"There is no exception to the rule that every organic being naturally increases at so high a rate, that, if not destroyed, the earth would soon be covered by the progeny of a single pair." Charles Darwin, 1859, The Origin of Species

An essential condition of evolutionary change, Darwin recognized, was that all organisms produce far more young than the environrnent can possibly support. For exarnple, if a single pair of houseflies began breeding in April, and if all their eggs hatched and all the young survived to reproduce, by August they would have 191,010,000,000,000,000,000 descendents. Thus there is intense competition among the members of a species for survival and reproductive opportunities. Some individuals possess characteristics that give them an advantage in this competition--disease resistance, camouflage, the speed to escape predators, etc.--and pass these characteristics on to their offspring. Hence the population shows evolutionary change from generation to generation.

The growth rate (G) of a population depends on four factors:

• B, Birth rate (mean number of offspring per individual)
• I, Immigration (new members moving into a habitat from neighboring areas)
• D, Death rate (from such factors as predation and starvation)
• E, Emigration (individuals moving away)

INSTRUCTIONS

A POPULATION UNCHECKED BY PREDATORS

a ) Initially, the meadow was populated by 10 immigrants.

b) Each mouse averages 2 offspring (that is, 4 offspring per pair), which constitute the breeding population of the next generation. Assuming the parents die, the population size doubles each generation--2 parents leave 4 offspring in the second generation, these leave 8 offspring in the third, 16 in the fourth, and so on. In other words, if N is the population size of one generation, the population size of the next generation is 2N. Such a rate of population increase is called exponential growth.

c) Whenever the population of the meadow exceeds 500 mice, 98% of the mice die and only 2% survive. For example, if the population were 540, the number of survivors would be 540 x 0.02 = 11 mice. (Round any fractions to the nearest whole number.)

d) Any time the population falls below 10, another 10 mice immigrate into the meadow. For example, if the population falls to 4, these four reproduce and double their number, and another 10 mice immigrate, bringing the population size to 18.

These are the "rules" of the simulation "game" you are about to perform.

Assume the meadow is empty at the beginning of the simulation, so 10 mice immigrate into it from neighboring areas. Starting with these 10 as Generation 1, calculate the population size through 30 generations of mice. Fill in your data here for your own reference.

Generation Population

• 1. 10
• 2.
• 3.
• 4.
• 5.
• 6.
• 7.
• 8.
• 9.
• 10.
• 11.
• 12.
• 13.
• 14.
• 15.
• 16.
• 17.
• 18.
• 19.
• 20.
• 21.
• 22.
• 23.
• 24.
• 25.
• 26.
• 27.
• 28.
• 29.
• 30.

2. Although the reproductive rate of your mice is constant (2N), how would you describe their population growth? That is, as the population gets bigger, does it grow at a constant rate, faster, or slower?

3. How many times does the population crash in 30 generations? In a natural setting, what do you think might be causing the population to crash whenever it gets too large? What types of resources in the environment might place a limit on population size? Discuss this in class and list all the reasons the class could think of.

4. Ecologists have developed the concept of carrying capacity to describe the number of organisms of a given species that a habitat can support on a long-term basis. What is the carrying capacity of the meadow in this simulation?

INTERACTIONS BETWEEN POPULATIONS

Predators obtain their energy by eating primary consumers (and each other--for example a snake may eat a mouse and then a hawk may eat the snake). Predators therefore reduce the population of breeding mice. Death rate due to predation is called predator pressure and is one of the major selection pressures that drive evolutionary change. The act of finding food, including a predator's hunting behavior, is called foraging.

Predator populations grow, too, and the habitat must have a carrying capacity for them as well. Discuss the following points within your group, and answer these items in the lab report.

5. How would you expect predators to affect the rate at which your mouse population grows?

6. Compared to the population crashes you observed in the absence of predators (Fig. 1), would you expect larger or smaller crashes when predators are present? Why?

7. Do you think the carrying capacity of this habitat for predators will be greater than, less than, or equal to its carrying capacity for mice? That is, can the habitat support more mice, more foxes, or about equal numbers of both? Why?

Now we are going to introduce a simulated predator, a fox, into your meadow. The biological characteristics of the fox--the "rules" of the next simulation--are as follows:

a) For each generation of mice, if there are no other foxes in the meadow, one fox will immigrate from a neighboring area.

b) The fox must eat 4 mice in order to survive, and it produces 1 offspring for every 5 mice it consumes. For example, if the fox captures 4 mice, it survives, but does not reproduce. If it captures 5-9 mice, it produces an offspring and there are 2 foxes in the next generation; if it captures 10-14 mice, it produces 2 offspring and there are 3 foxes in the next generation, and so on.

In this simulation, a shallow, flat-bottomed dish or bowl will be the meadow, the mice will be beans in the dish, and the fox will be a spoon. For each generation of mice, a fox gets to forage across the meadow once. To simulate this, look away from the dish, gently shake the dish to distribute the "mice," and then run the "fox" across the dish once, scooping up as many "mice" as possible without looking. Pass the spoon straight across the dish not around the edges.

To start, place 10 mice in the meadow. A single fox immigrates into the meadow. Let the fox forage once.

In the table on the following page, record the number of mice it catches and the number of mice that survive. Add 10 more mice (immigrants), double the number of survivors left from the previous generation (for a reproductive rate of 2N), and enter the total number of offspring + immigrants in the first row for the next generation.

Determine whether the fox survived or not (did it catch at least 4 mice?). If not, enter 1 in the first row for the next generation (because a new fox would immigrate to your meadow from a neighboring area). If your fox did survive, determine how many offspring (if any) it produced (one for every 5 mice). In the first row of the next generation, enter the sum of the survivors and offspring.

For the next generation of foxes and mice, continue to let each fox forage across the meadow once to capture mice. Remember, if the fox population has grown, that generation of mice has to endure more than one foraging attack. For example, if there are 3 foxes at some point, you sweep through the dish three times with the spoon to simulate foraging by all three foxes. Keep the beans for each fox in a separate little pile, so after all the foxes have foraged you can determine how many survived and how many reproduced. To avoid bias, never look at the dish while you are "foraging," and be sure you gently shake the dish to redistribute the beans after each foraging attack.

Also remember that if the only fox in the meadow dies (captures fewer than 4 mice), another fox will immigrate to the meadow and take its place in the next mouse generation. And, if the mouse population ever drops below 10, another 10 mice will immigrate into the meadow (add 10 more beans to the dish). The class will do the first four generations of mice together. Each group of students will get similar, but not necessarily identical results. After doing those four generations, each group should continue at its own pace to complete the remainder of the 20 generations of mice.

Data Table for recording predations and calculating number of mice and foxes in the next generation.

1. Starting with generation 2, this is No. of offspring + No. of immigrants from previous generation.

2. Equals twice the number of survivors.

3. Add 10 immigrants only if number of survivors was 9 or fewer.

4. Starting with generation 2, this is No. of survivors + No. of offspring from previous generation. If there were no survivors, make this number 1 fox (by immigration).

5. Number of foxes that caught 4 or more mice.

6. Each fox produces 1 offspring for every 5 mice it caught.

In the lab report (Item 8), graph the mouse and fox populations generation by generation. Use pencil only (no ink). Connect the data points and label the two lines "mice" or "foxes" to distinguish them. Compare this to the graphs generated earlier when the mice existed without predators.

AN EXAMPLE FROM NATURE

CONCLUDING INTERPRETATIONS

9. Reconsider the predictions you made at Items 5-7. Which of your predictions were true? Which were false? Did the results differ from what you expected? If so, how and why?

10. What do you estimate to be the meadow's carrying capacity for foxes?

11. Describe or summarize how the mouse population graphs differed with and without predation.

12. In what generations did the mouse population reach its highest and lowest numbers? In what generations did the fox population reach its highest and lowest numbers? Do they agree? If not, can you detect a pattern?

PRE-LAB QUIZ

Data Table to calculate changes in the population of mice.

[Editor's Note: This image is 6" x 3.5" and will be largely off screen when viewed, a size appropriate for importing into a text file.]

_ 2. To assure you understand the rules governing fox populations, complete the following table. Some of the cells are filled in for you. From the data given there, you should be able to compute the data for the empty cells.

Data Table to calculate changes in the population of foxes.

[Editor's Note: This image is 4.5" wide x 3.5" tall and will be largely off screen when viewed, a size appropriate for importing into a text file.]

3. This exercise deals with predation and starvation as causes of death when a species becomes overpopulated. What other causes of death can you think of?

4. Over the course of a particular weekend in Baldwin County, five babies were born, four people moved into the county, six people moved away, and three died. What was the growth rate of the county's human population?

5. Why should you look away from the dish while "foraging" through it with the spoon?

LAB REPORT

1. Figure 1--Population growth of mice unchecked by predators.

Chart to graph of mouse population size by generation

[Editor's Note: This image is 6" wide x 3.5" tall and will be largely off screen when viewed, a size appropriate for importing into a text file.]

2. As the population grows, its growth rate (check one):

O remains uniform O becomes faster O becomes slower

3. Number of population crashes in 30 generations? Possible reasons conceived of in class discussion?

4. Carrying capacity of the simulated meadow for mice?

5. How would you expect predators to affect growth of the mouse population?

6. Would you expect larger or smaller population crashes? Why?

7. For which species do you think the carrying capacity will be higher? Why?

8. Figure 2--Population growth of coexisting mice and foxes.

9. Evaluation of your earlier predictions.

10. What do you estimate to be the meadow's carrying capacity for foxes?

11. Contrast the mouse population curves with and without predation.

12. In which generations did populations reach their highest values?

For Mice:

For Foxes:

In which generations did they reach their lowest values?

For Mice:

For Foxes:

Can you detect a pattern here? Explain.