T. Scott Rupp
This paper integrates two mathematical dispersal models into a GIS and outlines the initial development of a spatially explicit model for white spruce seed dispersal in interior Alaska. Integration of models revealed several benefits of modeling with a GIS. These benefits include simulation of dispersal upon a defined landscape unit, the ability to describe the effects of source shape upon dispersal patterns, simulation of the natural variation in seed density, and the application of dispersal simulations to aid resource managers with silvicultural decisions. Development of a spatially explicit model for interior Alaska demonstrates the potential for simulating the effects of seed crop periodicity and the use of a wind friction parameter to describe the influence of wind upon general dispersal patterns. The lack of data for interior Alaska is a major limitation to the modeling effort. This model is still under development, but at the very least demonstrates the potential of a GIS for environmental modeling of spatially explicit processes such as seed dispersal.
Understanding the controls upon landscape-level vegetation patterns is crucial to successful ecosystem management. An in-depth knowledge of regeneration dynamics is a prerequisite to such an understanding. Seed dispersal patterns are a critical factor affecting colonization patterns. These patterns directly influence subsequent processes within the regeneration phase. Therefore, a spatially explicit understanding of dispersal will help our understanding of controls upon these landscape patterns.
The landscape of interior Alaska is characterized by a mosaic of forest types. The fire history of the last 200 years is closely related to this vegetation mosaic (Viereck 1973). Recolonization of a burned site depends on several factors including the availability of seeds from adjacent communities (Zasada et al. 1983). The ability to model dispersal patterns upon the landscape would improve our knowledge of boreal forest regeneration dynamics and provide land managers with a useful management tool.
Improved understanding of seed dispersal mechanics would be a great benefit to the land manager. Past studies have sought to mechanistically model the dispersal process by identifying parameters such as height of release, settling velocity, wind speed and turbulence, and seed structure (Greene and Johnson 1989 and 1995, Okubo and Levin 1989, and Sharpe and Fields 1982). The advantage of such models are the ability to apply the model to any species or situation. This approach differs from the traditional area specific physical parameters of numbers of seed and distance from the source which must be measured for each specific situation (Okubo and Levin 1989). Mechanistic models of point source dispersion have been developed and show promise, but area source models have yet to be developed at a practical level useful to the land manager.
Traditional modeling studies of seed dispersal for most tree species have been largely restricted to mathematical expressions of seed dispersed, as a function of distance from the source, into a spatially undefined clearcut opening. Studies involving seed traps in clearcuts have been conducted by researchers for decades. Dobbs (1976) and Youngblood and Max (1992) investigated seed dispersal of white spruce. These studies have provided valuable information on seed production, dispersal distances, and subsequent seedling densities. Although these studies describe seed dispersal they lack the ability to be applied to a spatially defined landscape.
Geographic information systems (GIS) offer the ability for simulating general seed dispersal patterns upon a spatially defined landscape. This approach allows for simulation of variability in seed numbers at a given distance, effects of wind upon seed distribution, and influences of seed source shape. Although such a model is not as powerful and robust as the above mentioned mechanistic approach, it does provide a silvicultural management tool of an applied nature for the resource manager.
Our goal is to model regeneration of interior Alaska white spruce forests, solely within a GIS. The regeneration routine is being developed for integration into a GIS based forest ecosystem model. This paper describes the initial subroutine development of seed dispersal. The development process began by integrating previous models into a GIS. This integration effort was utilized to investigate the potential advantages of modeling within a GIS. The actual subroutine development of white spruce seed dispersal in interior Alaska is ongoing. The dispersal routine will model seedcrop periodicity and the subsequent dispersal patterns from the seed source into a post-disturbance clearing.
The dispersal distance of seeds into a clearcut is an important factor in the ability of natural regeneration to provide adequate restocking levels. Informed decisions regarding clearcut size, seedbed preparation, and whether or not to regenerate artificially depend on having a good measure of seed dispersal densities (Dobbs 1976). Integrating dispersal equations of previous white spruce seedfall studies into a GIS can provide more detailed information for such decisions. Two different dispersal equations were used to investigate the benefits of modeling dispersal on a GIS. The model was developed as an ARC/INFO arc macro language (AML) routine within the GRID package.
Our initial code used Dobbs (1976) quadratic equation for white spruce seed dispersal in central British Columbia. The objective was to disperse seeds on a defined landscape unit and simulate seedfall differences associated with various source shapes.
Dispersal of seed upon a defined landscape provides specific information about a physical location. The AML inputs a grid identifying the source cells. The euclidean distance of each cell to the closest source cell is then determined. The distance grid is then applied to the dispersal equation from which an output grid defines seed numbers for each cell. Describing the source shape allows for simulation of dispersal patterns specific to the seed source (Figure 1). This model provides information about seed density upon a defined landscape unit and the effects of source shape which the original equation of Dobbs (1976) cannot provide.
Dispersal of interior Alaska white spruce seed was also integrated. The negative exponential equation, of Youngblood and Max (1992), for floodplain white spruce seed dispersal in interior Alaska was utilized. The objectives were to simulate seed density variance at a given distance and to provide information which can be utilized by the resource manager to assist in silvicultural decisions.
The ability to describe seed density variance upon the landscape provides another layer of information. Using the original data set, the variance in seed numbers as a function of distance was calculated. Within a given distance seed was dispersed upon the cells by applying a normal distribution with the model mean and standard deviation associated with that distance interval (Figure 2).
The above information, coupled with information on seed to germinant ratios and stocking requirements, would allow the manger to obtain a visual model of potential natural regeneration following a harvest of given size and shape. Using information from Zasada (1971) a 24:1 seed to germinant ratio was applied to create a grid of successful germinants for each cell. Full stocking was assumed to represent 2500 trees/ha (Cleary et al. 1978). A stocking grid was then created to identify four stocking levels as defined by Reynolds et al. (1953). Stocking regions are developed through the use of several focal functions. Analyzing neighboring cells by calculating mean values and using majority grouping allows for a description of generalized stocking patterns. The output grids allow for the analysis of potential stocking following a harvest (Figure 3). This model provides a more detailed and realistic description of dispersal upon the landscape than the original model of Youngblood and Max (1992) and provides information that can be applied by the resource manager in silvicultural decisions.
Integration of seed dispersal equations into a GIS allows for modeling on a spatially defined landscape. The dispersal routine simulates both the periodic nature of seed production and the subsequent dispersal of the seedcrop. The work of Youngblood and Max (1992) is being incorporated with current field study work to model seedfall patterns as a function of seedcrop quality, distance from the source stand, and wind direction.
White spruce cone crops are periodic in nature, being influenced heavily by annual temperature and precipitation regimes (Zasada 1971). Cone crop periodicity is modeled with a Monte Carlo simulation technique following the work of Fox et al. (1984). The subroutine simulates the probabilistic nature of white spruce cone crops. The seed crop is classified as either good-excellent or poor-moderate. A probability of 0.25 for a good-excellent seed year was projected (Zasada and Viereck 1970 and Zasada 1980). Furthermore, successive good-excellent seed years do not occur and the interval between them is irregular (Zasada 1971, 1980). This periodic nature has a big impact on potential stocking levels. Seed densities associated with cone crops were estimated based on limited data available (Zasada and Viereck 1970). The AML subroutine used scalars and the random number function to simulate seed crop quality. Seed density is then calculated from the best estimated mean and standard deviation for that cone crop rating. This variable is then input into the dispersal AML. By determining seed density ranges associated with the two quality classes, cone crop influences on dispersal density and associated stocking levels can be described (Figure 4).
Winds influence general dispersal patterns. Most studies have implicitly modeled this influence by deploying seed traps from the windward edge into the clearing in the direction of the prevailing winds. The ability to model wind influences in a simplistic manner would benefit the resource manager. This model attempts to use a wind friction parameter to describe the negative influence upon general dispersal in non- windward directions. The parameter reduces the distance and associated density of seeds dispersing in directions from the source other than that of the defined wind direction. This parameter allows for the potential simulation of wind patterns upon general seed dispersal patterns. The development of a wind friction parameter is ongoing and much of the field work portion has yet to be completed.
This first generation dispersal subroutine for interior Alaska white spruce is still in a developmental stage. Due to the relative lack of data much field work must be completed before the dispersal routine can be finished and tested.
The ability to apply a model upon a defined landscape unit is an improvement over most modeling efforts which work within an undefined landscape. Current GIS packages, such as ARC/INFO, have many functions and utilities that lend itself to developing simple AML's that can model certain biological processes upon a given landscape. This paper provides such an example. Integration of prior seed dispersal models demonstrates the advantages of modeling in a GIS and the model development shows the potential for development of a silvicultural tool easily applied by the resource manager to aid in decision making.
Integration of mathematical models of white spruce seed dispersal into a GIS was relatively easy. The modeling effort provided information about the dispersal process beyond that of the original mathematical models. The most identifiable advantage is the ability to disperse seeds upon a specific landscape unit and provide information about a physical location. This point is further demonstrated by the ability to describe source shape and its influence upon dispersal patterns. Providing dispersal distributions associated with seed number deviations at a given distance interval relates a more realistic view of the dispersal process. Utilizing all this information, along with stocking level information, demonstrates the potential for use as a silvicultural tool by the resource manager. Information on disturbance size and shape and possible stocking levels could help in the development of specific harvesting schemes and decisions.
The seed dispersal routine for interior Alaska incorporates seed crop periodicity, providing description of another important factor in the seedfall dynamics of white spruce. Modeling the influence of winds upon dispersal patterns will further benefit the resource manager. Application of a wind friction parameter can help describe seedfall patterns and help in the creation of harvesting schemes and making silvicultural decisions about stocking levels. The lack of seedfall data sets for Alaska white spruce is a major limitation. Data acquisition will provide for further model development and testing.
This paper provides an idea of the potential of a GIS for modeling biological processes upon the landscape and for use of such models by the resource manager to aid in decision making. Benefits of modeling with a GIS include the ability to simulate biological processes upon a defined landscape unit, provide for natural variation across the landscape, and provide simulations for decision making purposes.
Influence of source geometry upon dispersal patterns. Seed density is displayed as a surface upon the landscape. Areas of greatest elevation identify the source. Dispersal AML uses equation from Dobbs (1976).
Output grids of dispersal AML using the equation of Youngblood and Max (1992). Colors represent the percent values of filled seed dispersed at a given distance from that dispersed within the source. A) Output grid from negative exponential model. B) Output grid showing density variance within a given distance interval.
Output grid cell color values represent stocking levels (Blue = good, Green = medium, Red = poor, White = nonstocked). A) Initial stocking grid calculated from successful germinants. B) General stocking regions as determined by focal functions application.
Stocking regions for different seed crop classifications. Simulates the effects of cone crop periodicity upon regeneration. A) General stocking regions resulting from a poor-moderate cone crop. B) Stocking regions resulting from a good-excellent cone crop.
Cleary, B.D., Greaves, R.D., and Hermann, R.K. (1978) Regenerating Oregon's forests. Oregon State Univ., Ext. Serv., Corvallis, OR.
Dobbs, R.C. (1976) White spruce seed dispersal in central British Colombia. For. Chron. 52: 225-228.
Fox, J.D., Zasada, J.C., Gasbarro, A.F., and Van Veldhuizen, R. (1984) Monte Carlo simulation of white spruce regeneration after logging in interior Alaska. Can. J. For. Res. 14: 617-622.
Greene, D.F., and Johnson, E.A. (1989) A model of wind dispersal of winged or plumed seeds. Ecology. 70: 339-347.
Greene, D.F., and Johnson, E.A. (1995) Long-distance wind dispersal of tree seeds. Can. J. Bot. 73: 1036-1045.
Okubo, A., and Levin, S.A. (1989) A theoretical framework for data analysis of wind dispersal of seeds and pollen. Ecology. 70: 329-338.
Reynolds, C., Jeffers, N., Borisquet, V., and Stien, R. (195 3) Reforestation surveys. Chapter VII. In Reports of the Pacific Northwest seeding and planting committee on various recommended reforestation practices and techniques. pp. 61- 69.
Sharpe, D.M., and Fields, D.E. (1982) Integrating the effects of climate and seed fall velocities on seed dispersal by wind: a model and application. Ecol. Mono. 17: 297-310.
Youngblood, A., and Max, T.A. (1992) Dispersal of white spruce seed on Willow Island in interior Alaska. Res. Pap. PNW-RP-443. Portland, OR. USDA For. Serv., Pacific Northwest Res. Sta.
Viereck, L.A. (1973) Wildfire in the taiga of Alaska. Quatern. Res. 3: 465-495.
Zasada, J.C., and Viereck, L.A. (1970) White spruce cone and seed production in interior Alaska, 1957-1968. USDA For. Serv. Res. Note PNW-129, Pac. Northwest For. Range Exp. Stn., Portland, OR.
Zasada, J.C. (1971) Natural regeneration of interior Alaska forests - seed, seedbed, and vegetative reproduction considerations. In Fire in the northern environment, a Symposium. Pac. Northwest For. Range Exp. Stn., Portland, OR. pp. 231-246.
Zasada, J.C. (1980) Some considerations in the natural regeneration of white spruce in interior Alaska. In Forest regeneration at high latitudes. Proceedings of an International Workshop. USDA For. Serv. Gen. Tech. Rep. PNW-107, Pac. Northwest For. Range Exp. Stn., Portland, OR. pp. 25-29.
Zasada, J.C., Norum, R.A., Van Veldhuizen, R.M., and Teutsch, C.E. (1983) Artificial regeneration of trees and tall shrubs in experimentally burned upland black spruce/feather moss stands in Alaska. Can. J. For. Res. 13: 903-913.