Mortality behaviors

In this document:
Mortality parameters
Adult Self Thinning
Adult Stochastic Mortality
Aggregated Mortality
BC Mortality
Browsed Stochastic Mortality
Competition Mortality
Density Self-Thinning Mortality
Exponential Growth and Resource-Based Mortality
GMF Mortality
Growth and Resource-Based Mortality
Height-GLI Weibull Mortality with Browse
Juvenile Self Thinning
Juvenile Stochastic Mortality
Logistic Bi-Level Mortality
NCI Mortality
Senescence
Stochastic Bi-Level Mortality
Weibull Snag 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 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 existing 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.

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.

Aggregated Mortality

Aggregated Mortality is similar to the Adult Stochastic Mortality behavior in that it kills trees randomly to match a predetermined mortality rate. However, Aggregated Mortality clumps together the deaths in both time and space.

How it works

Mortality occurs in discrete episodes, which have an average return interval. For any timestep, the probability that a mortality episode will occur is T/RI, where T is the number of years per timestep and RI is the Aggregated Mortality Return Interval (years) parameter. Each timestep, this behavior uses a random number to decide if a mortality episode occurs. Between mortality episodes, this behavior does not kill any trees.

If a mortality episode occurs, this behavior kills some of the total pool of trees to which it has been applied. The base annual mortality rate proportion is given in the Aggregated Mortality Annual Kill Amount (0-1) parameter. Since the parameter gives an annual rate, the actual mortality rate is 1-(1-AD)T, where AD is the annual amount to kill and T is the number of years per timestep.

During a mortality episode, this behavior kills the trees in discrete clumps. The behavior uses a random number with each tree in its pool of eligible trees to decide if that tree dies. If it dies, the behavior also kills the trees closest to it. Only trees to which this behavior has been applied are killed; other neighbors are left alone. The size of these clumps of dead trees can either be deterministic or drawn from a negative binomial probability distribution. This option is set in the Aggregated Mortality Clump Size parameter. If the size is deterministic, the size of all clumps is given in the Aggregated Mortality Number of Trees To Aggregate parameter. If the size is from a negative binomial distribution, that parameter gives the mean, u, for the function

Negative binomial function

where k, the clumping parameter, is the Aggregated Mortality Clumping Parameter parameter.

If the Aggregated Mortality Return Interval (years) and Aggregated Mortality Number of Trees To Aggregate parameters are both set to 1, then this behavior functions exactly like the Adult Stochastic Mortality behavior.

How to apply it

This behavior can be applied to seedlings, saplings, and adults of any species. Only those trees to which this behavior has been applied will be killed. This behavior can be combined with other mortality behaviors, but for best results, it should be the first one to occur.

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:

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.

Browsed Stochastic Mortality

This simulates the effects of herbivory by allowing different background mortality rates for browsed and unbrowsed trees.

How it works

Whether or not a tree is browsed is determined by the Random browse behavior. For each tree, if it has not been browsed, that species's Juvenile Background Mortality Rate parameter is used; if it has been browsed, the species's Browsed Juvenile Background Mortality Rate parameter is used. A random number is compared to the appropriate rate to decide if the tree 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 the Random browse behavior applied.

Exponential Growth and Resource-Based Mortality

This behavior calculates probability of mortality 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 mortality for a tree is calculated with the following equation:

Prob = (d + a * R) * exp( -( b + c * R) * G)
where:

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 mortality probability as calculated above is an annual probability. For multi-year timesteps, the timestep probability is 1 - (1 - AP)X, 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.

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:

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.

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:

Growth and resource mortality equation
where:

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.

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 existing 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.

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.

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:

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.

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:

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 * Size Effect * Shading Effect * Crowding Effect * Storm Effect

Max Survival is the NCI Max Survival Probability (0-1) parameter. Storm Effect, Shading 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:

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.

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 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.

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:

NCI size effect equation

where:

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:

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:

Density self-thinning equation

where:

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:


Logistic Bi-Level Mortality Equation

where

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 with Browse

This behavior calculates the probability of mortality using a Weibull function of tree height and GLI (light level). It can also simulate the effects of herbivory by using different parameters for browsed and unbrowsed trees.

How it works

The same function is used to calculate the probability of mortality for both browsed and unbrowsed trees, but the parameters are different. The function is:

p = Mmax * exp(-a * H b - c * GLI d)

where

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.

Whether or not a tree is browsed is determined by the Random browse behavior. If the Random browse behavior does not apply to a tree, or is not present in the run, the unbrowsed parameters are always used. The other parameters can be ignored.

How to apply it

This behavior can be applied to seedlings, saplings, and adults of any species. You must also use a light behavior. If you wish to include the effects of herbivory, also include the Random browse behavior in the run.


Last updated: 03-Apr-2007 07:39 AM