition Mortality Maximum Parameter (max) The maximum relative increment of growth subject to mortality. Used by the Competition Mortality behavior.
- Competition Mortality Shape Parameter (Z) Determines the shape of the mortality function. Used by the Competition Mortality behavior.
- DBH at Onset of Senescence, in cm DBH at which senescence takes effect. Used by the Senescence behavior.
- DBH of Maximum Senescence Mortality Rate, as an integer in cm The DBH at which maximum mortality occurs. Trees with a DBH greater than this value experience no further increase in the mortality rate. Used by the Senescence behavior.
- Density Self-Thinning Asymptote (A) The asymptote of the density self-thinning function. Used by the Density Self-Thinning Mortality behavior.
- Density Self-Thinning Density Effect (S) The parameter controlling the density effect of the density self-thinning function. Used by the Density Self-Thinning Mortality behavior.
- Density Self-Thinning Diameter Effect (C) The parameter controlling the effect of neighbor mean diameter of the density self-thinning function. Used by the Density Self-Thinning Mortality behavior.
- Density Self-Thinning Minimum Density for Mortality (#/ha) The minimum density of neighbors, in stems/ha, for density self-thinning mortality. A tree with a lower density of neighbors than this value will not die. Used by the Density Self-Thinning Mortality behavior.
- Density Self-Thinning Neighborhood Radius, in m The maximum radius, in m, within which to search for neighbors to calculate neighbor density for density self-thinning. Used by the Density Self-Thinning Mortality behavior.
- Growth/Resource - Scaling Factor (rho) Scaling factor to reduce survival at the mode of the survival probability function. Used by the Growth and Resource-Based Mortality behavior.
- Growth/Resource - Function Mode (mu) Determines the mode of the function along a gradient of the resource R (the mode is the optimal niche of a species). Used by the Growth and Resource-Based Mortality behavior.
- Growth/Resource - Survival Increase with Growth (delta) Specifies the increase in survival caused by amount of growth. Used by the Growth and Resource-Based Mortality behavior.
- Growth/Resource - Low-Growth Survival Parameter (sigma) Affects the shape of the survival probability distribution in low-growth conditions. Used by the Growth and Resource-Based Mortality behavior.
- Height-GLI Weibull - a The "a" parameter in the Weibull function for calculating annual mortality. Used by the Height-GLI Weibull Mortality behavior.
- Height-GLI Weibull - b The "b" parameter in the Weibull function for calculating annual mortality. Used by the Height-GLI Weibull Mortality behavior.
- Height-GLI Weibull - c The "c" parameter in the Weibull function for calculating annual mortality. Used by the Height-GLI Weibull Mortality behavior.
- Height-GLI Weibull - d The "d" parameter in the Weibull function for calculating annual mortality. Used by the Height-GLI Weibull Mortality behavior.
- Height-GLI Weibull - Max Mortality (0 - 1) The maximum mortality probability for a species, expressed as a proportion between 0 and 1. Used by the Height-GLI Weibull Mortality behavior.
- Include Snags in NCI Calculations Whether or not to include snags when finding competitive neighbors for NCI. Used in the NCI mortality behavior.
- Juvenile Background Mortality Rate The proportion of trees that die each year, as a value between 0 and 1. Used by the Juvenile stochastic mortality behavior.
- Juvenile Self-Thinning Intercept Intercept of the juvenile self-thinning linear function. Used by the Juvenile self-thinning behavior.
- Juvenile Self-Thinning Slope Slope of the juvenile self-thinning linear function. Used by the Juvenile self-thinning behavior.
- Light-Dependent Mortality Light-dependent mortality. Used by the GMF mortality and BC morality behaviors.
- Logistic Bi-Level - Low-Light "a" The "a" parameter used in low-light conditions. Used by the Logistic Bi-Level Mortality behavior.
- Logistic Bi-Level - Low-Light "b" The "b" parameter used in low-light conditions. Used by the Logistic Bi-Level Mortality behavior.
- Logistic Bi-Level - High-Light "a" The "a" parameter used in high-light conditions. Used by the Logistic Bi-Level Mortality behavior.
- Logistic Bi-Level - High-Light "b" The "b" parameter used in high-light conditions. Used by the Logistic Bi-Level Mortality behavior.
- Logistic Bi-Level - High-Light Mortality Threshold (0-100) The threshold between low-light and high-light parameters, as a value between 0 and 100. Used by the Logistic Bi-Level Mortality behavior.
- Maximum DBH for Adult Self-Thinning Maximum DBH at which adult self-thinning applies. Above this value, no mortality occurs. Used by the Adult self-thinning behavior.
- Mortality at Zero Growth Mortality rate at zero growth. Used by the GMF mortality and BC morality behaviors.
- NCI Crowding Effect Slope (C) The slope of the curve for neighbor effects. Used in the NCI mortality behavior.
- NCI Crowding Effect Steepness (D) The steepness of the curve for neighbor effects. Used in the NCI mortality behavior.
- NCI Max Radius of Crowding Neighbors, in m The maximum distance from a target tree at which neighbors can have a competitive effect. Used in the NCI mortality behavior.
- NCI Max Survival Probability (0-1) The maximum annual probability of survival, as a value between 0 and 1. Used in the NCI mortality behavior.
- NCI Minimum Neighbor DBH, in cm The minimum DBH for trees of that species to compete as neighbors. Used for all neighbor species, not just those using NCI mortality. Used in the NCI mortality behavior.
- NCI Neighbor DBH Effect (alpha) The effect of the DBH of a neighbor tree on its competitiveness for a target species. Used in the NCI mortality behavior.
- NCI Neighbor Distance Effect (beta) The effect of the distance of a neighbor tree on its competitiveness for a target species. Used in the NCI mortality behavior.
- 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. Used in the NCI mortality behavior.
- 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. Used in the NCI mortality behavior.
- 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 mortality behavior.
- 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 mortality behavior.
- NCI Size Effect Mode, in cm The mode of the size effect curve. Used in the NCI mortality behavior.
- NCI Size Effect Variance, in cm The variance of the size effect curve. Used in the NCI mortality behavior.
- NCI Size Sensitivity to NCI (gamma) The sensitivity of a tree's survival probability to its DBH. Used in the NCI mortality behavior.
- NCI Storm Effect - Complete Damage (0-1) The fraction by which a tree's survival probability is reduced when it has sustained complete storm damage. Used in the NCI mortality behavior.
- NCI Storm Effect - Medium Damage (0-1) The fraction by which a tree's survival probability is reduced when it has sustained medium storm damage. Used in the NCI mortality behavior.
- Species i NCI Lambda The scale of the competitive effect of a neighbor tree's species on the target tree's species. Used in the NCI mortality behavior.
- Senescence Mortality Alpha Controls the senescence mortality rate. Used by the Senescence behavior.
- Senescence Mortality Beta Controls the senescence mortality rate. Used by the Senescence behavior.
- Stochastic Bi-Level - High-Light Mortality Probability (0-1) The annual probability of mortality under high-light conditions, as a proportion between 0 and 1. Used by the Stochastic Bi-Level Mortality behavior.
- Stochastic Bi-Level - High-Light Mortality Threshold (0-100) The threshold between low-light and high-light mortality rates, as a value between 0 and 100. Used by the Stochastic Bi-Level Mortality behavior.
- Stochastic Bi-Level - Low-Light Mortality Probability (0-1) The annual probability of mortality under low-light conditions, as a proportion between 0 and 1. Used by the Stochastic Bi-Level Mortality behavior.
- Weibull Annual "a" Parameter for Snag Size Class 1 Mortality Weibull annual "a" parameter for those trees whose DBH is less than or equal to the value in "Upper DBH of snag size class 1". Used by the Weibull snag mortality behavior.
- Weibull Annual "a" Parameter for Snag Size Class 2 Mortality Weibull annual "a" parameter for those trees whose DBH is greater than the value in "Upper DBH of snag size class 1" but less than or equal to the value in "Upper DBH of snag size class 2". Used by the Weibull snag mortality behavior.
- Weibull Annual "a" Parameter for Snag Size Class 3 Mortality Weibull annual "a" parameter for those trees whose DBH is greater than the value in "Upper DBH of snag size class 2". Used by the Weibull snag mortality behavior.
- Weibull Annual "b" Parameter for Snag Size Class 1 Mortality Weibull annual "b" parameter for those trees whose DBH is less than or equal to the value in "Upper DBH of snag size class 1". Used by the Weibull snag mortality behavior.
- Weibull Annual "b" Parameter for Snag Size Class 2 Mortality Weibull annual "b" parameter for those trees whose DBH is greater than the value in "Upper DBH of snag size class 1" but less than or equal to the value in "Upper DBH of snag size class 2". Used by the Weibull snag mortality behavior.
- Weibull Annual "b" Parameter for Snag Size Class 3 Mortality Weibull annual "b" parameter for those trees whose DBH is greater than the value in "Upper DBH of snag size class 2". Used by the Weibull snag mortality behavior.
- Weibull Upper DBH of Snag Size Class 1 The upper DBH value of trees in size class 1. Used by the Weibull snag mortality behavior.
- Weibull Upper DBH of Snag Size Class 2 The upper DBH value of trees in size class 2. Trees with a value greater than this are considered to be in size class 3. Used by the Weibull snag mortality behavior.
GMF mortality
GMF mortality is a growth-based mortality behavior.
How it works
The GMF mortality model evaluates the following function to determine the probability of a tree's mortality:
m = m1*e-m2G
where:
- m is the probability of mortality
- m1 is the Mortality at Zero Growth parameter
- m2 is the Light-Dependent Mortality parameter
- G is amount of radial growth, in mm/yr, added to the tree's diameter
this timestep
Once the probability of mortality is calculated for a tree, SORTIE generates a random number to which to compare it to determine whether the tree will live or die.
This model was originally described in Kobe et al 1995.
How to apply it
The GMF mortality function assumes a timestep length of five years, so that must be your timestep length in order to use this behavior. 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 growth behavior applied.
BC mortality
BC mortality is a growth-based mortality behavior.
How it works
The BC mortality model evaluates the following function to
determine the probability of a tree's mortality:
where:
- m is the probability of mortality
- T is the number of years per timestep
- m1 is the Mortality at Zero Growth parameter
- m2 is the Light-Dependent Mortality parameter
- G is amount of radial growth, in mm/yr, added to the tree's diameter
during T
BC mortality is described in Kobe and Coates 1997.
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 growth behavior applied.
Adult self thinning
Self-thinning is a behavior that uses a pseudo-density
dependent function designed to increase the death rate in dense
uniform-age stands. You specify a maximum DBH at which to apply
it - above this DBH a tree will not die. There is nothing in this
behavior which makes it specifically for adult trees - the name
is to match the old SORTIE conventions.
How it works
Self-thinning uses a simple linear function of probability of
mortality as a function of DBH, assuming the tree is below the
maximum DBH at which to apply self-thinning. After evaluating
this function for a tree, it uses a random number to determine
whether the tree dies.
How to apply it
This behavior can be applied to seedlings, saplings, and
adults of any species.
Juvenile self thinning
Self-thinning is a behavior that uses a pseudo-density
dependent function designed to increase the death rate in dense
uniform-age stands. Unlike adult self-thinning, there is no upper
DBH limit applied. There is nothing in this behavior which makes
it specifically for juvenile trees - the name is to match the old
SORTIE conventions.
How it works
Self-thinning uses a simple linear function of probability of
mortality as a function of DBH. After evaluating this function
for a tree, it uses a random number to determine whether the tree
dies.
How to apply it
This behavior can be applied to seedlings, saplings, and
adults of any species.
Senescence
Senescence mortality provides for an uptick in mortality
rates. It is meant to slightly increase the death rate among
large adult trees.
How it works
All trees to which senescence is applied are evaluated for
senescence mortality. In practice, trees below the onset of
senescence DBH very rarely die. The probability of death rises
with DBH until the DBH of maximum senescence rate is reached, at
which point it levels off.
To assess whether a tree will die due to senescence, the
following function is evaluated:
where:
- ms is the probability of mortality
- α (Senescence Mortality Alpha parameter) and β (Senescence Mortality Beta parameter) control the magnitude of the uptick
- DBH is the tree's DBH, in cm
- DBHs is the DBH at Onset of Senescence, in cm parameter
The probability is compared to a random number to determine whether the individual tree will die.
How to apply it
Senescence may be applied to saplings and adults of any
species. It cannot be applied to seedlings.
Adult stochastic mortality
This behavior produces a background mortality rate. Individuals within the pool of trees to which this behavior applies are randomly selected to die. There is nothing about this behavior which makes it only applicable to adults. The name conforms to old SORTIE standards and allows it to be
distinguished from the Juvenile stochastic mortality behavior, so that two different rates can be applied to two different groups of trees.
How it works
For each tree, a random number is compared to that species's Adult Background Mortality Rate parameter to determine if it falls in the pool of trees that die.
How to apply it
This behavior can be applied to seedlings, saplings, and
adults of any species.
Juvenile stochastic mortality
This behavior produces a background mortality rate. Individuals within the pool of trees to which this behavior applies are randomly selected to die. There is nothing about this behavior which makes it only applicable to juveniles. The name conforms to old SORTIE standards and allows it to be distinguished from the Adult stochastic mortality behavior, so that two different rates can be applied to two different groups of trees.
How it works
For each tree, a random number is compared to that species's Juvenile Background Mortality Rate parameter to determine if it falls in the pool of trees that die.
How to apply it
This behavior can be applied to seedlings, saplings, and adults of any species.
Weibull snag mortality behavior
This behavior controls snag fall. Snags are standing dead trees. Obviously, they can't die again, so the word "mortality" is a bit of a misnomer. We call the behavior a mortality behavior because it functionally fits in this behavior class.
Snags that are "killed" by this behavior are considered to have fallen over. If Substrate behaviors are enabled, then these fallen trees are available to become new fresh log substrate. Any that are not picked up by substrate will be dealt with by the Dead tree remover behavior.
How it works
The behavior uses a Weibull function to determine the number of snags of a certain age left standing at a given time. The equation is:
where:
- S is proportion of snags still standing, between 0 and 1
- a and b are Weibull parameters (Weibull Annual "a" Parameter for Snag Size Class X Mortality parameter and Weibull Annual "b" Parameter for Snag Size Class X Mortality parameter)
- T is the snag age in years
Different sizes of snags fall at different rates. This behavior allows you to define three snag size classes and enter different "a" and "b" parameters for each.
A random number is used against this equation for a given tree to determine if it falls in the current timestep.
How to apply it
This behavior can be applied to snags of any species.
NCI mortality
This behavior uses the effects of neighbor competitiveness to influence tree survival ("NCI" stands for neighborhood competition index). A tree's maximum potential probability of survival 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 annual probability of survival is calculated as:
Prob. Survival = Max Survival * Storm Effect * Size Effect * Crowding Effect
Max Survival is the NCI Max Survival Probability (0-1) parameter. Storm Effect, Size Effect, and Crowding Effect are all factors which act to reduce the maximum survival probability and will vary depending on the conditions a tree is in. All values are bounded 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 parameter
- Xb is the NCI Size Effect Variance, in cm
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
- D is the NCI Crowding Effect Steepness (D) 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
- 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.
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 neighbor species. If the neighbor has complete damage, the value is the NCI Neighbor Storm Damage (eta) - Complete (0-1) parameter for the neighbor 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 survival probability as calculated above is an annual probability. For multi-year timesteps, the timestep probability is APX, where AP is the annual probability and X is the number of years per timestep. Once a tree's timestep survival probability has been calculated, it is compared to a random number to determine whether the tree lives or dies.
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.
Growth and Resource-Based Mortality
This behavior calculates probability of survival as a function of growth and some second resource. The identity of the second resource is unimportant and could be anything, from exchangeable calcium levels to soil moisture.
How it works
The probability of survival for a tree is calculated with the following equation:
where:
- Prob is the annual probability of survival, as a value between 0 and 1
- R is the amount of the second resource
- G is the amount of radial growth, in mm/yr
- ρ is the Growth/Resource - Scaling Factor (rho) parameter, which is a scaling factor to reduce survival at the mode of the survival probability function
- μ is the Growth/Resource - Function Mode (mu) parameter, which determines the mode of the function along a gradient of the resource R (this corresponds to the optimal niche of a species, meaning where it is the top competitor, the absolute winner of competition)
- δ is the Growth/Resource - Survival Increase with Growth (delta) parameter, which specifies the increase in survival caused by amount of growth
- σ is the Growth/Resource - Low-Growth Survival Parameter (sigma) parameter, which affects the shape of the survival probability distribution in low-growth conditions
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.
The survival probability as calculated above is an annual probability. For multi-year timesteps, the timestep probability is APX, where AP is the annual probability and X is the number of years per timestep. Once a tree's timestep survival probability has been calculated, it is compared to a random number to determine whether the tree lives or dies.
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 growth behavior applied. You must also enter a map of second resource values into the Resource grid.
Competition Mortality
Competition mortality is a growth-based mortality behavior. It uses the results of the NCI growth behavior.
How it works
NCI growth in SORTIE is calculated in the following way:
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 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.
In the Competition mortality behavior, the following measure is used as predictor variable for probability of mortality:
Relative increment = Growth / PG
The relative increment is the ratio between the growth for an individual tree and the maximum growth possible for that tree. The Growth is the tree's growth for the previous timestep. PG is calculated as follows:
PG = Max Growth * SE
where Max Growth is the NCI growth parameter NCI Maximum Potential Growth, cm/yr, and SE is the Size Effect. Size Effect is calculated as follows:
where:
- DBH is of the target tree, in cm
- X0 is the NCI Size Effect Mode, in cm (X0) NCI growth parameter
- Xb is the NCI Size Effect Variance, in cm (Xb) NCI growth parameter
Once the relative increment for an individual tree has been calculated, the probability of mortality for that individual is calculated in the following way:
Prob = Z relative increment / max
where:
- Prob is the probability of mortality
- Z is the Competition Mortality Shape Parameter (Z) parameter
- max is the Competition Mortality Maximum Parameter (max) parameter, which indicates the maximum relative increment subject to mortality
-
All trees with a relative increment greater than or equal to max will live.
How to apply it
This behavior can be applied to saplings and adults of any species. It cannot be applied to seedlings. Any tree species/type combination to which it is applied must also have NCI growth. This behavior can only be applied with a one year timestep.
Density Self-Thinning Mortality
This behavior calculates the probability of mortality of an individual juvenile tree as a function of the density and mean diameter of the neighborhood trees. Only neighborhood seedlings and saplings are taken into account in this behavior.
How it works
The probability of mortality is calculated with a double Michaelis-Menton function:
where:
- Pm is the probability of mortality for an individual tree
- density is the density of neighboring seedlings and saplings, in stems/ha, within a radius defined in the Density Self-Thinning Neighborhood Radius, in m parameter
- diam m is the mean diameter of neighbors, measured 10 cm above root collar in cm
- A is the Density Self-Thinning Asymptote (A) parameter
- C is the Density Self-Thinning Diameter Effect (C) parameter
- S is the Density Self-Thinning Density Effect (S) parameter
If the value of density is less than the value in the Density Self-Thinning Minimum Density for Mortality (#/ha) parameter, the tree does not die.
How to apply it
This behavior can be applied to seedlings and saplings of any species. It cannot be applied to adults. This behavior can only be applied with a one year timestep.
Logistic bi-level mortality
This behavior calculates the probability of survival according to a logistic 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 calculate survival probability is:

where
- p - annual probability of survival
- a - in high-light conditions, this is the Logistic Bi-Level - High-Light "a" parameter; in low-light conditions, this is the Logistic Bi-Level - Low-Light "a" parameter
- b - in high-light conditions, this is the Logistic Bi-Level - High-Light "b" parameter; in low-light conditions, this is the Logistic Bi-Level - Low-Light "b" parameter
- D - tree diam, in cm; diam10 for seedlings, DBH for others
If the timestep length is not one year, the actual probability of survival for the timestep is calculated as p' = p T, where p is the annual probability of survival, p' is the timestep probability of survival, and T is the number of years per timestep. Once the survival probability for the timestep is known for a tree, then a random number is compared to this probability to determine if the tree lives or dies.
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 Logistic Bi-Level - High-Light Mortality Threshold (0-100) parameter.
This behavior can also be used without Storm Light. In this case, only the low-light mortality 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.
Stochastic bi-level mortality
This behavior applies a constant rate of mortality to trees, with different rates for high-light and low-light conditions.
How it works
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 Stochastic Bi-Level - High-Light Mortality Threshold (0-100) parameter.
For each tree, a random number is compared to that species's probability of mortality to determine if it dies. If light levels qualify as high light, the probability of mortality is the value in the Stochastic Bi-Level - High-Light Mortality Probability (0-1) parameter; if the light levels are low, the probability of mortality is the value in the Stochastic Bi-Level - Low-Light Mortality Probability (0-1) parameter.
If the timestep length is not one year, the probability of mortality is adjusted from an annual mortality probability to a timestep probability.
How to apply it
This behavior can be applied to seedlings, saplings, and adults of any species. You must also use the Storm Light behavior.
Height-GLI Weibull Mortality
This behavior calculates the probability of mortality using a Weibull function of tree height and GLI (light level).
How it works
The equation used by this behavior to calculate mortality probability is:
p = Mmax * exp(-a * H b - c * GLI d)
where
- p - annual probability of mortality
- Mmax - the Height-GLI Weibull - Max Mortality (0 - 1) parameter
- a - the Height-GLI Weibull - a parameter
- b - the Height-GLI Weibull - b parameter
- c - the Height-GLI Weibull - c parameter
- d - the Height-GLI Weibull - d parameter
- H - tree height in meters
- GLI - light level, between 0 and 100% of full sun
If the timestep length is not one year, the actual probability of mortality for the timestep is calculated as p' = 1 - (1 - p) T, where p is the annual probability of mortality, p' is the timestep probability of mortality, and T is the number of years per timestep. Once the mortality probability for the timestep is known for a tree, then a random number is compared to this probability to determine if the tree lives or dies.
Light levels can come from any of the light behaviors that directly assign a tree its light level. It is expected that this is a GLI value, from 0 to 100% of full sun.
How to apply it
This behavior can be applied to seedlings, saplings, and adults of any species. You must also use a light behavior.
Last updated: 26-Jan-2006 03:17 PM