NOTE: In these experiments you will use computer software to simulate different types of growth models. HYPOTHESES: The experimental hypothesis might be that if we increase either R, the reproductive rate or the initial population size, NT, that this will increase the population size after 10 generations in an exponential growth model compared to unmanipulated control populations. The null hypothesis may be that populations of different R and initial population size will have the same population size as control groups after 10 generations.
To build an exponential population growth model, first open a new workbook in Excel.
Save the file to a secure location and name it “exponential growth”.
Label cell A1 “generation”, and cell B1 “population size”.
Type the number zero into cell A2. This row will represent the initial generation.
In cell A3 type this formula: = 1 + A2
Now hit enter.
Click on cell A3 and drag the small box in the bottom right corner to cell A12 for 10 generations.
Type the number two in cell B2. This will represent the initial population size in the model.
Label cell E1 “growth rate”, and in cell E2 type the number 0.05. This value represents the proportion of new offspring produced by each individual for each generation, or R in the exponential growth model.
NOTE: In the classic exponential growth equation, T is the generation, and NT is the number of organisms in the current generation. NT+1 will be is the number of individuals in the next generation.
Enter the exponential growth equation in cell B3 as the formula shown here: = B2 + (1 + E2) * B2
Now, hit enter.
Click cell B3 and drag the small square in the bottom right corner down to cell B12 to simulate 10 generations of exponential growth.
To observe the results, select all data, along with the headers, in columns A and B.
Click “insert” and select “scatter plot with smooth lines and markers” from the toolbar. A scatter plot should appear in the sheet. TIP: If it does not, check to see if a new sheet was created in the workbook.
Label the Y axis “population size” and the X axis “generation”. Title the chart “exponential growth of a population”.
Observe how the population increases in a classic exponential growth pattern.
Next, create Table 1 labeling the “growth rate R” as the header of column A, and “population size after 10 generations” as the second column.
Record the population size at generation 10 for the growth rate of 0.05, the rate we just simulated.
Now, set the growth rate in cell E2 to 0.1, and repeat the steps to generate a new scatter plot.
Record the population size at generation 10.
Continue to alter the growth rate using the values in table one, noticing how the Y axis changes to accommodate the increasing values.
After completing Table 1, set the growth rate back to 0.05 and change the initial population size in cell B2 to 100 individuals.
Record the population size at generation 10 in a new table, Table 2.
Proceed to change the initial population size using the values in Table 2. Once the table is complete, save the Excel sheet and close it.