Tree allometry
Encyclopedia
Tree allometry establishes quantitative relations between some key characteristic dimensions of tree
Tree
A tree is a perennial woody plant. It is most often defined as a woody plant that has many secondary branches supported clear of the ground on a single main stem or trunk with clear apical dominance. A minimum height specification at maturity is cited by some authors, varying from 3 m to...

s (usually fairly easy to measure) and other properties (often more difficult to assess). To the extent these statistical relations, established on the basis of detailed measurements on a small sample of typical trees, hold for other individuals, they permit extrapolations and estimations of a host of dendrometric
Dendrometry
Dendrometry is the branch of botany that is concerned with the measurement of the various dimensions of trees, such as their diameter, size, shape, age, overall volume, thickness of the bark, etc., as well as the statistical properties of tree stands, including measures of central tendency and...

 quantities on the basis of a single (or at most a few) measurements.

The study of allometry is extremely important in dealing with measurements and data analysis in the practice of forestry. Allometry studies the relative size of organs or parts of organisms. Tree allometry narrows the definition to applications involving measurements of the growth or size of trees. Allometric relationships are often estimating difficult tree measurement, such as volume, from an easily-measured attribute such as diameter at breast height
Diameter at breast height
Diameter at breast height, or DBH, is a standard method of expressing the diameter of the trunk or bole of a standing tree. DBH is one of the most common dendrometric measurements....

 (DBH).

The use of allometry is widespread in forestry
Forestry
Forestry is the interdisciplinary profession embracing the science, art, and craft of creating, managing, using, and conserving forests and associated resources in a sustainable manner to meet desired goals, needs, and values for human benefit. Forestry is practiced in plantations and natural stands...

 and forest ecology
Forest ecology
Forest ecology is the scientific study of the interrelated patterns, processes, flora, fauna and ecosystems in forests. The management of forests is known as forestry, silviculture, and forest management...

. In order to develop an allometric relationship there must be a strong relationship and an ability to quantify this relationship between the parts of the subject measured and the other quantities of interest. Also when developing this equation one must play in factors which affect tree growth such as age, species, site location, etc. Once all these guidelines are met, one may attempt to develop an allometric equation.

First thing to do is select a group of some subject (for forestry: trees). Then measure several easily measured attributes such as DBH, height, species, etc. Graph the results and perform a regression analysis and transform some of the variables until a correct regression
Regression analysis
In statistics, regression analysis includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables...

 is found.
There are different tree species compositions in each region in the world and most of those regions have at least one equation that estimates tree volume from DBH. Research and the application of forest allometry have meshed over time to develop these quick equations to accurately estimate how much volume a particular forest stand holds.

The general allometric equation for mathematics and science is

Y = β Xα

where "Y" is an biological variable (such as tree height or DBH), "β" is a proportionality coefficient, "α" is the scaling exponent (which is equal to the slope of the line when plotted on logarithmic coordinates), and "X" is some physical measure such as body volume or body mass(M). While α is often quite similar between very diverse organisms, β differs from species to species. Because the proportionality constant(β) and the scaling exponents(α) are often denoted using Greek letters, it is desirable to use β as the proportionality coefficient versus α, since α could be misread as the symbol for "proportional".

A well-known allometric equation relates metabolic rate to body mass: Y = βM 3/4.

In forestry
Forestry
Forestry is the interdisciplinary profession embracing the science, art, and craft of creating, managing, using, and conserving forests and associated resources in a sustainable manner to meet desired goals, needs, and values for human benefit. Forestry is practiced in plantations and natural stands...

the equation takes on many forms in order to represent relationships between the many various attributes of tree size and growth. Below is an example:

Y = b0 + b1 X
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