Diversity
Student Worksheet 4

Activity 4: Dispersal and Diversity Simulation Model

Preparation
Before you begin working on the dispersal and diversity simulation model, you should have read the Background Information of Unit 4. Your instructor may have assigned additional readings on diversity, dispersal, and disturbance. All of these will help your understanding of this activity.

Purpose of this Activity
This activity is intended to show that diversity is the result of many individual events of dispersal. The dispersal process requires gene pools in one place with connections to other places. When such connections are destroyed along with the local diversity, diversity is regained only very slowly. The simplified model we will use here shows how corridors or barriers constructed by humans can alter the biodiversity of places. We will manipulate the environmental factors that govern spatial change of multiple organisms vying for the same spaces and examine how the changed factors affect the dispersal processes of species.

Introduction
Let's use an example to explain what we will look at in this activity. Imagine an individual farmer who plows 40 acres annually and thereby creates a small barrier to perennial plants that migrate across the field. If many adjacent farmers do this or if the field size is even larger, you have a situation like that of Midwestern farmers in the U.S. (This is common, however, in many parts of the US as well as in countless other countries): the aggregate impact of many human decisions to cultivate land has created vast barriers to plant dispersal. Again, in many Midwestern counties, 95% of the land is now cultivated annually. This severely isolates the tiny remnants of pre-cultivation vegetation from the exchange of genetic materials that occurred prior to intensive agriculture. Other land cover changes like the creation of long reservoirs can be just as devastating to the migration fish and terrestrial animals.

The impact of land use changes on genetic and species diversity is the central theme of this activity. Understanding these impacts through simulations requires that we model the spatial distribution of species, their spatial behavior (e.g., how fast they can spread), and the occurrence of barriers or corridors that will alter this spatial behavior. So, modeling the spatial behavior of individual species allows us to articulate the spatial outcomes of this behavior.

The DIVERSE3.wb1 simulation model is a relatively simple method to visualize how the diversity of organisms in one place is a result of interactions with adjacent places and how biodiversity is affected by habitat constraints and chance.

A site's adjacent places are those most likely to contribute new genetic material. Habitat constraints (like rooting depth or disturbance frequency) make the site more suitable to some organisms than to others. Chance governs the combined probabilities of the timing of an opportunity for a new organism to enter and the readiness of a plant or animal to occupy that newly available space. The model we use here intentionally simplifies reality in order to illustrate the principles of chance, spatial variability of site characteristics, and the varied genetic contexts of each potential invasion site at each time step. The model does not include a so-called local "extinction function" (a separate programmed step that removes some of the population). Such an extinction function would reduce the diversity of spaces and allow subsequent new immigrants. The model does, however, have a "random chance function," which allows the removal of some species from the competition for space. It does that by adding up the species in the eight spaces (cells) surrounding a central cell (the "target cell") and multiplying that number by a randomly chosen number. If the sum of the species in the cells surrounding a target cell times the random number totals less than 1 (rounded up from 0.5), then the species becomes extinct in the target cell in that step (see Figure 2 below and a sample screen capture from the DIVERSE3.wb1 spreadsheet).

Figure 2: Excerpt of the DIVERSE3.wb1 model

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Target cell

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Cells surrounding the target cell to be added up and multiplied by a random number

1,2,3... Number of species initially present in a cell

Instructions

Opening the Spreadsheet: Use a spreadsheet program such as Quattro Pro 5.0 for Windows to open the spreadsheet notebook DIVERSE3.WB1 or import the file into a Mac-program like Excel 4.0. To download the DIVERSE3.WB1 file on to your disk or hard drive hold down the shift key and click on the hotlinked file with your left mouse button.

Important Spreadsheet Terminology: Before we run the simulation, let's familiarize ourselves with this particular spreadsheet. If you do not recall the general terms used to describe a spreadsheet -- row, column, cell, cell address, cell entry, and cell formula -- consult the explanation on the NUTCY4 worksheet of Unit 2. In addition to those terms, we will use several new ones here; grid and block. The term grid is any space segmented into smaller rectangular pieces. Grids are commonly laid over landscapes as an aid in systematically collecting data. In our case, we would use the grid to count the members of a particular species per grid cell. The number of species members is then entered into the spreadsheet. A block, on the other hand, refers to a portion of a spreadsheet: when you mark a portion of a spreadsheet that encompasses parts of several rows and of several columns, e.g., a block spanning from G2 - G8 (rows) and from G2 - K2 (columns) you are marking a 7 by 7 cell block. In a spreadsheet you would use a block to represent a grid. Thus, you may think of the spreadsheet blocks for a particular species as a map that shows how frequently a particular species is found in different portions of the modeled landscape.

The Spreadsheet Layout: The DIVERSE3.wb1 spreadsheet is laid out vertically as 5 blocks of 5 columns each (separated by small gray-shaded columns) that represent different time periods (Time1, Time2, etc.) for a 5 by 5 cell grid. Horizontally, the spreadsheet is divided into a top portion that shows blocks of numbers of real, potential, and unsuccessful species, and a lower portion with a five-row block each for Species1 through 13. In the upper left corner of the spreadsheet you see a 5 by 5 cell grid of the site that we will focus on (the shaded block); it contains the constraints of the model area. We refer to this block from here on as the "habitat types block." The numbers in this block tell the maximum number of species that can live in a grid cell (hence a "constraint"). The simulation model is illustrated in the first 98 rows and tracks 13 species. Below row 100 is a duplication of the first 98 rows. Use the space in rows 101 to 198 for experimentation; rows 22-99 are a backup, should you need to copy beginning values of formulae to start over. Finally, beginning in cell AK23, column AK contains random numbers -- representing the model's random chance function -- that are recalculated each time the spreadsheet goes through a recalculation cycle.

Let's take a closer look at the top portion of the spreadsheet which is in bold type (see print-out on the spreadsheet, Supporting Material 4, if you don't follow the explanations on the computer screen). The top three block rows are accounts of what happens in the 13 species blocks below. The first row, POTENTIAL Species#, shows the number of species that have dispersed to that cell. The second row of blocks, REAL Species#, is the POTENTIAL Species# minus the limit placed by the Habitat types block on the number of species the habitat is likely to contain. This is a gross simplification of reality. A place with 10 habitat types able to hold 10 plant species each, could hold a maximum of 100 species. That level of diversity may be unstable and thus has a very low likelihood of occurrence. In this model the number of species possible is 1 per habitat type. The third row of blocks contains the UNSUCCESSFUL Species#, which is the POTENTIAL Species# minus the REAL Species#. The model does not keep track of which of the species are the unsuccessful ones. The REAL species# block is the one that tracks the diversity of the spaces.

Now let's look at the lower portion of the spreadsheet. The processes that are at work in the dispersal of multiple organisms take place in the 5 by 5 row blocks starting with row 22 for Species1 and continuing through Species13. Beginning patterns for each species are supplied in the Time1 block. The formula that governs how species are spread starts with cell E21 and is a relational formula (in which the mathematical procedure, i.e., the type of equation, stays the same, but depending on where in the spreadsheet you are, the cells that enter into the equation change). The relational formula is copied to each cell of each block for Time2 through Time5.

Simulation Inputs: So now let's see what we need to run the simulation. Recall that in order to understand dispersal and diversity, you need to know three basic elements (of course, this is the simplified world of the model): the species we begin with, how they are disturbed, and what the random chance function is. The DIVERSE3.wb1 model uses exactly these three types of inputs:

A beginning distribution map for each species being considered

(the 5 column block starting with the column labeled Time1). Our example uses 13 different species with a fixed starting condition (only 2 of which could be shown in the screen image print-out included here). In the example, the starting condition maps for Species1 and Species2 assume that a major disturbance has removed all organisms from the center 9 cells. The numbers 1 or 0 indicate the presence or absence of the species in that space at Time1. What you see on theat print-out is that Species1 and Species2 start to invade the space, but chance outcomes cause their local extinction. A map of habitat/disturbance regimes (habitat types in the upper left corner). This map differentiates the resources and hazards of the study space. The map has 25 cells with different niche opportunities that can support from 1 to 9 species at a time. In this abstraction of reality the number of species is limited by the diversity of local resources and hazards. A random number that can vary the outcomes of the model This part of the model recognizes the randomness in nature. If we started any process of dispersal over again with all environmental traits constant, the outcomes would be slightly different because of the complexities of multiple conditional probabilities. At each time period, the random number is used to define the probability that a species invaded a cell from any of the surrounding 8 cells. This implementation of the random chance process uses one random number per row to govern the outcome of all spaces for a time period (column AK). Obviously, this part of the simulation can have much more complexity by providing a separate random probability for each species to invade each cell. In the real world most invasions come from immediately adjacent spaces, but distant spaces have some small chance of supplying invaders. In this model the spatial linkage is kept simple to allow the model to minimize computer memory requirements. Move to the bottom half of the spreadsheet DIVERSE3.wb1 by using the page down key. The TEST portion of the page is a copy of the top 98 rows and can be altered for experimentation. The model inputs can be altered by the user in three ways without altering the equations.

Change of the starting patterns

The starting patterns of individual species can be changed by changing the 1's and 0's of species in the Time1 column. Change of the random chance elements Place the cursor on a blank cell and press the delete key to change the random number that governs the chance element for invasions. This action causes the entire spreadsheet to go through a recalculation cycle. The random number that affects each individual species invasion process changes, altering all of the species outcomes and the diversity (REAL Species #) maps. Change of the habitat constraints By changing the habitat type map cells, you can alter the constraints on the number of species that can be accommodated in a space. These numbers should be from 0 to 13 (the number of species used in this model). 5. Running the Simulations: Following the instructions below, use the model and the various change options to explore the following questions about the development of diversity. Analyze the results and write down your answers on an extra sheet of paper. 1. Examine the series of Species# maps. How does diversity of the 9 center cells change through time?

2. Change the random number in the method described above until you get a high number of UNSUCCESSFUL Species# recorded in Time5. You are essentially rolling five dice 13 times each time the spreadsheet recalculates. It may take many tries to get extremely high or low numbers of UNSUCCESSFUL Species. Print or record the patterns of the series of Species# maps. What is the difference in effect of high and low probabilities of invasions and resulting diversity patterns?

3. Change all beginning maps (Time1, columns G through K) for Species1 to Species13 maps to have only 1's in the 2 left columns (G and H) and 0's in the 3 right columns (I, J, K). What is the effect on the development of diversity if you start the species invasions from the same side?

4. Change the middle column of habitat types (C104 to C108) to accommodate no species at a time (only 0's). By doing this, you are constructing an absolute barrier like a long reservoir that is too wide for terrestrial organisms to cross. What is the effect of this absolute barrier on the development of diversity on the right side of the map?

5. Change two cells (cells C105 and C107) in the middle column of habitat types (which, after the last run, should have only zeros) to accommodate one species at a time. This changes the absolute barrier to a high-resistance barrier. The cells changed to 1's are limited-capacity bridges. What is the effect of this high resistance barrier on the development of diversity on the right side of the map?

6. Change all of the middle column of habitat types (C104 to C108) to accommodate one species at a time. What is the effect of the low-resistance barrier you have constructed on the development of diversity on the right side of the map?

7. This experiment asks you to test accelerated dispersal. Human environmental changes often create corridors of high-disturbance frequency that speed the migration of organisms. For example, a road construction corridor that is stripped of vegetation, if not seeded promptly, provides excellent opportunities for species to move along that corridor. Similarly a river that remains flooded for several weeks kills much of the floodplain vegetation, leaving an extensive corridor for plant dispersal. Change all of the middle row of habitat types (A106 to E106) to accommodate all 13 species at a time. What is the effect of the no-resistance corridor on the development of diversity on the right side of the map?

8. For each of the different types of interference with dispersal you have just modeled, think of some examples of human actions that would have the same effect.

The answers to your questions should either be synthesized in a summary paper or presented in a useful way to the class. Your instructor will let you know which formats s/he can accommodate.