Appendix. Structure of the spatially explicit model.
Impact of Water Depth on Demographic Processes
We incorporated effects of water depth on species performance in two ways. In the simplest case, seeds could germinate only in cells without standing water because even shallow flooding inhibits the germination of most emergent plant species (van der Valk and Davis 1978, Seabloom et al. 1998). The effects of water depth on other demographic traits were linked to species-specific, water-depth response curves. These curves were made by scaling the logistic regression curves used in the niche model so that the maximum value was set equal to 1.0 (Fig. 3). These water-depth response curves represent realized niches rather than strict physiological responses and represent the long-term (20 years) competitive outcome of the interactions among species with different tolerances for flooding along a stable water-depth gradient.
The curves were used to determine the demographic response of a species in a grid cell as a function of water depth (see below). This was done using Monte Carlo techniques; i.e., a random number, varying uniformly from 0.0 to 1.0, was drawn and compared to the value of the water-depth response curve (which ranged from 0.0 to 1.0) corresponding to the depth of the water in the cell. The demographic response then depended upon whether the height of the response curve was less than or equal to or greater than the random number. From a biological perspective, species in the model had an annual survivorship of 1.0 at the water depth where they were most common in the MERP wetlands prior to the experiment and a survivorship less than 1.0 elsewhere.
We could not calculate water-depth response curves directly for either S. validus or Mudflat Annuals, because they were very rare at the start of the Delta Marsh experiment. For Mudflat Annuals, this was a trivial problem. In the simulations, seeds only germinate in unflooded areas, and adult annuals die before water levels change. On the other hand, it was critical to estimate a water-depth response curve for S. validus. To do this, we assigned S. validus the same response as Scolochloa, because both species are similarly intolerant of flooding. S. validus stands cannot persist in permanently flooded conditions for longer than 1 or 2 years (van der Valk and Davis 1980), and Scolochloa is rarely found in permanently flooded conditions (Fig. 3).
Model Initialization
The initial distribution of adults in each simulation was determined in one of two ways. For the simplest models, the logistic regressions (Eq. 2) were used to predict species distributions as in the niche model. Alternately, the model was initialized to have the same distribution of dominant plant species as the Delta Marsh experimental wetlands during 1980. For either initial distribution, the dominant species in a cell was capable of spreading rhizomatously, if water depth was shallower than the species optimum. However, if water depth exceeded the species' optimum in the cell, the probability that the species could spread rhizomatously was equal to the height of the water-depth response curve for that depth. The actual reproductive state was set using Monte Carlo techniques, as described above.
For model runs that did not incorporate seed or seedling density data, all species in the seed bank were set to have a density equal to the average total density divided by the number of species (1,995 seeds*m-2*species-1). For the model runs that incorporated seed and seedling distributions, we used parameter estimates obtained from three sources: Pederson (1983) and Welling (1987) for annuals and van der Valk and Welling (1988) for perennials. Each of these sources presents mean density of seeds or seedlings by species at 0.1 m elevation intervals. We fit quadratic linear regressions to the log10(x + 1) transformed seed and seedling densities and used the resulting models to predict seed density as a function of elevation (Fig. 2). During the initialization, the variability in density at a fixed water depth was modeled by adding a normal deviate with a zero mean and a variance equal to the mean squared error of the regression.
Dynamic Behavior
After initialization, the state of cells in the spatial model was changed using the following ordered set of rules applied once for each year of the MERP experiment:
Set Water Depth
Water depth for each model wetland was set to the depth occurring in the corresponding experimental MERP wetland for the same time period.
Rhizomatous Dispersal
We modeled rhizomatous dispersal as occurring prior to seed germination, because seedlings are generally unsuccessful in competition with clonal growth from already established plants (Crawley and May 1987).
Rule 1: Only cells unoccupied by a dominant adult species could be colonized through rhizomatous spread.
Rule 2: Rhizomatous spread into an unoccupied cell could only occur from eight neighboring cells.
Rule 3: Adult stands could spread rhizomatously only if they were in a reproductive state and were composed of a species capable of rhizomatous dispersal. Determination of whether a stand was reproductive or dormant was made either at the time of model initialization (see above) or in the prior time step, using rules described under Flooding Damage (see below).
Rule 4: Successful colonization of an unoccupied cell through rhizomatous spread from an adjacent cell was determined as follows:
4a) Determine which of the neighboring cells meet criteria in Rule 3.
4b) Select the cell from which colonization might occur by random draw, weighting the probability of invasion by the heights of the water-depth response curves for the potential colonizers at the water depth occurring in the unoccupied cell.
4c) Determine if the species selected in 4b successfully colonizes the empty cell by using a random draw weighted so that species growing at a non-optimal water depth will have less capacity to spread into an empty cell than those growing near the water depth where they occurred most frequently. Specifically, the probability that the species chosen in (4b) colonizes the cell is either proportional to the height of the water depth response curve, for model runs incorporating a fast rate of spread, or to one-third the height of the curve, for models incorporating a slow rate of spread. The fast growth rate corresponds to rates of spread determined for Typha (Yeo 1964), and all rhizomatous species were assigned this growth rate due to a lack of species-specific data.
4d) If colonization is successful the empty cell is now occupied, and if it is unsuccessful, the cell remains unvegetated.
Seed Germination
Rule 1: Germination only occurs in cells with no standing water, because standing water greatly inhibits germination of most emergent plants (Seabloom 1997).
Rule 2: Germination only occurs in cells currently unoccupied by living plants and litter, because litter and living plants greatly inhibit germination in wetland plants (van der Valk 1986).
Rule 3: In cells where germination is allowed, a fixed proportion (0.1) of each species' seeds in the seed bank germinate.
Seedling Competition
Rule 1: In cells with germinating seedlings, one species grows to dominate a cell. The successful species is chosen by a random draw of all germinated seedlings in a cell. This rule ensures that the species with the largest number of seedlings has the highest probability of being chosen to dominate the cell.
Flooding Damage
Rule 1: Flooding damage occurs in a cell under two circumstances: (1) water depth in the cell is greater than the depth associated with optimal performance of the dominant species, as determined from its water-depth response curve; and (2) a random number between 0.0 and 1.0 is greater than or equal to the height of the water depth curve for the dominant species at the water depth found in the cell. The upper areas of wetlands are mesic and water depth only limits species distributions when it is excessively deep (Seabloom 1997).
Rule 2: Flooding damage will make a reproductive stand dormant.
Rule 3: Flooding damage will kill a dormant stand. Studies show that emergent plants are killed only after two full years of flooding (Squires and van der Valk 1992).
Rule 4: Dormant stands unaffected by flooding damage are returned to a reproductive state.
Mortality of Annuals
Rule 1: All annuals die at the end of each annual time step.
Model Output
Vegetation maps used in subsequent analyses were exported each year of the model run prior to implementation of flooding damage rules. Each cell of the exported map was occupied by a dominant plant species or was empty. However, for water depths greater than 70 cm, the cell was listed as empty in output maps to be more consistent with maps derived from field collected data. The ability of emergent species to produce leaves above water declines rapidly at water depths greater than 70 cm (Squires and van der Valk 1992), and as a consequence maps of vegetation from field data show empty cells for areas of a wetland under deep water even though live plants may be present. In contrast, model simulations predict the presence of a stand of live plants, regardless of whether the stand would be visible on an aerial photograph. For this reason, the models would appear to overestimate vegetative cover in deeply flooded areas if we did not adjust the output to account for this bias in the field data.
Crawley, M. J., and R. M. May. 1987. Population dynamics and plant community structure: competition between annuals and perennials. Journal of Theoretical Biology 125:475-489.
Pederson, R. L. 1983. Abundance, distribution, and diversity of buried seed populations in the Delta Marsh, Manitoba, Canada. Dissertation. Iowa State University, Ames, Iowa.
Seabloom, E. W. 1997. Vegetation dynamics in prairie wetlands. Dissertation. Iowa State University, Ames, Iowa.
Seabloom, E. W., A. G. van der Valk, and K. A. Moloney. 1998. The role of water depth and soil temperature in determining initial composition of prairie wetland coenoclines. Plant Ecology 138:203-216.
Squires, L., and A. G. van der Valk. 1992. Water-depth tolerances of the dominant emergent macrophytes of the Delta Marsh, Manitoba. Canadian Journal of Botany 70:1860-1867.
van der Valk, A. G. 1986. The impact of litter and annual plants on recruitment from the seed bank of a lacustrine wetland. Aquatic Botany 24:13-26.
van der Valk, A. G., and C. B. Davis. 1978. The role of seed banks in the vegetation dynamics of prairie glacial marshes. Ecology 59:322-335.
van der Valk, A. G., and C. B. Davis. 1980. The impact of a natural drawdown on the growth of four emergent species in a prairie glacial marsh. Aquatic Botany 9:301-322.
van der Valk, A. G., and C. H. Welling. 1988. The development of zonation in freshwater wetlands: an experimental approach. Pages 145-158 in H. J. During, M. J. A. Werger, and J. H. Willems, editors. Diversity and pattern in plant communities. Academic Publishing. The Hague, The Netherlands.
Welling, C. H. 1987. Reestablishment of perennial emergent macrophytes during a drawdown in a lacustrine marsh. Thesis. Iowa State University, Ames, Iowa.
Yeo, R. R. 1964. Life history of the common cattail. Weeds 12:284-288.