Is there a relationship between canopy breadth, height, and the trunk diameter of specific species of trees in Oxford, Ohio, and does this change with the surrounding environments? We hypothesize that a positive correlation exists among these factors. We also hypothesize that these comparisons change according to the location of the tree,
either in a forest or in an open environment. This topic interests us because we are curious to know if there is a consistency among tree growth.
The purpose of our experiment, therefore, is to find a mathematical correlation between these three measurements, and not to determine, necessarily, the environmental factors leading to these results. Conducting this study may lead us to better understand the growth of different species of trees in the two environments. This, in turn, may be useful to the professions involving reforestation and landscaping.
Sufficient evidence supports the fact that there is a relationship between canopy breadth, height, and the diameter of the trunk at breast height (dbh) within a particular species of trees.
Most of our sources suggest that there is a constant ratio among each of the three relationships (canopy breadth to trunk diameter, trunk diameter to height, and height to canopy breadth). For example, there is a positive relationship between the trunk diameter and the height within the species of the Giant Sequoia, a cousin of the Redwood. They may grow to reach a height of 350 feet with a trunk diameter of up to twenty-two feet (Dold 120). Similarly, smaller trees are more likely to have a smaller trunk diameter.
The reasons for these correlations may not be solely due to common growth patterns within a particular species of trees. For example, many scientific sources give sufficient evidence as to the adaptation of trees to their surrounding environments, which may alter the normal growth patterns. Such factors affecting the growth patterns within a species may include the location, the competitive forces among neighboring trees involving sunlight and water, and age. We are excluding all such variables in our measurements except the species of the trees and the locations of these trees.
One source states there is a strong correlation between the three measurements both within and across species, “suggesting that many species have similar allocation patterns” (O’Brien 1928). Another source states that there is little size dependency within a species.
Location is an important factor in determining tree measurements. In a closed canopy, there is a lot of competition among trees for such things as sunlight, water, and growing space. In a dense forest it is likely that there will be little foliage near the forest floor and the trees will tower because of their need for sunlight. However, in an open environment it is not necessary for a tree to be as tall because sunlight is abundant. The location concerning different parts of the country also affects tree growth. The palm tree, for example, is likely to grow into a mature tree in California, but in Ohio it may only tolerate weather conditions in a green house, where the amount of sunlight and temperature can be replicated like that of California. For example, Ryan states in “Hydraulic Limits to Tree Height and Tree Growth;”
“In the front range of the Colorado Rocky Mountains, a seed from a twenty-five meter tall ponderosa pine may fall into a rocky crevice and never grow more than one to two meters. On the eastern slope of the Cascade Mountains of Oregon, ponderosa pine soar to fifty meters. Thirty kilometers farther east in a drier climate, the same species struggles to attain ten meters…maximum height and the rate of height growth vary remarkably from place to place.”
Also, little wind reaches the center of the forest, meaning that there is little obtrusion in the direction of growth.
Age has been proven to slow the upward growth of a tree, even though the tree trunk diameter may continue to grow, which would change the constant ratio between the three measurements. At a certain age, the tree stops growing completely in height. A young mountain ash may grow up to two to three meters per year in height. By 90 years of age, height growth slows to 50 centimeters per year, and by 150 years, height growth stops, although the tree may live for another century or more (Ryan 235). Factors of age that affect the growth may be slowed photosynthesis, lack of nutrient availability, or a lack of carbon for multiple trees to flourish. For reinforcement, these considerations will not be taken into account, but may ultimately be a factor in why certain trees grow the way that they do.
Materials and Methods:
The materials we used in this experiment included: protractor; string and weight (clinometer); tape measure (in metric); calculator; chalk; leaf guide; and maples, oaks, and ashes.
Using a field guide, we identified if the type of tree was a maple, oak, or ash. If so, we recorded the species on the data sheet. We determined whether or not it was in a forest. At least five trees within a 6.1-meter (20-foot) radius constituted a forest.
To measure the height of the tree we stood at a point away from the tree (at least a few meters) in which the top of the tree could be seen. We measured this point's distance from the center of the trunk and recorded this under the column "Point Distance" in our data sheet. We then stood at this point and used the clinometer.
By extending the clinometer up towards the tree so that there is a direct line of sight with the straight edge and the top of the tree (the highest point), we measured the angle the string made with the protractor. We subtracted this number from 90 degrees to find the angle from the "Point Distance" to the top of the tree. We let this be called angle “Q,” and recorded it as such.
We then measured the height of the person from his/her angled arm, and used this height as a reference for all protractor readings. This was recorded under "Height of Person." To determine the height we first used the trigonometric equation: tanQ = Height/ Point Distance.
This determined the height from the protractor (at 0 degrees) to the top of the tree. To find the total height of the tree, we added the height found using the trigonometric equation to the "Height of Person." This was recorded under "Tree Height."
To measure the diameter at breast height (dbh), we first positioned the tape measure around the trunk of the tree at breast height to avoid the butt swell (the wide bottom part of the trunk). We recorded this under "Circumference." By using this measurement as the circumference, we used the formula: Circumference = Diameter * Pi,
to determine the diameter of the trunk, with pi being 3.14. This was recorded under "Diameter."
To measure the canopy breadth (overall width of tree), we stood underneath the furthest point out from the trunk, taking into account branches and leaves. We then measured the distance from this point to the center of the tree to the opposite point out from the trunk. We moved a little to one side and measured the canopy breadth using the
measuring tape. This avoided measuring a path that would interfere with the trunk. Then we recorded it under "Canopy Breadth."
After having measured a tree, we drew a ring around the trunk of the tree with chalk to indicate that tree was already measured. This avoided the same tree being measured twice. We followed these steps to arrive at the height of the tree, the diameter of the trunk, and the canopy breadth.
The class helped us gather data by finding tree measurements and by later doing calculations. The class was divided into three groups. Each of our group members accompanied a group to ensure their data was collected accurately. Those in the forest group measured 6 trees, collecting 2 measurements for each type of tree. The open environment groups measured 9 trees, 3 of each type of tree. Each group took
measurements of varying sizes of trees during class.
After information was gathered, we used scatter plots to compare two sets of data. The factors plotted were within a species. Those being compared were tree height and trunk diameter, tree height and canopy breadth, and trunk diameter and canopy breadth. A trendline was used on each graph to find the relation between the two variables. The Pearson Correlation Coefficient was used to find the probability of a line being accurate for any given data.
For actual data obtained, refer to the open access spreadsheet under the heading: “rachel”. The following tables include examples that the data was recorded on.
Table 1- Measurements
Height of Person: ________m
Type Forest? Point Dist.(m) Angles(degrees) Cir.(m) Canopy Breadth(m)
Type Q(degrees) Tree Height(m) Diameter(m)
(90-angle=Q) ((tanQ=(ht./pt.dist.))+person's ht.) (cir.=pi*dia.)
Trendlines indicate the average relation between the two variables measured in each graph. Trendlines are in slope-intercept form (y = mx + b). The “m” is the deciding factor in the relation between the two variables. Any “m” value above 0 indicates a positive correlation. All of our graphs indicated a positive correlation, which is to say that as the “x” variable increased, the “y” variable also increased. Because our “b” values were relatively small among all graphs, we excluded this value and used only the slope (“m” value) to determine the relationship between the two variables. By using these linear regression models, if one variable is known, the other variable can be estimated.
In order to compare data, it must be significantly comparable, which is to say, the plotted points must be relatively close to the trendline. The “R^2” value (Pearson Correlation Coefficient) indicates this closeness to the trendline. “R^2” values range from
0 to 1. One indicates a perfect correlation, in which all points lie on the trendline, and 0 indicates that the data points have no relation to one another. We chose to compare only sets that had an “R^2” value equal to or greater that .5, in which data centralized around a given value so comparisons could be trusted. The graphs that indicated correlations (above .5) were those comparing canopy breadth and tree diameter. These included all three species in the forest and in the open. Surprisingly, therefore, no correlations existed between height and canopy breadth or height and tree diameter. The comparisons proved some interesting correlations between and among trees. By comparing slopes, we found positive correlations between canopy breadth and the trunk diameter. Comparing maples and oaks in the open showed that canopy and dbh correlated strongly, with slopes of 20.63 and 22.198, respectively. Also, looking at open maples and forest maples, our data showed a strong correlation (20.63 and 24.514). Open oaks and forest oaks had a similar relationship (22.198 and 22.559), as did forest maples and forest oaks (24.514 and 22.559). The previous information is compared below.
Open Maple Open Oak
Forest Maple Forest Oak
All relationships between canopy and dbh relate similar findings among open maples, open oaks, forest maples, and forest oaks. The strongest of all these correlations included the open oaks and forest oaks. We can conclude, therefore, that the location (forest or open) is not significant concerning the growth of both the canopy breadth and the tree diameter. Open maples and forest maples did not prove as strong a correlation as did open oaks and forest oaks.
Forest ashes, with an “R^2” value of .4851, did not meet the strength of the correlation we set to determine it comparable data. The open ashes had an “R^2” value of .6254. But if we chose to compare these sets of data regardless, we would see that the growth of canopy breadth and of tree diameter of forest ashes and open ashes did not
correlate as strongly (20.906 and 13.385). Ashes, unlike the maples and oaks, may not correlate as strongly in our data because the “R^2” value indicates a less determinant set of data points.
Discussion and Conclusion:
From the information that was obtained, we were able to find strong correlations between the trunk diameter and the canopy breadth. However, there may have been some factors that skewed our data. In gathering our information, we tried to be as consistent as possible, however, factors dealing with human error may have had a slight impact on some of our data. This may further indicate why our hypothesis was false with regard to positive correlations involving height. If we were to continue this investigation, we would build a stand for the clinometer for readings to be read off of to avoid this type of error.
Also, it is assumed that all readings are taken from a flat plain, without hills. Error may have resulted from this as well, although we did try to measure in order to overcome this.
As previously stated, the height did not have strong relations with other variables across species or within species concerning the location. This disproved our hypothesis. Once again, reasons may be offered for this surprising discovery. Age, as stated by Ryan,
is a cause for the upward growth of a tree to slow, while the canopy breadth and trunk diameter continue to grow. This, therefore, may be the reasoning behind this. If we were to do a follow-up study, we could explore the relationship of these factors within age groups of trees, so that conclusions could be drawn more inclusively.
In conclusion, strong correlations existed between the canopy breadth and diameter at breast height between the maple and oak species, and between the forest and open locations. Height did not seem to relate to any other measurements. The trees that we measured, while in some areas may seem varied, did contain certain uniform qualities.
Dold, Catherine A. “The Largest Tree on Earth.” Audubon. May 1990: 120.
Hara, Toshihiko, et al. “Growth Patterns of Tree Height and Stem Diameter in Populations of Abies Veitchii, A. Mariesii and Betula Ermanii.” Journal of Ecology. Dec. 1991: 1085-1098.
O’Brien, Sean T., et al. “Diameter, Height, Crown, and Age Relationships in Eight Neotropical Tree Species.” Ecology. Sept. 1995: 1926-1929.
Ryan, Michael G. and Barbara J. Yoder. “Hydraulic Limits to Tree Height and Tree Growth.” BioScience. Apr. 1997: 235.
Thomas, Sean D. “Asymptotic Height as a Predictor of Growth and Allometric Characteristics in Malaysian Rain Forest Trees.” American Journal of Botany. May 1996: 556-563.
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