United States 

Department of 

Agriculture 

Forest Service 

Southern 

Research Station 

Research Paper 

SRS-3 

Stand-Yield Prediction for 

Managed Oca a Sand Pine 

D.L. Rockwood, B. Yang, and K.W. Outcalt 
Stand-Yield Prediction for Managed 

a Sand Pine 

D.L. Rockwood, B. Yang, and K.W. Outcalt 

Abstract 

Sand pine is a very important species in Florida, producing significant 

quantities of fiber. The purpose of this study was to develop the site index 

and stand-level growth and yield equations managers need to make 

informed decisions. Data were collected from 35 seeded plots of Ocala sand 

pine covering a rmge of site indexes, ages, and densities in 1982-83. These 

plots were remeasured 5 and 10 years later and the data used to develop 

growth and yield equations by tree component. Equations for both current 

and future yields in volume and weight measures are given. These 

equations gave very good results when tested by comparing actual yields 

with predicted yields for a second set of 22 sand pine plantations measured 

in the panhandle area of Florida. 

Keywords: Biomass, growth, site index, survival, yield. 

Materials and Methods 

Study Area 

Ocala sand pine stands were randomly selected to represent 

a range of stand densities and ages (table 1). Most of the 

stands were less than 20 years old because few stands in the 

older age classes (20 to 40 years) could be located. The 35 

stands in Marion County, located in the center of Florida on 

the Ocala National Forest, had originated from direct 

seeding afier clearcutting or from natural regeneration. 

Planting had established the stands located in nearby 

Putnam and St. Johns Counties. Planted stands located in 

the panhandle area of west Florida made up the remainder 

of the sample. 

Introduction 

Sand pine stands in the Ocala National Forest and those 

Sites with deep, sandy soils form a small but significant land nearby in Putnam and St. Johns Counties were growing on 

resource [3.2 million hectares (ha)] in the Southeastern Astatula or Paola sand soils (hyperthermic, uncoated 

United States. The Choctawhatchee (Pinus clausa var. Quartzipsamments). These soils consist of deep, droughty 

immuginata D.B. Ward) and Ocala (P. clausa var. clausa) sand deposits from former dunes, offshore bars, and barrier 

varieties of sand pine grow naturally on these dry, sandy sites 

in northwestern and peninsular Florida, respectively. Many Table 1-Distribution of 57 Ocala sand pine biomass 

of the sandy sites in Florida, once occupied by low-quality plots by initial age and location in Florida 

scrub oaks generally unsuitable for forest products, have 

been converted to sand pine. Sand pine has also been 

extensively planted on sandy sites in Georgia and South 

Carolina (Bums 1973, Hebb 198 1, McNab and Carter 198 1, 

Preston and Price 1979). 

Producers and managers are interested in expected growh 

and yield for these sand pine stands. Prediction equations for 

individual tree contents have been developed (McNab and 

others 1985, Rockwood and others 1987, Taras 1980), but 

equations for site index (SI) and stand-level yields from 

Ocala sand pine are not available. This paper presents 

equations developed to quantify SI, tree momlity, 

aboveground biomass, and growth and yield for Ocala sand 

pine stands in Florida. 

Age (years) 

Location 

Bay 

Gilchrist 

Marion 

Okaloosa 

Putnam 

St. Johns 

Taylor 

W a1 ton 

Washington 

Number ofplots 

Total 17 17 17 5 1 5 7 
islands. The complex, undulating topography generally has 

slopes from 0 to 8 percent with occasionally steeper areas 

near sinks and lakes. Planted smds in the panhandle area 

were on Lakeland sand (tbemic coated typic 

Quartzipsamment). Ldeland soil formed from sad 

deposited by oceans, rivers, and wind. The terrain is broad, 

nearly level to gently sloping with gradients from 0 to 12 

percent. 

Inventory 

Betvveen June 1982 and December 1983,57 pemanent plots 

were installed in the study area+ne plot per stand (table 1). 

Square 15- by 15-meter (m) plots were installed in low 

density stands (<2,000 trees per ha). Smaller 10- by 10-m 

plots were installed in high density stands (22,000 trees per 

ha). All trees on these plots were tagged and numbered, and 

diameter at breast height (d.b.h.) was measured to the nearest 

millheter (mm). Total height and height to the base of the 

live crown were measured to the nearest 0.5 rn for all trees. 

Trees on the 35 plots located on the Ocala National Forest 

were remeasured 5 (1987-88) and 10 (1992-93) yeus after 

initial plot establishent. 

Data Surnmary and Analysis 

Using equations developed by Rockwood and others (19871, 

20 biomass components were estimated for every tree on 

each sample plot: stem wood volume inside bark (SVIB), 

stem volume outside bark (SVOB), and green and dry weight 

for stem wood, stem bark, stem, branch wood, branch bark, 

branch, foliage, crown, and tree (table 2). Summing values 

for all trees on a plot provided yields on a per area basis. 

Site index function and curves-Polmorphic SI curves 

were developed using the initial height and age of up to 10 

dominant and codominant trees on each of the 35 Ocala 

National Forest plots. Our height-age model was based on a 

modified form of the equation used by Bailey and Clutter 

(1 974) and Cao and Durand (1 99 1): 

H = exp [a + b * (1 i A?], (1) 

where 

Applying the namral logarithm to equation (1) produced the 

following equation: 

where 

ln (frd) = the natural logarithm of H. 

Assuming b from the above equation (2) vaies with 

different plots, b was expressed in terms of SI and base age 

(SA): 

Repiacing b in equation (2) resulted in the polymorphic SI 

model: 

Survival prediction-A fairly broad spectrum of tree 

survival data were gathered from the Ocala National Forest 

plots over the 10-year period of the study. Initial tree ages 

ranged from 5 to 40 years, and initial densities fkom 444 to 

22,000 trees per ha. The survival model of Clutter and Jones 

(1 980) and Pienaar and others (1 990) was applied to these 

data: 

N2 = N1 * {exp [a + In 142 / 10Ib 

+ In W>fI / exp [a 

+ In @I / 10)b + In WIH~ , (4) 

where 

A I = initial stand age in years, 

NI = the initial number of trees per ha, 

A2 =. future stand age in years, 

N2 = survivkg trees per ha at age AZ, md 

a, b, and c - c0efficient.s esthateb f om the BaB, 

N -- average height 51 m of the dombant and codornhmt 

trees, 

A = stand age in years, and 

a, b, and c = coefficients esthated fiom the data. 
-? 'f? 2 2 'f? '=? 

8 2 V3 N 

t- m m c~ 0 00 s 2 Vl cn N 

--r-oO 

VS - c9 ~mcm 

"? 'f? r-: 

ZZIS" 
Basal area prediction-Basal area (B in m2 per ha) 

calculations were based on live tree data. A basal area 

prediction model was developed using SI, density 0, and 

age (A?) as independent variables: 

B = exp la + in lSnb 

+ 1nW + d *(I /A) 

+ In&* ~IAYI, 

where 

a, b, c, d, and f = coefficients estimated from the data. 

Stand-level growth and yield equations-Equations, based 

on the data collected from the Ocala National Forest plots at 

time 0,5, and 10 years, were developed to predict yield. 

Using age, surviving trees per ha, SI, and basal area, the 

following equations were generated: 

In (ff) = 6.435 + fln (58 

- 6.4351 * (50 / A)~.'~~~ . (8) 

Site index in m for Ocala sand pine at SA 50 years was 

determined by solving equation (8) for SI: 

In (Y) = a + In {b * N 

+ c * exp iF (N, SI, B, A)lj , (6) 

where 

Y = the stand yield per ha, and 

a, b, and c = coefficients estimated from the data. 

I;- (Nj SI, B, A) = a1 + In @fY2 + 1n (SV + 172 (By4 

+a5*(l/A), 

where 

al, a2, a3, a4, and a5 = coefficients esthated from the 

data. 

Model evaluation and verification-To test agahst an 

independent data set, the models developed from the 35 

Ocala National Forest plots were tested against the values 

measured in 1982 and 1983 on the 22 plots in the plmted 

stands. To test actual and predicted data, they were 

compared using the following equation: 

where 

ResuIts and Discussion 

Site index-Data from the 35 sites on the Ocala National 

Forest provided the following solutions to equation (3): 

SI = exp I6.435 + [ln @d 

- 6.4351 * C4 / / 10 (9) 

Site index estimates for each plot and SI curves were 

constructed from equation (9). 

The seeded and planted plots represented a range of site 

indices (fig. 1). Within the 35 seeded stands, the youngest 

plots were on sites with indices ranging widely &om 14 to 

32 m. Plots in lower density stands initially 16 to 25 years 

of age had SIs from 20 to 30 m. A trend toward decreasing 

SI with increasing age suggests a possible bias in the data; 

the oldest seeded stand was located on a poor site. 

Plots in planted stands represented a somewhat similar 

range of site conditions. Plantations from I1 to 25 years of 

,age were on sites predicted to grow trees 20 to 30 m tall in 

50 years. Plots in the youngest plantations had high SIs. 

The SI curves presented in figure 2 show the polymorphic 

height growth expected over a 50-year period. Height 

growth an good sites is predicted to be rapid at early ages, 

with decreasing rates at older ages. On poorer sites, height 

growth is expected to be less but more consistent over time. 

Suwival prediction-ne survival equation generated from 

equalion (4) for initial densities of less than 18,200 trees per 

ha follows: 

N2 = NI * exp 11.681'7 

+ In iA2 1 1 o)-~.~~~ 

+ In L?il~0~7g5'1 / (exp C1.6817 

+ In C4f 1 10)-~.~~~~ 

+ In W1j0.~~~~11 , 

P (y) = the predicted volume, and 

A fy) = the actual volume. with R2 = 0.946. 
Figure I-Distribution of seeded (top) and planted (bottom) Ocala sand pine plots by initial age, density, and site index. 
0 5 10 15 20 25 30 35 40 45 50 

Age (years) 

Age (years) 

Figure 2-Bse-age 50 yeas site index curves fir Bcala sand pine: site indices 14, 16, k8,20. md 22 (top): site indices 24, 26,28, 30, 

and 32 (bomm). 
The high R2 is important because survival prediction is 

critical to accurate growth and yield prediction. 

Figure 3 shows survival curves for six initial densities 

ranging from 1,100 to 1 8,000 trees per ha from ages 6 to 50. 

Survival is predicted to drop significantly for initial 

densities 2 12,000 such that by age 50 stand densities are 

near 4,000 trees per ha. 

Basal area prediction-A simultaneous estimation 

procedure following techniques of Pienaar and others 

(1990) was used to estimate parameters in equations (1 1) 

and (12). Applying model (51, current sand pine basal area 

in m2 per ha can be predicted: 

BI = exp 1- 0.030 + in (S1)1.3915 

+ In (N)0.7487 - 16.9491 

* (1 I A) - ln (Nl 

* 1 / ~)~.~~~~1 1 100 , (1 1) 

with R2 = 0.8263, and future basal area (B2) can be 

projected: 

B2 = Bl * exp [- 0.030 + ln m1."15 

+ In (N2)0.7487 - 16.9491 

* (1 I A2) - In h'2 * 1 I ~2)~.~~~~l 

/ exp [- 0.030 + ln 6%1.3915 

+ In h'l)0.7487 - 16.9491 * (1 I Al) 

- 1n GrVll * I I AI)~.~~~~~ . (12) 

These two equations are compatible because the projection 

equation uses the same coeficients in a different form of 

the prediction equation. This ensures that the basal area 

projected at age A2 from the basal area at age A1 with 

equation (12) will be the same as the predicted basal area at 

age A2 given by equation (1 1) with N2 and SI. Figure 4 

shows stand basal areas for six initial densities and four SIs. 

Stand-level growth and yield equations-Stand average 

tree contents (Rockwood and others 1987) were 

successfully modeled as functions of stand basal area, SI, 

and age. For example, a stand's average tree SVOB (m3) can 

be calculated: 

In &FOB) = - 13.8155 + In {1,728 * lo3 

+ exp L2.7610 + In @)1.28766 

+ In - 5.3366 

* (1 / A) + ln (N"1°.06s281) , (1 3) 

with R2 =: 0.986 

n = 3525. 

Stand SVOB (SSVOB in m3 per ha) (table 2) can then be 

calculated: 

I~&sv(~B) = - 13.8155 + InI1.728 

* lo3 * N + exp (14.5251 - in ~~30.206 + ln CSI)~.~~~ 

+ In - 4.5986 

* (1 i A)]) , (14) 

with R2 = 0.987. 

Using equation (14) in a simultaneous estimation procedure, 

the future SSVOB projection model was developed: 

SSVOB2 = SSVOBI * ((1.728 * 10' * N2 

+ exp i14.5251 - In (N2?.206 

+ In @I)~.~~~ + In @2)1.323 

- 4.5996 * (1 I ~2)l) 1 1.728 

* lo3 * Nl + exp L8.4808 

- In (N1)0.206 + ln @I)~.~~~ 

+ In @1)1.323- 4.5986 

* (1 I A~)II) . (15) 

Stand growth and yield models can be applied to various 

basal areas, SIs, initial stand densities, and ages. For 

example, at SI = 28, stand volume ranged from 4 m3 per ha 

at age 6 years and an initial density of 1,100 trees per ha to 

3 19 m3 per ha at age 50 with an initial density of 18,000 

trees per ha at age 6 years (table 3, fig. 5). For SI = 24 at 

age-6 densities of 1,100 and 18,000 trees per ha, the 

expected yields are 85 m3 per ha and 228 m3 per ha at age 

50 years, respectively. At SI = 16, stand volume ranged 

from 35 m3 per ha to 99 m3 per ha (N= 1,100 - 18,000) at 

age 50 years. 

Model evaluation-Model (I 5) provided good estimates at 

the initial and at future ages. In the case of SSVOB, 

volumes predicted by model (15) were typically within 5 

percent of the observed volumes. Using the actual data from 

the 35 Ocala National Forest plots to test the model: 

P (SSVOB) = 7.3399 + 0.8767 * A (SSVOB) , 

with R2 = 0.942 1. 
Age (years) 

Figure 3-Survival of Ocala sand pine through age 50 years for initial age-6 stand 

densities ranging from 1,100 to 18,000 trees per hectare. 

Table 3-Predicted Ocala sand pine stand total stem In the 22 plantation plots, the predicted and actual values 

volumes outside bark (m3/ha) at six ages for four site did not differ significantly and were randomly distributed 

indices and four initial stand densities at age 6 years (fig. 6). 

Stand densities hlpplication Site 

index Age 1,100 7,200 12,000 18,000 Model (15) may be used to predict future yields when SI 

SI = 16 6 2.5 13.5 22.0 32.6 and present stand density and age are known. For example, 

10 5.1 16.5 24.2 33.4 if initial stand density = 5,400 trees per ha at age 12 years 

20 15.5 34.2 44.0 54.5 

3 0 24.0 49.5 61.5 73.9 and SI = 28, after 6 years (A2 = IS), SSVOB can be derived 

40 30.2 60.6 74.4 88.3 by (a) estimating future stand density, (b) calculating 

50 34.7 68.9 84.1 99.0 current and fbture stand basal area, and (c) converting these 

estimates to stand volume: 

SI = 20 6 2.9 14.2 22.9 33.6 

a) N2 = 5,400 * exp L1.6817 - In (18 / 10i0.5M)5 

+ ln (5,400)0.~~~~1/ exp1.68 17 

== 4,408 trees per ha, 

20 36.6 74.3 91.6 109.2 

30 57.9 113.7 137.9 161.6 b) Bl = exp 1-0.03007 + h (281' 3915 + ln 15,400~'~~ 

40 73.2 142.2 171.5 199.8 - 16.949 *: (1 / 12) - h (5,400 * 1 / 12P33571 ! / 100 

50 84.6 163.4 196.5 228.1 

= 19.6 m2 per ha, 


Observed volume (cubic meters per hectare) 

Figure 6---(Predicted-observed) versus observed volumes in Ocala sand pine plantation plots 

82 = B1 * exp 14.5785 + In (28)' "" + ln (4,408)'~'~~ LOWS, or EXCEL version of the spreadsheet for yields in 

- 16.949 * (1 / 18) - ln (4,408 * 1 / 18r.'33571/ metric format, and K.W. Outcalt, the third author, will 

exp L4.5785 + ln (28)' "" + In (5,400)'~'~~ provide a LOTUS or EXCEL version in English format. 

- 16.949 * (1 / 12) - In (5,400 * 1 / 12)033571 

= 3 1 .O m2 per ha, and Acknowledgments 

c) SSVOB2 = exp (-13.8155 + ln (1.728 * lo3 * 4,408 

+ exp L14.5251 - ln (4,408)"'~ + In (28)' 394 

+ ln (31.0)"~~ -4.5986 * (1 / 18) I 11 

= 105.2 m3 per ha. 

For different management objectives, the best stand option 

can be selected based on these yield predictions. 

Equation (6) can be used to predict stand contents for all 

traits that can be predicted on an individual tree basis, i.e., 

the 20 volumes and weights in table 2. By combking 

volumes and weights with energy values (Rockwood and 

others 19801, stand energy components can be estimated. 

These estimates reflect stand yields possible with the seed 

sources used for direct seeding or nursery propagation until 

the late 11970's; improved seed could result in different 

paaerns of stand development (Rockwood and Goddard 

1980). 

The equations in table 2 have been inco~porated hto a 

computer spreadsheet to facilitate yield projections. By 

speeiQhg initial stand condition and hwre ages, current 

and Euhrre growth and yield may be readily calculated (table 

4). Table 5 displays in English forma, cuarent and projected 

yields for a, range of Sls and hitial densities. D.L. 

Rockwood (senior author) will provide a QUATTRO, 

Research support was provided through the project 

"Biomass Production of Sand Pine Planted on Scrub Oak 

Sites in the Southeastern United States" under Supplement 

5 1 dated March 1, 1982 through December 3 1, 1984 of 

Cooperative Agreement A8fs-9,96 1. This research was 

supported by knds provided by the U.S. Department of 

Agriculture, Forest Service, Southeastern Forest 

Experiment Station (now Southern Research Station), 

Asheville, NC. 

We are indebted to W.H. McNab, K.V. Reddy, C.W. 

Comer, M. Allen, and Lake City Community College for 

assistance in conducting this research and to Container 

Corporation of America, Union Camp Corporation, 

Buckeye Cellulose Corporation, St. Regis Paper Company, 

ad the U.S. Depament of Agriculture, Forest Service, 

Ocala National Forest. for provision of research plots. This 

manuscript is also journal series paper R-04772 of the 

Florida Agsiculterral Experiment Station. 
Table 4--Representative output from the growth and yield spreadsheet for managed Oeala sand pine 

Weight of 

Volume 

Trees Basal whole stem Stem wood Stem bark Whole stem Branch wood Branch bark Branch Foliage Crown Tree 

SI(50) Age perha area OB IB &en Dry Green Dry Green Dry Green Elry OB 1s Green Dry Cireen Dry Qeen Dry Green by 

------------------ Metric tom - - .. - - - - - - - - 

OB = outside bark; IB = inside bark. 
Table 5a4tem volume and weight for managed Ocata 

sand pine stands by site index 50, age, and density 

tern volume and weight for managed Ocafa 

sand pine stands by site index 55, age, and density 

Basal Stem volume 

area OB IB 

Stem weight 

Green Dry 

Basal Stem volume Stem weight 

Age Density area OB IB Green Dw Density 

Treesiac 

404 

350 

313 

285 

264 

247 

233 

22 1 

21 1 

202 

600 

520 

465 

424 

393 

367 

346 

329 

3 13 

300 

800 

693 

620 

566 

524 

490 

462 

438 

418 

400 

1,000 

866 

774 

707 

654 

612 

577 

547 

522 

500 

OB = ourside bark; IB = inside bark. OB = outside bark; 1B = inside bark. 
Table Sc4tem volume and weight for managed Oealai Table Sd--Stern volume and weight for managed Ocaatla 

sand pine stands by site index 60, age, and density sand pioe stands by site index 65, age, and density 

Stem volume Basal 

Density area OB 1B 

Trees/ac F8 - - - -Fr' - - - - 

Stern weight Stem volume 

OB IB 

- - - -I;t3 - - - - 

Stem weight Basal 

area 

FrZ 

26 

3 7 

45 

52 

5 7 

6 1 

64 

67 

69 

7 1 

3 1 

44 

53 

6 1 

6'7 

72 

76 

79 

82 

85 

3 5 

49 

60 

69 

76 

8 1 

86 

89 

92 

95 

3 8 

54 

66 

75 

83 

89 

94 

98 

101 

104 

OB = outside bark; IB = inside bark. OB = oubide bark; IB = inside bark. 
tern volume and weight for managed Ocala 

sand pine stands by site index 70, age, and density 

Stem volume Basal 

Density area OB IB 

Stem weight 

Green Dry 

OB = outside bark; IB = inside bark. 
Literature Cited 

Bailey, R.L.; CIutter, J.L. 1974. Base-age invariant polymorphic site 

curves. Forest Science. 20: 155-159. 

Burns, R.M. 1973. Comparative growth of planted pines in the sand-hilts 

of Florida, Georgia, and South Carolina. Gen. Tech. Rep. SE-2. 

Asheville, NC: U.S. Dep ent of Agriculture, Forest Service, 

Southeastern Forest Experiment Station: 124-1 33. 

Cao, Q.V.; Durand, K.M. 1991. Site index curves for eastern cottonwood 

plantations in the Lower Mississippi Delta. Southern Journal of 

Applied Forestry. 15(1): 28-30. 

Clutter, J.L.; Jones, E.P. 1980. Prediction of growth after thinning of 

old-field slash pine plantations. Res. Pap. SE-217. Asheville, NC: U.S. 

Department of Agriculture, Forest Service, Southeastern Forest 

Experiment Station. 14 p. 

Hebb, E.A. 1981. Choctawhatchee sand pine growth on a chemically 

prepared site - 10-year results. Southern Journal of Applied Forestry. 

5(4): 208-2 1 1. 

McNab, W.H.; Carter, A.R. 1981. Sand pine performance on South 

Carolina sandhills. Southern Journal of Applied Forestry. 5(2): 84-88. 

Pienaar, L.V.; Page, H.; Rheney, J.W. 1990. Yield prediction for 

mechanically site-prepared slash pine plantations. Southern Journal of 

Applied Forestry. 14(3): 104-109. 

Preston, D.N.; Price, T.S. 1979. Sand pine in Georgia: A look at a tricounty demonstration program. Georgia Forestry Commission. Georgia 

Forest Research Paper 5(June). 13 p. 

Rockwood, D.L.; Conde, L.F.; Brendemuehl, R.H. 1980. Biomass 

production of closely spaced Choctawhatchee sand pine. Res. Note 

SE-293. Asheville, NC: U.S. Dep ent of Agriculture, Forest 

Service, Southeastern Forest Experiment Station. 5 p. 

Rockwood, D.L.; Goddard, R.E. 1980. Genetic variation in Ocala sand 

pine and its implications. Silvae Genetica 29(1): 18-22. 

Rockwood, D.L.; Reddy, KV.; Comer, C.W.; McNab, W.H.; Outcalt, 

KW. 1987, Weight and volume prediction equations for sand pine 

trees in Florida. Tech Bull. 869. Gainesville, FL: Florida Agricultural 

Experiment Station, University of Florida, Institute of Food and 

Agricultural Sciences. 16 p. 

Taras, EM.A. 1980. Aboveground biomass of Choctawhatchee sand pine in 

northwest Florida. Res. Pap. SE-210. Asheville, NC: U.S. Department 

of Agrricuftun, Forest Sewice, Soueheastem Forest Experiment Station. 

23 p. 

McNab, W.H.; Outcalt, KW.; Brendemuehl, R,H. 1985. Weight md 

volume of plantation-grown Choctawhatchee sand pine. Res. Pap. 

SE-252. Ashevitfe, NC: U.S. Department of Agriculture, Forest 

Service, Southeastern Forest Experiment Station. 44 p. 
Rockwood, D.L.; Yang, B.; Outcalt, K.W. 1997. Stand-yield prediction for managed 

Ocala sand pine. Res. Pap. SRS-3. Ashevilre, NC: U.S. Department of Agriculture, 

Forest Service, Southern Research Station. 16 p. 

Sand pine is a very important species in Florida, producing significant quantities of fiber. 

The purpose of this study was to develop the site index and stand-level growth and yield 

equations managers need to make informed decisions. Data were collected fiom 35 

seeded plots of Ocala sand pine covering a range of site indexes, ages, and densities in 

1982-83. These plots were remeasured 5 and 10 years later and the data used to develop 

growth and yield equations by tree component. Equations for both current and future 

yields in volume and weight measures are given. These equations gave very good results 

when tested by cornparing actual yields with predicted yields for a second set of 22 sand 

pine plantations measured in the panhandle area of Florida. 

I Keywords: Biomass, growth, site index, survival, yield.