I. Introduction and backdrop

A number of recent events and trends have prompted me to attempt to develop a spatially- explicit, individually-based forest disturbance simulator. First, ecologists in a number of disciplines now recognize that spatial considerations may be essential to explain and understand a variety of ecological phenomena. Second, large disturbances in particular are typically infrequent and it is therefore difficult to quickly assemble a sufficiently large database from which to derive generalizations. Third, several of the factors that may be important to forest disturbance and subsequent early (first several decades) recovery dynamics, are difficult to manipulate in controlled and replicated experiments. Finally, the continued rapid progress of desktop computing capabilities makes possible and even practical the sort of realistic simulations that would have been impractical just a few years ago. I have spent much time and thought recently pondering what characteristics of large and small wind disturbances distinguish them from other types of disturbances, and what might be the consequences for subsequent forest recovery. This simulation is an attempt to formulate current information into a format that would allow researchers and managers to generate hypotheses and ask questions about possible successional outcomes under a variety of possible disturbance and subsequent management scenarios.

The model is conceptually rather akin to the very successful SORTIE model developed by Pacala, Canham, Silander, and colleagues, although I have not seen any of the SORTIE code, and don't know exactly how the various subroutines were implemented in their simulator beyond what is described in the published journal articles. In its current form, the simulator described here has a less detailed routine for calculating light availability for the growing plants, and currently does not simulate nutrient availability, or any plant influence on soil moisture. Another distinction of this model from SORTIE is that my goal was to create a simulator that explicitly addressed what happened during and immediately after a disturbance, because I believe that such initiating and early recovery events "set the stage" for much of the forest structure, composition, and dynamics that follow. Thus the focus here is on simulating the disturbance itself, and on seed dispersal, seedling establishment, and early seedling/sapling growth and mortality. Realistically-simulated trees produce realistic numbers of seeds that are dispersed to real locations, and germinate subject to realistic constraints to produce seedlings that must compete with herbaceous vegetation and other seedlings to reach the sapling stage.

The model is called BLOWDOWN, for obvious reasons, although it is quite flexible and can simulate numerous small gaps on a modest landscape, e.g. seedling distribution in several, arbitrarily- sized gaps in a simulated area up to 16ha; three gaps are illustrated in Figure 1 below for an area 200 m x 200 m. BLOWDOWN is written in the C++ programming language, for which I have used Visual C++, version 6.0 from Microsoft.

Figure 1. This figure shows the locations of 2000 trees in a simulated area of 200 m x 200 m. Also shown are some of the microsite types that are created in the simulation when trees are blown down by the simulated winds. To maximize clarity, crowns of both standing and fallen trees are not shown in this figure. Down trees can be either trunk broken (blue squares) or uprooted (red open circles). Areas covered by trunks of fallen trees are shown as black linear microsites adjacent to trunk broken or uprooted trees. Disrupted soil is shown as treefall pits and mounds at the bases of fallen trees (red and light blue irregular patches).

II. Structure

The essential structure of the BLOWDOWN simulation consists of two components: The first is an array of all saplings and trees (stems > 2 cm dbh) in the simulated area, as shown in Figure 2.

Figure 2. This figure shows the locations of trees in a subarea of 50 m x 50 m, with a 10m gap in the center of the simulated area. Standing trees shown as solid black dots; trunk-broken trees as triangles; uprooted trees as diamonds. Spatial locations were randomly-determined. Within the potential gap area, fates of trees are determined by an empirically-based algorithm that determines, first, if the tree is to fall, and then whether it will be trunk-broken or uprooted. These relationships are species and size (dbh) specific, and can be chosen from among several probability functions based on different blowdowns studied.

Tree and sapling sizes can be randomly created or read from a data file based on actual mapped and measured trees (Figure 2 shows random locations). The second component is a detailed two-dimensional (x,y) array consisting of 50 cm x 50 cm "grid cells" (Figure 3). Each grid cell has a true x,y location within the simulated area, and contains environmental data (canopy openness, microtopographic elevation, microsite type, and soil moisture), herbaceous percent cover, number and species of tree seeds, as well as the species and height of up to 75 tree seedlings. Microsites are currently one of the following: intact, treefall pit, treefall mound, under a fallen tree crown, under a fallen trunk, and stump. Figure 3 shows categories by color for grid cells in a 50 x 50 m subarea simulated with gaps in the lower left, center, and lower right.

Figure 3. Here is a representation of the types of microsites of the grid cell array, in an area of 50 m x 50 m. Of course, this is only a small subsection of the entire simulated area, but serves to show the variety of microsite types possible for cells of the grid array. Green cells are under the canopies of standing trees, which are indicated by the light blue hexagons. Trunk-broken and uprooted trees are indicated by yellow circles and violet diamonds, respectively. Irregular dark blue patches are treefall pits at the base of uprooted trees. Cells that were under tree canopies before disturbance but now are in "gap" area are shown in reddish-brown. Black cells indicate those cells covered by trunks of fallen trees. Uncolored (white) cells show areas not under tree canopies -- these would be very scarse in intact, closed-canopy forest, and the density of trees was intentionally kept low in this simulation.

Tree seedlings do not have individual x,y coordinates beyond that of the cell itself, but they do experience thinning and growth, and when large enough (about 3-4 m tall) they get "promoted" to the sapling/tree array, freeing some of the seedling slots for that grid cell and gaining their own x,y coordinates and dbh. Obviously this grid structure results in numerous routines being very computationally-intensive, since a 4 ha simulation has 160,000 grid cells and a 25-ha simulation has 1 million grid cells. Because of hardware constraints, I have not yet (as of mid April 2000) attempted to simulate areas larger than 16 ha.

The sapling/tree array (Figure 2) contains the coordinates of the plant, along with its size (cm diameter at 1.4 m), species, total height, crown radius, and crown depth. A number of additional characteristics are indirectly known for each sapling or tree based on its species: shade tolerance, growth rate, empirical dbh-fecundity relationships, vulnerability to windthrow, empirical dbh-root pit size relationships, and empirical dbh-type of treefall relationships (uproot or trunk break). Note in Figure 2 that among the trees in the gaps, some were trunk broken, some uprooted, and some remained standing. Species and size-specific probabilities of these 3 alternatives are determined for each tree based on one of several sets of logistic regressions from different blowdowns I have studied.

III. Interaction with users

The program/user interaction is currently via a boring text interface in which a question is asked, the program waits for an answer, and then execution resumes after the user provides some input. There is little in the way of error checking at the moment, so if the user inputs strange values for something, unknown results may follow. A priority for program improvement, once the essentials are more firmly established, will be to make BLOWDOWN more robust and resistant to user blunders.

IV. Options

As currently implemented, BLOWDOWN has substantial flexibility. When the program executes, the user is asked a series of questions about what values should be used for assorted variables in the simulation, allowing a huge number of permutations. Note that the actual processes simulated are phenomenological, not mechanistic (i.e. growth does not simulation photosynthesis, carbon allocation, root uptake, etc, etc). Users can specify all of the following:

a) Number of trees

b) Number of tree species present in the sapling/tree array

c) Relative abundances of the above*

d) Beta value in the function determining seed output (fecundity) from tree size

e) Number of species in the soil seed bank, and density of seeds of each of these species

f) Seed maximum germination percentage*

g) Choice of whether or not germination is responsive to microsite type*

h) Relative growth rates of seedlings*

i) Choice of constant vs fixed percent cover of herbaceous species (and the cover value if constant is chosen)*

j) Competition (shade) tolerance for growth of seedlings of each tree species (value of 1-10)*

k) Number and size (radius in meters) of gaps

l) Choice of one of three sets of logistic regression parameters to specify risk of treefall as a function of tree size and species

m) Choice of whether or not to remove herbs*

n) Choice of whether or not to remove seed bank*

o) Number of years of post-disturbance seedling growth

Items marked with an asterisk above have default values that the program uses if the user does not input anything.

V. Pre-disturbance processes

The simulation subroutines more-or-less follow the course of events in an actual forest disturbance/recovery sequence. The first two subroutines establish initial conditions for the grid array and tree array.

Grid cells all start out as being intact, having a 0 relative microelevation, with some herbaceous cover (unless the user says this is removed), some seeds in the soil seed bank (unless the user says this is removed, or specifies none), with no fresh seedlings, no microsite, etc. Based on the user's desired seed bank seed density, each cell begins with that density of seeds already present. Seed bank species are currently modeled as species that are NOT present in the living sapling/tree array (i.e. species that had previously been present on the site, but were no longer present as living stems). Pre-disturbance conditions for selected cells are written to an output file called "prestat.dat".

Trees are established by dividing the total number of trees into the appropriate number of each species, then x,y coordinates are randomly assigned to each. If the user lets the program use default species relative abundances, the total number of trees is divided equally into however many species are specified; e.g. if 5 species and 4000 total trees are specified, the default is equal abundance or 800 trees of each species. The user can specify relative abundances, but must do so such that the total proportions sum to unity. Alternatively, tree locations and species can be read from one of several files containing actual x, y coordinates for real trees mapped in situ.

Simulating a realistic size distribution is accomplished by dividing trunk diameter (dbh) into eight size classes (2.5 - 100 cm dbh), and creating the appropriate number of trees within each size class to mimic the size distribution found in my research in the old-growth hemlock- northern hardwoods forest at Tionesta Scenic Area, Pennsylvania. Actual dbh values within each size class (e.g. 30-40 cm dbh) are randomly assigned. In this approach, size distributions are currently fixed and identical for all species. Again, as an alternative to creating size distributions, tree sizes can be read (along with coordinates and species) directly from one of several files containing real sizes of mapped and measured trees. Pre-disturbance circumstances (size, species, coordinates) for each sapling/tree in the array are written to an output file called "early.dat".

There is one seed dispersal season prior to the wind event in BLOWDOWN. All standing, live trees (which is all of them at this time) produce seeds based on a fecundity relationship as parameterized by Clark and colleagues from Coweeta Hydrologic Lab in North Carolina (Ecological Monographs 1998 68: 213-235). Users can modify the default fecundity parameters, which use trunk diameter (dbh) to determine fecundity on a species- specific basis, based on the relationship: fecundity = beta * radius2 * pi. Default values of beta for each species are those published by Clark et al from Coweeta where applicable, or averaged across species if a species-specific value is not available.

Seeds are dispersed for each tree, one tree at a time, utilizing the tree size to determine fecundity, and from that tree's rooted x,y coordinate. Direction of dispersal is randomly chosen from 0 to 2pi radians. Distance of dispersal is calculated as a Gaussian distribution, modified to have a longer-than normal tail. Figure 4 shows post-dispersal locations of just a few of the seeds produced by five trees.

Figure 4. Seed distribution around five randomly-positioned parent trees. Seeds of a given parent tree are shown as small crosses of a particular color; parent tree locations indicated by large black dots. The dispersal probability density function was intentionally constrained for this figure, so there are no distantly-dispersed seeds. However, even for severely-constrained dispersal distances, it does show how seed shadows can thoroughly intermingle for trees located close to one another (e.g. the trees in upper left with red and dark green "seeds").

A clever computing trick that produces a Gaussian distribution is to utilize the sum of a fixed number of random numbers (e.g. 6) between zero and unity, minus 1/2 of that number, since the average expectation of six random 0-1 numbers is 3. The sum of the 6 minus 1/2 of the number of numbers, though, has a Gaussian distribution centered on zero. The simulation uses the absolute value of the sum, multiplied by a species-specific conversion factor to mimic different distance-dispersal probabilities for various species (e.g. small, winged Betula seeds disperse much farther than large, heavy oak acorns). The conversion factors were chosen to produce a Gaussian distribution that was as close as possible to the exponential decay model in Clark et al. (1998, Ecological Monographs), based on visual inspection of the published probability density functions in the Clark et al. paper. This produces a Gaussian distribution with slightly less of a concentration at zero distance (the center of the standing tree crown), a thicker tail at moderate-to-long distances, and a slightly more rapid drop off toward zero at large distances, compared to the exponential. However, these disadvantages are small in comparison to the computational benefits of the Gaussian approach.

The positions of adults of a species combine with dispersal distances to produce variation in seed density among grid cells that differs among species. For example, the high seed production and wide dispersal of Betula alleghaniensis (Figure 5) results in a high and spatially rather uniform seed density among grid cells. However, Fagus grandifolia trees produce fewer seeds, which disperse only short distances from the parent, resulting (Figure 6) in lower seed density, but with pronounced variation in density from cell to cell.

Figure 5. Seed abundances of Betula alleghaniensis seeds in a small subsection (25 m x 25 m) of a simulated forest. Note both the abundance and relative homogeneity of seed abundance of this widely-dispersing and very fecund species compared to the more locally-dispersed species in the next figure.

Figure 6. Seed abundances of Fagus grandifolia seeds in a small subsection (25 m x 25 m) of a simulated forest. For this species with more restricted dispersal distances, there is much greater heterogeneity in seed abundance from cell to cell, and the influence of individual parent trees can be clearly seen; in this particular case, several Fagus parents happened (by chance) to have been aligned just above 5 m on the x axis, and the "ridge" of seed abundances near 5m x values reflects those locations.

Seeds are dispersed individually for trees producing < 20,000 seeds, in pairs for trees producing 20,000 to 30,000 seeds, and so on, up to dispersal in groups of 10 seeds for trees producing > 100,000 seeds. This is a compromise with the computational burden of this step, which is the time-consuming function within the simulation, and needs to be done for each living tree before the disturbance, and for each surviving tree for a given number of years after the disturbance. The number of seeds of each of the canopy tree species in each cell is written, for selected cells, to an output file called "seedout.dat".

VI. The disturbance event

Wind disturbance occurs in BLOWDOWN by simulating realistic treefalls of the trees in the sapling/tree array. When the main program calls the "disturb" function, the function runs through the tree array, and for each individual within the disturbed area, calculates a probability of treefall (Figure 2). The user chooses the number and size of gaps to be created in the simulation. If multiple gaps are chosen (Figure 1) they are all the same user-chosen radius (in m), and area randomly positioned within the simulated area such that none are closer than 15 m to the edges of the simulated stand boundaries. If a single gap is chosen, it is positioned in the exact center of the simulated stand area. All trees are examined to determine if they are within the gap(s), by calculating distance from the gap center to that tree:

Dist[g,t] = ((xg - xt)[^2] + (yg - yt)[^2])[^1/2]

where g = center of gap, and t = position of focal tree. If the distance is less than the user-chosen gap radius, then the focal tree is considered within the gap, and vulnerable to treefall.

Probability of treefall is determined from that tree's size and species, based on logistic regression parameters from one of three sources: 1) the 1985 Tionesta tornado blowdown (386 ha in the preserve alone); 2) the 1994 Tionesta tornado blowdown (2 ha in the preserve about 3 km south of the 1985 swath); or 3) the 1989 Cathedral Pines (CT) Nature Conservancy Preserve tornado blowdown (8 ha). For each of these three cases, logistic regressions have been fit to observed stand vs. fall responses of numerous trees of several species, resulting in best-fit parameter values of a and b (see below) for the common species. Other parameterizations need to be implemented soon. Severity of disturbance is not explicitly stated by the user, because the logistic treefall-risk relationships embody the severity aspect of the disturbance: using different treefall-risk parameters results in different severity of disturbance. As with the fecundity parameters, species-specific values for the treefall-risk logistics are used when available, otherwise a given tree's risk is calculated from an across-species average, as follows:

logiti,j = aj + bj*dbhi,j

Riski,j = 1.0 - e[^logit] / (1 + e[^logit])

where i = sapling/tree individual; j = species; e = base of natural logarithms; and dbh = tree trunk diameter in cm at 1.4m height. This is the typical logistic relationship between a binary response variable (in this case, stand or fall) and a continuous predictor variable (in this case, tree size as measured by dbh). After the risk is calculated for a given tree, a random number between 0 and 1 is chosen, and if the risk is greater than the random number, then the tree is declared fallen. Since in the limit many truly random numbers between 0 and 1 will average 0.5, this effectively allows stochasticity in the treefall function, while maintaining the desired pattern that trees with a treefall risk > 0.5 will usually fall (Figure 2).

Whether a tree suffers trunk breakage or uprooting has important consequences for the creation of microsites in the post-disturbance landscape, so the type of treefall is determined by assigning each tree about to fall, a probability for breakage or uprooting, based on size and species. These probabilities are simply the empirically-observed probabilities from my research in the blowdown at the Tioenesta Scenic Area tornado blowdown of May 1985. Probabilities differ for each 10-cm dbh size class. At Tionesta, the majority of fallen trees uprooted (roughly 66%), and this trend was most pronounced in intermediate size classes, so the simulation break/uproot function reflects the same pattern. For each falling tree, a random number is chosen and compared to the probability of uprooting for that 10-cm size class; if the probability is greater than the random number, then the falling tree is declared uprooted, otherwise it is declared trunk broken.

In nature when a tree falls, regardless of the type of fall, the trunk and crown land on and cover areas of the ground, and this forms crown and trunk microsites. In the simulation, each potentially-covered grid cells is examined for its location, and if the center of the grid cell is covered by the fallen tree trunk or crown, then the cell is declared "trunk" or "crown" microsite. Figure 7 illustrates a subarea around a large gap, showing cells covered by tree crowns (green) and trunks (black), as well as the original rooted locations of the fallen trees. Tree crowns are currently considered to be spherical, and when on the ground, the trunk is simply a long, narrow rectangle from the base to the crown (no taper built in to simulation yet). Cells declared "trunk" are given a relative elevation of 2. Original location, dbh, species, and type of fall for each fallen tree is written to an output file called "treefall.dat". Currently, fallen trees fall in random directions; future program enhancements will incorporate trees falling in the same approximate direction.

Figure 7. Here the microsites created on the ground by treefalls in a gap are illustrated, without canopy circumstances shown. This gap was created in a simulation consisting of 5 species of trees, with complete treefall in the gap area, although lesser severities in the affected (gap) area can be specified. The open circles, squares, up-triangles, and down-triangles indicate the original rooted locations of trees of the five species within the gap area (trees of the surrounding intact forest are not shown, for clarity). Trunks of fallen trees are shown in black, and crowns of fallen trees are shown in green. Trunk and crown sizes are proportional to tree size (dbh), based on empirical relationships. Pits and mounds of uprooted trees are red and blue, respectively, and are proportional to the size of the fallen tree. In this simulation, direction of treefall was random.

If the fallen tree is declared trunk broken, the cell containing the tree's pre-disturbance standing location is declared "stump" microsite if the tree is > 35 cm dbh. The x,y coordinate and the microsite type ("stump") for each stump cell is written to an output file called "stump.dat".

If the fallen tree uproots, a treefall pit and mound are created (Figure 7). The pits and mounds are offset (0.5 - 1.5 m depending on size of the tree) from the point of origin where the tree originally was standing, the mound in the direction of treefall, and the pit away from the direction of treefall. These microsites are modeled as ellipses, whose size is determined from the dbh of the uprooted tree. Pit and mound dimensions are derived from my empirical findings of the relationship between tree dbh and pit or mound length and width in the 1985 Tionesta blowdown (see, e.g. Peterson & Pickett 1991 Forest Ecology & Management). Working out from the center point in the pit or mound, each cell less than the distance of the predicted radius from the central point, is declared of that microsite type. Figure 7 shows the cells that comprise pits (red) and mounds (blue) at the bases of fallen trees. All vegetation growing in the cells that are declared pit or mound is removed. Pit cells are assigned a local relative elevation of -2, and mounds are assigned relative elevation of 3. The cell x,y coordinates for all cells declared to be of each type are written to a series of output files (trunkout.dat, crownout.dat, moundout.dat, pitout.dat), which simply contain the coordinates and the microsite type of the cells.

After the disturbance, canopy openness is calculated, for each grid cell, as:

Openness = cellsopen / cellstot

where cellsopen is the number of cells within 7.5 m of the focal cell that have no canopy directly over them, and cellstot is the total number of cells within 7.5 m of the focal cell. Effectively, this is the proportion of area within 7.5 m of the focal cell that has no canopy directly overhead, and takes on values between 0 and 1.0, with 960 possible values. Figure 8 shows openness values (blue) for cells in a single gap, in this case without showing locations of surrounding trees. Openness values for each cell are written to an output file called "openness.dat".

Figure 8. This figure illustrates the amount of canopy openness for each cell in and around a 10 m radius gap. Openness is shown in blue for each cell, ranging from 0 to 1.0. The values peak in the center of the gap because in a sufficiently large gap, the cells in the center of the gap are > 7.5 m from any intact canopy and thus reach openness values of unity.

VII. Post-disturbance processes

Once the disturbance is accomplished and microsites created, there is another round of seed production and dispersal by the surviving trees (these would be mostly outside of the gap if a high-severity blowdown is simulated using the Tionesta 1985 or Cathedral Pines 1989 logistic parameters for treefall risk), conducted the same as before the disturbance but using only surviving trees. Consequently, gaps often have greater density of seeds around the periphery (Figure 9), where distance to surviving/standing trees is small.

Figure 9. Seed abundances per cell, for a simulation using 500 trees in a 100 x 100 m simulated area, with 5 gaps each 15.2 m in diameter. Trees arbitrarily dispersed 500 seeds each, with a decay beta of -0.30. Note that with a few exceptions, seed abundances were greatest around the edges of gaps -- closer to surviving intact canopy trees. In more realistic circumstances with trees producing several orders of magnitude more seeds, per-cell seed abundances could be much higher. Where the decay in dispersal with distance is less than this, more seeds will reach the interior of gaps and the gap edge-to-interior difference will be reduced.

Seeds germinate based on inherent species characteristics and the ambient conditions within the grid cell where the seed is located. For a given grid cell, the number of germinants of a given species is the product of the number of seeds of that species present in the cell, a random cell-variation factor, canopy openness, seed viability, herbaceous species cover, species shade tolerance, and the identity of the microsite for that cell, as follows:

New seedlingsj = seednumj * inherentj * modifiermicro * opennessi * compherb

where j = species, i = focal cell, seednumj = number of seeds of species j in the focal cell, inherentj = proportion of dispersed seeds still viable for species j ; modifiermicro = germination modifiers specific to various microsite types, opennessi is a value from 0 to 1.0 as described previously, and compherb is a value from 0 to 1.0 as described previously. Each cell is assigned to be one of several microsite types (intact, crown, mound, pit, stump, trunk, stump), which are arbitrarily assigned inherent germination probabilities of 1.0, 0.2, 1.0, 0.1, 0.9, and 0.1. Species- specific values of typical seed viability are derived from the 2-year average seed viability found by Houle (1994, Journal of Ecology), for Betula alleghaniensis, Acer rubrum, Acer saccharum, and Fagus grandifolia; other species' values are the average across these values.

After the first post-disturbance year, information on the newly-germinated seedlings is written to the output file "freshsdl.dat". All of the above factors can interact to influence the density and composition of new seedlings colonizing the disturbed area. Figures 10 and 11 show, for a small subarea, the effect presence or absence of herbaceous plants on the proportion of newly- germinated seedlings that are pioneer species. Note that when herbaceous cover is removed in the simulation (reducing shading), light-demanding pioneers make up a much larger proportion of the new seedlings (Figure 11), showing the influence on future forest composition of only one of multiple factors that influence events soon after disturbance.

Figure 10. Here we see the first of two figures illustrating variation in the proportion of new, post-disturbance, seedlings that are of pioneer species, vs intermediate or late-successional species. In this figure we see the results of a simulation in which a 25 m radius gap was formed, centered on the x,y coordinates of 100, 100. The figure shows only cells from the center of the gap. In this run of the simulation, time was initiated with an existing seed bank of 50 seeds per cell, microsites were considered in calculating germination probabilities, and a uniform cover of 10% by herbaceous species was established. The result was a rather low relative abundance of pioneer species among the new seedlings that established in the first year after disturbance.

Figure 11. This figure is identical to Figure 10, except that the simulation was run with no cover by herbaceous species. As a result, pioneer species make up a much larger proportion of the cohort of new tree seedlings establishing in the first year after disturbance.

Newly-germinated seedlings grow and experience mortality during the years after disturbance. Mortality is a stochastic probability calculated from species-specific overal survival rates, seedling density (crowding) in that cell, and the cell openness, using the formula:

Probability of survival = cellprobi * inherent survivalj * crowdingi * opennessi

where i = grid cell, j = species, cell probability varies stochastically from 0.9 and 1.1, and openness ranges from 0.0 to 1.0.

Growth is calculated as the product of density of other seedlings in the cell, shade tolerance, the species' inherent maximal relative growth rate, and competition from herbaceous species (if the seedling is < 75 cm tall), as follows:

Height i,t+1 = Height i,t * ratej * compsdl * compherb

where i = focal seedling, j = species, t+1 = this year, t = last year, ratej = species' j inherent maximal relative growth rate, compsdl = interference from other seedlings, and compherb = interference from herbaceous species. Herbaceous competition is simply the inverse of percent cover of herbs in this cell, and is not included if the focal seedling is > 0.75 m tall. Competition from other seedlings is calculated as:

compsdl = 1 - (total seedling density in cell * tolerancej * 0.005)

where tolerancej = species' j ability to grow under shading vegetation. It is based approximately on values published by Canham et al. (Canadian Journal of Forest Research 1994 24: 337-349) for fitted probabilities of mortality in five years for 2 cm dbh saplings at 0.5% of full sun light levels. Species for which they published values were: Acer rubrum, Acer saccharum, Betula alleghaniensis, Fagus grandifolia, Fraxinus americana, Pinus strobus, Prunus serotina, Quercus rubra, and Tsuga canadensis.

After each year, the status (alive or dead) and height (in cm) of the seedlings of each species per grid cell is updated. After all the simulated years have concluded, the information on relative proportions of pioneer, mid-seral, and climax spp seedlings per cell is written to the output file "finalsdl.dat".

When seedlings reach a certain size (typically 3-4 m height), they are assigned their own beginning dbh (2 cm) and x,y coordinates somewhere within the boundary of the cell in which they originated; size, species, and coordinates for each newly-"promoted" sapling are then added to the sapling/tree array. They are then removed from the collection of seedlings for that grid cell.

VIII. Output

Upon execution of the program, several output files are generated, and written as text files to the default hard drive directory. These output files and their contents are:

freshsdl.dat -- relative abundances of three categories (pioneer, mid-seral, and climax) of species of new post-disturbance seedlings, for each of a selected number of grid cells in the center of (one of) the disturbed area(s). finalsdl.dat -- similar to freshsdl, but contains seedlings surviving to the end of the post- disturbance period (x years) simulated.

seedout.dat -- density of seeds of each tree species present in each grid cell in selected area (typically the center of one of the disturbed areas).

prestat.dat -- pre-disturbance characteristics of selected grid cells.

openness.dat -- x,y and % canopy openness for grid cells in disturbed areas.

crownout.dat -- x,y of grid cells that are covered by fallen tree crowns (post- disturbance).

moundout.dat -- x,y of grid cells that are treefall mounds (post-disturbance).

pitout.dat -- x,y of grid cells that are treefall pits (post-disturbance).

trunkout.dat -- x,y of grid cells covered by fallen trunks (post-disturbance).

early.dat -- pre-disturbance location, size and species of sapling/tree array members.

treefall.dat -- post-disturbance tree info, including type and direction of fall.

IX. Usefulness

The BLOWDOWN simulation should prove very valuable for formulating testable hypotheses of how forest disturbance and recovery patterns should really occur in nature. With accurate parameters, it will allow users to vary numerous aspects of the forest composition, size structure and density, severity and size of disturbance, and fecundity and availability of propagules. It is likely that these characteristics of the trees, the forest, and the disturbance event have profound influence on the subsequent composition and dynamics of forest regeneration, and the output of BLOWDOWN can make predictions of the consequences of changing any of the above characteristics. Because most forests experience disturbances and undergo subsequent recovery at various temporal and spatial scales, BLOWDOWN should offer valuable insight and facilitate increased understanding of these important ecosystems.