Academic journal article
By Lau, Joann M.; Korn, Robert W.
The American Biology Teacher , Vol. 69, No. 2
An important aspect of biology is spatial distribution and patterns of distribution can be either ordered, random, or clustered. For examples, deployment of mature trees in a forest is ordered, occurrence of zebras on a savannah is clustered, and location of clams on the ocean floor is random. Deployment can be examined in two directions; first is down the scale of order to study arrangement of organisms (trees, zebras, trout) in a population, leaves on a branch, stomates on a leaf, chloroplasts in a cell, etc. The second approach to the study of deployment is to provide a quantitative measure of a pattern. One means of quantifying space is by tile dispersion index, DI, which is tile variance over the mean, ([[sigma].sup.2]/m; a value greater than 1.0 indicates an ordered arrangement, a value of about 1.0 denotes a random pattern, and a D1 noticeably' less than 1.0 comes from clustering.
An interesting example of all three patterns is the occurrence of clustered stomates on leaves in some Begonia cultivars (Figure 1). In this figure stomates are found in clusters and the arrangement of these clusters is indicated by the DI which is 0.64/3.25, or 0.19, much less than 1.0. Also notice that clusters are usually separated by one cell, again, a relation that gives an ordered pattern. For the arrangement of stomates the DI is 74/13, or 5.7, much greater than 1.0 and so the pattern is one of order. Finally, the number of stomates per cluster has a D1 of 3.1/3.6 (Table 1), or 0.87 close to 1.0 for a random number of stomates per cluster.
[FIGURE 1 OMITTED]
Data collection and statistical analysis of the data is the hallmark of modern science but few teaching exercises are designed lot students to experience this approach. The difficulty with handling data is that it requires either too many organisms or the technological requirements are unrealistic. For a class to study the spatial distribution of trees, animals in a herd, or clams on the sea floor is unrealistic both with respect to travel and to have sufficient numbers to make sound conclusions. One example where many data points can be collected with minimal equipment is that of stomates (Greek for "openings") on the leaves of plants. In some cultivars of Begonia, stomates occur in clusters ranging from one to as many as ten (Payne, 1970) and these can be seen by a permanent preparation of a microscope slide as a fingernail polish imprint (Sampson, 1961) as shown in Figure 1. Seen under the microscope, 100 clusters can be counted for the number of stomates per cluster in only 15 minutes and, if desired, 500 within an hour. This data set can then be analyzed statistically by, calculating the average as well as variance and then tested to see if they fit a particular expected distribution, in this case the Poisson distribution. The exercise can be done in middle school classes by students making their own slides and seeing imprints of ceils, or at the high school level through collecting data of number of stomates per cluster and graphing the results, or in a college laboratory by comparing collected data to an expected Poisson distribution and doing a [chi square] test for goodness of fit.
Begonia (B. X semprflorens) plants can be purchased in the spring at a local nursery or are grown indoors year round. Some cultivars have stomatal clusters, such as "Vodka," "Whiskey," or "Lady Carol," while others, B. X tuberhybrid, have the more typical solitary stomates, so plants have to be checked well before class. A piece of leaf about the size of a postage stamp is cut off the plant and the imprinting method of Sampson (1961) is run as follows. The lower epidermis is swabbed with clear fingernail polish, left to dry for about 15 minutes, and then peeled off with a pair of forceps. This imprint is then placed on a dean microscope slide, a coverslip is placed over it, and a small dab of the fingernail polish is placed at two diagonal corners and allowed to dry in order to hold down the coverslip. …