Friday, June 18, 2010

An Adult Completes Yet Another Science Fair Project

Grass is to have on the ground with dirt under it and clover in it.

~ Ruth Krauss, A Hole Is To Dig: A First Book of First Definitions

For three years now, I have been watching a small 64 square (well, roughly square) foot portion of my front yard. This little plot slopes from one section of a retaining wall to the street in front of the house. Three years ago, after the rupture of a large water pipe and the ensuing repairs, that little plot was nothing more than a pile of dirt and rock. Anticipating the initiation of a much delayed county project to build a sidewalk that would consume that plot, I left it alone, save for an occasional pass of a weed-wacker and the pulling up of a dandelion or two.

(Uprooting dandelions would have not sat well with Emily Dickinson who was fond of the weed, describing it in one poem as a signal of the end of winter and, even more, a symbol of immortality. The poem begins: “The Dandelion’s pallid tube/Astonishes the Grass, . . . .”. When it recreated her garden for its exhibit entitled Emily Dickinson’s Garden: The Poetry of Flowers, the New York Botanical Garden carefully nurtured dandelions, apparently a first for its gardeners.)

Clearly, nature abhors (loves) a vacuum. My plot is now populated with a rich array of wildflowers, though, I agree, many of them are what others would call “weeds.”

How to capture the transformation of this piece of land located in the mid-Atlantic area? I will try pictures, a list, and graphs.


During the first week of this June, the slope offered up a flowery show. A few pictures might tell part of the tale.

A List

A list of those wildflower species in bloom at that point can tell another part of the story, giving some sense of the diversity. After trying my hand at identifying fossils for several years, it seemed a remarkably similar process to work with extant plants. Though there’s something to be said about having the entire organism at hand in its “natural” environment, the identification can still depend upon subtle distinctions that require expertise (as the “unknown” entry below attests). In this list, the identifications, scientific names, and categorizations as “Native” or “Alien” are all based on A Field Guide to Wildflowers by Roger Tory Peterson and Margaret McKenny (copyright 1968). In general, I’m confident in the identifications, well, as confident as one who only dabbles in botany can be.

Common NameScientific NameNativeAlien
BugleAjuga reptans*
Common NightshadeSolanum nigrum*
Field Sow-ThistleSonchus arvensis*
Grass-Leaved Golden-AsterChrysopsis graminifolia*
Hop CloverTrifolium agrarium*
Indian StrawberryDuchesnea indica*
Lance-Leaved Coreopsis (Tickweed)Coreopsis lanceolata*
Long-Bristled SmartweedPolygonum cespitosum*
White CloverTrifolium repens*
Whorled Wood AsterAster acuminatus*
Yellow Wood-SorrelOxalis stricta*
Unknown 1???

Species-Area Curves

I very much like to wear the “citizen scientist” mantle, but pictures and a list don’t quite entitle me to wear it. Rather, a yellowing 17-year-old article, uncovered during a recent spring cleaning of my files, offered the necessary inspiration and tools. The piece, entitled Biodiversity in the Backyard ran in the January 1993 issue of the Scientific American as that issue’s The Amateur Scientist column, and was written by Henry S. Horn, Princeton University professor of ecology and evolutionary biology. In it, he described a wonderful ecology activity exploring the calculation and meaning of a species-area curve, an activity he developed originally as part of a summer program for grade school teachers. Pretty heady stuff for grade school teachers and, by extension, their students. Over the years, the project has reached many higher level students as well. It’s an inspiring blend of field work, mathematical analysis, and hypothesizing. And, when I tore it out of the magazine those many years ago, I thought that this would make a grand science fair project for me and one of my children. When the time came, my children, rightly suspicious of my enthusiasm, declined the invitation.

So, a week ago, I (alone) finally followed the steps of the project described by Horn. My effort differed in key, possibly “fatal” ways. First, the sheer size of the terrain under analysis was dramatically different. His participants worked on a stretch of lawn on the Princeton campus that was 256 square meters, not something paltry like my 64 square foot plot. Horn’s folks inventoried all vegetation found, while I restricted myself to those plants that were in flower. [Later edit: I should clarify that Horn's folks did not worry about identifying the correct common or scientific names for their individual species. Rather, they distinguished separate species solely on the basis of leaf shape and gave species new informal names for the project. Frankly, part of the fun for me was the process of trying to affix the correct scientific label to each species. Limiting myself to plants presently in flower made this much easier.]

Regardless of the possible misguided nature of my venture, I plowed ahead. A comment at the outset on the species-area curve. Though, as I will describe below, there isn’t just one such curve, they all are graphic representations of the relationship between changes in the area under analysis and the number of unique species found. These curves are not restricted to plants. Insects and animals are fair game, though a more difficult prey given their mobility. The basic message of species-area curves is that as area increases the likelihood of encountering more species also increases. More on that message later.

I inventoried the plant species that were flowering during the first week of June in my plot, after I subdivided the plot into a nested sequence of smaller square blocks as shown below. The initial four blocks (numbered 1 through 4) were each one foot by one foot squares, the next three (5-7) were each two by two squares, and the next three (8-10) were four by four squares. Horn subdivided his plot similarly, though his initial blocks were one meter by one meter, and he created three additional blocks, each eight meters by eight meters.

The key piece of calculated data was a running cumulative total of unique species found, beginning with the smallest block (1) and ending with the largest (10). The table below shows the distribution of the species by block. The number in the block in which a species first appears is colored red – these are the species identifications that were added to the running total. (The use of the number "1" in the species' blocks was a matter of convenience for calculating the running totals. More than one specimen of a particular species might well have been found in a particular block.)

From these data, I graphed the relationship between the increasing cumulative total number of species (Y axis) against the increasing cumulative area (X axis). Plotting these data points and connecting them with straight lines produced a species-area curve (its “Type I – Horn Variation” label will come clear in a bit) that has a definite stair step aspect to it at the outset (where the number of species remained static while the area was increasing) and approaches a smooth curve as the area increases.

What does this graph convey? (Besides that I am devoting a lot of time to this little exercise.) Not unexpectedly, its message is that, as the cumulative area rises, the cumulative number of species found is likely to rise. Seemingly a truism, this relationship between area and number of species has a prominent place in ecology. Samuel M. Scheiner, biologist in the National Science Foundation’s Division of Environmental Biology, has written:

This increase of species number with area has been called one of the few laws of ecology, making species-area curves a prime measure of ecological patterns. (Six types of species-area curves, Global Ecology and Biogeography, 2003, p. 441.)

According to Scheiner, at its most basic level, this growth in the number of species is a function of two developments related to expanding the area analyzed. First, a larger area is likely to have more individual specimens, raising the probability that new species will be found. Further, as the reach of the sampled area is increased, the likelihood that environmentally different locations will be included rises, and such locations are more likely to be occupied by species different from those already encountered.

In the article cited above, Scheiner analyzed six different species-area curves, asserting that the appropriate use of each may vary. They differ in terms of the arrangement of individual blocks within the area being analyzed – a uniform grid of contiguous blocks of the same size is at one end of the spectrum while noncontiguous blocks of differing sizes (think islands) is at the other. The Type I curves (of which Horn’s is a variation) involve single counts and may result in the stair step pattern; most of the others are based on averages of the number of species found in various blocks of the same size and generate smooth curves. These curves differ in other dimensions, including whether they are sensitive to spatial arrangements of species within the area.

For the sport of it, I tackled the calculation of a Type IIA species-area curve for my plot. This curve is generated by calculating the average number of species in contiguous blocks of different sizes across the entire area under analysis. I began with one foot square blocks of which there were 64 in the 8 foot by 8 foot plot. I then calculated the average number of species in all possible two foot by two foot squares within the plot – 49 such squares exist. Similar calculations were made for squares of increasing sizes up to eight by eight foot squares (obviously, just one in this plot). Here are my calculations:

Block Dimensions (Ft.)Avg. # Species Per Block
1 x 11.23
2 x 22.71
3 x 34.50
4 x 46.28
5 x 57.88
6 x 69.11
7 x 710.75
8 x 812.00

And then I graphed the average number of species by block size. A very nice species-area curve emerges, one that is actually a smooth (well, almost smooth) curve.

So what’s been gained by all of this? Well, I had some fun. I made some sense of a baffling riot of colorful plants that colonized a patch of dirt and rock. And even this small plot appears to support the basic message of the species-area curve. And, yes, it would have been a winning science fair project for child . . . and father.

Later Postscript
I've been thinking about the consequences of limiting my sample to those plants in bloom at a particular point in June. To the extent that a species-area curve is a measure of the distributional patterns of all of the species occupying a specified area, the inventory I made of the plant species in bloom on my plot raises some concerns. Is there any reason to suspect that, by limiting my sample as I did, that the core relationship of number of species to cumulative area should be different? Certainly, none of the methods I used would allow for the number of species to decrease as the area grew. Further, it shouldn't affect the logic that using average counts of species would smooth out the stair steps of the Type I curve and yield a smooth curve that was likely to show fewer new species added after an initial steep climb. Limiting my inventory to plants in bloom certainly made identification of species easier (my guide is keyed to flower colors), but the attribute of being in bloom was in addition to the fundamental one of having established a foothold in my plot of land, and it certainly had consequences for the species counts in each block. I don't know its consequences for overall results. Still, there are myriad variables to consider. When a plant is in bloom is a function of many factors, presumably including when other plants are in bloom, when and where pollinators are active, rainfall, sunlight, temperature, . . . . Does this change the meaning of what I've calculated? Ah, part of the beauty of the effort is revealing the questions after questions.


  1. What a great summer science project! Thanks! I would like to share a list of Middle School Science Projects at

    Pragmatic Mom
    Type A Parenting for the Modern World
    I blog on education, parenting and children's lit

  2. Pragmatic Mom: Thanks for your comment. This project could be a fun summer activity, but, be warned, the inventory process can get tedious. In fact, Horn notes that one group of his grade school teachers slacked off late in the inventorying and may have messed up the data a bit. You might want to check the later edit I made to the posting [it's in brackets] which describes how Horn's students went about distinguishing among separate species. As for science fair projects, they are a rite of passage for parent and child. I appreciate that your list includes many that don't involve much of a cash outlay and can be handled at various levels of analysis. As one who briefly taught at the elementary school level, I don't think much science is really done in elementary or middle school science fair projects, and I wonder what impact they actually have on students' views of doing science. I suspect there's research out there about that.


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