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
--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 and Anisotropic disperse, these PDFs are always the ones used. Used by the Non-gap spatial disperse, Gap 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 The annual STR 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. (In the case of the last two, the canopy probability distribution function is the only one used for a species.)
- Lognormal Canopy X0 The mean of 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 Xb The variance of 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 Gap Annual STR The annual STR 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.
- 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 for Stumps The annual STR 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 The annual STR 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 (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 Theta The θ 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 Gap Annual STR The annual STR 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 undergo
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 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 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 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)
- 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.
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.
Last updated: 22-Aug-2004 08:36 PM