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. Then the Germination behaviors and Seed Predation behaviors act to reduce the number of seeds. Finally, the Establishment behaviors turn the seeds in the grid 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:

Normal function

where σ is the function standard deviation. Mean is zero.

The lognormal distribution is:

Lognormal function

where ζ is the function mean and σ is the standard deviation.

The Poisson distribution is:

Poisson function

where λ is the function mean.

The negative binomial distribution is:

Negative binomial function

where u is the function mean and k is the clumping parameter. This is Equation 3.103 from Hilborn and Mangel.

Disperse parameters

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: 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:

Weibull function

where,
Weibull normalizer

and where:

The lognormal function is as follows:

Weibull function

where,
Lognormal normalizer

and where:

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:

Weibull anisotropic function

where
Weibull anisotropic normalizer

and where For lognormal:
Lognormal anisotropic function

where
Lognormal anisotropic normalizer

and where As an example, the lognormal function produces the following graph:
Lognormal anisotropic 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.



22-Aug-2004 08:36 PM