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The Regulation of Yield

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            A loose term generally applied to determine the yield and the means of achieving it. Yield regulation means to estimate the amount of yield ie how much should be harvested (cut), where to harvest, when t harvest and also ‘in which form’, ie either main felling, intermediate felling, etc.

Objects of cutting:

There is a no of reasons why a forest is harvested:

  • To supply forest produce to the market to meet the various requirements.
  • To develop a proper structure/ design of crop. It means that sometimes money is not needed but the need is the structure adornment ie to have proper crop conditions or size conditions.
  • To reduce the length of rotation.
  • To remove low inferior growing trees.
  • To remove defective trees.

But the basic question is that how much should be cut? This is prescribed by various methods of yield regulations.

Methods of yield regulation:

  1. Area Method
  2. Volume Method
  3. Use of Formulae
  4. By Number of Trees
  5. By Stimulation Modes

Area Method:

This is the simplest method of Yield Regulation. It tells that how much area should be harvested.
Area to be harvested = Total Area (At) / Rotation (R)
Or, Ah = At / R
This method can be applied for Irrigated Plantations, Riverain forests, and chir pine forests.
This method is applied only to even-aged forests provided the SQ, the area occupied b each age class and the stocking is same. If variations of the SQ are present then adjustments are made accordingly.
Thus SQ I may require less area to be harvested than SQ II, or SQ III.

Site Quality Area Final yield/ acre Ratio of Yield
I 1050 2536 1
II 5700 2036 0.80 (1.25acre)
III 3850 1330 0.520(1.30 acre)

For finding ratios or adjustments, take SQ I as one unit and find out the ratio of the others with one. So far the circumstance of production or cutting the 1.25 acres of SQ II is equal to 1 acre of SQ I. Similar is the case with SQ III (1.90 acres of SQ II = 1 acre of SQ I)

The advantage of Area Method:

  1. It is the simplest method because no knowledge of growing stock is needed, no increment is needed.
  2. It is suited to even-aged crop.
  3. This method is most suitable when our main objective of mgt is the silvicultural improvement of the growing stock because each coup can be intensively treated.

Disadvantages of Area Method:

  1. Vol of thinning is problematic ie because the only area to be harvested is prescribed by this method.
  2. It does not reckon the vol of increment growing stock which may vary from one place to the other.
  3. It is not suited to uneven-aged forests.
  4. In this method, the final and intermediate yields have to be determined separately.

Volume Method:

In this method, the vol is also taken into account. The annual yield should be equal to the vol of the actual growing stock divided by rotation.
Annual yield = Vol of actual growing stock / Rotation
Ya = Va / R
This method is an improvement over the area method however in different stand types.
Ya = (V1/R1 + V2/R2 + V3/R3 + ……… + Vn/Rn)
There can be different stand types in a forest eg Chir pine + Blue pine, etc.

Disadvantages of This method:

  1. It does not take into account the growth and increment of the crop.
  2. This method will give yield even if there is no mature tree ie when the young crop is present and old is absent.
  3. The problem of location of yield area is also faced.
  4. SQ is not considered.

Use of Formulae:

The formulae used for regulation of yield have been divided into two categories, ie

  1. Without Increment (I) or Formula-based or growing stock or the volume.
  2. Volume and Increment (both)

Without Increment:

  • Von Mantel’s Formula:

This formula which is based on the relationship b/w vol and increment was introduced by Mantel in 1852.
The relationship b/w vol and increment is;
I = 2Vn / R
(Note: For the derivation of this formula see previous chapter; Relation b/w Vol and Increment of Normal Forest)
It means that if the forest is normal, we will be cutting twice the normal value. Von Mantel said, “Replace the increment with annual yield.”
Ya = 2Va / R
ie If we put the yield equal to increment, then we will be cutting yield exactly equal to the increment put on, each year. However, it is commonly called;
Annual Yield = Volume / 0.5 R
Annual Yield = 2Va / R

Merits and Demerits of Von Mantel’s Formula:

  • It is simple to evaluate.
  • The only information required is the vol of growing stock
  • It is extensively used in Pakistan.
  • It is derived from the normal forest model, so it is not suited to irregular and uneven-aged forests.
  • It works out final yield only. The thinning yields are not calculated here.
  • It usu gives a low yield.
  • Hundeshogen’s Formula:

Hundeshogen, in 1826, said that the ratio of actual yield to actual vol should be same as that of normal yield and normal volume, ie
Ya / Va = Yn / Vn
(Where; Ya = Actual yield; Va = Actual vol; Yn = Normal yield; Vn = Normal vol)
One has to know the actual vol (Vn) only and the Yn and Vn are taken from the Yield Table. Thus,
Ya = Va Yn / Vn
Now it can also be said that Yn / Vn * 100 is the utilization percentage of a normal forest eg 5 / 100 * 100 (5 percent) means that utilization is 5 because how much percent of vol we can remove is our yield, since the utilization percentage, say, is already known so we can calculate the yield of our actual forest by:
Ya = 5 / 100 * Va [utilization % * Va]

Merits/ Demerits/ Comments:

  • Yield is based on the standing vol of actual growing stock so only the final yield is calculated and thinning yields are excluded. (Standing vol given in the YT is after thinning but this formula does not contain thinning vol).
  • Yield is fixed by a percentage of actual growing stock. The yield is greater if the growing stock is in excess and vice-versa. So the general principle of yield regulation is observed.
  • Point no2 stated above has certain problems that the basic assumption of the formula is not correct. The young crop grows faster while the old crop grows slower. So the ratio Ya/ Va does not remain constant. It means that Ya/Va = Yn/Vn, only when we have a young crop. The more of the old crop means that Ya/Va is less and vice versa. It is only correct when the crop is like a normal forest.
  • The formula gives absurd results because sometimes the yields are shown even when no mature trees are available.


  • With Increment (Volume and Increment) (both):

This includes the following formula:

  1. Austrian’s Formula
  2. Cotta’s Formula

Out of these formulae, the Austrian’s Formula is the most famous.

  1. Austrian’s Formula:

In this formula, the actual or annual yield is equal to
Ya = Ia + (Va – Vn)/ P
Where; Ya = Annual yield; Ia = Annual increment; Va = Actual vol; Vn = Normal vol; P = Adjustment period viz usu 1/3rd of R
This formula gives us the amount of wood which we will be removed each year. This is the virtue of this formula that both the vol as well as the increment are taken into account.
This formula shows that if the actual vol (Va) is more than the normal vol (Vn), the figure obtained will be positive and the ‘cut’ will be more than the increment and it the actual vol (Va) is less than the normal vol (Vn), the figure obtained will be negative and the ‘cut’ will be less than the increment.
‘P’ is the period during which we bring our forest to the level of the normal forest. It was previously kept equal to Rotation (eg 100 in case of chir). But what is meant by 100 yrs.? It actually means all our adjustments for 100 yrs will make it a normal forest. However, there are definite principles for ‘P’. Today they are used for 30 – 40 yrs.

  • If a forest is deviating slightly from the normal forest, the ‘P’ should be small it should be larger because the difference is very small and it can be adjusted during rotation.
  • If the deviation is stronger, it should be reduced as one should cut more or less in a greater amount.
  • No difference is exactly like the normal forest.

Now the problem is with the increment. When the crop is mature, Ia is smaller. When the crop is young what happens that Ia is more and the volume is small and even then we will be cutting more because the young crop put more increment. Since the Ia varies with the age, the need is how to balance and this situation? The answer lies in another formula viz called Gehrhardt Formula. According to this formula;
Ya = (Ia + In)/2 + (Va – Vn)/ P

  1. Cotta’s Formula:

This formula is widely used for the determination of yield among the periodic blocks particularly the regeneration blocks. So in regeneration block;
Ya = (V + ½ I) / P
Where; I = estimated growth of the initial growing stock in the Reg block; P = reg period which is usu one-fourth of the rotation (1/4 R)
For the yield regulation in the PBs, the PB method was used in 1820. There are three kinds of PBs.

  1. Permanent PBs: These are sub-divisions of felling series and have permanently allotted area on the ground and are not altered later. They are compact and equiproductive. They comprise the relevant age classes in requisite proportion. They do not move from their place but are transferred into the next form.
  2. Revocable PBs: These are equiproductive but need neither to be compact nor permanent. The areas are not fixed. In every mgt plan, all the areas are visited and new allotments are made. Generally the SQ of different areas intervenes to suggest these allotments. Incase of good SQ, one PB takes shorter period to get transformed into next PB and vice-versa. So at each compartment, go and make judgment whether it is suitable for PBI, PBII, or some else.
  3. Sing PB or Floating PB: This includes PBI only viz the regeneration block. Rest of all the areas are called un allotted (PBs). Regeneration block is the only subject of attention; we look only at the mature trees and are never concerned with other blocks, etc.

Use of Cotta’s Formula:

In the regeneration block, final felling is done whereas in other blocks only thinning is done.
Calculate yield for it. The calculation says that cut V/P but since the felling are completed during the ‘P’, so some of the increment will be put on by the trees and at the end of 25 yrs, the total increment will be available. In other words, the vol (v) has put some increment so it should also be included.
Logically we say that 50% of the trees are putting increment. If we take 100% increment, it means that we will be taking a little bit more than the estimation. So the formula including increment becomes
Ya = (V + ½ I) / P

                        Merits/ Demerits/ Comments:
  • This formula gives an estimate of the final yield only. The intermediate yields (thinning yields) are estimated from the past records or from yield tables. The intermediate yields are in other PBs and not in the PB in question.
  • This formula is widely used in Pakistan for the chir forests and normally the increment is not included. (In any mgt plan, the increment has not been used because forests are exposed to depletion, damages and other hazards. If includes increment, it means that the cutting is too much).
  • In Pakistan, the common method in PBs is the addition of advance growth and vol. normally seed bearers put 25% of the vol which is excluded. Thus annual yield becomes:

Ya = (Vol + Advance growth – Seed bearer vol) / Reg period (P)
From PB II and PB III, 10cft per acre per yr is cut and from PB IV we cut 8 cft per year.

By Number of Trees:

This method is very helpful for uneven-aged or selection forest. If we have the no and dia of the crop, the derived form of the forest will be as shown in the graph.
Yield Measurement - Forestrypedia
The above graph is self-explanatory showing the amount of ‘cut’ in a refined manner. The shaded portions should be cut. In 1, 2 and 3 the above-shaded portions should be removed and in 4, nothing should be removed.
In other countries, continuous forest inventories are made and all know that what no should be placed in which dia class. If permanent \cut and remove’ are known by the records kept, then the number can easily be kept in balance (eg in last yr such no was removed and now this yr so much will be removed or even nothing will be removed etc.)
Again if we have several forests, we should compare them and think about which the best is. Now make calculations on the basis of best eg which is thinning vol, which is the final vol, etc.

By Stimulation Modes:

These are also called computer models. They not only give yield but also the future development of forest over a longer period of time. This is very interesting to note to turn over the brain of the computer by prosecuting it in different ways. Actually all the data of the area, spp composition, growth of different spp, intensity of thinning, age and classes etc in fed to the computer. Now it makes calculations of its own and tells in a precise way what will be the condition of our crop in future. What is the effect of a mixed number of factors like SQ, spp composition, the intensity of mgt, etc on the crop and so on?
Then there may be different rotations, different areas, different compartments, what will happen after rotation, etc.
It is clear that a normal human mind cannot think of these possibilities, so the computer tells what the human mind can just imagine.
The yield which the computer tells may be like;
Yield Measurement 1 - Forestrypedia


High Hill Forests: (Deodar, fir, spruce)

Different methods can be used. Nowadays 50cm dia is mature, so 50cm dia is exploitable. Then all the formula ie Austrian’s, Hundeshagesn’s, Von Mantel’s etc can be applied except Cotta’s Formula because Cotta’s formula deals with mature crops only and out forests contain all age classes.

Chir Pine Forests:

(Since there are clear-cut age classes, the above all formulae cannot be used because they are for the whole of the crop. There should be a separate method for a mature crop so it is always in PBI
PBI = Ya = V/P
Here the increment is excluded because these forests are under depletion and damages. Moreover, PB-II thinning, PBIII thinning. But PBIV has certain problems). If the mature crop has not been removed, the vol of mother trees creates difficulty. S actual vol of these trees should be taken. Thus PBIV = thinning vol + mature trees vol, but how much is the thinning vol depends upon past records. PBII and PBII = 10 cft/ acre and PBIV = 6-8 cft / acre excluding mature tree vol.
The area method can also be applied.

Irrigated Plantations:

Here the area method is logical. The area under different ages should be known. If all the classes occupy the equal area, it should be divided by rotation. The area under clear felling should be multiple of rotation. So
Vol to be cut = Total vol – Vol of standard trees.

Scrub Forests:

Area divided by rotation. No concept of age. Coppices selection system is used just like the high hill forests. If 30 acre cut one acre each year; 30 is the rotation.

Riverain Forests:

Area method but it is much more problematic because it depends on the flood and the age classes are not uniformly distributed to the area method is abandoned but it is still being used. However in Babul forests, determine the area under different age classes, do mapping work, the density of the crop, etc and then vol method should be evolved.

Mangrove Forests:

A clearfelling system cannot be allowed so selection system. Vol, the calculation is difficult and problematic but Von Mantel’s formula can be used. No other.

For correction and improvements please use the comments section below.

Naeem Javid Muhammad Hassani is working as Conservator of Forests in Balochistan Forest & Wildlife Department (BFWD). He is the CEO of Tech Urdu ( Forestrypedia (, All Pak Notifications (, Essayspedia, etc & their YouTube Channels). He is an Environmentalist, Blogger, YouTuber, Developer & Vlogger.

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