We're expecting word any day about the departure of monarch butterflies from Angangueo. In the meantime, as you and other students across the United States and Canada prepare to report sightings of monarch butterflies, you may be wondering: "How many monarchs will be coming from Mexico anyway?" Before reading the description below, imagine how you might go about counting all the butterflies wintering in the mountains in Mexico! Discuss this as a class now, before reading further.....
Estimating the Size of Wildlife Populations
It's important for scientists to have good methods of estimating population sizes. This information can tell whether a population is increasing, decreasing or remaining stable. One of the standard methods for estimating wildlife populations is known as "Mark, Release, Recapture (MRR)". We've included an activity below so you can try it yourself and see how close your estimate comes to an actual count.
As you probably know, there was a snowstorm in the monarch sanctuaries on December 31, 1995. In an effort to measure the effect of this storm on the butterflies, scientists visited the Chincua reserve to estimate mortality. Teacher Jon Dicus of Blake School visited the sanctuary while this research was underway. Here he describes the method the scientists used:
"The scientists marked out small plots on the forest floor of about 2 meters by 2 meters. Within these squares or plots they counted all the dead butterflies. They looked at each butterfly to determine how it had died, either by bird predation, predation by some other animal, or by freezing. They then totaled the number of butterflies which were killed by freezing, compared it with normal rates of mortality and then made their estimate for the entire colony in Cerro Chincua.
"The quality of forest differs in each area. So, in addition to counting dead butterflies they also made estimates of forest density and tree cover to determine the impact the forest had on butterfly mortality during the snowfall. If there are less trees to protect the butterfly, it is very likely that many more died. For this reason the number of trees and the height and number of branches in these trees is an important factor to consider."
Dr. William Calvert of Austin, Texas described the methods he used to estimate the size of the monarch population during the 1994/1995 wintering season:
"The estimates are the simplest possible. In 1986 we did a mark & recapture study at one of the sites in January. On the basis of that study we estimated 13,000,000 monarch per hectare. Since then, off and on, we have measured the total surface area of all the colonies in Mexico. Simple multiplication gives an estimate, albeit crude, of the total monarch population for that year. There are certain factors we must take into account. Packing is the most dense in January and early February. Therefore we must measure the colonies in that time period. The reliability of the estimates is off course dependent on the assumptions made. I'm sure our reviewers will have much to say about these assumptions."
Counting all Butterflies:
Now it's your turn! In this lesson you will use two of the same methods biologists use when estimating the number of monarchs at the over-wintering sanctuaries. In the first method, you'll count a known number of individuals and extrapolate to make an estimate. The second methods is known as "Mark, Release, Recapture (MRR)". After trying both methods you can make an actual count and test the accuracy of each method.
But first, see if you can answer Challenge Question #32:
Assume there were 60,000,000 butterflies in Mexico. If you were to give one butterfly to everyone in your state or province--and continue giving butterflies to people in neighboring states and/or provinces--
"In how many states/provinces could you all the people have their own monarch butterfly?"
How to Respond to Challenge Question # 32:
1. Send your answer to jn-challenge@learner.org
2. In the subject line of your message write: Challenge Question #32
3. In the body of your message give the answer.
********** E S T I M A T I O N *** A C T I V I T Y *************
Materials needed for student groups
1 cup of rice
1 small glass jar
Note paper
Calculator
Activity
1. Put 1 cup of rice into a jar. Have students imagine the kernels of rice are monarchs in a wintering sanctuary. Give each student a slip of paper. Have them number from 1-3 and label:
1) Count and Extrapolate
2) Mark, Release, Recapture (MMR) Estimate
3) Actual count
2. Count and Extrapolate
Have students take out a small number of rice kernels, count them,
and put them back into the jar. Encourage them to notice the amount
of space the small number of rice kernels occupies in the jar. Now,
have them extrapolate in order to estimate the number of rice
kernels in the full jar.
3. Mark, Release, Recapture (MRR)
Next, "capture" a number of rice kernels and mark them with a
colored marker. Students should capture and mark at least 100 pieces
of rice. Put all the rice back into the jar. Record the number of
pieces you captured and marked on your "1st Visit".
Now go back for a "2nd Visit". Record the number of MARKED individuals you recaptured on the 2nd visit. Also record the TOTAL NUMBER of individuals you captured. (Do not return the rice to the jar until you have captured the full number.)
Now, figure your estimate according to the MRR equation. Remember, you are solving for "Total Population Size", or "b" in the equation below. The basic idea is that the number of individuals marked on the first visit (a) is to the total number in the population (b), as the number of marked individuals captured on the 2nd visit (c) is to the total number of individuals captured on the 2nd visit (d).
MRR Equation: a/b = c/d
a= # Individuals Marked on 1st Visit
b= Total Population Size
c= # Marked Individuals Recaptured on 2nd visit
d= # Individuals Captured on 2nd Visit, in Total
Here's an example:
a=100 Individuals Marked on 1st Visit
b= Unknown (Total Population Size)
c= 20 Marked Individuals Recaptured on 2nd visit
d= 100 Individuals Captured on 2nd Visit, in Total
4. Actual Count
Divide the rice among the students in the group. Have them count
the actual number of objects in the jar.
Discussion
1. How did your 2 estimates compare to the actual number of objects? Which method of estimation was more accurate?
2. What assumptions are made in the MRR method? List as many as you can. (For example, between the 2 visits there are *no births or deaths, * no arrivals or departures, * there's equal chance of capture and recapture, * monarchs don't learn to avoid being captured, etc.)
3. Do you think MRR is a reliable method?
4. Does the estimate become more accurate if you mark a greater number of individuals? Why?
The Next Monarch Butterfly Migration Will be Posted on March 19, 1996.
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