Disperse behaviors
In this document:
Seed randomization
Disperse parameters
Non-spatial disperse behavior
Spatial disperse behaviors
--Non-gap spatial disperse behavior
--Gap spatial disperse behavior
--Masting spatial disperse behavior
--Anisotropic spatial disperse behavior
Disperse behaviors create and distribute tree seeds around the plot. Dispersal is the first step in seedling recruitment.
Seed totals for different species are stored in the Dispersed Seeds grid. You can change this grid's cell resolution. Each of the disperse behaviors adds seeds to this grid. The Establishment behaviors decide which seeds in the grid turn into new seedlings.
For these behaviors, "parent trees" refers to trees over the minimum reproductive DBH for a species. These are the only trees which can contribute new seeds to the plot.
While there is support in the model for seeds to act as individuals (see Trees), these seeds are not individuals but merely numbers in a grid. You could not, for instance, create a list of individual seed positions.
Seed randomization
The numbers of seeds added by the disperse behaviors can be randomized. You choose how randomization will be applied. If the seed distribution is deterministic, no randomization is done. Otherwise, you can choose a probability distribution function and the number of seeds is treated as the mean of that function. You
may need to supply additional parameters, depending on the probability distribution function you choose. This randomization applies to the seeds from all disperse behaviors that you have chosen.
There are four choices for probability distribution functions: the normal, the lognormal, the Poisson, and the negative binomial.
The normal distribution is:
where σ is the function standard deviation. Mean is zero.
The lognormal distribution is:
where ζ is the function mean and σ is the standard deviation.
The Poisson distribution is:
where λ is the function mean.
The negative binomial distribution is:
where u is the function mean and k is the clumping parameter. This is Equation 3.103 from Hilborn and Mangel.
- Amplitude of Anisotropic Effect The amplitude of the anisotropic effect (how strongly the distances differ in the maximum and minimum directions). Used by the Anisotropic spatial disperse behavior.
- Azimuth Direction of Max Dispersal Distance, in rad The azimuth direction in radians (north zero, east positive) of the maximum dispersal distance. Used by the Anisotropic spatial disperse behavior.
- Beta for Stumps The β value for stumps. Stumps use the same probability distribution function as the live members of their species. Only required if a behavior is being applied to stumps. Used by the Gap spatial disperse and Non-gap spatial disperse behaviors.
- Canopy Function Used The probability distribution function to be used to distribute seeds in canopy conditions. For the behaviors Non-gap spatial disperse, Masting spatial disperse, and Anisotropic disperse, these PDFs are always the ones used. Used by the Non-gap spatial disperse, Gap spatial disperse, Masting spatial disperse, and Anisotropic spatial disperse behaviors.
- Gap Function Used The probability distribution function to be used to distribute seeds in gap conditions. Used by the Gap spatial disperse behavior.
- Intercept of Mean Non-Spatial Seed Rain, seeds/m2/yr The intercept of the non-spatial seed rain function. This is the bath seed rain term. Set this value to zero to turn off bath non-spatial seed rain. Used by the Non-spatial disperse behavior.
- Lognormal Canopy Annual STR/n The annual STR/n value (Standardized Total Recruits, or all seeds produced by a 30 cm DBH tree in one year) for the lognormal function under canopy conditions (see equation below). This is only required if the canopy probability distribution function is lognormal. Used by the Gap spatial disperse, Non-gap spatial disperse, and Anisotropic spatial disperse behaviors. (In the case of the last two, the canopy probability distribution function is the only one used for a species.)
- Lognormal Canopy Beta The β for the lognormal function under canopy conditions (see equation below). This is only required if the canopy probability distribution function is lognormal. Used by the Gap spatial disperse, Non-gap spatial disperse, and Anisotropic spatial disperse behaviors.
- Lognormal Canopy X0 The mean of the lognormal function under canopy conditions, or under non-masting conditions in the case of Masting spatial disperse (see equation below). This is only required if the canopy probability distribution function is lognormal. Used by the Gap spatial disperse, Non-gap spatial disperse, Masting spatial disperse, and Anisotropic spatial disperse behaviors.
- Lognormal Canopy Xb The variance of the lognormal function under canopy conditions, or under non-masting conditions in the case of Masting spatial disperse (see equation below). This is only required if the canopy probability distribution function is lognormal. Used by the Gap spatial disperse, Non-gap spatial disperse, Masting spatial disperse, and Anisotropic spatial disperse behaviors.
- Lognormal Gap Annual STR/n The annual STR/n value (Standardized Total Recruits, or all seeds produced by a 30 cm DBH tree in one year) for the lognormal function under gap conditions (see equation below). This is only required if the gap probability distribution function is lognormal. Used by the Gap spatial disperse behavior.
- Lognormal Gap Beta The β for the lognormal function under gap conditions (see equation below). This is only required if the gap probability distribution function is lognormal. Used by the Gap spatial disperse behavior.
- Lognormal Gap X0 The mean of the lognormal function under gap conditions (see equation below). This is only required if the gap probability distribution function is lognormal. Used by the Gap spatial disperse behavior.
- Lognormal Gap Xb The variance of the lognormal function under gap conditions (see equation below). This is only required if the gap probability distribution function is lognormal. Used by the Gap spatial disperse behavior.
- Masting Disperse - Masting Beta The β value under masting conditions. Used by the Masting spatial disperse behavior.
- Masting Disperse - Masting CDF "a" The "a" value in the cumulative density function that is used to decide when masting events occur. Used by the Masting spatial disperse behavior.
- Masting Disperse - Masting CDF "b" The "b" value in the cumulative density function that is used to decide when masting events occur. Used by the Masting spatial disperse behavior.
- Masting Disperse - Masting Group Species in the same group always mast together. If all the group numbers are different, then each species masts separately. The actual numbers do not matter, just whether species have identical numbers. Used by the Masting spatial disperse behavior.
- Masting Disperse - Masting Lognormal X0 The mean of the lognormal function under masting conditions. This is only required for a species if the canopy probability distribution function for that species is lognormal. Used by the Masting spatial disperse behavior.
- Masting Disperse - Masting Lognormal Xb The variance of the lognormal function under masting conditions. This is only required for a species if the canopy probability distribution function for that species is lognormal. Used by the Masting spatial disperse behavior.
- Masting Disperse - Masting STR/n Mean The mean annual STR/n value under masting conditions. If the Masting Disperse - STR Draw PDF is Deterministic, then this is the STR/n value used. Used by the Masting spatial disperse behavior.
- Masting Disperse - Masting STR/n Standard Deviation The standard deviation of the STR/n value under masting conditions. If the Masting Disperse - STR Draw PDF is Deterministic, then this value is not used. Used by the Masting spatial disperse behavior.
- Masting Disperse - Mast Proportion Participating (0-1) The proportion of all adults for a species that participate in disperse during a masting timestep, as a value between 0 and 1. Used by the Masting spatial disperse behavior.
- Masting Disperse - Non-Masting Beta The β value under non-masting conditions. Used by the Masting spatial disperse behavior.
- Masting Disperse - Non-Masting STR/n Mean The mean annual STR/n value under non-masting conditions. If the Masting Disperse - STR Draw PDF is Deterministic, then this is the STR/n value used. Used by the Masting spatial disperse behavior.
- Masting Disperse - Non-Masting STR/n Standard Deviation The standard deviation of the STR/n value under non-masting conditions. If the Masting Disperse - STR Draw PDF is Deterministic, then this value is not used. Used by the Masting spatial disperse behavior.
- Masting Disperse - Non-Mast Proportion Participating (0-1) The proportion of all adults for a species that participate in disperse during a non-masting timestep, as a value between 0 and 1. Used by the Masting spatial disperse behavior.
- Masting Disperse - Masting Weibull Dispersal The dispersal value for the weibull function under masting conditions. This is only required for a species if the canopy probability distribution function for that species is weibull. Used by the Masting spatial disperse behavior.
- Masting Disperse - Masting Weibull Theta The θ for the weibull function under masting conditions. This is only required for a species if the canopy probability distribution function for that species is weibull. Used by the Masting spatial disperse behavior.
- Masting Disperse - Stochastic STR Draw Frequency If the STR/n value is stochastic, this determines whether a new value is generated once per species per timestep or once per tree per timestep. If the Masting Disperse - STR Draw PDF is Deterministic, then this value is not used. Used by the Masting spatial disperse behavior.
- Masting Disperse - STR Draw PDF Whether the STR/n value should be deterministic, or generated each timestep using a normal or lognormal distribution. Used by the Masting spatial disperse behavior.
- Maximum Parent Trees Allowed in Gap Cell Maximum number of trees above the minimum DBH for reproduction that are allowed in a grid cell for that cell to still have gap status (as opposed to closed canopy). Used by the Gap spatial disperse behavior.
- Maximum Search Distance for Neighbor Parents, in m
The maximum distance that the Anisotropic disperse behavior will look for neighbor parents from a particular point. Used by the Anisotropic spatial disperse behavior.
- Minimum DBH for Reproduction, in cm The minimum DBH at which a tree can reproduce. This value does not have to match the Minimum adult DBH. Used by all disperse behaviors.
- Seed Distribution The distribution method to be applied to seeds (randomization). Used by all disperse behaviors. Choices are:
- Deterministic - no randomization.
- Poisson - use the number of seeds as the mean in a Poisson probability distribution function. See the equation above.
- Normal - use the number of seeds as the mean in a normal probability distribution function. You must then supply a standard deviation for the function. See the equation above.
- Lognormal - use the number of seeds as the mean in a lognormal probability distribution function. You must then supply a standard deviation for the function. See the equation above.
- Negative binomial - use the number of seeds as the mean in a negative binomial probability distribution function. You must then supply a clumping parameter. See the equation above.
- Seed Dist. Clumping Parameter (Neg. Binomial) If you have chosen the negative binomial probability distribution function for "Seed distribution", this is the clumping parameter of the function, in seeds per m2. If you have not chosen that PDFs, then this parameter is not required. Used by all disperse behaviors.
- Seed Dist. Std. Deviation (Normal or Lognormal) If you have chosen the normal or lognormal probability distribution functions for "Seed distribution", this is the standard deviation of the function, in seeds per m2. If you have not chosen these PDFs, then this parameter is not required. Used by
all disperse behaviors.
- Slope Mean Non-Spatial Seed Rain, seeds/m2/ha of BA/yr The slope of the non-spatial seed rain function. This is the basal-area-dependent seed rain term. Set this value to zero to turn off basal-area-dependent non-spatial seed rain. Used by the Non-spatial disperse behavior.
- STR/n for Stumps The annual STR/n value (Standardized Total Recruits, or all seeds produced by a 30 cm DBH tree in one year) for stumps. Stumps use the same probability distribution function as the live members of their species. Only required if a behavior is being applied to stumps. Used by the Non-gap spatial disperse, Gap spatial disperse behaviors.
- Weibull Canopy Annual STR/n The annual STR/n value (Standardized Total Recruits, or all seeds produced by a 30 cm DBH tree in one year) for the Weibull function under canopy conditions (see equation below). This is only required if the canopy probability distribution function is Weibull. Used by the Gap spatial disperse, Non-gap spatial disperse, and Anisotropic spatial disperse behaviors. (In the case of the last two, the canopy probability distribution function is the only one used for a species.)
- Weibull Canopy Beta The β for the Weibull function under canopy conditions (see equation below). This is only required if the canopy probability distribution function is Weibull. Used by the Gap spatial disperse, Non-gap spatial disperse, and Anisotropic spatial disperse behaviors. (In the case of the last two, the canopy probability distribution function is the only one used for a species.)
- Weibull Canopy Dispersal The dispersal value for the Weibull function under canopy conditions, or under non-masting conditions in the case of Masting spatial disperse (see equation below). This is only required if the canopy probability distribution function is Weibull. Used by the Gap spatial disperse, Non-gap spatial disperse, Masting spatial disperse, and Anisotropic spatial disperse behaviors.
- Weibull Canopy Theta The θ for the Weibull function under canopy conditions, or under non-masting conditions in the case of Masting spatial disperse (see equation below). This is only required if the canopy probability distribution function is Weibull. Used by the Gap spatial disperse, Non-gap spatial disperse, Masting spatial disperse, and Anisotropic spatial disperse behaviors. (In the case of the last two, the canopy probability distribution function is the only one used for a species.)
- Weibull Gap Annual STR/n The annual STR/n value (Standardized Total Recruits, or all seeds produced by a 30 cm DBH tree in one year) for the Weibull function under gap conditions (see equation below). This is only required if the gap probability distribution function is Weibull. Used by the Gap spatial disperse behavior.
- Weibull Gap Beta The β value for the Weibull function under gap conditions (see equation below). This is only required if the gap probability distribution function is Weibull. Used by the Gap spatial disperse behavior.
- Weibull Gap Dispersal The dispersal value for the Weibull function under gap conditions (see equation below). This is only required if the gap probability distribution function is Weibull. Used by the Gap spatial disperse behavior.
- Weibull Gap Theta The θ value for the Weibull function under gap conditions (see equation below). This is only required if the gap probability distribution function is Weibull. Used by the Gap spatial disperse behavior.
Non-spatial disperse
The "non-spatial" in non-spatial disperse refers to the fact that this behavior ignores the location of parent trees and scatters seeds uniformly across the plot. Non-spatial disperse has two components: basal-area-dependent seed rain and non-density-dependent (bath) seed rain, the two of which are independent and can be used together or separately. For basal-area-dependent seed rain, the number of seeds added is in direct proportion to the amount of basal area of parent trees of a given species. Bath seed rain adds a constant number of seeds each timestep, even if there are no parent trees of that species in the plot.
How it works
Non-spatial disperse calculates how many seeds to distribute as:
λ = μ*BA + κ
where:
- λ is the mean number of seeds per m2
- μ is the Slope Mean Non-Spatial Seed Rain, seeds/m2/ha of BA/yr parameter
- BA is the basal area of the parent species in
m2
- κ is the Intercept of Mean Non-Spatial Seed Rain, seeds/m2/yr parameter
From this, the number of seeds per grid cell of the Dispersed Seeds grid is
calculated, and then that number is added to each grid cell.
In the equation above, μ is the basal-area-dependent seed rain term. Setting this value to zero turns off density-dependent seed rain. κ is the bath seed rain term. Setting this value to zero turns off bath seed rain.
How to apply it
Apply this behavior to adults of the species you wish to use non-spatial disperse.
Spatial disperse behaviors
Spatial disperse behaviors rely on the location and size of parent trees to determine the number and placement of seeds. The placement of the seeds is controlled by a probability distribution function. You can choose between the Weibull and lognormal functions.
The Weibull function is as follows:
where,
and where:
- Ri is the density (#/m2) of seedlings at a given
point i
- STR, the "standardized total recruits", is the number of seedling recruits produced by a 30 cm DBH parent tree. The STR/n value is entered as either the Weibull Canopy Annual STR/n or Weibull Gap Annual STR/n parameters
- n is a normalizer, discussed further below
- DBHk is the DBH in cm of the k = 1…T parent trees within a specified radius of location i
- D is a species-specific dispersal parameter (the Weibull Canopy Dispersal or Weibull Gap Dispersal parameters)
- mik is the distance (in meters) from point i to the kth parent tree
- θ and β are disperse parameters (the Weibull Canopy Theta or Weibull Gap Theta and Weibull Gap Beta or Weibull Canopy Beta parameters)
The lognormal function is as follows:
where,
and where:
- Ri is the density (#/m2) of seedlings at a given
point i
- STR, the "standardized total recruits", is the number of seedling recruits produced by a 30 cm DBH parent tree. The STR/n value is entered as either the Lognormal Canopy Annual STR/n or Lognormal Gap Annual STR/n parameters
- n is a normalizer, discussed further below
- DBHk is the DBH in cm of the k = 1…T parent trees within a specified radius of location i
- mik is the distance (in meters) from point i to the kth parent tree
- X0 is the mean of the function (the Lognormal Canopy X0 or Lognormal Gap X0 parameters)
- Xb is the variance of the function (the Lognormal Canopy Xb or Lognormal Gap Xb parameters)
- β is a disperse parameter (the Lognormal Canopy Beta or Lognormal Gap Beta parameters)
The normalizer (Equation 3 of Ribbens et al 1994) serves two functions. It reduces parameter correlation between
STR and the dispersion parameter (D); and scales the distance-dependent dispersion term so that STR is in meaningful units - i.e. the total # of seedlings produced in the entire seedling shadow of a 30 cm DBH parent tree. It is up to you to calculate the normalizer and divide STR by n for each species before entering that parameter.
Non-gap spatial disperse
Non-gap spatial disperse is called "non-gap" to distinguish it
from "gap" disperse. The "non-gap" means that forest cover is
ignored.
How it works
For each tree greater than reproductive age, the number of
seeds produced is calculated as
seeds = STR*(DBH/30)β
These seeds are cast in random azimuth directions from the tree, and at random distances that conform to the chosen probability distribution function.
How to apply it
Apply this behavior to all trees of at least the minimum reproductive age for your chosen species. If the minimum
reproductive age is less than the Minimum adult DBH, be sure to apply this behavior to saplings as well as adults. In the parameters, choose the appropriate probability distribution function for each species under "Canopy function used".
This behavior can be used to simulate the suckering of stumps. Apply this behavior to tree type "stump"of your chosen species. Stumps reproduce like other parent trees. They use the same probability distribution function and parameters as live members of their species, but they get their own β and STR values so that they can produce different numbers of seeds.
Gap spatial disperse
Gap spatial disperse takes forest cover into account when determining the number and placement of seeds. The two possible forest covers are gap and closed canopy. A "gap" is defined as a cell in the Dispersed Seeds grid with no more adults than the value of the "Maximum adults allowed
in gap cell" parameter, above.
How it works
The behavior starts each timestep by updating the forest cover of each cell (gap or canopy). It counts all trees above the minimum DBH for reproduction in each cell and compares that number to the Maximum parent trees allowed in gap cell parameter. The behavior will count trees of all species to determine gap status. However, if it finds a tree of a species that is not one of the ones this behavior is assigned to, it will use the tree's minimum adult DBH parameter instead of the minimum DBH for reproduction.
For each tree greater than the reproductive age, the number of seeds produced is calculated as
seeds = STR*(DBH/30)β
using the higher of gap or canopy STR along with its matching
β.
Each seed is given a random azimuth angle. It is then given a random distance that conforms to the probability distribution function of the current forest cover of the parent. Once the seed has an azimuth and a distance, the function determines which grid cell it should drop in.
Once the seed has a target grid cell, that cell's cover is checked. Then the seed's survival is evaluated. If the seed is in the cover type with the higher STR, it automatically survives. Otherwise, a random number is compared to the ratio of the lower STR to the higher STR to determine if it survives.
If the seed survives, it may need to be repositioned. If both parent and seed are under closed canopy, the seed is dropped where it is. If the parent is in gap and seedling is in canopy, a new distance is calculated as though the parent was also in canopy. The shortest of the two distances is used to determine where the seed lands. If the seed lands in a gap cell, the behavior "walks out" the line of the seed's path from parent to target landing cell, checking each intermediate grid cell's cover along the way. If any of the grid cells in the line are under canopy cover, the seed drops in the first canopy cell it reaches.
How to apply it
Apply this behavior to all trees of at least the minimum reproductive age for your chosen species. If the minimum
reproductive age is less than the Minimum adult DBH, be sure to apply this behavior to saplings as well as adults. In the parameters, choose the appropriate probability distribution function for each species for each forest cover type.
This behavior can be used to simulate the suckering of stumps. Apply this behavior to tree type "stump" of your chosen species. Stumps reproduce like other parent trees, except they always assume they are in a gap. They use the same probability distribution function and parameters as live members of their species, but they get their own β and STR values so that they can produce different numbers of seeds.
Anisotropic spatial disperse
Anisotropic spatial disperse allows for a directionality in the seed probability distribution function. Seeds are still evenly distributed at all azimuth angles around a parent tree, but the distance varies with azimuth direction. This behavior can simulate things like prevailing wind direction.
IMPORTANT: This behavior does not yet yield good results and needs tweaking. It is recommended that you NOT use it.
How it works
Extra parameters are added to the Weibull and lognormal
probability distribution functions to allow for anisotropy. For
Weibull:
where
and where
- Ri is the density (#/m2) of seedlings at a given
point i
- STR, the "standardized total recruits", is the number of
seedling recruits produced by a 30 cm DBH parent tree (the Weibull Canopy Annual STR or Weibull Gap Annual STR parameters)
- DBHk is the DBH in cm of the k = 1…T parent
trees within a specified radius of location i
- D is a species-specific dispersion parameter (the Weibull Canopy Dispersal or Weibull Gap Dispersal parameters)
- mik is the distance (in meters) from point i to
the kth parent tree
- θ and β are disperse parameters (the Weibull Canopy Theta or Weibull Gap Theta and Weibull Gap Beta or Weibull Canopy Beta parameters)
- μ is the amplitude of the anisotropic effect (the Amplitude of Anisotropic Effect parameter)
- φ is the azimuth angle of maximum dispersal distance (the Azimuth Direction of Max Dispersal Distance, in rad parameter)
- δ is the azimuth angle from the kth parent tree to point i
For lognormal:
where
and where
- Ri is the density (#/m2) of seedlings at a given
point i
- STR, the "standardized total recruits", is the number of
seedling recruits produced by a 30 cm DBH parent tree (the Lognormal Canopy Annual STR or Lognormal Gap Annual STR parameters)
- DBHk is the DBH in cm of the k = 1…T parent
trees within a specified radius of location i
- mik is the distance (in meters) from point i to
the kth parent tree
- X0 is the mean of the function (the Lognormal Canopy X0 or Lognormal Gap X0 parameters)
- Xb is the variance of the function (the Lognormal Canopy Xb or Lognormal Gap Xb parameters)
- μ is the amplitude of the anisotropic effect (the Amplitude of Anisotropic Effect parameter)
- φ is the azimuth angle of maximum dispersal distance (the Azimuth Direction of Max Dispersal Distance, in rad parameter)
- δ is the azimuth angle from the kth parent tree to point i
As an example, the lognormal function produces the following
graph:
For each grid cell in the Dispersed Seeds grid, all neighbor parent trees within a certain radius are found and the appropriate function above is applied to calculate the seed density at that point. That number of seeds is added to the grid cell.
How to apply it
Apply this behavior to all trees of at least the minimum reproductive age for your chosen species. If the minimum reproductive age is less than the Minimum adult DBH, be sure to apply this behavior to saplings as well as adults. In the parameters, choose the appropriate probability distribution function for each species for each forest cover type. This behavior cannot be applied to stumps.
Masting spatial disperse behavior
This behavior is a variant of the Non-gap spatial disperse behavior that adds masting and more stochasticity in seed production.
How it works
Deciding when to mast. For each timestep, the probability of masting for each species is calculated from the following cumulative distribution function:
where:
- y is the probability of masting
- X is the number of years since last mast
- a is the Masting Disperse - Masting CDF "a" parameter
- b is the Masting Disperse - Masting CDF "b" parameter
When the run starts, it is assumed a masting last event took place in timestep -1. A random number is used to determine whether a mast occurs in the current timestep. Disperse happens the same way in mast and non-mast timesteps, but the parameters used are different.
Species may be organized into groups to create synchrony in masting. The Masting Disperse - Masting Group parameter allows you to assign group numbers to species. The actual value of the group number is not important. It only matters if more than one species has the same number. If one species in a group masts, all species in that group do. Each group's mast decision is made separately, so sometimes more than one group may mast at a time. If all species have a different group number, then they all mast independently of one another.
Which trees disperse. Of the group of trees eligible to disperse (those with DBHs above the value in the Minimum DBH for Reproduction, in cm parameter), some can be randomly selected to participate in disperse. The proportion dispersing is set in Masting Disperse - Mast Proportion Participating (0-1) for mast timesteps, and Masting Disperse - Non-Mast Proportion Participating (0-1) for non-mast timesteps. The group of trees participating is chosen again each timestep. No adjustment is made to the number of seeds produced per tree. Fewer trees participating in disperse means fewer total seeds will be produced.
STR/n stochasticity. The STR/n value may be randomized each timestep. Use the Masting Disperse - STR Draw PDF parameter to choose from a normal or lognormal probability distribution. You can then set the mean and standard deviations for each species, which are different in masting and non-masting timesteps. You can also leave the STR/n value deterministic, in which case the mean STR/n value is used directly.
If you choose to use a stochastic STR/n, the STR/n value can be generated once per species per timestep, or once per tree per timestep. If the value is generated once per species, all individuals of that species use the same STR/n value that timestep.
Once the behavior has decided whether masting occurs, and what the STR/n values are, then disperse proceeds exactly as described in the Non-gap spatial disperse behavior.
How to apply it
Apply this behavior to all trees of at least the minimum reproductive age for your chosen species. If the minimum
reproductive age is less than the Minimum adult DBH, be sure to apply this behavior to saplings as well as adults.
Last updated: 16-May-2007 08:36 PM