Stand Density Management for Optimal Growth Micky G. Allen II 12/07/2015
How does stand density affect growth? Langsaeter s Hypothesis (1941) Relationship valid for a given tree species, age and site Source: Daniel, T.W., J.A. Helms and F.S. Baker. 1979. Principles of silviculture. Second Edition, Mc Graw-Hill.
Thinning and Growth: A full turn around Patterns for periodic annual total and merchantable volume increment (Gross volume) How is stand density defined? How is merchantable volume defined? Source: Zeide, B. 2001. Thinning and growth: A full turnaround. J. For. 99(1):20-25.
Post-thinning relationship between growth and density Only a graphical representation Relative density? Total stem volume or merchantable volume? Source: Nyland, R.D. 2002. Silviculture: Concepts and applications. Second Edition, McGraw-Hill. 682p.
Research Purpose Determine stand density that optimizes volume increment in loblolly pine plantations Use multiple operational studies Thinning vs. No Thinning Compare multiple definitions of stand density Commonly used measures of stand density Determine which is more correlated with volume increment Compare multiple definitions of volume increment Total vs. Merchantable Gross vs. Net
Data: Non-intensively managed plantations Thinning study established 1980-1982 in 8-25 year old plantations Designed to examine thinning across a range of ages 186 permanent plots established across the natural range of loblolly pine Treatments: Unthinned control Light thin removing 30% of basal area Heavy thin removing 50% of basal area Management: Site preparation No genetic improvement No fertilization or weed control
Data: Intensively managed plantations Thinning study established 1996-2000 in plantations 3-8 years old Stands thinned at a common point in stand development (45 ft, 13.7 m) 170 permanent plot locations across the natural range of loblolly pine Treatments: Unthinned control Light thin removing 30% basal area Heavy thin removing 50% basal area Management: Pruned, removing dead branches only Site preparation Genetically improved seedlings Fertilization and weed control
Data: Region Wide 19 Thinning Study Thinning and fertilization study established 2007-2012 in plantations 10-16 years old 8 permanent plot locations across natural range of loblolly pine Treatments: Thin to 1235 (500), 741 (300), 494 (200), and 247 (100) stems per hectare (acre) No fertilization or fertilization with N and P Four replications of each thin+fert combination at each location Management: Genetically improved seedlings Site preparation
Data: Spacing Study Trials designed to examine effects of different planting densities established in 1983 Four locations established in Virginia and North Carolina 3 replications of study design at each location Base design: Grid with four spacings (4, 6, 8, 12 ft) (1.2, 1.8, 2.4, 3.6 m) Spacing varies in two-dimensions for a total of 16 plots Ex: 4x4, 4x6, 4x8, 4x12, etc. In this work only the initial planting density was considered 4x6 = 6x4 = 1815 stems/acre 9 initial planting densities 2722, 1815, 1361, 1210, 907, 680, 453, and 302 stems/acre 6727, 4484, 3363, 2989, 2242, 1681, 1494, 1121, and 747 stems/hectare
Definitions of Stand Density Stems per Hectare (SPH) Basal Area per Hectare (BPH, m 2 /ha) Relative Spacing Diameter: RSD = 10,000/SPH d q, d q = quadratic mean diameter (m) Height: RSH = 10,000/SPH H d, H d = dominant height (m) Stand Density Index * Diameter: SDID = SPH 25 d q 1.43089 1.42324 Height: SDIH = SPH 30 H d Volume: SDID = SPH 0.65 v 0.48895, v = mean tree volume (ft 3 ) * Parameter estimates from: Burkhart, H.E. 2013. Comparison of maximum size density relationships based on alternate stand attributes for predicting tree numbers and stand growth. Forest Ecology and Management 289(0):404-408.
Volume Estimation Total volume (ft 3 /acre) * Unthinned: V u = 0.21949 + 0.00238D 2 H, D = diameter(in), H = height (ft) Thinned: V t = 0.25663 + 0.00239D 2 H Merchantable volume (ft 3 /acre) * Unthinned: MV u = V u exp 0.78579 d 4.9206 D 4.55878 Thinned: MV t = V t exp 1.04007 d 5.25569 D 4.99639 Volumes converted to metric (m 3 /ha) Pulpwood: Trees in the 13 cm DBH class and greater to 7.6 cm top(d) Sawtimber: Trees in the 20 cm diameter class and greater to 15.2 cm top (d) * Volume equations from: Tasissa, G., H.E. Burkhart, and R.L. Amateis. 1997. Volume and Taper Equations for Thinned and Unthinned Loblolly Pine Trees in Cutover, Site-Prepared Plantations. Southern Journal of Applied Forestry 21(3):146-152.
Growth Definition Net Productivity: Standing volume + Volume removed in thinning Gross Productivity: Net + Volume of mortality Productivity = Periodic annual increment (PAI) PAI = Volume 2 Volume 1 Time 2 Time 1 Measurement periods ranged from 2 to 3 years
What kind of pattern? V a1 V a Density exp( a 2 Density) 0 Increasing Optimum Stand Density
Hypothesis Testing PAI a1 a 0 Density exp( a 2 Density) Test of hypothesis: Ho : Optimum pattern between volume increment and stand density HA : Increasing pattern between volume increment and stand density or Ho : all coefficients are significant HA : all coefficients, except, are significant
Results: Definitions of Growth and Density Measures Based on diameter were more correlated with growth BPH, RSD, SDID Consistently explained the most variation in volume increment (20-30%) Net and Gross growth had similar relationships in most cases
Results for Total Volume Increment
Results: Is there a stand density that optimizes total volume increment? Dataset NIMP PAI Density SPH BPH RSD RSH SDID SDIH SDIV Gross Net 291 NIMP1t Gross 69.5 10.65 Net IMP Gross 1476 5.77 560 909 Net 1498 5.70 554 896 IMP1t Gross 733 7.72 791 585 711 Net 731 7.76 766 590 693 RW19 Gross 1622 53.8 8.84 7.03 1297 718 1027 Net 1520 44.9 7.82 6.23 1065 587 837 Spacing Study Gross 37.3 6.82 5.84 1282 765 1098 Net 27.7 5.87 4.66 1108 491 843 Hypothesis test concluded an optimal relationship Density values that optimize total volume increment
Results for Pulpwood Volume Increment
Results: Is there a stand density that optimizes pulpwood volume increment? Dataset PAI Density SPH BPH RSD RSH SDID SDIH SDIV NIMP Gross 3.31 Net 324 345 NIMP1t Gross 75.8 Net IMP Gross 35.96 6.76 5.21 953 504 749 Net 35.42 6.70 5.18 949 502 746 IMP1t Gross 737 7.70 792 584 711 Net 736 7.75 768 590 695 RW19 Gross 1636 53.9 8.85 7.01 1296 714 1024 Net 1602 45.6 7.89 6.32 1090 605 859 Spacing Study Gross 2150 36.5 6.68 5.22 1084 570 803 Net 2440 28.4 5.93 4.28
Results for Sawtimber Volume Increment
Results: Is there a stand density that optimizes sawtimber volume increment? Dataset PAI Density SPH BPH RSD RSH SDID SDIH SDIV NIMP Gross 877 58.48 8.96 Net 935 58.92 8.94 NIMP1t Gross 701 46.9 7.95 Net 727 48.7 8.12 7.21 IMP Gross 356 Net 350 IMP1t Gross 684 804 586 720 Net 689 804 601 725 RW19 Gross 1374 57.4 9.27 6.82 1438 679 1046 Net 1385 53.9 8.85 6.69 1346 662 993 Spacing Study Gross 877 38.9 7.05 5.53 773 462 634 Net 915 39.4 7.09 5.47 776 457 633
Conclusions Results of hypothesis test were different depending on the dataset, measure of growth, and measure of density Approach was inconclusive at determining the relationship between growth and density Stand density measures based on diameter (BPH, RSD, and SDID) consistently explained the most variation in volume increment (20% 30%) No consistent solution between these measures
Different Approach #1 Zeide (2004) argues that optimal density cannot be determined as in the previous manner Relating volume increment as a function of density alone does not account for the effects of age and average tree size (quadratic mean diameter) Age: as stands age any gaps in the canopy created by mortality become more difficult to fill by the residual stand Volume increment can only be optimized when the canopy is full Any gaps in the canopy reduce the total amount of light interception Average tree size: Stands at similar densities can have largely different average diameters Average diameter and density can determine diameter increment which is related to volume increment Source: Zeide, B. 2004. Optimal stand density: A solution. Canadian Journal of Forest Research 34(4):846-854.
Formulating a model: Define the volume of an average tree Using a local volume equation v = αd q β Using the combined variable equation v = αd q 2 H d Where v = mean total tree volume (m 3 ) D q = quadratic mean diameter (cm) H d = mean tree height (m) α,β = parameters to be estimated
Formulating a model: Differentiate to obtain individual tree volume increment equations dv = αβd β 1 dd q dt q dt dv = α 2D dd q dt qh d + D dt q 2 dh d dt Where dv dt = individual volume increment (m3 / year) dd q dt = diameter increment (cm / year) dh d dt = height increment (m / year)
Formulating a model: Multiply volume increment of average tree by Stems per Hectare dv dt = SPH αβd q β 1 dd q dt dv = SPH α 2D dd q dt qh d + D dt q 2 dh d dt Where dv dt = volume increment per hectare (m3 / hectare / year)
Formulating a model: Add modules to account for the effects of age and density dv dt = SPH αβd q β 1 dd q dt exp γ age exp( Dens ) δ dv = SPH α 2D dd q dt qh d + D dt q 2 dh d dt exp γ age exp( Dens ) δ Where γ,δ = parameters to be estimated
Formulating a model: Formulate SPH as a function of commonly used measures of density BPH = BA tree SPH SPH = BPH = BPH 2 2 = c BPH d BA q tree d q c RSD = 10,000/SPH d q SPH = c RSD 2 d q 2 SDID = SPH 25 d q 1.43089 SPH = c SDID d q 1.43089
Formulating a model: Replace SPH in volume increment equations dv = α BPH D dt q c dd q dt exp γ age exp( BPH ) δ dv = α dt RSDθ c D dd q q dt exp γ age exp( RSD δ ) dv = α SDID D dt q c dd q dt exp γ age exp( SDID ) δ
Results: Is there a stand density that optimizes volume increment? Both local and combined variable formulations with all measures of density resulted in optimal relationships between density and volume increment (for all measures compared here) In all cases the optimal density was well outside the commonly held theoretical maximum SDI for loblolly pine in the southern U.S. of 450, as defined by Reineke (1933) which equates to 450 10-inch trees per acre or 1112 25-centimeter trees per hectare. Using this approach it appears that maximum volume increment occurs near the maximum observed densities
Different Approach #2 Use the RW19 data Individual plots were thinned to a common number of stems per hectare Treatments: 1235, 741, 494, and 247 residual SPH Spacing Study data Nine different planting densities 6727, 4484, 3363, 2989, 2242, 1681, 1494, 1121, and 747 SPH Fit 2 nd degree polynomial to each thinning treatment and planting density PAI = B0 + B1 Density + B2 Density 2 Useful for determining if different relationships exist among treatments
Results from the RW19 Study
Results: Fitting 2 nd degree polynomial to thinning treatments Dens. Thinning Total Gross PAI Pulpwood Gross PAI Sawtimber Gross PAI Treatment R 2 OptD OptP R 2 OptD OptP R 2 OptD OptP BPH 247 SPH 0.6823 0.6766 0.5011 494 SPH 0.4929 39.60 27.89 0.4795 39.69 27.96 0.4008 27.67 26.74 741 SPH 0.3605 40.81 27.47 0.3421 41.24 27.69 0.3562 33.74 29.65 1235 SPH 0.0897 44.00 28.00 0.0850 44.06 28.23 0.1986 42.60 32.65 RSD 247 SPH 0.6818 0.6762 0.5010 494 SPH 0.4913 0.4777 0.4069 6.06 26.64 741 SPH 0.3604 7.90 29.05 0.3416 0.3599 6.62 29.45 1235 SPH 0.0930 7.48 27.90 0.0881 7.49 28.14 0.2012 7.37 32.47 SDID 247 SPH 0.6670 0.6616 0.4902 494 SPH 0.4806 0.4674 0.3993 549.23 26.65 741 SPH 0.3586 841.62 28.26 0.3403 854.60 28.62 0.3617 704.28 29.68 1235 SPH 0.0684 0.0660 0.1701 977.26 33.20 OptD = optimum density, OptP = PAI at which density is optimized
Results from Spacing Study
Conclusions
Total Volume Increment Maybe Langsaeter (1941) was partially right Volume seems to become near optimal over a wide range of densities although not necessarily constant A decrease in volume production at higher levels of density may not be observable Before a reduction in volume increment can occur stands self-thin Adjustment to Langsaeters Hypothesis
Merchantable Volume Increment Relationship between pulpwood volume increment and density is similar to that of total volume increment Merchantable volume increment can become optimal Depends on: Initial planting density Thinning Intensity
Is this the final answer?
Questions?