View source for Periodic annual increment

{{Short description|Forestry term for change in size of tree on annual basis}}

In [[forestry]], '''periodic annual increment''' (PAI) is the change in the size of a tree between the beginning and ending of a growth period, divided by the number of years that was designated as the growing period.<ref>Avery, T.E.,B.E. Harold. 2002 Forest Measurements, fifth edition. New York: McGraw-Hill. 426 p.</ref> For [[sigmoid function|sigmoid]] growth, the graph of PAI increases rapidly and then quickly declines, approaching zero. PAI may go negative if a tree loses volume due to damage or disease. 
Periodic annual increment is commonly used instead of current annual increment as a basis for computing growth ''per cent''. Growth ''per cent'' indicates the rate of increase with relation to the wood capital required for its production, this is usually based on a single year's growth.<ref>Chapman, H.H.,1921, Forest Mensuration, second edition. p315 New York: Wiley & Sons, Inc.</ref>

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== Equation ==

<math>PAI= \frac {Y_2-Y_1} {T_2-T_1} </math>

Where: Y is the yield (volume, height, [[diameter at breast height|DBH]], etc.) at times 1 and 2 and T<sub>1</sub> represents the year starting the growth period, and T<sub>2</sub> is the end year.

Example: Say that the growth period is from age 5 to age 10, and the yield
(height of the tree), is 14 feet at the beginning  of the period and 
34 feet at the end. 
Then: <math> \frac {34-14} {10-5} = 4 feet/year </math>

==Uses==

The maximum point on the curve of PAI is the same as the [[inflection point]] on a graph of yield versus time. The inflection point is the point corresponding to the fastest change in yield.

When [[mean annual increment]] (MAI) and periodic annual increment (PAI) are graphed together, the point in which they intersect is called the biological rotation age. The biological rotation age is the age in which a stand should be harvested to maximize long-term yield.

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==References==
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{{Forestry}}

[[Category:Forest modelling]]