Timber wolves once ranged throughout Wisconsin. However, early settlers viewed wolves as a threat to livestock, and, as a result, a bounty was placed on wolves. By 1957 no more wolf packs existed in the state of Wisconsin and the last wolves were killed in 1959. However, thanks to the protection afforded by the federal Endangered Species Act of 1973, the Minnesota wolf population was allowed to expand and in 1975 a wolf pack was discovered in northern Wisconsin. In 1989 the Wisconsin Wolf Recovery Plan was approved by the Department of Natural Resources to monitor and protect the state’s wolf population. Today the timber wolf ranges throughout much of northern Wisconsin. They have maintained high enough numbers in the state for a long enough period of time to now be considered for down-listing from the designation of "endangered" to "threatened".

In this activity, students will learn about wolf biology and incorporate ecology principals in the analysis of data collected from the Internet. Statistical methods will be used to estimate wolf population size.

This activity is designed for a high school Environmental Biology course, but could be modified for use in a history, statistics or mathematics course.

Previous Knowledge Needed.

Students should know how to access a given website on the Internet. They should understand percent and average. They should be able to plot points on a graph.

Materials.

Internet access. Timber Wolf Activity Sheet and graph paper. TI-83 (or other calculator that can fit logistic curves) recommended. Video: "Never Cry Wolf" recommended.

To use the Internet to access information and data about Wisconsin timber wolves.

To gain knowledge about wolves and their place in our state.

To discuss the history of the wolf population in Wisconsin.

To learn about the logistic population curve.

To predict Wisconsin wolf population for the next few years using a fitted logistic curve to wolf population data.

In the computer lab, students will search the Internet for the required information about the Wisconsin wolf population and complete the attached Wisconsin Timber Wolf Activity Sheet. In class, students will share and discuss the information they have found about the Wisconsin wolf population. The teacher will explain and discuss the logistic curve for describing population growth. Students will plot wolf population data on graph paper, draw a logistic type curve to describe it and then predict the wolf population for the next few years.

See points on the Activity Sheet and the Logistic Population Curve worksheet.

Students may wish to view the video "Never Cry Wolf" or explore more wolf activities at other websites.

Students may wish to explore other endangered animals in the state of Wisconsin and predict their population growth.

!!!! Warning !!!! The Web sites given in this lesson may have changed! Before using this lesson with your students, be sure to check if the sites are still working or if you must find another site. Sometimes the sites still have the relevant data but you may need to change the directions to access the data.

To learn more about the logistic curve, see, for example, the website

http://www.bioss.sari.ac.uk/smart/unix/mgrow/slides/intro.htm

Some graphing calculators, like the TI-83 will fit logistic curves. In order to fit a logistic curve to the wolf population data, you will need to enter a point close to the maximum population value. For example, add the population 380 (approximately the maximum) in, say, year 2030 or later. Also you should not enter the exact values of the years, but designate them by small numbers. For example, designate 1979 by, say 1, 1980 by 2, etc.

Other websites with wolf information are the following:

http://www.timberwolfinformation.org

http://www.timberwolfinformation.org/updates

http://www.wolf.org

http://www.wolftracker.com

http://www.forwolves.org

http://www.wolfsanctuary.org

http://www.rr.gmcs.k12nm.Us/domagala.wolves.htm

If you wish more background about the statistical concepts involved in the lesson, some good sites to check are:

http://davidmlane.com/hyperstat/index.html

http://www.anu.edu.au/nceph/surfstat/surfstat-home/surfstat.html

http://www.math.unb.ca/~maureen/SSCEdCom/basicstats/basicstats.html

http://www.math.unb.ca/~knight/BasicStat/$content.htm

http://www.bbns.org/us/math/ap_stats

http://www.grad.cgs.edu/wise/linksf.shtml

http://www.cvgs.k12.va.us/DIGSTATS

http://www.statsoft.com/textbook/stathome.html

http://www.stats.gla.ac.uk/steps/glossary/index.html

http://www.crpc.rice.edu/CRPC/GT/sboone/Lessons/lptitle.html

http://forum.swarthmore.edu/library/topics/statistics

http://www.psychstat.smsu.edu/introbook/skb00.htm

TI-83 instructions:

http://www.ti.com/calc/docs/act/koehler001.htm

http://www.wku.edu/~neal/manual/ti83.html

The Calculator website at the Mathematics Department of the University of Wisconsin-La Crosse will perform basic statistical calculations. If you do not have access to a simple statistical computer package or calculators with statistics options, your students may access http://www.compute.uwlax.edu/stats_htdocs/newmenu.html to perform statistical computations on-line.

In order to print out just a copy of the student worksheet, highlight this section, then copy and paste it into your word processor. You may then revise the worksheet if you wish.

Activity Sheets. 

When you take a sample of items from a population, you obtain information about a relatively small group of items relative to the whole population size. For example, you may be interested in the areas of cities throughout the United States. There are thousands of U.S. cities and you probably don’t have time to find the areas of all of them. Hence you take a small sample of cities and just find the areas of these cities.

Next you may want to report what the average or mean area of all U.S. cities is. You would average the areas of the cities in your sample and report that this is approximately the average area of all U.S. cities. If the average area of the cities in your sample was, say 40 square miles, then it seems reasonable to say that the average area of all U.S. cities is approximately 40 square miles. However we don’t expect to be very accurate. So statisticians will report a "confidence interval" instead.

If you use a confidence interval, you might report the mean area of all U.S. cities as likely to be between 35 and 45 square miles. Or statisticians may say, "a 95% confidence interval for the mean area of all U.S. cities is (35,45)." This means that it is very likely that the mean area of all U.S. cities is between 35 and 45 square miles. Or we are "95% confident" that the mean area of all U.S. cities is between 35 and 45. If we want to be more sure, we might find a 99% confidence interval, which might be (30, 50). We would say that we are 99% sure that the mean area of all U.S. cities is between 30 and 50.

It is a little tricky to interpret a confidence interval in a mathematically correct way. The correct interpretation is based on repeated sampling. If samples of the same size are drawn repeatedly from a population, and a "95% confidence interval" is calculated from each sample (these will all be somewhat different since each sample is different), then 95% of these intervals should contain the population mean.

You can easily find confidence intervals using the TI-83. Enter your sample data in a list and use the command Tinterval in the STAT > TESTS menu. Choose the confidence coefficient you wish (90%, 95%, or 99% are often used).

Excel will also calculate confidence intervals. In the Tools menu, chose Data Analysis and then Descriptive Statistics.

Read more about confidence intervals in

http://curriculum.qed.qld.gov.au/kla/eda/ws_ci.htm

http://www.stat.ucla.edu/textbook/introduction/inference/Confidence_Intervals.html

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Use the web site: http://www.dnr.state.wi.us/org/land/er/publications/wolfplan/toc.htm Scroll down to the table of contents.

1. (3 points) Prior to the settlement of Wisconsin, how many wolves are estimated to have ranged in the state? (Click on History of Wolves in Wisconsin to answer this and the following questions.)

2. (3 points) As a result of a bounty placed on them, wolves were completely exterminated from Wisconsin. When did the Wisconsin legislature institute a bounty on the timber wolf and why?

3. (3 points) What legislation was enacted by the federal government that protected wolves from hunting? When was it enacted?

4. (5 points) When did the Wisconsin Department of Natural Resources (WDNR) begin monitoring wolves? Summarize the goals of its Wolf Recovery Plan.

5. (5 points) How many wolves were living in Wisconsin since 1979? (Click on Figure 3.)

6. (3 points) Wolves live in family groups called "packs". What is the average size of a pack and how much territory does each pack occupy? (Use Wolf Biology and Ecology.)

7. (3 points) Do all sexually mature members of a wolf pack breed? Approximately how many pups does a wolf pack raise in one year?

8. (3 points) What diseases have been observed in Wisconsin wolves?

9. (3 points) In recent years what was the most common cause of death of Wisconsin wolves?

10. (3 points) What are the primary foods for Wisconsin wolves?

11. The issue of wolf depredation on domestic livestock has been an issue with the wolves since early settlement of the state. During the period 1990-1997 there were 103,800 cattle and 3,700 sheep located in Wisconsin wolf pack territories. (Click on Appendix A.)

a. (5 points) How many cattle were killed by wolves from 1990-1997? What percent of all cattle were killed?(Click on Table A1.)

b. (5 points) How many sheep were killed by wolves from 1990-1997? What percent of all sheep were killed?

c. (5 points) How many dogs have been killed by wolves during the period 1990-1997? What was the average number of dogs killed per year?

d. (5 points) The DNR reimburses owners for wolf depredation losses. How much were these reimbursements for all losses in 1997? What was the average cost of these losses per wolf?

12. The potential size of the Wisconsin wolf population will be primarily limited by the amount of land available for wolf habitat. (Use Appendix C.)

a. (3 points) What type of land is best suitable for wolf habitat in Wisconsin?

b. (3 points) What is the total number of square miles of land in Wisconsin that has a 50% probability or more of being settled by wolf packs?

c. (3 points) Using the "Habitat Area Model", what is the approximate potential size of Wisconsin’s wolf population? (Click on Table C3.)

d. (5 points) Table C3 also gives "90% confidence interval" predictions for the wolf population. The estimate using the Habitat Area Model is 324 to 461 wolves. This means that we can be 90% sure that the potential wolf population is between 324 and 461 wolves. The Prey Based Model predicts between 262 and 662 wolves. Which estimate do you think is more accurate? Why?

13. Shade in current wolf habitat areas in Wisconsin on the following map. (Use Figure C1.) Which counties have large wolf habitat areas (more than about half of the county)?

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If conditions are suitable, a population will often grow following a "logistic" curve. A logistic curve looks like the one in the following graph. The vertical axis represents the number in the population and the horizontal axis represents time.

You can see from the graph that at first the population is small, then increases quite rapidly and finally levels off to some maximum value. This type of growth pattern is quite common. At first it takes a while for a species to become adapted to the environment. Hence population growth is small. Afterwards, as long as there is enough space and resources, the population "takes off". However there is a limit to growth because the amount of space and resources is finite. At this stage, the population has reached its maximum sustainable value and remains approximately constant.

In the above graph, we see that the population started out quite small for the first 20 years or so, then experienced rapid growth for the next 40 years or so, and finally reached an equilibrium at about 250 members in the group.

1. (10 points) Plot the wolf population numbers that you found in Question #5 (from the previous worksheet) on the attached graph paper. Then draw a horizontal line across the graph at height equal to the maximum potential population you found in Question #12c. Finally draw a curve that looks like the logistic curve shown above. The curve that you draw should go approximately through the points you plotted and level off at the maximum population.

2. (5 points) In order for wolves to be delisted (no longer considered endangered or threatened in Wisconsin), the population must remain at 300 wolves for 3 consecutive years. Using the graph that you drew, estimate the earliest delisting time of Wisconsin timber wolves.

3. (5 points) During which years will the wolf population be growing most rapidly?

4. (5 points) After what year will the wolf population remain approximately constant?

Years

Use the web site: http://www.dnr.state.wi.us/org/land/er/publications/wolfplan/toc.htm Scroll down to the table of contents.

1. (3 points) Prior to the settlement of Wisconsin, how many wolves are estimated to have ranged in the state? (Click on History of Wolves in Wisconsin to answer this and the following questions.)

3000 – 5000 wolves

2. (3 points) As a result of a bounty placed on them, wolves were completely exterminated from Wisconsin. When did the Wisconsin legislature institute a bounty on the timber wolf and why?

3. (3 points) What legislation was enacted by the federal government that protected wolves from hunting? When was it enacted?

The Endangered Species Act of 1973

4. (5 points) When did the Wisconsin Department of Natural Resources (WDNR) begin monitoring wolves? Summarize the goals of its Wolf Recovery Plan.

In 1979. The goals were to support 80 wolves for 3 consecutive years

in order to downlist them to "threatened".

5. (5 points) How many wolves were living in Wisconsin since 1979? (Click on Figure 3.)

6. (3 points) Wolves live in family groups called "packs". What is the average size of a pack and how much territory does each pack occupy? (Click on Wolf Biology and Ecology.)

Averaging 4.3 wolves per pack covering about 70 square miles per pack.

7. (3 points) Do all sexually mature members of a wolf pack breed? Approximately how many pups does a wolf pack raise in one year?

No, generally only the alpha pair breed, bearing 4 to 8 pups.

8. (3 points) What diseases have been observed in Wisconsin wolves?

Distemper, parvovirus, Lyme disease, blastomycosis, parasites, mange.

9. (3 points) In recent years what was the most common cause of death of Wisconsin wolves?

50% of wolf mortality is caused by humans.

10. (3 points) What are the primary foods for Wisconsin wolves?

Mostly deer, beaver and hare.

11. The issue of wolf depredation on domestic livestock has been an issue with the wolves since early settlement of the state. During the period 1990-1997 there were 103,800 cattle and 3,700 sheep located in Wisconsin wolf pack territories. (Use Appendix A.)

a. (5 points) How many cattle were killed by wolves from 1990-1997? What percent of all cattle were killed?(Click on Table A1.)

21 calves; 21/103800 = .0002 = .02%

b. (5 points) How many sheep were killed by wolves from 1990-1997? What percent of all sheep were killed?

10 sheep; 10/3700 = .0027 = 0.27%

c. (5 points) How many dogs have been killed by wolves during the period 1990-1997? What was the average number of dogs killed per year?

14 dogs or 14/8 = 1.75 dogs per year.

d. (5 points) The DNR reimburses owners for wolf depredation losses. How much were these reimbursements for all losses in 1997? What was the average cost of these losses per wolf?

3600 + 400 + 6250 + 2318.15 = $12,568.15; $12568.15/148 = $84.92 per wolf

12. The potential size of the Wisconsin wolf population will be primarily limited by the amount of land available for wolf habitat. (Use Appendix C.)

a. (3 points) What type of land is best suitable for wolf habitat in Wisconsin?

93% of the wolves live in forest land.

b. (3 points) What is the total number of square miles of land in Wisconsin that has a 50% probability or more of being settled by wolf packs?

5739 square miles

c. (3 points) Using the "Habitat Area Model", what is the approximate potential size of Wisconsin’s wolf population? (Click on Table C3.)

380 wolves

d. (5 points) Table C3 also gives "90% confidence interval" predictions for the wolf population. The estimate using the Habitat Area Model is 324 to 461 wolves. This means that we can be 90% sure that the potential wolf population is between 324 and 461 wolves. The Prey Based Model predicts between 262 and 662 wolves. Which estimate do you think is more accurate? Why?

The Habitat-Based model is more accurate since its confidence interval is narrower. The width of the Habitat-Based model is 137 (= 461 – 324) while the width of the Prey-Based model is 400 (= 662-262). Also since wolves need both habitat and a food supply to exist, the smaller prediction should be used.

13. Shade in current wolf habitat areas in Wisconsin on the following map. (Use Figure C1.) Which counties have large wolf habitat areas (more than about half of the county)?

Iron, Forest, Florence and Menominee have large wolf habitat areas. Also Langlade, Price, Sawyer and Ashland have quite large areas.

Figure C1
Primary and secondary wolf habitat in Wisconsin

If conditions are suitable, a population will often grow following a "logistic" curve. A logistic curve looks like the one in the following graph. The vertical axis represents the number in the population and the horizontal axis represents time.

You can see from the graph that at first the population is small, then increases quite rapidly and finally levels off to some maximum value. This type of growth pattern is quite common. At first it takes a while for a species to become adapted to the environment. Hence population growth is small. Afterwards, as long as there is enough space and resources, the population "takes off". However there is a limit to growth because the amount of space and resources is finite. At this stage, the population has reached its maximum sustainable value and remains approximately constant.

In the above graph, we see that the population started out quite small for the first 20 years or so, then experienced rapid growth for the next 40 years or so, and finally reached an equilibrium at about 250 members in the group.

1. (10 points) Plot the wolf population numbers that you found in Question #5 (from the previous worksheet) on the attached graph paper. Then draw a horizontal line across the graph at height equal to the maximum potential population you found in Question #12c. Finally draw a curve that looks like the logistic curve shown above. The curve that you draw should go approximately through the points you plotted and level off at the maximum population.

2. (5 points) In order for wolves to be delisted (no longer considered endangered or threatened in Wisconsin), the population must remain at 300 wolves for 3 consecutive years. Using the graph that you drew, estimate the earliest delisting time of Wisconsin timber wolves.

After 2008

3. (5 points) During which years will the wolf population be growing most rapidly?

Approximately 1995-2005

4. (5 points) After what year will the wolf population remain approximately constant?

After about 2020.