Counting Caterpillars

by Dr. Bruce Barkstrom

An Experience

To illustrate how informal science can work, we need some specific examples. The first one is an expansion of something that happened to our family on a trip from Virginia to Illinois late one May.

If your family is like ours, travelling along the Interstate can seem like one of the sentences to limbo: hours of boring, never changing pictures of distant landscapes. The Sun pores through the windows. The children exhibit the lunatic's excruciating ability to whine, grumble, and argue their parents' into insanity. Highway hypnosis sets in, so that all that is remembered is that the Sun finally set and the trip came to an end (justifiable homicide for the trip?).

We had started on one such episode, when we noticed fuzzy, black and orange caterpillars crawling across the road. This was certainly a temporary relief from the deadened landscape -- something living, something different than the endless perspective of trees and fields and white concrete. One of the interesting aspects of this encounter was how many of them there seemed to be. There weren't enough to cover the highway. However, there were enough to be noticeable.

How many were there, anyway? That wouldn't be too hard to answer. I set the car speed to 60 miles per hour (one mile per minute) and counted the number of caterpillars in a minute. One, two, three, .... At the end of the first mile, I had about 150 caterpillars and the attention of the rest of the family. Father had found something more interesting to do than hit a sibling over the head with the books. We all counted. The next mile had about 130. We tried again - 160.

Let's see. The road had two lanes, each about twenty feet wide. That means our two lanes were about forty feet wide altogether. One mile of two lane highway has an area of 40 times 5280 square feet. Gus got out his calculator, and we found the answer was 211200 square feet. That's about 200,000. Now we know there are about 150 caterpillars per 200,000 square feet, or about 3 caterpillars for every 4000 square feet. This would be a strip of land 1 foot wide and 4000 feet long. 4000 feet is about one mile (OK, 5280 is right, but when you are bored, 4000 isn't far from 5000). That means that one square mile has about 4000 such strips, each containing about three caterpillars. That means that a square mile has 3 times 4000 caterpillars -- 120,000 caterpillars per square mile! (We ask you to imagine Anne's reaction to having that many wriggly, squiggly, squishy, orange and black, hairy caterpillars.)

Alice got out the road map of Virginia. In the upper corner, where the legend was, she found that Virginia had an area of about 40,000 square miles. We could really get into big numbers. If each square mile had 120,000 caterpillars, that would be a total of about 5,000,000,000 of the beasties. For those of you with a calculator, you can get a number with more digits. For our purposes, five billion was a big enough number. The point is not whether it was 4,973,253,105 or 6,201,884,230. The real question is whether the number is close to 1 or 1000 or 1,000,000, or 1,000,000,000 or 1,000,000,000,000. We had our answer.

What could we use it for? Well, those caterpillars had developed over the last month or so, I guessed. They weighed an ounce or so each. For this kind of work, it is easier to use grams or kilograms. An ounce is about 30 grams, so the total mass of these orange-black caterpillars in Virginia could be estimated to be 30 times 5,000,000,000 grams or 150,000,000,000 grams. There are 1000 grams per kilogram and 1000 kilograms per tonne (about 2200 pounds). If our estimate were close to correct, there were about 150,000 tonnes of caterpillars moving from one part of Virginia to another on that particular Saturday.

Since caterpillars get to be as big as they are by eating (leaves, thank goodness), they must have eaten at least this weight of leaves in the previous month. If they only weighed one tenth of what they had eaten, there must have been 1,500,000 tonnes of leaves consumed by these insect larvae over the preceding month. The family sat in stunned silence for a quarter of an hour. We weren't bored, we were stunned.

Then the second thoughts set in. How representative were our numbers? Did we really believe that there were as many caterpillars in the mountains where we could see that the leaves hadn't quite opened up? Would we have the same density in Tidewater, where it had been Spring for more than a month? Then we started to notice differences in the numbers of caterpillars between sunny parts of the road (where there seemed to be more than average) and shaded parts of the road (where there were less). We also noticed that where the wind seemed strongest, there were more caterpillars than where the wind was not so strong. There seemed to be more caterpillars opposite fields than woods. What controlled the distribution of caterpillars?

Extending the Experience

This experience certainly livened up our trip from Virginia to Illinois. It started simply by taking a little more careful look at the surroundings. Perhaps we could have made it sound more scientific if we had stopped the car and identified the species of caterpillar. The first point is that we did some simple measurements and used our imagination to extend these measurements to the whole state. The second is that we began to ask what might be wrong with the numbers, and how far we could trust them. This lead to more careful looking at what we had measured. It opened up the countryside, and made us see things with a deepened sense of what was going on. "The hills are alive ..." takes on whole new universes of meaning when you consider how many caterpillars have their residence there.

In other words, we have started with an observation, tickled our fancy with some extrapolation, and come back asking for better observations. We have also developed a rough idea of what the numbers mean and some idea of how they are related to other phenomena. If we wanted to be fancy, we could use the language of hypothesis and experiment. But that's textbook language. The process is a bit more complex than that, and simpler, as well.

Where does this lead? Several directions. If you have children that are interested in biology, you could try becoming more specific about the species of plants or animals. Keep a diary of plants or animals identified. Find their universal biological names (the Latin ones for genus and species).

On a more quantitative note (and for me, the more interesting aspect of this episode is quantitative), try counting plants or animals of a given species in a particular area. If you live in a city, find a vacant lot and keep track of the number of different kinds of plants that appear. If you live in a suburb, use your lawn as a laboratory. Even the most perfect gardener is likely to have a weed here or there. At our house, we have more than a few different kinds of weeds in the public part of the lawn. We may even have poison ivy under the trees in the back. If you live in the country, you can find all sorts of areas.

Lay out a convenient square and count the number of oaks or dogwoods or timothy grass stalks. How many seeds were there in the square before Spring started? How many germinated? Of those that germinated, how many were able to get to the point of having full leaves and flowers? Were there some that made seeds? How many seeds did these plants produce?

If your children are more interested in animals, count those. Can you find out what they eat? How do they die? Of the tadpoles that hatch in the Spring, how many become frogs? Do the frogs live from one year to the next? Don't just go down to the library, see if you can actually measure what is going on.

Much ingenuity may be needed. How do you estimate the number of frogs that a given clump of frog eggs will produce? Take them home and incubate them through the tadpole stage? If you do, have you really represented the hazards of tadpole life? When Anne brought home a bunch of tadpoles and tried to get them to grow in a coffee can, all of them apparently died. Is this dismal statistic true of wild tadpoles? How do you take a frog census?

If you are interested in birds, how could you keep track of the density of swamp hawks or sparrows over a whole year? Similar questions arise for possums or skunks or raccoons.

Observe that these kinds of scientific activity do not involve any expensive equipment. A notebook and pen, a calculator, and a yardstick (or meterstick) are all that are needed to start. For more quantitative work, a plant or animal identification guide would certainly be helpful.

Furthermore, this kind of activity can actually be useful to professional scientists. We can use the same numerical extrapolation techniques that we explored with caterpillars. There are perhaps 10,000 professional botanists in the United States. There are about 200,000,000 square miles in the country. If we assign each botanist a standard area to cover, we will have one biologist per 2,000 square miles. If we allow several hundred plants per square foot, and have 25,000,000 square feet per square mile, we can see that each biologist would have a few trillion individuals to look after each year. Needless to say, recording where they were and how many of their seedinglings germinated wouldn't leave much time for sleeping and eating, as well as going to meetings or teaching. In other words, you don't need to worry about duplicating the work of other biologists if you choose to examine your own area.

Some More Advanced Material

If you have older children to teach, you might want to have them try a more challenging investigation: the study of energy and water flow in some part of their environment. Some of the magic of this study was put down by a scientist nearly a century ago:

"Did the reader ever consider that next to the mystery of gravitation, which draws all things on the earth's surface down, comes that mystery -- not seen to be one because so familiar -- of the occult force in the sunbeams which lifts things up? The incomprehensible energy of the sunbeam brought the carbon out of the air, put it together in the weed or the plant, and lifted each tree-trunk above the soil. The soil did not lift it, any more than the soil in Broadway lifted the spire of Trinity. Men brought stones there in wagons to build the church, and sun brought the materials in its own way, and built up alike the slender shaft that sustains the grass blade and the column of the pine. If the tree or the spire fell, it would require a certain amount of work of men or horses or engines to set it up again. So much actual work, at least, the sun did in the original building; and if we consider the number of trees in the forest, we see that this alone is something great. But besides this, the sun locked up in each tree a store of energy thousands of times greater than that which was spent in merely lifting the trunk from the ground, as we may see by unlocking it again, when we burn the tree under the boiler of an engine; for it will develop a power equal to the lifting of thousands of its kind, if we choose to employ it in this way. This is so true, that the tree may fall, and turn to coal in the soil, and still keep this energy imprisoned in it, -- keep it for millions of years, till the black lump under the furnace gives out, in the whirling spindles of the factory or the turning wheel of the steamboat, the energy gathered in the sunshine of the primeval world.

The most active rays in building up plant-life are said to be the yellow and orange, though Nature's fondness for green everywhere is probably justified by some special utility. At any rate, the action of these solar rays is to decompose the products of combustion, to set free the oxygen, and to fix the carbon in the plant. Perhaps these words do not convey a definite meaning to the reader, but it is to be hoped they will, for the statement they imply is wonderful enough. Swift's philosopher at Laputa, who had a project for extracting sunbeams out of cucumbers, was wiser than his author knew; for cucumbers, like other vegetables, are now found to be really in large part put together by sunbeams, and sunbeams, or what is scarcely distinguishable from such, could with our present scientific knowledge be extracted from cucumbers again, only the process would be too expensive to pay. The sunbeam, however, does what our wisest chemistry cannot do: it takes the burned out ashes and makes them anew into green wood; it takes the close and breathed out air, and makes it sweet and fit to breathe by means of the plant, whose food is the same as our poison. With the aid of sunlight a lily would thrive on the deadly atmosphere of the "black hole of Calcutta;" for this bane to us, we repeat, is vital air to the plant, which breathes it in through all its pores, bringing it into contact with the chlorophyl, its green blood, which is to it what the red blood is to us; doing almost everything, however, by means of the sun ray, for if this be lacking, the oxygen is no longer set free or the carbon retained, and the plant dies. This too brief statement must answer instead of a fuller discription of how the sun's energy builds up the vegetable world.

But the ox, the sheep, and the lamb feed on the vegetable, and we in turn on them (and on vegetables too); so that, though we might eat our own meals in darkness and still live, the meals themselves are provided literally at the sun's expense, virtue having gone out of him to furnish each morsel we put in our mouths. But while he thus prepares the material for our own bodies, and while it is plain that without him we could not exist any more than the plant, the processes by which he acts grow more intricate and more obscure in our own higher organism, so that science as yet only half guesses how the sun makes us. But the making is done in some way by the sun, and so almost exclusively is every process of life.

...

Since, then, we are the children of the sun, and our bodies a product of its rays, as much as the ephemeral insects that its heat hatches from the soil, it is a worthy problem to learn how things earthly depend upon this material ruler of our days. But although we know it does nearly all things done on the earth, and have learned a little of the way it builds up the plant, we know so little of the way it does many other things here that we are still often only able to connect the terrestrial effect with the solar cause by noting what events happen together. We are in this respect in the position of our forefathers, who had not yet learned the science of electricity, but who noted that when a flash of lightning came a clap of thunder followed, and coucluded as justly as Franklin or Faraday could have done that there was a physical relation between them."

pp. 72-75, The New Astronomy (1889)
Samuel Pierpont Langley

Here, in a few pages, Langley has summarized much of the technical study of ecology - the way energy flows through an ecosystem. If you want to study this, you can begin by trying to measure how much sunlight falls on a particular area. This may require some ingenuity, because the available energy depends on cloudiness and haze, as well as the time of year. Still, it should be possible to build a simple lightmeter that could be placed outside to measure how much sunlight is falling on a given area. Look around your library or your local Radio Shack store for simple circuits for measuring light.

Try starting your measurements early in spring, before any plants have sprouted or leaves appeared. Do the seeds sprout before the leaves come out? Do some plants wait to sprout until the forest canopy has come out fully? Often, in our area, there is a three-layered structure of vegetation: a top canopy (Oak or Beech), an understory (Dogwood and Holly), and a surface layer (blueberries, poison ivy, etc.). The top layer gets more light than the next one down, and so on, at least most of the summer. Can you measure the changes through the year?

Let's take this a little more slowly, so you can be sure to get the flavor of what's being suggested. There are two ways to get a light meter. The fastest is to find a camera store that has new or used light meters. These are light operated meters that require no batteries, and are quite portable. They are also reasonably well calibrated. I have a Weston Master 6, but any inexpensive meter will do for a start. If you don't want to buy a light meter (about $30 or so for a new one), go to Radio Shack and find one of their circuit design books for photocells. Assemble it from the design.

Let's assume that you have a light meter, and talk about the next part of the measurement process. If you aren't familiar with sunlight, try using your new meter several times during the day. Walk outside and hold the active part of the meter face up and level with the horizon (or the ground - as long as you aren't on a mountain side -- If you are on a mountain side, make the face as level as you can). Take a reading, following the directions in the manual. If you've made your own photocell device, you will probably have a meter attached, from which you can get a number. Try doing this about once an hour over the course of the whole sunlit day.

Take a piece of paper and use it to write down the time and meter reading in two columns. One column should be the time, the second the meter reading. When you finish the day, you will probably have six to twelve pairs of numbers. As a next step, plot them. Find a sheet of paper and draw a line about an inch in from the long edge and parallel to it. Mark a point about one inch from the left edge. Now, find your largest light reading. Make a third column of numbers on your page by dividing each reading by the largest reading (please use your calculator, don't do it by hand). The numbers in this column will be fractions, the largest being 1.000 (keep three numbers to the right of the decimal point). We call this a Normalized Reading. After you have done this, make a fourth column of numbers by multiplying each of the numbers in the third column by 7.0. You should have a table that looks like the one below:

We also need to build another column showing how many minutes have elapsed from the time of the first measurement. The easiest way to do this for me is to convert all of the times to a 24 hour clock. The morning times are not affected. For those in the afternoon, add 12 to the hours. This means 1:14 pm is 13:14. Then multiply the number of hours by 60 and add the product to the minutes after the hour. 9:15 am becomes 9 * 60 + 15 = 555. 1:14 pm becomes 13 *60 + 14 = 794. What you have computed is the number of minutes past midnight. Make this your fifth column, as shown above. Make a sixth column by subtracting the first number in the fifth column from each number below it. This is the number of minutes from your first measurement. Finally, make a seventh column by dividing each number in the sixth column by 60. This last column is the number of hours from the first measurement.

The fourth column is labelled "Y" because that is how far above the line you will want to put a point. "Y" is what that axis is called for historical reasons. Where you have marked a point on the line parallel to the long side of the paper, measure up the length (in inches) that represents the number in the first line of the fourth column (1.34 inches for the hypothetical numbers in the table above). Next, make a mark on the base line a distance in inches equal to the number of hours from the first measurement. At this point, measure up a number of inches equal to the second line of the fourth column (2.26 inches for the table above). Continue this process until you have plotted all of the numbers in the columns labelled "X" and "Y". You should have a page that looks a little like

           1.0 |     X 
Normalized     | 
Reading        |   X 
               |       X X 
           0.5 |           X 
               | X           X 
               X 
               |_______________
               0 1 2 3 4 5 6 7 
                 Hours Diff

This plot shows when your measurement of sunlight was highest, and when it was lower. Notice that we have added labels to the axes to help understand what we have plotted.

Now that you have tried this for one day, repeat the process for a number of successive days, preferably over several months. Look at your plots. What do you see from them? Is there a steady change with days? Are some days higher than others? Do you remember what the weather was on the low days? Incidently, you will need to make measurements when the weather is bad, as well as when it is good. As far as we know, plants do not decide not to accept sunlight when there is bad weather during the summer or early fall.

What you have plotted on each day is how much solar energy was falling when you made the measurement. We expect the total energy to add. In other words, if there was one unit of energy the first half of the day, and two units the second half, there would be a total of three units for the day.

Let us make a new, very long table. In the first column, mark down each day in the year. Starting with 1 in the first row of the second column, give each day in the year a consecutive number. January 2 will be day 2; January 5 will be day 5; February 1 will be day 32; etc. In the third column, mark with an X each day on which you have a measurement.

For each day you made a measurement, add the raw measurements (the numbers in your second column of the first kind of table) and divide by the number of measurements. If you are unfamiliar with statistics, this is called computing the mean. Some days will probably have missing hours. Find the previous day with a measurement at this hour and the next day with the same thing. Add these two measurements together and divide the sum by 2, then add this to the day's accumulated measurements and compute the mean. When you have filled in all of the missing hours, place the day's mean in the fourth column of the new table. Do this for all the days you have measured.

You will probably have some missing days to be filled in. One way of doing this is to put the first measurement in half of the days between and the later measurement in the other half. When you have to fill in, put parentheses around the number.

Once this is done, you can compute a fifth column. Make the first row of this column equal to the first daily average. The second row of the new column should have the sum of this column's first row and the second day's daily mean. The third row should have the sum of this column's second row and the third day's daily average. In other words, this column should have the accumulation of solar energy.

Your table may look a little like the following hypothetical example:

Now, make a plot of Cumulative Sunlight (on the "Y" axis) against day of the year (on the "X" axis). You will probably have a chart that looks a bit like the example below:

         | YYYYYYYY
         | YYYY
Cumulat  | YYY XXXXXXXXXXX
Sunlight | XXXXXXXXXXXXXXXXX
         | XXXX
         | XXXXX X - under canopy
         | XXXX Y - open field
           XXX________________________
           1 30 60 90 120 150 Day

What good is this chart? Well for one thing, it shows you how much solar energy has been available below where you made the measurements. If you have made them at several different locations, put all of the measurements on the same chart, connecting each locations points with a line. We have tried to indicate this in the graph by letting"X" be measurements made under a forest canopy and"Y" be measurements made in an adjacent open field. You can see from just this simple type of graph where the forest canopy leaves opened in March. It also suggests that by late spring, the field had about one and one-half times as much solar energy available for making plant material as did the forest floor. See if you can imagine other things that you might understand and predict from this simple set of measurements.

As an aside, all you have had to do so far was to get a light meter and take the time to record the amount of sunlight on a regular schedule. You could even build your own light meter and cut the cost. You are likely to have more data in your table than many professional botanists have. Your major expense has been the time it takes you to make the measurements.

Just to help you remember what kind of conditions you had as you went along, you might want to take photographs of the plants whose energy input you are recording. If you decide to do this, I would suggest trying to record about once or twice a week (i.e. every seventh day or every third day) at about the same hour of the day. Put the camera in the same place, looking in the same direction, as well. That way, you will know what has changed.

Measuring sunlight is a start. The next step in the process is to find out how efficiently the sunlight is converted to plant material (often called biomass). Probably the simplest measure of this is weight of leaves and stems. Can you take a census of biomass development in different layers over an entire year? Try selecting a certain area and sampling leaves. Weigh your samples, and plot the weight as a function of time. Is most of the weight contributed by one specie of plant, or are several responsible? Note that you might have hundreds of individual tiny plants that produce less mass than one or two large trees.

If you want a more quantitative measure of what is going on, divide your plants into trees and shrubs (on the one hand) and understory plants (on the other). Trees produce one set of leaves in the spring, and do not appreciably add any over the rest of the year. Thus, if you can get a good estimate of how many leaves have come out in the spring, you only have to measure how big a typical leaf is to be able to estimate the biomass produced by the tree.

I aksed Gus about this when he was standing next to a Betina bush that hides our garbage cans from the neighbors. He looked at the tree and said "Maybe 4000."

"But why do you think that?" I responded.

He shrugged. "Just seems like a good guess. But if you really insist, maybe I could estimate it. 4000 does seem like a lot of leaves." He looked at the bush, which was about fifteen feet high and maybe ten feet across at the top. Then, he grasped a small branch and looked at the gathering of leaves at its end. "One, two, three, ..., eight. Eight leaves in one cluster." He continued "each big trunk has about -- one, two, three, ..., twenty four, twenty five clusters. At least this one does. Twenty five times eight is ... um ... one hundred times two. Two hundred leaves on each big trunk." He looked deeply into the mass of the bush, counting trunks about two inches in diameter. "Twenty trunks. That makes two hundred times twenty ... um ... ah ... four thousand! Boy that is a lot of leaves."

We leave it to your ingenuity to figure out how many leaves there are on an Oak or a beech that can't be reached from the ground. Maybe you would want to try using a pair of binoculars and counting leaves on twigs, twigs on branches, and branches on trees. Maybe you would want to find a downed branch and count twigs and leaf scars from that. The point to remember is that you want a good estimate, not an exact number.

For plants in the ground cover, it isn't clear that they only have one set of leaves. Grass in what a good imagination might call our "lawn" gets run over by the lawn mower and cut off. I have a distinct feeling that the grass responds by sending out more leaves. Besides, I wouldn't want to guarantee that even the weeds survive long enough to last through the whole summer.

Gus provided the sensible answer again. He walked over to a patch of "grass" near the mailbox (which is not under our oaks) and walked off an area about one meter by one meter (four paces by four paces, to be more exact). Then, he got down and looked at the mat of tiny plants. "Let's see, eight plants along one side. Eight times eight is sixty four. Each plant has maybe eight leaves? That's about five hundred leaves."

The next job in tracing energy transformation is to measure the amount of material that is growing. For trees, try to get a few leaves and measure the mass of a leaf. Estimate the thickness (say 1 mm), and measure the area. This is not too difficult if you are after a rough number. Simply measure the length of the green part of the leaf and multiply by the width. This is the area of a rectangle. If you think the leaf is closer to a circle in shape, multiply length times width by 3/4. For an oak leaf, trace out a leaf outline on a sheet of graph paper. Measure the length in units of sides of one of the squares, and do the same for width. Then, count the number of squares within the outline you have drawn. If you divide this number by the product of length times width, you will have a fraction (probably close to 1/2). Do this for a few leaves and take the average fraction as your factor to multiply length times width to get leaf area.

You can apply the same principle to the lower layers. Estimate the number of plants per square meter (or square yard). Select a sample of these plants, and count the number of leaves and their area. Write this down about once a week during the course of the growing season. As you go along, plot this estimate against your measurements of cumulative light meter readings. What do you notice? (I can't fill you in with a textbook answer, I haven't made the measurements.)

Again, for more quantitative work, you might want to try building a cumulative biomass table. For example, if you have the estimated leaf area every third day, try building a table with the first row being the first area, the second row the sum of the first and second areas, the third the sum of the the first three areas, etc. You might then want to divide the cumulative leaf area by the cumulative sunlight. If you think of what you are computing, you can see that it is total area per total sunlight. This is a sort of efficiency. If you do it by weight (mass of leaves per sunlight), you may be able to directly compare how efficient forests are in comparison with ground cover. Is a forest as efficient as a fertilized lawn in utilizing sunlight?

The culmination of biomass measurements comes in the fall (at least in deciduous forests) -- at leaf raking time. The world is full of overly serious adults (who want nothing except to get the lawn cleared of leaves) and of kid sisters (who only want to run and jump in your carefully gathered piles of leaves). If you want some relief (and have seriously maintained your measurements through the summer), think of this harvest of leaves as stored sunlight. You will want to estimate the number and mass of leaves per area (and perhaps per tree). If you can be reasonably sure that you have gotten all of the leaves (and haven't had them blown to the neighbor's), try to actually measure the number of leaves that have come down, as well as their weight. Does your estimate agree with your estimates based on observing leaves all summer? If you burn the leaves, how much heat do you think they give off? Is it a large or small amount compared with the amount of sunlight that fell on the forest?

If you have also kept records on an adjacent clear area, how much material has been produced over the summer? Is the forest more productive than the meadow?

After you have measured the rate of plant material production, try to find out how many seeds are produced by all of this activity. How is seed production timed with respect to solar energy input, or with respect to the state of the forest canopy? Ditto with respect to water. If you have a drought, can you measure the reduction in the rate of biomass production? Do some plants increase productivity in this period?

How about insects? Can you determine how much of the biomass has gone into insect flesh? Suppose, for example, that you could keep insects from eating some leaves. If you could compare the rate at which these leaves grew with the rate for leaves that could be eaten, you might be able to estimate how much material the insects and their larvae consume. Could you sample the insect population (say with a trap or with fly paper) over time to determine how much various species weigh? If you use this technique, you may have to do the same kind of extrapolation we used on the caterpillars in the example at the beginning of the chapter.

What controls the number of insects? Birds? Bats? Spiders? Disease? Which of these is most important? I am not a biologist, but I suspect this is barely touched in professional science, simply because of the sheer number of different kinds of insects and habitats. Certainly, for crops, this question is studied. However, if you are interested in what goes on outside of your back door, you can probably find questions which have never been studied by any scientist before you happened to ask them.