• Increment: Increase in diameter basal area, height, volume, quality, price or value of trees or crops during a given periodCAI: current annual increment is defined as the increase in tree size in one year.
• PAI: it is difficult to measure the increment annually, the average annual growth over a period of 5 to 10 years is commonly substituted instead. The difference in tree size between the start and end of a growth period divided by a number of years involved is properly termed as periodic annual increment.
• MAI: is derived by dividing total tree size at any point to time by total age.
• Total increment: it is the increment of a tree from origin to age when trees cut

CAI and MAI Relationship

CAI is small in early stages (seedlings and saplings), increases slowly at first, then more rapidly to the maximum, after which it begins to decline, and finally ceases with its mortality. The sum of CAIs laid on for the entire period gives the total volume, which when divided by the age gives the MAI. It is an arithmetically derived value and coincides only twice in the life of a crop; once at the end of the first year and once later, when culminates and equals the CAI.

A time may come when there may be no growth at all and so the CAI will be zero. Unless the tree or stand is cut, loss in volume may start taking place due to rot or other damages and then CAI will become negative. But the value of MAI is never zero. In other words, until the tree or stand is cut or destroyed, the MAI is always positive.

The curves of CAI and MAI cross each other at the maxima of MAI curve. The age at which they cut, is the age of maximum production. In short,

• To begin with the MAI, keeps below the CAI
• While the CAI is more than MAI, the MAI is rising
• The CAI attains the maximum before MAI
• The CAI is falling when the MAI is still rising

When the CAI is equal to the MAI (the two curves intersect), the MAI is stationary, and has attained its culmination point.The MAI curve is flat at this point and the MAI is about the same for some years and some years after it. If the crop is felled at this age, at which the MAI is maximum.

Increment Percent

It is defined as the average annual growth in diameter, basal area or volume over a specified period expressed as percentage of diameter, basal area or volume

A. Diameter increment percent

1. Pressler’s formula

based on simple interest rate,

Mean of two diameter = (d+D)/2

Annual increment in diameter = (D-d)/n

As I=PTR/100, R=I*100/PT

so, P (increment) =200(D-d)/ (d+D)*n

2. Compound interest formula

The increment of a diameter, ht & volume in tree is like the increase in capital at compound interest

So, D= d(1+p/100)ⁿ how to derive p

Where, D is diameter after n years, d is dia at initial year, p rate of increment in % and n is number of years

D= d(1+p/100)ⁿ how to derive p

by compound interest formula

(1+p/100)= n√D/d

P= (n√D/d-1)*100

B. Volume increment percent

a) Compound interest formula

D= d(1+p/100)ⁿ how to derive

P= (n√V/v)-1*100

b) P (increment) =200(V-v)/ (v+V)*n

Therefore, p= 200(V2-v2)/ (v2+V2)*n

c) Schneider’s formula simpler formula

P=400/nD,

Where, D is the present diameter at the point of boring, n is number of rings in the outer most centimeter in the radius