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

	2	1	0
	4	1	3
	1	0	0

iii iiiiii

Target cell

iiii iiiiii

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.

ƒ 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

Change of the starting patterns