The Concept of Increment in Forest Management
Table of Contents
GROWTH:
“The increase in dry weight of a tree throughout its active life is called growth.”
INCREMENT:
From Forest mgt point of view, the increment is important rather growth.
“Increment is the increase in growth, diameter, BA, ht, vol, quality or value of individual trees r crops during a given period.”
Growth is important because it tells us how much crop is to be harvested or cut, what the condition of the site is and what the comparative efficiency of different spp. is Moreover, it is important for making judgments about various silvicultural practices being done or to be done.
Each yr in each growing season, the trees put a new layer on all of its parts (ie stem, branches, and roots). In other words, every entity increases its size and vol within a due course of time. However in Forest mgt, the interest lies in the growth of dia, girth, vol, and BA ie the increment.
Forest spp have two types of increments ie

Current Annual Increment (CAI)

Mean Annual Increment (MAI)
CAI is the increment of a tree or stands of trees during each yr whereas the MAI is equal to the total vol divided by age or no of years in which the vol was attained.
If the volume is plotted against age the curve will show the increase in age increases the volume.
Periodic Increment:
“An average increment put on during a particular period is called PI”. Eg from 40 – 45 yrs. ∆n is the change during ‘n’ number of years.
PI = (Vol at any age + n – Vol at start) / n
The period is usu taken 510 yrs. PI is preferred because it is very difficult to measure increment for each yr.
RELATIONSHIP B/W CAI AND MAI:
An increment is always in the form of vol. CAI starts slowly at the initial stage but rises quickly and touches the climax from where it culminates (comes down) fast. CAI can also be negative sometimes when the crop reaches maturity or over maturity and at this stage the growth is negative.
MAI is more or less smooth in the track. It starts rising smoothly and cut CAI at point A which is the age of maximum vol production. Eg in chir pine SQ I point A is at the age of 90 yrs with vol of 7.6 m^{3}.
CAI is always higher than MAI and CAI is always greater than zero and smooth in nature because it is an average of a number of yrs. The point A indicates that the crop should now be harvested. Beyond A, the growth is lesser. Nevertheless, the vol production may not be economical. If maximum revenue is needed than rotation age is important. Here the total cost and total revenue are compared and it is calculated
DETERMINATION OF ECONOMIC ROTATION AGE:
Rotation:
 Planned number of years b/w regeneration of the crop and its final cutting at a specified stage of maturity.
 A rotation is the period of years acquired to reproduce, grow and harvest evenaged stands of timber in order to best accomplish definite objectives of mgt, namely, maximum production of vol and value, or, maximum profit; while maintaining the forest on a permanent basis.
Current and Mean Annual Increment:
 For determination of economic rotation age of evenaged stand, we should know CAI and MAI.
 The increment is the growth in height, dia, and volume of a tree in relation to time.
 One year’s growth is called CAI, this term is generally used for volume increment. CAI is the amount by which the vol of a stand increases in one year.
 One year’s growth is generally too small for accurate measurement, it is measured over a period of years and the average obtained from that is referred as Periodic Mean Annual Increment (PMAI).
 CAI is, however, used most often and in practice is always taken as an average annual increment over a short period.
 If the time to which growth is related is the age of the tree, the average obtained by dividing the total vol by the total age and is termed as Mean Annual Increment (MAI).
 According to the biological phenomenon, the CAI remains slow in the early age, becomes faster beyond that and shoots up in the youth to maturity period until it reaches culmination point from where it decreases onwards.
 The MAI, on the other hand, increases at a steady rate and reach the culmination point much later than CAI.
 The point of intersection of CAI and MAI indicates the age beyond which it is not economical to retain the tree in the forest; it is called the Economic Rotation for that particular spp at a site.
 This phenomenon is shown in fig.
 Consider the following example:
Years  Volume (cft)  MAI (cft)  CAI (cft) 
1  2  2  2 
2  4  2  2 
3  7  2.3  3 
4  10  2.25  3 
5  14  2.8  4 
6  18  3  4 
7  22  3.15  4 
8  25  3.125  3 
9  28  3.11  3 
10  30  3  3 
11  33  3  2 
12  33  2.75  1 
13  33.5  2.75  0.5 
14  34  2.43  0.5 
15  34.3  2.16  0.3 
 From the above example, it is clear that suppose we cut the tree at the age of 15 years, the total volume of the tree is 34.3 cft. While in other cases if cut the tree at the age of 10 yrs, total volume is 30 cft and replant the area, after 5 years the volume of the plant will be 14 cft. So from the same site, we can get 44 cft (ie 30 + 14) instead of 34.3 cft.
Need for information on Increment:
Information on increment is necessary due to the following reasons:
 It gives a check on the correctness of past mgt.
 It serves as a predictive tool for the future planning and mgt.
 Having knowledge of increment, suitable silvicultural and mgt practices can be applied.
 Various tending operations can be judged.
 Increment decides the length of rotation.
 The increment is a dominant factor in deciding the optimum level of residual growing stock in selection forests.
 The rate of increment is a guide to check the correctness of the mgt practices being applied.
 Increment helps to estimate the forest area required to meet the future requirements.
 Forest industries can be established only if their requirements (means raw material ie wood) are guaranteed and such guaranteed and such guarantee can be given only if the information about the increment is available.
 The increment is also useful is several methods of yield regulation.
 Economic rotation age can be determined.
MEASUREMENT OF INCREMENT:
The following are used for determination of increment.
 Yield Table Method
 Spur’s TwoWay Method
 Stand Table Projection Method
 Continuous Forest Inventory Method
 Increment Determination by Control Method
Yield Table Method:
If valid yield tables are available, the future increment of evenaged forest can be estimated. To determine increment from yield table we should have knowledge of spp, SQ or site index, age, and density. If the stand has the same stocking (density) as of the yield tables then increment for the prediction period can be directly estimated from the yield tables.
But actual stands never have the stocking as the YT. YTs are made for 100% stocking (or 1 density) and the actual stands never have 100% stocking so vol is calculated from YT by the stocking of the stand in question and compare it with the stocking of YT.
Suppose;
Spp Chir
SQ I
Age 60 yrs
Density 0.7
At 60 yrs age YT standing vol per ha of SQ I of Chir = 207.82 m^{3}.
This is for 100% stocking and here density = 0.7, so standing vol of the actual stand of chir, SQ I, 60 yrs age.
= 0.7 * 207.82 / 1
= 145.47 m^{3}/ ha

YT showing vol at 70 yrs (for 1 density) = 252.6 m^{3}/ ha
So for 0.7 density à vol = 0.7 * 252.6 / 1
= 176.82 m^{3}/ ha
Now 10 yrs increment = 176.82 – 145.47 = 31.35 m^{3}/ ha
The approach towards Normality:
The phenomenon of understocked stands tending to approach fully stocked stand with an increase in age is called Approach towards normality.
Spur’s TwoWay Method:
Spur in 1952 stated that growth is the vol of a stand is a function of its growth in BA and ht assume that no material change occurs in the stand form factor in the prediction period eg 10 yrs.
The actual stand ht and stand BA are measured stand vol computed from vol tables.
The ht 10 yrs here is estimated from SQ curves. Then the growth in BA can be estimated from increment cores by the following formula.
G_{BA} = ∑D^{2} (∑d_{1}^{2} – ∑d_{2}^{2}) / 183.3465 ∑d_{1}^{2}
Where G_{BA} = Growth in the basal area; ∑D^{2}= Sum of squares of dia over the bark of all trees enumerated; ∑d_{1}^{2} = Sum of squares of present dia under the bark of all trees bored; ∑d_{2}^{2 }= Sum of squares of dia under bark 10 yrs age of all trees bored.
Knowing present ht (h_{1}), present BA (B_{1}), present vol (V_{1}), future BA (B_{2}), and future ht (h_{2}), and we can estimate future vol (V_{2}) as;
h_{1} B_{1} / V_{1} = h_{2} B_{2} / V_{2}
V_{2} = h_{2} B_{2} V_{1} / h_{1} B_{1}
Stand Table Projection Method:
This method is applied to working plans. In this method, the stand whose growth is to be predicted is enumerated into one or twoinch dia classes. Then 10yrs (prediction period) increment of every dia class is calculated. Increment borer is taken and a core of wood is taken out of all the dia classes.
Moreover, the length of the core of wood taken out by the increment borer up to 10 rings ie 10 yrs growth say it is 1.6 cm. so growth in 10 yrs from both sides = 1.6cm + 1.6cm = 3.2cm
A number of trees in the same dia class are similarly measured and the average of their growth is calculated eg 12 – 14 or 14 – 16.
Dia Class Average increment for 10 yrs
12 – 14 3.2
14 – 16 3.3
16 – 18 3.4
. .
. .
. .
.
.
78 – 80
There is error in this method because it relates growth in the past (ie 1991 – 2001) with growth in the future (ie 2001 – 2011) which may be different because the various growth conditions may not be same in past and future.
The numbers of trees which will move onto the next higher classes during growth prediction period are estimated in terms of Moment Ratio which is the percent ratio b/w average increment for prediction period and diameter interval.
Moment Ratio (%) = Average increment for 10 yrs / dia interval * 100
For the data the MR of 12in – 14in dia class = 3.2 * 100 / 2 à 160%
(60% will move two classes and the remaining 40% will move 1 class up)
Continuous Forest Inventory Method:
100% enumerations are not feasible in large forest areas. To avoid this difficulty permanent sample plots are laid out and measured at 510 yrs intervals. The information thus collected is applied to large forest tracts for the purpose of mgt and planning. For this purpose either fixed area plots or prism sample plots may be employed. To ensure that the sample plots may be employed. To ensure that the sample plots receive the same treatment the plots are usu not visibly marked on the ground but are traced by various devices eg map position, reference trees, etc.
The sample plots are measured after regular intervals of time ie 5 to 10 yrs eg in 1980 the vol was V_{1} and in 1985 it became V_{2}. The increment is the difference of these two vol ie
Increment = V_{2 (1985)} – V_{1 (1980)}
Increment Determination by Control Method:
In this method, the compartments are enumerated at 100% at intervals of 5 – 8 yrs. Careful records are kept by compartments of all mortality and all trees cut in the interval b/w successive counts.
In growth is estimated by a process of accounting for every tree which is present at the second count or which has died or has been removed in the period since last inventory.
Then with the help of a local vol table, the no of trees is converted into vol and from the vol, the increment for the required period is calculated.
Brief Glimpse:
Out of all the methods stated above for calculation of increment, the method of continuous forest inventory is the most accurate. It enables the determination of increment under the actual conditions of forest working and is superior to the YT method in which the plots are given ideal treatment (ie stocking 100%).
COMPONENTS OF INCREMENT:
In a stand, individual trees put some increment and not the total forest. The total increment is not the same as increments of these. So there are some terminologies regarding the matter under consideration.
Ingrowth:
“It is the vol of those trees which were small ie <8inch dia during the first measurement but will enter into 8” dia in the second measurement is called Ingrowth or Recruitment. ”
Eg if in 1990 some sample plots are enumerated and in these plots, the trees having 5”, 6” dia are not enumerated but when enumeration is done in 2000, the trees which were 5”, 6” etc may now have more than 8” dia, so they will be enumerated in 2000. This is called Ingrowth.
Gross Growth including Increment:
= V_{2} + M + C – V_{1}
(V_{2 }= Future vol, M = mortality trees, C = trees harvested; cut down, V_{1} = Initial vol)
Means total growth including everything viz there are some trees which have died but were included in the measurement. Similarly, some trees might have cut down.
Gross Growth of Initial Volume:
= V_{2} + M + C – I – V_{1}
(Where; I = Ingrowth)
Net growth including Ingrowth:
= V_{2} + C – V_{1}
Since dead trees have no more ‘net’ growth, so they are not taken into account
Net Increment of Surviving Trees:
In Initial Volume:
= V_{2} – M – C – I – V_{1}
Net Growth in Growing Stock:
= V_{2} – V_{1}
Net growth in initial volume:
= V_{2} + C – I – V_{1}
SILVICULTURAL OR PHYSICAL ROTATION:
 The silvicultural or physical rotation are the basis for the final choice of a rotation, is that dictated by the forest as a plant community and best suited to its perpetuation and maximum vigor of growth and reproduction.
 The elements to be considered are as under:

Reproduction:
 Were clearcutting and planting practice, this factor is negligible, but their natural seeding is depended on a considerable degree of maturity that may be required to produce a sufficient quantity of seed.

Preservation of Productiveness of Type:
 Too long rotation may result in site deterioration by opening up of the stand favoring the entrance of weed trees and brush, or by increasing the proportion of undesirable invaders.

Protection against destructive agents:
 Short rotation tends in some cases to the establishment of stands of less desirable spp; more susceptible to damage. The term natural rotation is sometimes used to designate the period through which a natural stand of a gives spp or mixture may be expected to survive and occupy the soil in the absence of lumbering, fire, insect devastations or abnormal winds, etc.
For correction and improvements please use the comments section below.
Thank you sir for providing lots of information..Really appreciate it as a forestry student of IOF Nepal..Sir,which is the best method of determination of crop increment?
You’re welcome, dear. Back in days students from Nepal used to come to Pakistan and study in PFI (Pakistan Forest Institute Peshawar). Our teachers/seniors have friends in Nepal who have completed B.Sc / M.Sc Forestry from here.
So far as your question is concerned, out of all the methods stated above for the calculation of increment, the method of continuous forest inventory is the most accurate. It enables the determination of increment under the actual conditions of forest working and is superior to the YT method in which the plots are given ideal treatment (ie stocking 100%).
I feel honoured,thanks for your prompt response!
You’re always welcome 🙂
Hey mate,
Thanks for this. What would you say is the difference between MAI and CAI for an even aged forest?
Cheers
please give the link for this book i am a student
https://forestrypedia.com/download/theforestmanagementnotesbynaeemjavidmuhammadhassani/
At the age , at 9 years the volume is 28 , and at 10 years the volume is 30 , so the current annual increment at ten years should be 2 years, there is mistake , the CAI is written here 3 instead of 2.
Let me check it plz