1. Approaches to regulation in the selection method and maintaining a balanced stand with sustainable yield
Area regulation
Volume regulation
Structural regulation

2. Area regulation: this is the simplest, and is fairly easy with a group selection system, but it is difficult with the single-tree approach.
Combined area of all trees removed in each cutting cycle

3. Exercise 1 - Area Regulation:
Stand Size: 75 acres
Rotation Length: 80 years
Cutting Cycle: 10 years
Calculate the proportion of the area that will be cut at each entry ___________________
How many acres will be harvested at each entry? ____________________

4. Exercise 1 - Area Regulation:
Stand Size: 75 acres
Rotation Length: 80 years
Cutting Cycle: 10 years
Calculate the proportion of the area that will be cut at each entry
Interpretation: 12.5% of the area will be cut every 10 years with a 80 year rotation age
How many acres will be harvested at each entry? ____________________
75 acres * = 9.4 acres

5. Volume regulation: harvest the allowable cut each cutting cycle
If a stand is balanced, this is equal to the growth during the cutting cycle period

6. Volume Regulation: An Example
Volume-Guiding Diameter-limit (VGDL) approach
Determine a maximum stocking level for the stand
Estimate the annual stand volume growth rate
Set the cutting cycle length
Minimum feasible cutting cycle length is set by minimum volume acceptable for an operable cut divided by the stand's annual growth rate
Annual growth multiplied by the cutting cycle length equals the allowable cut
A guiding diameter limit is calculated so that harvesting trees in this diameter class and larger will provide the allowable cut

7. Volume Regulation: An Example
Volume-Guiding Diameter-limit (VGDL) approach
VGDL diameter limit is only intended as a guide
High-quality trees with acceptable growth may be retained above the limit, while an equal volume of lower quality trees may be cut below the limit
To avoid problems and diameter distribution imbalances, apply thinning and improvement cutting to all size classes
If the stand is understocked, remove less than the allowable cut by reducing the harvest in under-represented sizes

8. Exercise 2 - Volume Regulation
Assume:
Maximum stocking levels: 80 ft2 ac-1 basal area, 7,000 board feet/acre
Minimum volume for operable cut is 1,600 board feet/acre/year
Annual stand volume growth rate: 400 board feet/acre/year
5 year cutting cycle
What is the allowable cut (board foot volume)?

9. Exercise 2 - Volume Regulation Assume:
Maximum stocking levels: 80 ft2 ac-1 basal area, 7,000 board feet/acre
Minimum volume for operable cut is 1,600 board feet/acre/year
Annual stand volume growth rate: 400 board feet/acre/year
5 year cutting cycle
What is the allowable cut (board foot volume)?
Annual volume growth x cutting cycle = allowable cut
400 x 5 = 2000 board feet/acre

10. Exercise 2 - Volume Regulation Assume:
Maximum stocking levels: 80 ft2 ac-1 basal area, 7,000 board feet/acre
Minimum volume for operable cut is 1,600 board feet/acre/year
Annual stand volume growth rate: 400 board feet/acre/year
5 year cutting cycle
What is the allowable cut (board foot volume)?
Annual volume growth x cutting cycle = allowable cut
400 x 5 = 2000 board feet/acre
Does the allowable cut meet minimum volume for operable cut? YES
2000 board feet/acre > 1600 board feet/acre

11. Exercise 2 - Volume Regulation
In the Volume/Guiding-Diameter-Limit regulation method a guiding diameter limit is calculated so that harvesting trees in this diameter class and larger will provide the allowable cut.
Using the given stand data, What is the determine the guiding diameter limit?
DBH
Volume/Acre
(in)
(board-feet) 10
197 11
278 12
336 13
385 14
411 15
400 16
505 17
624 18 19
604 20
712 21
350 22
478 23
546 24
618
7,013

12. Exercise 2 - Volume Regulation
In the Volume/Guiding-Diameter-Limit regulation method a guiding diameter limit is calculated so that harvesting trees in this diameter class and larger will provide the allowable cut
Allowable cut = 2000 bdft/ac
Using the given stand data, What is the determine the guiding diameter limit?
21 inches dbh
DBH
Volume/Acre
(in)
(board-feet) 10
197 11
278 12
336 13
385 14
411 15
400 16
505 17
624 18 19
604 20
712 21
350 22
478 23
546 24
618
7,013
 = 1,992

13. Structural regulation: use a reverse J-shaped curve of residual diameter distribution as a guide.

14. Balance vs. Irregular (unbalanced) uneven-aged stands

15. Structural regulation and reverse J-shaped curve
In balanced uneven-aged stands with an reverse-J shape distribution, a constant ratio exists between the number of trees in successive diameter classes.
This relationship defines the curve’s shape (steepness or flatness) and is called q (or quotient)
where,
TPAi = number of trees in the ith diameter class
TPAi+1 = number of trees in next largest diameter class

16. Influence of q on Target Diameter Distribution
A smaller q value more large trees and fewer smaller trees
A larger q leaves fewer large trees, more smaller tree (i.e. less sawtimber)

17. Structural regulation: BDq Method
The BDq method of regulation:
B is the target residual basal area (after harvest)
D is the maximum retained (after harvest) diameter class
Maximum diameter or largest diameter tree)
q is the ratio of numbers of stems (target-after harvest) of each DBH class to the next higher DBH class
BDq Method is being researched at the Crossett Experimental Forest (Arkansas) for loblolly and shortleaf pines. Information and recommendations from their research is used as examples for the following discussion.

18. Exercise 3 – Structural Regulation The BDq Method
For this exercise, assumptions
Target residual basal area (after harvest) = 60 ft2 ac-1 basal area
Maximum retained (after harvest) diameter class = 21 in
q-value = 1.2
Based upon the above assumptions, how many trees per acre should be retained (Target TPA) in the largest diameter class (21 in DBH)?

19. Exercise 3 – Structural Regulation The BDq Method
Based upon the above assumptions, how many trees per acre should be retained (Target TPA) in the largest diameter class (21 in DBH)?
TPAdbhmax = the number of trees in the largest diameter size clas
BA = target residual stand basal area
dbhi = diameter class
bai = basal area of diameter class midpoint
w = width of diameter class (usually 1 or 2 inches)
dbhmax = largest diameter to be retained in the stand
dbhmin = smallest diameter class

20. Exercise 3 – Structural Regulation The BDq Method
For this exercise, assumptions
Target residual basal area (after harvest) = 60 ft2 ac-1 basal area
Maximum retained (after harvest) diameter class = 21 in
q-value = 1.2
Based upon the above assumptions, how many trees per acre should be retained (Target TPA) in the largest diameter class (21 in DBH)?
The Easy Way:
BDq Structural Regulation Spreadsheet

21. Exercise 3 – Structural Regulation The BDq Method
DBH
Pre-Harvest
Target
Removal
 (in)
TPA 4 30 5 20 6 18 7 16 8 14 9 12 10 11 13 15 17 3 19 2 1 21
Complete the table
Pre-Harvest TPA is from the stand’s current inventory data.
Target residual TPA is the number of trees by diameter class in the target guiding curve for the stand
Removal TPA is the number of trees (by diameter class) that must be removed in a selection harvest to meet the target diameter curve distribution.

22. Exercise 3 – Structural Regulation The BDq Method
DBH
Pre-Harvest
Target
Removal
 (in)
TPA 4 30 5 20 6 18 7 16 8 14 9 12 10 11 13 15 17 3 19 2 1 21
1.0
Knowing TPA in largest dbh class (21”) and q we can calculate remaining Target TPAs
Recall that:
where,
TPAi = number of trees in the ith diameter class
TPAi+1 = number of trees in next largest diameter class
Therefore: TPAi = q * TPAi+1

23. Exercise 3 – Structural Regulation The BDq Method
DBH
Pre-Harvest
Target
Removal
 (in)
TPA 4 30 5 20 6 18 7 16 8 14 9 12 10 11 13 15 17 3
1.72 19 2
1.44 1
1.2 21
1.0
Knowing TPA in largest dbh class (21”) and q we can calculate remaining Target TPAs
For example,
TPA20” dbh = q * TPA21” dbh
= 1.2 * 1
=1.2 trees per acre
TPA19” dbh = q * TPA20” dbh
= 1.2 * 1.2
=1.44 trees per acre
TPA18” dbh = q * TPA19” dbh
= 1.2 * 1.44
=1.72 trees per acre