MODELING FOREST SUCCESSION

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1 MODELING FOREST SUCCESSION Steven K. Rice Dept. of Biological Sciences Union College Schenectady, NY Notice: The author retains all rights to this document. The exercise or portions of it may be copied and used for educational purposes as long as it is distributed free of charge and author is acknowledged. If you would like a WORD version of this exercise, please write to the author at rices@union.edu. Forest Succession Forest succession can be modeled using a simple approach that considers succession as a tree by tree replacement process. Each canopy individual will be succeeded by a sapling. The chance of this happening on average throughout the forest can be modeled by calculating transition probabilities. These probabilities can be estimated by the relative densities of saplings of different species present below each canopy species. If one assumes that the transition properties can be estimated based on knowledge of the present observed state and that these do not change with time, then the future steady-state composition of the forest can be predicted (i.e., it is characterized as a stationary Markov chain). You collect data that will allow you to calculate transition probabilities and use them to parameterize a STELLA model to predict successional change within the two forest types. Data Collection and Analysis 1. You will collect information on tree and sapling composition by sampling canopy trees in each stand in a stratified random manner. Lay out a 100 m transect in each forest stand. Think of this as a line that runs down the middle of a 20 x 100 m plot or a set of twenty 10 x 10 m plots. You will sample a tree in each of these plots. Using a random number table, choose two numbers from 0 to 9. The first number represents the number of meters you will go along the midline and the second number is the number of meters from the midline you go into each plot. From that point, locate the nearest canopy tree to sample and identify it. 2. For each sample canopy tree, identify and count all saplings beneath its crown. You will have to estimate this. Define saplings as any potential canopy species that is greater than 1 m in height and less than 10 cm diameter at breast height. Record your data in the table provided. 3. You have a table of 20 canopy trees and the number and type of each sapling beneath it. For each individual canopy tree, calculate the relative density of saplings of each type beneath it. To do this, divide the number of each sapling species by the total number of saplings. This represents the sapling relative density beneath each canopy tree. 4. You may have more than one than one individual of each canopy species in your sample. In these cases, average the sapling relative densities for each canopy species. These numbers represent estimates of the transition probabilities and will be used to parameterize your forest succession model. 1

2 Forest Stand Record the number of each sapling species found beneath each canopy tree in your sample canopy sample number of individuals of each sapling species sample species sum Transition Matrix canopy species average relative density of each sapling species beneath each canopy species 2

3 Modeling Forest Succession: Refer to the appendix for an introduction to STELLA if you are unfamiliar with the package. 1. Use the model toolbar to construct an initial model that shows the transitions for red maple and red oak as shown at the right. This model shows that red maple canopy trees (in the rectangular stock ) leave the canopy through RMloss and enter through the process of RMgain. These represent tree death and the transition of a seedling to a canopy tree. 2. You will now enter relationships within this by clicking on the world icon until you see the χ 2 icon that means you are in the modeling mode. Double click on each? and enter the appropriate data or equation. For red maple and red oak stocks, enter the number of trees of each type. 3. Of course, it is necessary to add values for the transition from seedlings to canopy trees for each species. You will enter the transition probabilities derived from your field data collection. Double-click on the RMgain flow and enter an equation that looks something like this: 0.5*red maple + 0.4*red oak. Your equation will differ as the transition probabilities (0.5 and 0.4 will not likely be the same). This equation describes the number of red maple in the next generation as the sum of the probability that red maple saplings replace both red maple and red oak canopy trees. 4. There are, of course, many more species in the forest plots than is shown in this simple diagram. You will be provided with summary data from your field study with transition probabilities already calculated. Using the transition matrix, construct a full STELLA model. Once constructed and parameterized, use the graph icon to place a graph on the model. Double-click on the graph and move all the canopy tree stocks to the display window. Run the model by double clicking on the run icon on the lower left corner. Change the time specs to 50 years so the model will stabilize. 5. Construct and run a model to simulate forest succession in each of the forest stands. Let the model equilibrate and record the final densities for each species in the table below. 3

4 Model Output Species final density forest stand 1 final density forest stand 2 Useful References: Acevedo, M.F., D.L. Urban and M. Alban Transition and gap models of forest dynamics. Ecological Applications 5: Frelich, L.E Forest dynamics and disturbance regimes: studies from temperate evergreen-deciduous forests. Cambridge University Press, Cambridge, UK. Hibbs, D.E Forty years of forest succession in central New England. Ecology 64: Horn, H.S Markovian properties of forest succession. Pg in M.L. Cody and J.M. Diamond (eds.), Ecology and evolution of communities. Harvard University Press, Cambridge, MA. Runkle, J.R Gap regeneration in some old-growth forests of the eastern United States. Ecology 62:

5 Names Questions: 1. Is forest history or environmental factors most responsible for the differences in forest composition and structure of the two forest communities? Explain. 2. Look at the table of transition probabilities and describe why the two forests types end up with different compositions. 3. What ecological processes does the modeling approach we used do a good job of simulating and what ones does it do a poor job? 5

6 APPENDIX: STELLA MODELING TOOL The STELLA modeling software is a flexible, powerful tool that will allow you to develop dynamic simulations that retain enough reality to be usefully applied to the systems you will study in BIO 153. To get you started programming, you must first familiarize yourself with the modeling approach using the information below. Model Building Blocks Stocks: Flows: The basic building block is the stock that is used to represent anything that accumulates (populations, biomass, nutrients, water). These are tangible, countable, physical accumulations. You can also use stocks to represent the degree of non-physical accumulations such as knowledge or fear. The second building block is the flow that is used to represent activities that lead to inputs and outputs. Flows include births, migration and nutrient or biomass transport. These activities will change the magnitude of stocks in the system. You can think of flows as being pipes. Whatever is associated with the stock(s) flows through them and causes the magnitude of stock(s) to increase or decrease. The circular portion represents the regulator and contains an algebraic expression that controls the volume of flow through the pipe. Connectors: Connectors look like wires and transmit information to regulate flows. Connectors can connect into flows or converters but never into stocks. Only flows affect the magnitude of stocks. However, connectors can affect both input and output flows. Converters: Converters contain equations that generate an output value during each time interval of a simulation. Converters often take in information and transform it for use by another variable in the model. They are also handy for storing constant values. Now, you should proceed with your first modeling effort. The first stage is to map out the scheme of relationships that affect the stock of interest. The building blocks are found in the upper left side of the toolbar and look like: Use the building blocks to construct the map shown below. Helpful hints 1. Rename blocks by clicking on the blocks and typing in the new name. 2. If you make a mistake, use the dynamite tool to blow it up. Do this by clicking on the dynamite stick and placing it over the item and clicking again. 3. If you hold down the <alt> key, the last building block you used will be retained. flow converter connector dynamite stock 6

7 Sample Model Structure Sample Model Parameters: These data are for a deciduous forest near Mechanicville, New York. Seedling Transition Probabilities Initial tree Canopy Red maple Red oak Big toothed Paper birch American American density species aspen ash beech 12 R ed maple Red oak Big toothed aspen 0 Paper birch American ash 0 American beech 7