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Learning Landscapes |
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Learning Landscapes |
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Discuss what keeps populations of plants and animals from exploding. List both natural factors (disease, predators, fire, insects, etc.) and human barriers (herbicides, collecting, habitat destruction, etc.). Which of these controls is absent in the case of weeds? Discuss other populations that have not been kept in control, and reasons for this. (For example, many populations of white tailed deer in the East are exploding because natural predators such as mountain lions have been eliminated and the deer have adapted to human presence. )
To illustrate the exponential explosion of invasive weeds, have students calculate the rate of reproduction of one knapweed over 10 years given the following hypothetical but realistic example. (Note that seed germination depends on many variables, such as climate or soil type.) One hundred knapweed seeds are inadvertently dropped in an area. A knapweed plant produces 1,000 seeds per plant. Four percent of knapweed seeds in the seedbank germinate (sprout) each year, leaving 96 percent for next year's seedbank. About 25 percent of the seedlings that sprout survive to become mature plants. Knapweed seeds remain viable in the soil for 8 years. It takes 1 year for knapweed to germinate and produce seed. Knapweed plants live for 5 years. How many plants and seeds will be produced in the area over 10 years?
Answer: From 100 seeds, four (four percent) will germinate the first year. Ninety-six will remain in the seed bank. Twenty-five percent of the sprouts (one of the four) will survive. That one surviving knapweed plant will produce 1,000 seeds the next year. In the second year, 44 (four percent of 1096) seeds from the seed bank will sprout and 11 of those plants will survive. Add to the first year plant to get a total of 12 plants. These produce 12,000 new seeds plus 96 percent of last year's seedbank for a total of 13,052 seeds. Continue for 5 years, taking one percent of the previous year's seedbank and adding to the previous year's plants for the new number of plants. Multiply plants times 1,000 and add to 96 percent of the previous year's seedbank for the new seedbank. Since the plants only live for 5 years, you must subtract year 1 from year 6, year 2 from year 7, etc. Also, the seeds are viable for only 8 years, so you must subtract 100 from year 8 seedbank; year 1's seedbank from year 9's seedbank, etc.
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Year |
Plants |
Seeds |
|---|---|---|
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0 |
0 |
100 |
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1 |
1 |
1096 |
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2 |
12 |
13,052 |
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3 |
143 |
155,530 |
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4 |
1,698 |
1,847,309 |
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5 |
20,171 |
21,944,417 |
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6 |
239,614 |
260,680,640 |
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7 |
2,846,408 |
3,096,661,414 |
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8 |
33,812,879 |
36,785,673,858 |
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9 |
401,667,920 |
436,982,165,807 |
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10 |
4,771,469,407 |
5,190,972,273,123 |
Note: If this problem is too difficult for younger students, give them the answers and have them create graphs showing the rate of growth over time. They could turn the graphs into visuals to use in a public awareness campaign.
Extra: Have students answer the following: If the site will support three mature knapweed plants per square foot, how many acres would be affected after 10 years? (There are 43,560 square feet in an acre. )
Answer: 4,771,469,407 plants divided by 3 (plants per square foot) equals 1,590,489,802 square feet divided by 43,560 (square feet per acre) equals 36,513 acres after 10 years.
