1. 1.Area regulation 2.Volume regulation 3.Structural regulation Approaches to regulation in the selection method and maintaining a balanced stand with sustainable yield

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 * 0.125 = 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-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 Volume Regulation: An Example

7. 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 Volume Regulation: An Example

8. Exercise 2 - Volume Regulation Assume: – Maximum stocking levels: 80 ft 2 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 ft 2 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 ft 2 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? DBHVolume/Acre (in)(board-feet) 10197 11278 12336 13385 14411 15400 16505 17624 18505 19604 20712 21350 22478 23546 24618 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 DBHVolume/Acre (in)(board-feet) 10197 11278 12336 13385 14411 15400 16505 17624 18505 19604 20712 21350 22478 23546 24618 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. 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, TPA i = number of trees in the ith diameter class TPA i+1 = number of trees in next largest diameter class Structural regulation and reverse J-shaped curve

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 RegulationThe BDq Method For this exercise, assumptions – Target residual basal area (after harvest) = 60 ft 2 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 RegulationThe 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)? The Hard Way: TPA dbh max = the number of trees in the largest diameter size clas BA = target residual stand basal area dbh i = diameter class ba i = basal area of diameter class midpoint w = width of diameter class (usually 1 or 2 inches) dbh max = largest diameter to be retained in the stand dbh min = smallest diameter class

20. Exercise 3 – Structural RegulationThe BDq Method For this exercise, assumptions – Target residual basal area (after harvest) = 60 ft 2 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 RegulationThe BDq Method DBHPre-HarvestTargetRemoval (in) TPA 430 520 618 716 814 912 10 118 127 136 145 154 164 173 183 192 201 210 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 RegulationThe BDq Method DBHPre-HarvestTargetRemoval (in) TPA 430 520 618 716 814 912 10 118 127 136 145 154 164 173 183 192 201 2101.0 Knowing TPA in largest dbh class (21”) and q we can calculate remaining Target TPAs Recall that: where, TPA i = number of trees in the ith diameter class TPA i+1 = number of trees in next largest diameter class Therefore: TPA i = q * TPA i+1

23. Exercise 3 – Structural RegulationThe BDq Method DBHPre-HarvestTargetRemoval (in) TPA 430 520 618 716 814 912 10 118 127 136 145 154 164 173 1831.72 1921.44 2011.2 2101.0 Knowing TPA in largest dbh class (21”) and q we can calculate remaining Target TPAs For example, TPA 20” dbh = q * TPA 21” dbh = 1.2 * 1 =1.2 trees per acre TPA 19” dbh = q * TPA 20” dbh = 1.2 * 1.2 =1.44 trees per acre TPA 18” dbh = q * TPA 19” dbh = 1.2 * 1.44 =1.72 trees per acre