The mean annual increment (MAI) or mean annual growth refers to the average growth per year a tree or
stand of trees has exhibited/experienced up to a specified age. For example, a 20-year-old tree that has a stem volume of has an MAI of /year. MAI is calculated as
where
= yield at time
. For a stand of trees the total stem volume (m
3) per area (ha) is typically calculated. Because the typical growth pattern of a forest is
sigmoidal, the MAI starts out small, increases to a maximum value as the trees mature, then declines slowly over time as some trees' canopies face competition for sunlight and older trees die off.
Throughout this, the MAI always remains positive. MAI differs from
periodic annual increment
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. For sigmoid growth, the graph of PAI in ...
(PAI) in that the PAI is the growth for one specific year or any other specified length of time.
The point where the MAI and PAI meet is at the point of maximum MAI and is typically referred to as the
biologically optimal rotation age. This is the age at which the tree or stand would be harvested if the management objective is to maximize long-term yield. The proof of this definition is shown by differentiating
with respect to
, and is shown by Husch, Miller, and Beers.
[Husch, B., Miller, C.I., and T.W. Beers. 1982. Forest Mensuration. Wiley. New York. 402 p.]
Notes
References
Avery and Burkhart. ''Forest Measurements''. Fifth Edition, McGraw Hill, New York. 2002.
Forest modelling
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