Revisiting the Southern Pine 

Growth Decline: Where Are We 

10 Years Later?

Gary L. Gadbury

 Michael S. Williams

Hans T. Schreuder

United States

Department

of Agriculture

Forest Service

Rocky Mountain

Research Station

General Technical

Report RMRS-GTR-124

February 2004
Gadbury, Gary L.; Williams, Michael S.; Schreuder, Hans T. 2004. Revisiting the southern pine growth decline: Where are we 10 years later? Gen. Tech. Rep. RMRS-GTR-124. Fort Collins, CO: U.S. Department of 

Agriculture, Forest Service, Rocky Mountain Research Station. 10 p.

Abstract

This paper evaluates changes in growth of pine stands in the state of Georgia, U.S.A., using USDA Forest 

Service Forest Inventory and Analysis (FIA) data. In particular, data representing an additional 10-year growth cycle has been added to previously published results from two earlier growth cycles. A robust regression procedure 

is combined with a bootstrap technique to produce estimates of mean growth with confidence intervals for the 

fourth, fifth, and sixth inventories of natural pine stands sampled between 1961 and 1990. Results suggest that 

sixth cycle growth rates of pine stands in Georgia remain fairly constant with rates observed in the fifth growth cycle, though they are not up to the level of growth observed in the fourth cycle. Overall, we conclude that growth in 

the stands screened for this analysis declined between the fourth and fifth cycles but stabilized in the sixth cycle. 

Inferences cannot be extended to the entire state of Georgia but only to the unknown population represented by 

the screened dataset of undisturbed natural pine stands. We highlight some specifics on what can and cannot be 

inferred from FIA data and recommend future actions to increase the chance of detecting changes and revealing 

factors that might be associated with the changes. The recent switch in FIA to annualized inventories will make it 

more likely that changes such as these will be easier to detect and interpret in the future.

Key words: bootstrap, cause-effect, forest inventory and analysis, robust regression

The Authors

Gary L. Gadbury is an associate professor of statistics at the University of Missouri at Rolla, Missouri. Michael 

S. Williams and Hans T. Schreuder are mathematical statisticians for the USDA Forest Service Rocky Mountain 

Research Station at Fort Collins, Colorado.

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Cover: Natural stand of 40-year-old loblolly pine by David J. Moorhead, 

The University of Georgia, www.forestryimages.org.
USDA Forest Service RMRS-GTR-124. 2004 1

Introduction

A controversial topic related to U.S. forest inventories 

was the southern pine growth decline issue in the 1980s. 

The U.S. Forest Service Forest Inventory and Analysis 

(FIA) program indicated that the growth of natural pines 

in Georgia and Alabama in the 1970s had decreased significantly from levels reported in the 1960s. In various 

newspapers articles, this was attributed to pollution.

FIA inventories were never designed to assess true 

cause and effect (Schreuder and Thomas 1991), just as 

the linkage between smoking and lung cancer could not 

be unequivocally confirmed from the numerous survey 

studies that suggested a connection between the two. 

Careful experimentation finally conclusively established such a link. Establishing cause-effect from observational survey data is difficult (Gadbury and Schreuder 

2003). Although cause and effect is beyond the scope 

of FIA, the FIA survey is suitable for assessing change 

in the forest resource over large areas. We document, as 

well as possible, what can be concluded from FIA data, 

a new procedure for analyzing FIA data, and a reanalysis 

that incorporates an additional growth cycle.

Literature Review

The FIA program, initiated in 1928, inventories the 

forest resources of the United States and regularly produces population estimates such as the total area of forest and timber volume as well as change over time. Until 

recently, FIA was a periodic inventory where states 

were visited one at a time every 7-22 years. A decline 

in growth of natural southern pine timber volume from 

the fourth cycle (1961-1971) to the fifth cycle (1972-

1982) was observed primarily in Georgia and Alabama. 

Concerns arose regarding the use of FIA data to conclude a growth decline. However, the findings were 

supported by several researchers (Sheffield and others 

1985; Sheffield and Cost 1987). The decline in growth 

was reported to be as much as 17-23% for natural loblolly pine and 27% for natural shortleaf pine (Zahner and 

others 1989; Bechtold and others 1991).

Ruark and others (1991) used FIA data to compare 

the periodic annual increment in basal area of selected 

naturally regenerated pine stands throughout Alabama 

and Georgia. Estimated growth rates between 1972 and 

1982 (fifth cycle) were compared with estimated growth 

rates obtained during the previous 10-year survey cycle (fourth cycle). Separate analyses were conducted for 

loblolly, longleaf, shortleaf, and slash pine cover types. 

Comparisons of growth rates yielded reductions ranging 

from 3% to 31% in both states. All reductions were statistically significant except for the 3% decline in natural loblolly pine in Alabama. Bechtold and others (1991) 

performed a similar study that focused only on the state 

of Georgia. Both Bechtold and others (1991) and Ruark 

and others (1991) developed models that adjusted the 

observed growth rates for changes in stand structure. 

T-tests were used to evaluate the significance of mean 

adjusted growth rates obtained from analysis of covariance models. The conclusion from both papers was that 

the declines could not be attributed to changes involving 

the modeled stand structural parameters; however, the 

agent(s) causing the decline were not identified.

A number of other studies examined possible explanations of a decline in growth. Knight (1987) attributed 

the decline to four factors: declining area of timberland, 

inadequate regeneration after harvest on non-industrial 

private forest lands, increased tree mortality, and a reduction in the rate of tree and stand growth. Zahner and 

others (1989), collecting tree-ring data on a 10% subsample of FIA field plots across the Piedmont region of 

Georgia, North Carolina, and South Carolina, developed 

tree-ring models to interpret the growth decline of loblolly pine. These authors attributed some of the decline 

to region-wide drought periods between 1950 and 1959 

and again between 1980 and 1983. Another important 

factor identified was the increase in average basal area 

and number of stems per hectare. This study concluded 

that the annual growth rate of trees in the early 1980s 

was about two-thirds that of trees growing in similar 

conditions 35 years earlier. Moreover, it concluded that 

a significant portion of the decline could not be attributed to either climatic or stand conditions but speculated 

that high levels of ozone in the region could have been 

a significant factor.

Czaplewski and others (1994) used the Georgia FIA 

data to look at spatial patterns to determine if atmospheric deposition from large metropolitan areas could be a 

factor in a growth decline. While there was a significant 

Revisiting the Southern Pine Growth Decline: 

Where Are We 10 Years Later?

Gary L. Gadbury, Michael S. Williams, and Hans T. Schreuder
2 USDA Forest Service RMRS-GTR-124. 2004 

spatial pattern associated with the growth decline, this 

pattern could also be explained by an unusually slowgrowing cluster of pine plots in the mountains approximately 100 km north of Atlanta. However, after using a 

regression model to adjust for local stand conditions, no 

significant spatial autocorrelation existed.

A number of concerns were raised regarding these 

findings. Hyink (1991), in a response to Bechtold and 

others (1991), was concerned about the differences in 

the distributions of age and site classes in data screened 

from the two growth cycles. He also noted that there was 

a troubling number of plots with atypically high growth 

rates in the fourth cycle in Georgia and that there is a 

lack of knowledge regarding what constitutes a “normal” growth rate for natural pine stands in the region.

Gertner (1991) commented on the analysis techniques 

used by Bechtold and others (1991) by noting that there 

are likely to be large amounts of error in some of the 

independent variables when a calibrated model is used 

to adjust mean logarithmic growth. He concludes that 

while there may have been a real reduction in growth 

rates, the possibility that the reduction may have resulted from biases caused by sampling errors and data transformations could not be ruled out.

Some of these concerns were addressed in subsequent studies. Ouyang and others (1991) used bootstrap 

and jackknife methods for inference since distributions of residuals from fitted models were often “heavy 

tailed.” Ueng and others (1997) used a robust regression technique to minimize the influence of outlying residuals from fitted models. Gadbury and others (1998, 

2002) used classification and regression tree methods 

to account for possible complex nonlinear relationships 

among variables describing growth, mortality, and stand 

structure. The results of each of these studies agreed with 

the results of Bechtold and others (1991) and Ruark and 

others (1991). Thus, some of the earlier concerns over 

the methods of analyses did not invalidate the findings.

Zeide (1992) performed an extensive analysis of data 

from the third to sixth cycles and pointed out that the reported changes were puzzling in light of the fact that the 

decline occurred only for naturally regenerated pines, 

but was unobserved in pine plantations. He suggested 

that either there was a growth decline before 1961, or 

more likely that there was no evidence of a growth decline and that the data were deficient for several reasons: 

(1) a drastic change from the fixed area plot sampling to 

variable radius plot sampling, (2) the presence of numerous outliers, and (3) inconsistencies in relationships between variables.

As noted in Schreuder and Thomas (1991) and affirmed in comments to that article by Clutter and Hyink 

(1991), screening of the data as done in both the Georgia 

and Georgia/Alabama studies make it difficult to assess 

the actual population for inference. So, was there a decline in growth in natural pine stands in the period from 

the 1960s to the 1970s? We believe there was for the 

screened data analyzed, but extension of these results to 

the entire population of natural pine stands in Georgia 

and Alabama is not warranted. What should be done to 

maximize the possibility of identifying and assessing 

meaningful hypotheses of change in the future and possible causes for them? We address that in the section on 

recommendations at the end of the paper.

Where Are We Today?

Some things have changed. First and foremost is the 

addition of the sixth cycle to the FIA inventory. From 

these data, the growth rate between the fifth and sixth cycle can be estimated and compared to that of the fourth. 

There are also new analytical techniques. Recently FIA 

procedures have changed drastically by going from a cyclical inventory to an annualized inventory where 20% 

of the plots will be measured in each state each year. FIA 

has also integrated with the Forest Health Monitoring 

(FHM) program and has dedicated a systematic subset of its plot network to investigating issues related to 

forest health (Stolte 2001). Ten years of research into 

cause-effect issues with FIA data has improved our 

understanding of the problem and going to an annualized inventory has provided us with improved ability to 

assess change. The goals of this study are to:

• Introduce robust methods for analyzing data from periodic surveys.

• Compare the growth rates between the fourth, fifth, 

and sixth cycles of the inventory to see whether perceived declines continued into the sixth cycle.

• Recommend possible methods to analyze such data in 

the future.

• Identify issues that arise when attempting to use observational data to attribute an observed change to potentially “causal” factors.

• Identify what can and cannot be accomplished with 

FIA-type observational data.

Data Description

Three types of naturally regenerating pine stands 

were studied and were designated by their dominant species: loblolly (Pinus taeda), shortleaf (Pinus 

echinata), and slash pine (Pinus elliottii). The data 
USDA Forest Service RMRS-GTR-124. 2004 3

represent growth rates and stand structure of forest 

plots in Georgia over three 10-year periods spanning the years 1961-1990. The three periods are 

referred to as the fourth, fifth, and sixth growth 

cycles. The data for cycles prior to the fourth were 

not suitable for assessing changes in growth rates. 

Additional information about the data can be found 

in Bechtold and others (1991).

Each growth cycle uses an independent sample of forest plots because the time lapse between 

samples and drastic changes in stand structure and 

disturbances made it unrealistic to follow the same 

plots over the three growth cycles. A total sample 

size of 692 loblolly plots was obtained, 235 from 

the fourth cycle, 104 from the fifth cycle, and 353 from 

the sixth, of which 11 were common to all three cycles. 

A total sample size of 258 shortleaf plots was obtained, 

127 from the fourth cycle, 45 from the fifth, and 86 from 

the sixth, of which three were common to all three. 

Finally, a total sample size of 401 slash pine plots was 

obtained, 84 from the fourth cycle, 83 from the fifth, and 

234 from the sixth, of which seven were common to all 

three. The plots common to all three growth cycles represented a small fraction of the total sample, and so they 

too were treated as independent observations across the 

three cycles.

The variables of interest are: GG = gross annual basal 

area growth per acre (survivor growth + ingrowth); S = 

site index representing volume growth potential (S represents a relation between age and height of dominant 

and co-dominant pines in each stand (base 50 years); A

= stand age (midpoint of 10 year class); N = number of 

stems per acre; P = ratio of yellow pine basal area per 

acre to basal area of all species; M = annual basal area 

mortality per acre of trees alive at initial inventory that 

die from natural causes prior to terminal inventory; net 

growth denoted NG, equal to GG – M . GG, N, M, and NG

are all based on trees 1.0 inches dbh and larger at the time 

of the initial inventory.

Variables GG, N, M, (and consequently NG) have 

separate data available for pine only and for all trees, 

denoted by the subscripts p and t respectively. These 

are represented as GGp and GGt for gross pine growth 

or gross total growth, respectively. Similarly, we use Np

and Nt, Mp and Mt, and NGp and NGt, the latter being net 

pine growth and net total growth. Summary statistics and 

sample sizes for the sixth growth cycle are shown in table 1. The corresponding results for the fourth and fifth 

growth cycles are reported in Bechtold and others (1991, 

page 708). Extreme data points at either of the fourth, 

fifth, or sixth growth cycles are handled with the method 

described below. In particular, variable transformations, 

diagnostic procedures, and robust fitting procedures 

should minimize the effect of extreme data values on 

any conclusions from the following analyses.

 Methods

The statistical methods discussed earlier have different strengths and limitations. We focus on a method that 

incorporates some of the advantages in Ueng and others 

(1997), Gadbury and others (1998, 2002), and Ouyang 

and others (1991). A linear model is fit relating a function of growth variables (i.e., response variables) to 

functions of covariates. We also explore more complex 

nonlinear relationships between covariates and the response in a second model and include these nonlinear 

terms if appropriate. The results then are a linear and a 

nonlinear model. The models are fit to the FIA data using a robust fitting algorithm to minimize the influence 

of large residuals, and interval estimates of growth are 

obtained using the bootstrap to minimize parametric assumptions. Results from inference using each of the two 

models are compared in order to evaluate the effect, if 

any, of the higher order nonlinear terms on conclusions 

from the analyses. The details of the method are described below.

Selecting a Model

Initially, the range of each covariate, i.e., A, P, S, and 

Nk, k = p, t, was studied to determine if transformations 

were necessary (Weisberg, 1985, p. 156). If, for a data 

set, the maximum of a covariate divided by its minimum 

was greater than 10, the natural logarithm was used. For 

all data sets, this resulted in ln(A) and ln(Nk) being used 

in place of A and Nk, respectively. These transformations helped to stabilize the variance of residuals and to 

Table 1. Sample size and summary statistics (mean and standard 

error) for variables from the sixth FIA growth cycle.

Loblolly Shortleaf Slash

n = 353 n = 86 n = 234

Variable mean SE mean SE mean SE

GGp 3.05 0.10 2.64 0.22 2.77 0.11

GGt 4.17 0.11 3.76 0.24 3.69 0.13

Mp 1.04 0.06 0.90 0.13 0.52 0.06

Mt 1.24 0.07 1.13 0.14 0.66 0.06

Np 442.8 20.1 437.2 36.7 345.1 19.2

Nt 834.9 24.4 858.2 46.3 688.7 32.0

A 28.7 0.7 27.4 1.4 30.4 0.8

S 73.0 0.5 67.0 1.1 71.4 0.6

P 0.79 0.01 0.77 0.02 0.83 0.01
4 USDA Forest Service RMRS-GTR-124. 2004 

control for influential observations (outliers in the values of a covariate) in model-fitting algorithms, and both 

were also used by Bechtold and others (1991) and Ruark 

and others (1991). Then, a model of the following form 

was considered:

g(Yk) = bo*T4 + b1*T5 + b2*T6 + b3*ln(A) + b4*ln(Nk) 

+ b5*S + b6*P + ε [1]

where Ti = 1 if a plot was sampled from the ith growth 

period and zero otherwise (i = 4, 5, 6), k = p or t for pine 

growth or total growth, Y is either GG or NG, and ε represents a random error term that need not be normally distributed for the method proposed here. Box-Cox 

transformations (Box and Cox 1964) were used with 

this model to determine a suitable transformation g(·) 

for Yk, the goal being stabilization of variances of residuals. Because NGk

 values were occasionally negative, a 

location transformation, NG*

k

 = NGk + | min(NGk)| + 1, 

k = p, t, was used when applying the natural logarithm 

transformation.

Since relationships between the predictor variables 

and the response variable appeared to be quite complicated, even after transformations, higher order terms 

were evaluated in a second model. In addition to the 

terms in model 1, two-way interactions and quadratic 

terms were selected using stepwise regression (Neter 

and others 1990, chapter 12). The objective of this step 

was to determine if any second order terms were important for capturing the complex relationship between covariates and response. There were, then, 22 additional 

terms in the pool of covariates that could be selected in 

this step. This model will be referred to as model 2.

Cook’s distance (Cook and Weisberg 1982) was used 

to identify any influential points in the models. These 

points may not only exert excessive influence on the fit 

of the model, but also the selected form for the model, 

i.e., they may suggest curvature in the model that is not 

really there. If such points were detected, they were investigated further to determine if they were valid and 

to assess their effect on conclusions from a model. 

Diagnostic plots were also used to evaluate equal variance of residuals and to identify any possible data points 

with high leverage.

A Robust Method for Fitting the Models

There were still outlying residuals in a model fitted 

by the usual least squares. To deal with this issue, both 

models 1 and 2 were fit to the data using iteratively reweighted least squares (Holland and Welsch 1977). The 

function to do this is available in the statistical analysis 

software S-Plus and is called rreg. We used a bi-square 

weighting function given by (1 – (u/c)

2

)2 if u < c and 

zero otherwise, where u is the residual scaled by a factor proportional to the median of the absolute deviations 

from the median of the residuals. The constant c was set 

equal to 4.685, the default value (Holland and Welsch 

1977), indicating that an observation with a scaled residual bigger than 4.685 received a weight of zero (i.e., 

it is removed from the data set), and is otherwise weighted by (1 – (u/c)

2

)2. After the observations are weighted, 

the model was fitted again to the data and the observations were re-weighted as described above. Eventually 

the model converged (i.e., there is negligible change in 

the regression coefficients).

Obtaining Estimates of Growth

The adjusted mean growth at each growth cycle was 

estimated at the mean value of the covariates over all 

three growth cycles. This is arbitrary, but some value 

of covariates or combination of values was necessary to 

obtain predictions from the models and the mean value of covariates is a reasonable choice (c.f., Bechtold 

and others 1991). Moreover, differences of estimated 

mean growth between cycles will be the same when using model 1 regardless of the choice of covariate values 

since no covariate by cycle interactions are included. If 

such interactions were included in model 2, the model 

coefficients would be less interpretable and estimated 

differences of growth between cycles would depend on 

the choice of covariate values. Thus, to compare growth 

rates between models 1 and 2, estimates were computed at the mean of the covariates over all three cycles. 

Some of the interactions that were included in model 2 

may have been spurious, primarily due to the large sample sizes. An advantage of reporting results from both 

models is to determine if any interaction terms in model 2 could alter conclusions obtained from the simpler 

model 1.

A disadvantage to the robust model fitting procedure 

is that certain features of classical parametric inference 

are not available. So to obtain confidence intervals, a 

bootstrap routine (Efron 1982) was conducted as follows. Suppose there are n1

, n2, and n3 observations from 

growth cycle 4, 5, and 6, respectively. A bootstrap sample was obtained by sampling n1

 observations with replacement from growth cycle 4, n2

 observations with 

replacement from growth cycle 5, and n3 observations 

with replacement from growth cycle 6. Iteratively reweighted least squares was used to fit a model to the 

bootstrap sample data, and the adjusted mean growth 

was estimated using each fitted model. This resampling 

technique was repeated 1000 times, thereby producing a 
USDA Forest Service RMRS-GTR-124. 2004 5

sampling distribution of adjusted mean growth estimates 

for each growth cycle and for each model. A family of 

three 95% confidence intervals was constructed for the 

mean growth at each growth cycle using a Bonferroni 

correction so that each individual interval had a 98.3% 

confidence level, i.e., since we are simultaneously estimating mean growth at three growth cycles, an individual confidence interval will have a confidence level 

of 100(1 – 0.05/3) = 98.3% (c.f., Christensen 1996, section 6.2). Using the bootstrapped sampling distribution, 

the eighth and 992nd sorted values represent the bootstrapped lower and upper confidence limits. See Efron 

and Tibshirani (1993, chapter 13) for more details on 

percentile bootstrap confidence intervals. Growth estimates from both models were transformed back to the 

original arithmetic units.

Results

 Estimated coefficients for model 1 are shown in table 2. With either gross growth or net growth as the dependent variable in the model, Box-Cox transformation 

analysis suggested that the natural logarithm transformation be used for most stand types. For some stand 

types, a square root transformation was suggested for 

net growth models, but the uncertainty in the maximum 

of the Box-Cox likelihood also indicated the logarithm 

would suffice. Thus, the dependent growth variable was 

transformed using the natural logarithm for all stand 

types for consistency. The signs and relative magnitudes 

of the coefficients generally agree with those of Bechtold 

and others (1991), who analyzed the natural logarithm of 

gross growth for the fourth and fifth cycles, but included 

mortality as a covariate in a standard analysis of covariance model. The coefficients for T4

, T5, and T6 in the net 

growth models appear different from those of the gross 

growth models due to the location transformation required in g(NGk

), k = p, t. It is the differences between the 

coefficients for T4, T5, and T6 that show differences in estimated growth between growth cycles because there are 

no covariate by cycle interactions in model 1.

Quadratic terms that commonly appeared in model 2 

for the different data sets were (lnA)2 and (lnNk)2. An interaction between S and ln(A) and between S and ln(Nk

) 

was commonly detected as was an interaction between 

ln(A) and ln(Nk). It was also not unusual to see S interacting with a growth cycle variable in some of the models. 

The other second order terms for model 2 varied with the 

data set and, for the sake of brevity, we do not list the details. Instead, the estimated mean growth using both models is shown in tables 3, 4, and 5. Estimates using model 2 

are always slightly greater than those using model 1 with 

the exception of net pine growth for slash pine (growth 

cycle 4) and gross growth shortleaf pine (growth cycle 

5). However, the estimates are close enough that the interval estimates using model 1 and model 2 easily overlap, 

indicating no significant difference between estimates 

obtained from the two models. Though significant interaction terms may be of biological interest and may suggest future studies to verify their significance, we focus 

on estimates from model 1 for a key reason. Estimated 

Table 2. Details of model 1 fitted by robust regression. The response variable, Y = GGk or NGk (k = p for pine growth and t for 

total growth), was transformed to g(GGk) = ln(GGk), and g(NGk) = ln[NGk + | min(NGk) | + 1], respectively, for gross growth 

or net growth analyses. 

Stand Response Estimated coefficients

 type variable T4 T5 T6 ln(A) ln(Nk) S P

Loblolly g(GGp) -0.343 -0.528 -0.480 -0.315 0.293 0.003 0.746

g(GGt) -0.025 -0.133 -0.090 -0.308 0.284 0.002 0.480

g(NGp) 2.015 1.933 1.882 -0.179 0.063 -0.001 0.282

g(NGt) 2.214 2.129 2.100 -0.159 0.072 -0.001 0.137 

Shortleaf g(GGp) -1.008 -1.271 -1.222 -0.282 0.347 0.005 0.704

g(GGt) 0.018 -0.246 -0.162 -0.268 0.262 0.003 0.312

g(NGp) 1.587 1.461 1.470 -0.137 0.092 0.001 0.198

g(NGt) 1.990 1.834 1.868 -0.167 0.066 0.001 0.123 

Slash g(GGp) -0.746 -1.064 -0.910 -0.216 0.399 0.003 0.140

g(GGt) -0.523 -0.788 -0.691 -0.258 0.346 0.004 0.332

g(NGp) 1.798 1.705 1.721 -0.089 0.094 -0.001 0.095

g(NGt) 1.452 1.319 1.317 -0.137 0.13 -0.002 0.146
6 USDA Forest Service RMRS-GTR-124. 2004 

growth at each cycle depends on the chosen values for the 

covariates at which the estimates are computed. However, 

differences in growth between cycles will be constant for 

any chosen values of covariates when using model 1, but 

not necessarily for model 2. In other words, in model 1 

the “slopes” of the fitted robust regression surfaces are the 

same for the three growth cycles.

Tables 3, 4, and 5 show the same decrease in growth 

from the fourth to the fifth cycle for all data sets and 

all analyses as was seen in Bechtold and others (1991). 

However, the family of three 95% confidence intervals 

based on the Bonferroni correction suggest the decrease 

is, at most, marginally significant after accounting for 

sampling variability. For most stand types and most analyses, the estimated growth for the 6th cycle represented 

a slight increase from the fifth cycle. An exception was 

loblolly net growth, which continued to decrease, though 

not significantly so, from the fifth cycle. Comparing the 

sixth cycle summary statistics in table 1 with those for 

cycles 4 and 5 given in Bechtold and others (1991, page 

708), one would observe that loblolly unadjusted gross 

growth for the sixth cycle was only slightly lower than 

that of the fifth, but mortality for the sixth cycle was 

higher than either the fourth or fifth cycles. This combination might explain the apparent continued estimated 

decline of loblolly net growth into the sixth cycle.

Table 3. Loblolly pine stands. Growth estimates from models 1 and 2. Estimates are given in original 

arithmetic units and they include a point estimate for mean adjusted growth for each growth 

cycle, μ$, and a family of three 95% confidence intervals (L,U). Interval estimates are computed 

with the bootstrap technique.

Growth Growth 

 type cycle Model 1 Model 2

μ$ , (L, U) μ$ , (L, U)

Gross pine 4 3.31,(3.07, 3.55) 3.59,(3.27, 3.92) 

growth 5 2.75,(2.44, 3.08) 3.03,(2.68, 3.41) 

6 2.89,(2.71, 3.06) 3.19,(2.92, 3.44)

Gross total 4 4.47,(4.16, 4.84) 4.63,(4.22, 5.09)

growth 5 3.81,(3.45, 4.22) 3.95,(3.52, 4.40) 

6 3.98,(3.80, 4.19) 4.22,(3.92, 4.54) 

Net pine 4 2.99,(2.65, 3.31) 3.15,(2.75, 3.59)

growth 5 2.42,(1.97, 2.81) 2.67,(2.28, 3.09) 

6 2.09,(1.83, 2.34) 2.40,(2.06, 2.71)

Net total 4 3.98,(3.58, 4.38) 4.18,(3.64, 4.74)

growth 5 3.19,(2.67, 3.69) 3.40,(2.78, 3.95) 

6 2.94,(2.68, 3.21) 3.24,(2.81, 3.66)

Table 4. Shortleaf pine stands. Growth estimates from models 1 and 2. Estimates are given in 

original arithmetic units and they include a point estimate for mean adjusted growth for each 

growth cycle, μ$ , and a family of three 95% confidence intervals (L, U). Interval estimates are 

computed with the bootstrap technique.

Growth Growth 

 type cycle Model 1 Model 2

μ$ , (L, U) μ$ , (L, U)

Gross pine 4 2.77,(2.47, 3.05) 2.99,(2.64, 3.37)

growth 5 2.13,(1.69, 2.61) 2.04,(1.60, 2.63)

6 2.23,(1.95, 2.56) 2.39,(2.06, 2.79)

Gross total 4 3.98,(3.65, 4.33) 4.30,(3.88, 4.77)

growth 5 3.05,(2.47, 3.72) 3.14,(2.50, 3.89)

6 3.32,(2.96, 3.70) 3.57,(3.08, 4.14)

Net pine 4 2.63,(2.22, 3.01) 2.76,(2.33, 3.24)

growth 5 1.79,(1.31, 2.39) 1.86,(1.29, 2.55) 

6 1.84,(1.38, 2.24) 2.09,(1.56, 2.67)

Net total 4 3.51,(3.05, 3.95) 4.12,(3.43, 4.85)

growth 5 2.33,(1.54, 3.26) 2.68,(1.61, 3.82)

6 2.57,(2.08, 3.11) 3.12,(2.50, 3.83) 
USDA Forest Service RMRS-GTR-124. 2004 7

A visual comparison of estimated growth for the three 

cycles can be seen in figures 1, 2, and 3. These are boxplots of an estimated bootstrapped sampling distribution 

of estimated mean growth. There are four subfigures 

in each figure and three boxplots in each subfigure for 

each of the three growth cycles. Each individual boxplot represents 1000 bootstrap estimates of adjusted 

mean growth from model 1 at a particular growth cycle. The lower and upper lines of the shaded region of 

a box are the first (Q1) and third (Q3) quartiles of the 

Table 5. Slash pine stands. Growth estimates from models 1 and 2. Estimates are given in original 

arithmetic units and they include a point estimate for mean adjusted growth for each growth cycle, 

μ$, and a family of three 95% confidence intervals (L, U). Interval estimates are computed with the 

bootstrap technique.

Growth Growth 

 type cycle Model 1 Model 2

μ$ , (L, U) μ$ , (L, U)

Gross pine 4 2.91,(2.47, 3.38) 3.03,(2.62, 3.61)

growth 5 2.12,(1.74, 2.56) 2.38,(1.96, 2.86)

6 2.47,(2.27, 2.68) 2.68,(2.42, 2.97)

Gross total 4 3.84,(3.33, 4.42) 4.32,(3.72, 5.05)

growth 5 2.96,(2.49, 3.52) 3.41,(2.82, 4.09)

6 3.26,(3.01, 3.52) 3.68,(3.30, 4.10)

Net pine 4 2.83,(2.43, 3.32) 2.79,(2.38, 3.33)

growth 5 2.16,(1.73, 2.61) 2.38,(1.78, 2.91)

6 2.27,(2.01, 2.54) 2.39,(2.10, 2.73)

Net total 4 3.66,(3.14, 4.20) 3.96,(3.45, 4.59)

growth 5 2.87,(2.31, 3.38) 3.14,(2.52, 3.81)

6 2.86,(2.58, 3.16) 3.14,(2.72, 3.59)

2.4 2.8 3.2 3.6

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Growth cycle

Estimated growth

Gross pine growth

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Gross total growth

2.0 2.5 3.0

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Growth cycle

Estimated growth

Net pine growth

2.5 3.5 4.5

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Growth cycle

Estimated growth

Net total growth

Figure 1. Loblolly pine: Box plot of a bootstrapped sampling distribution of estimated mean growth at each of the three 

growth cycles. Each box plot contains 1000 bootstrap estimates at each growth cycle.
8 USDA Forest Service RMRS-GTR-124. 2004 

Figure 3. Slash pine: Box plot of a bootstrapped sampling distribution of estimated mean growth at each of the three 

growth cycles. Each box plot contains 1000 bootstrap estimates at each growth cycle. 2.0 2.5 3.0

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Growth cycle

Estimated growth

Gross pine growth

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Growth cycle

Estimated growth

Gross total growth

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Growth cycle

Estimated growth

Net pine growth

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Growth cycle

Estimated growth

Net total growth

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Growth cycle

Estimated growth

Gross pine growth

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Growth cycle

Estimated growth

Gross total growth

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Net pine growth

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Growth cycle

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Net total growth

Figure 2. Shortleaf pine: Box plot of a bootstrapped sampling distribution of estimated mean growth at each of the three 

growth cycles. Each box plot contains 1000 bootstrap estimates at each growth cycle.
USDA Forest Service RMRS-GTR-124. 2004 9

1000 estimates, and the middle line in the box is the 

median. The extended lines stretch to the nearest value 

within a “step” below Q1 and a “step” above Q3 where 

a step is 1.5 multiplied by the interquartile range (IQR

= Q3 – Q1). Estimates outside the “steps” are plotted as 

points and are generally considered outside the normal 

“spread” of the data though this designation is somewhat 

arbitrary. The figures show that estimated growth for the 

6th cycle is slightly higher than the fifth, though not up 

to the level of growth in the fourth cycle. The exception, 

again, is loblolly net growth, which shows a continued 

decline at the sixth cycle, but the two distributions of estimated growth at the fifth and sixth cycles have a fair 

amount of overlap. As indicated earlier, this continued 

apparent decline is not significant after accounting for 

sampling variability.

Summary

Given the analyses performed, a summary of the results is as follows: 

1. There is no further significant decrease in either net or 

gross growth from cycle 5 to 6 as there was from 4 to 5. 

2. There is generally an interaction between S and A, S

and N, and A and N, as uncovered in model 2, though 

inclusion of these interactions did not significantly alter estimates of growth at each cycle. 

3. With the exception of loblolly net growth, there is 

a slight increase in growth for both net and gross 

growth from the fifth to the sixth cycle, but none of 

the growth differences are significant between any of 

the three growth periods as determined by a family of 

95% confidence intervals. 

4. Our inference space is quite limited due to the heavily 

screened data sets that were used. 

5. We are not accounting for a large amount of the variability observed with our models. There may be additional variables that need to be measured to account 

for this variability.

While the results are of interest in their own right, the 

more important issue is determining what the implications of the results are in terms of the southern growth 

decline issue. We conclude the following: 

1. Although there was a valid concern about a decline 

in pine growth in natural pine stands, this decline has 

not continued. 

2. We need to find ways to broaden our capability of inference to more general forest populations of interest.

3. We need to measure additional variables to sharpen 

the predictive ability of our models.

It should also be noted that the current annualized 

FIA inventories, although yielding a small sample size 

for a given year, may eliminate the need for screening 

the data to achieve comparability of results for each 

year. Hence, meaningful changes can be detected for a 

sufficiently large area (see Schreuder and others 2000). 

In addition, it may be possible to detect or assess changes more immediately by using additional samples of 

ground plots or by using alternative data sources such as 

large-scale aerial photography.

Recommendations

The southern growth decline is only one example 

of how observational survey data can become the focal point of a very contentious issue. Based on what has 

been learned in the last decade regarding this issue, we 

make the following recommendations.

1. Maintain clear and consistent sampling protocols as 

recommended by Zeide (1992). 

2. Develop a general analysis and sampling strategy to assess changes of interest from annualized inventories. 

3. Protect against results that are difficult to interpret, 

such as the growth decline in Georgia and Alabama. 

With the small sample size annually in each state, 

false alarms will happen, especially since many users 

will use the data themselves without realizing their 

limitations. Sampling strategies should be in place 

to follow up on interesting changes that are detected 

(see Schreuder and Wardle [1999] for an example related to similar issues). 

4. Measure key additional variables on the FIA plots 

as often as possible. With such variables, considerably improved prediction models could be developed 

making the detection and assessment of meaningful 

changes more likely. Though it is not feasible yet to 

obtain weather data for FIA plots, FIA data can be 

merged with climatic data to yield rough estimates of 

climatic influences. 

5. Emphasize quality design, analyses, and data collection. As recommended by Zeide (1992), data from 

forest inventories, such as FIA, need to be as good 

as research-quality data. It is possible that some of 

the growth decline detected in the earlier studies may 

have been due to unusual data points. 

6. Develop multiple working hypotheses and innovative analytical approaches. Such approaches are likely to provide the best scientific progress in assessing 

change or necessary “interventions.” 

7. Use a subjective checklist to form an elaborate theory that attempts to consider all possible variables 
10 USDA Forest Service RMRS-GTR-124. 2004

that could have produced an observed change (Olsen 

and Schreuder 1997). Remember that in surveys one 

does not know how “treatments” are assigned to response units, so results could be biased (Gadbury and 

Schreuder 2003). 

8. Have a clear understanding of what can and cannot be 

done with the data. Observational data are inadequate 

to establish cause-effect, but they can be used to identify interesting hypotheses. 

9. Publish controversial or important findings in refereed journals to ensure such analyses receive appropriate critical review.

Acknowledgments

Though the authors take full responsibility for the 

content herein, we are grateful to several individuals for 

their time in reviewing earlier versions of this work, including Tara Barrett, Rudy M. King, Francis A. Roesch, 

Stan Zarnoch, William Bechtold and Boris Zeide.

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