Tree Biometrics and Growth Sequences

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  .

Approximately 700 year old Douglas Fir in the Dalles                    Variably sized Douglas fir near the McCullough Tree Farm, White River.
Campground, Highway 410.  6 Billion students for scale.

 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.  Humans, for example, have an early period of fast increase in height which decreases to nearly zero and often reverses in old age.

 Organisms often change their "shape" over time, where shape is any two physical parameters such as height, weight, diameter of leg bone, wingspan, shell width, etc.  Humans, for example, typically increase their height at a fast rate relative to their girth during youth, then increase their diameter at a faster rate than their height during maturity, giving rise to pencil-shaped youth and barrel-shaped oldsters.  Some "shape" changes are dictated by biomechanics.  As an elephant grows in total body weight, the diameter of its leg bones must increase to support that weight without failure; the change in leg bone structure is dictated in part by the stress (force per unit area) that must be accomodated.

 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.  If you graph X = diameter and Y = height for a single conifer over a period of time, you will probably see a concave downward curve similar in form to a power law curve with the exponent less than 1.  Graph, for example, Y = X^0.5.  Of course, if you were to switch these variables, you would get a concave upward curve similar in form to an exponential curve with base greater than 1.  Graph, for example, Y = 1.5^X.  Either choice of graphical representation is valid  in this case, because neither diameter nor height can be considered the "independent" or "dependent" variable; height and diameter are just biometric parameters describing the shape of the tree.

 For conifers and other organisms with slow growth and long life spans, its 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 population) at one time, a snapshot.   The individuals in the population 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.

 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 diamters 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.  Perhaps you are studying the puaiohi (small Kauai thrush), of which there are fewer than 200 left only on the Hawaiian island of Kauai.  Has inbreeding in this tiny population affected the growth of this specie?  You might compare the growth curve of this remnant population with growth curves for museum specimens obtained many years previous.

go to top of page