About the Data

About Douglas fir biometrics:

Douglas fir (Pseudotsuga menziesii) is a common component of forests in the lowlands of western Washington and a native tree to forests of western North America (widely transplanted elsewhere). Douglas fir is an early colonizer of open spaces, and is typically succeeded by other species such as hemlock in the natural forest succession. Douglas fir grows very quickly, and therefore is often planted by foresters following harvesting. Information (including pictures) about Douglas fir and conifers in general can be found at the Gymnosperm Database,  http://www.conifers.org/index.htm 

The quantitative study of the growth of organisms (biometry) really got a boost from D'Arcy Wentworth Thompson's 2 volume treatise, On Growth and Form, first published in 1917. Other illustrious contributors to this field include the Harvard paleontologist Stephen J. Gould. Organisms typically change their growth patterns over time, often declining in growth rate as the organism ages. Trees change their height and diameter at differing rates over time. A typical conifer will increase its height relative to its diameter at a faster rate during its initial period of growth, and then add girth at a faster rate relative to its height change in maturity.

For conifers and other organisms with slow growth and long life spans, it is very cumbersome to measure a single organism over a long period of time. Furthermore, the resulting growth curves will be highly dependent upon all the other factors that influenced that particular individual specimen, including genetic makeup, local environmental factors, etc. Your single specimen might not be "average" or typical in its growth patterns. So instead of measuring one individual at many times, we can measure many individuals (a sample) at one time, a snapshot.  The individuals in the sample will exhibit a range of ages, to give us the full spectrum of growth. And the natural variability between individuals of the same age will be taken into account; mean values of any biometric parameter for any age can be determined.

Two of our students gathered data on the circumference (at chest height) and the height of about a two dozen Douglas fir trees along the White River valley in the Cascade foothills of Washington State. Circumference was measured directly; to calculate height, students measured the angle of inclination to the top of the tree from a location horizontal to the base of the tree. By using elevation angle, horizontal distance from the tree, and eye height, students calculated the height using simple right triangle trigonometry. See photos below.

Many questions can be asked about the student's sample of Douglas fir trees (or whatever tree is convenient for your students). Is the sample biased or unbiased? Is the sample stratified or unstratified? Is this a sample of convenience? How representative of the population of Douglas firs (along the White River valley) is this sample?

The Douglas firs show a typical growth pattern. Students can try curve fitting using a graphing calculator or Excel; what kind of functional model best describes Douglas fir growth?

Growth sequences can have all sorts of utility. For example, to determine the total amount of lumber in a particular stand of second growth Douglas fir, it is not necessary to measure the height of the trees, which is time consuming and difficult in thick forest. Instead, the diameters can be quickly measured, and using the growth sequence already established for this specie, the height can be read off the graph or calculated from the best-fit empirical formula. The volume of lumber can then be determined. The influence of growing parameters such as soil type, elevation or microclimate can be quantified by determining growth curves for trees in different areas.