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

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

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? ____________________

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

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

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

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

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)?

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

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

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

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

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

Balance vs. Irregular (unbalanced) uneven-aged stands

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

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)

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.

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)?

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

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

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.

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

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