Effects of Selection Logging on Rainforest Productivity

Australian Forestry 1990, 53 (3), 200-214
Effects of Selection Logging on Rainforest Productivity
Jerome K. Vanclay
Queensland Forest Service, GPO Box 944, Brisbane 4000 Queensland, Australia1
Abstract
An analysis of data from 212 permanent sample plots provided no evidence of any decline in
rainforest productivity after three cycles of selection logging in the tropical rainforests of
north Queensland. Relative productivity was determined as the difference between observed
diameter increments and increments predicted from a diameter increment function which
incorporated tree size, stand density and site quality. Analyses of variance and regression
analyses revealed no significant decline in productivity after repeated harvesting. There is
evidence to support the assertion that if any permanent productivity decline exists, it does not
exceed six per cent per harvest.
Introduction
Hilton (1987) claimed that rainforest logging could disrupt nutrient cycling and cause
impoverishment, and argued that new harvesting methods were required. He suggested that
rainfall made a considerable contribution to forest nutrition, and could replace the nutrients
removed or lost during harvesting, provided that the residual stand was well stocked. He
concluded that “so little hard information is available that no comparison can be made
between past and present yields in those areas of rainforest which are being logged for the
second time. Although the growing stock may have been accurately assessed before the first
harvest the rate of growth remains unknown. Thus it is impossible to see ... how much
productivity has been affected, if it has, by logging”.
Enright (1978) reported that the growth rates of individual trees in the residual stand dropped
markedly after logging. He also found that logging resulted in a temporary but marked
decrease in nutrient levels after logging. However, both these studies concerned heavily
logged stands. Enright (1978) reported that nearly all Araucaria cunninghamii (the dominant
species comprising 54% of the stand) individuals exceeding 40 cm dbh were removed, and
that extensive damage was caused to the residual stand.
Boxman et al. (1985) studied polycyclic logging followed by silvicultural treatment in
Suriname and concluded that these contributed minimally to the loss of nutrients. Claims that
polycyclic logging may lead to deterioration of the forest due to the progressive removal of
the better genotypes have been refuted by Whitmore (1984), who argued that this was
insignificant and academic.
The present study concerns the tropical rainforests of north-east Queensland. These forests
had been managed for conservation and timber production for more than eighty years (Just
1987), before logging ceased following their World Heritage nomination in 1988. Although
initial exploitation of these forests was largely uncontrolled, logging practices were
progressively improved and harvesting in recent years has caused little environmental impact

1 Revised manuscript received 14 September 1990

(Just 1987). The earliest exploitation caused relatively little damage because of the highly
selective nature of logging and modest horsepower involved. Environmental impacts probably
peaked during the mid-1960's with the ready availability of heavy earth moving machinery.
During the 1980's, timber harvests were obtained through selection logging which removed 7
to 10 trees per hectare, comprising not more than 25 per cent of the total standing basal area
(Vanclay 1989b). Guidelines (Preston and Vanclay 1988) ensured that not more than 50 per
cent of the canopy was removed. Such guidelines ensure rapid recovery of the rainforest
canopy (Horne and Gwalter 1982). Key components of this selection logging system as
practiced during the 1980's were:
• Logging guidelines were sympathetic to the silvicultural requirements of the forest,
viz. ensuring retention of vigorous advance growth, harvesting only defective and
fully mature trees, providing for adequate regeneration of commercial species and
discouraging invasion by weeds;
• Treemarking by trained staff specified trees to be retained, trees to be removed and
the direction of felling to ensure minimal damage to growing stock and minimal
opening of the canopy;
• Logging equipment was appropriate and driven by trained operators to ensure
minimal damage to the residual stand and minimal soil disturbance, compaction and
erosion;
• Prescriptions ensured that adequate stream buffers and steep slopes were excluded
from logging;
• Sufficient areas for scientific reference, feature protection and recreation were
identified and excluded from logging;
• Deficiencies in an evolving system were recognised and remedied, leading to an
improved system.
Several studies have examined impacts of timber harvesting in these forests. Gilmour (1971)
found that effects of logging on streamflow and sedimentation were small scale and short
lived. Gillman et al. (1985) examined soil chemical properties and found that most topsoil
nutrients regained their initial levels within four years of logging. Whilst nutrient cycles were
disrupted by logging, losses appeared to be small and quickly replaced by natural inputs,
provided that logging was of low intensity, short duration and infrequent (Congdon and Lamb
1990).
Nicholson et al. (1988, 1990) and Crome et al. (1990) reported that whilst timber harvesting
caused localized destruction, it did not lead to loss of any plant species. Logging tracks and
canopy loss were confined to 5 and 20 per cent of the area respectively (Crome et al. 1990).
However, the light climate may be altered in areas with no direct canopy loss. Stocker (1981,
1983), Unwin (1983, 1988) and Webb and Tracey (1981) have investigated other aspects of
the dynamics and regenerative capacity of these rainforests. Crome and Moore (1989, 1990)
discussed effects of logging on fauna.
It has been estimated that a timber harvest of 60 000 cubic metres per annum could be
sustained from these forests (Preston and Vanclay 1988). Vanclay and Preston (1989)
examined the long-term sustainability of such a harvest, and concluded that selection logging
could be sustained by the growth of residual trees and regeneration, and need not rely upon
trees missed during previous harvests. Research into the relationship between diameter (breast
high or above buttress, over bark) and log volume provided no evidence to suggest that there
was any increase in defect or any reduction in log length in trees harvested from previously
logged stands (Henry 1989).
Rainforests appear to have the regenerative capacity to cope with the effects of a single
selection logging, given sufficient time to recover (Hopkins 1990). Shugart et al. (1980) used
a succession model to examine the effects of comparatively intensive harvesting on a 30 year
cycle in subtropical rainforest in New South Wales, and concluded that such harvesting was

sustainable, although the structure and composition of the forest would be altered. The present
paper examines how the long term average growth rates of individual trees are influenced by
repeated selection logging.
Data
The Queensland Department of Forestry (1983) research programme has provided an
extensive database sampling virgin, logged and silviculturally treated forests. CSIRO (West et
al. 1988) have also established 20 plots in relatively undisturbed stands sampling the full
range of forest types in the region. The combined database represents over 250 permanent
sample plots with a measurement history of up to 40 years (Appendix). Permanent sample
plots range in size from 0.04 to 0.5 hectares, and have been re-measured frequently. All trees
exceeding 10 cm dbh (diameter over bark at breast height or above buttressing) were uniquely
identified and tagged, and were regularly measured for diameter (to nearest millimetre) using
a girth tape. To improve the consistency of diameter measurement, field crews had access to
previous records while in the field. Any trees exhibiting defects or bulges at or near the
measurement height were noted and so identified on computer. Such trees have not been used
in calculating diameter increments, and have only been used in calculating stand basal areas.
The data used in this study were identical to those used by Vanclay (1990) in developing a
growth model for yield prediction (Vanclay and Preston 1989). Pairs of plot remeasurements
were selected from the database to attain intervals between remeasurements of approximately
five years, which did not span any logging or silvicultural activity. Tree diameters do not
increase monotonically in size, but exhibit diurnal and seasonal fluctuations which may result
in measured diameters smaller than previous values (Lieberman 1982). These, and
measurement errors, may give rise to negative increments which may cause difficulties in data
analysis. Ensuring a long interval between remeasurements (e.g. 5 years) so that the growth is
large relative to the error, eliminates many of these decrements, but some remain. The
logarithmic transformation used in the present analyses has long been recognised as an
efficient way to satisfy assumptions implicit in regression analysis (linearity, normality,
additivity and homogeneity of variance) (e.g. Schumacher 1939, Clutter 1963), but cannot
accommodate negative increments. Some negative values can be accommodated by adding a
constant before transforming, but any decrements exceeding 0.01 were omitted from the
present analyses.
The data file created for statistical analysis contained 62 372 observations of diameter
increment derived from 28 123 individual trees. The file also contained records of tree species
and dbh, and stand variables such as site quality, stand basal area and soil parent material. Site
quality for each plot was estimated using Vanclay's (1989a) Equation 13:

where GI is the growth index of the plot, Dij is the diameter (breast high or above buttress,
over bark, in cm) of tree j of species i, DI is its diameter increment (cm y-1), OBAij is its
“overtopping basal area”, the basal area of trees within the plot that are bigger than tree ij (m2
ha-1), BA is the plot basal area (m2 ha-1), and the βs are parameters estimated by linear
regression. This equation estimates growth index, a measure of site productivity based on the
diameter increment adjusted for tree size and competition, of all trees of eighteen reference
species (Acronychia acidula, Alphitonia whitei, Argyrodendron trifoliolatum, Cardwellia
sublimis, Castanospora alphandii, Cryptocarya angulata, C. mackinnoniana, Darlingia
darlingiana, Elaeocarpus largiflorens, Endiandra sp. aff. E. hypotephra, Flindersia
bourjotiana, F. brayleyana, F. pimenteliana, Litsea leefeana, Sterculia laurifolia, Syzygium

kuranda, Toechima erythrocarpum, Xanthophyllum octandrum) using all available
remeasures for the plot (except that where plots were remeasured more frequently,
remeasurements were selected to achieve approximately 5 year intervals). The βs were
estimated by fitting the equation
Log (DI+ α) = Spp +D.Spp +Log (D).Spp +Log (BA).Spp +OBA.Spp +Log (D)Plot
(where Spp and Plot are qualitative variables) simultaneously for all these reference species in
the development data set (80 plots, a further 64 plots were used for validation studies). The
parameter α was assigned the value 0.02 after inspection of residuals and examining the
residual mean squares from a range of values (Vanclay 1989a). The value 0.08808 was
subjectively determined to scale the growth indices into the range 0-10.
Table 1. Size and History of Plots used in Analyses.
Measurement History (Years) Plot Area
(ha) 0.10 10-19 20-29 30+
Total
Plots
<0.10 2 31 3 2 38
0.1-0.19 4 47 6 10 67
0.2-0.29 15 42 3 27 87
≥0.30 5 9 0 6 20
Total 26 129 12 45 212
The present study omitted any plots for which the estimated site quality exceeded the range 0-
10, or for which the variance of the estimated site quality exceeded 2. Valid estimates of site
quality were obtained for 212 plots (Table 1).
Table 2. Logging History for Plot Data used in Analyses.
Harvests prior Total Harvests at Last Measure Total
to First Measure 0 1 2 3 Plots
0 9 1 10
1 - 136 38 174
2 - - 26 2 28
Total 9 137 64 2 212
Table 3. Logging and Measurement Profile for Data used in Analyses
Total Harvests prior to Measure Year of
Measure 0 1 2 3
Total
Plots
-1949 6 1 7
1950-54 4 45 1 50
1955-59 5 72 7 84
1960-64 5 86 6 97
1965-69 6 127 14 147
1970-74 6 121 27 154
1975-79 9 61 43 2 115
1980- 4 23 21 2 50
Unfortunately, no continuous record of growth data spanning two successive harvests was
available (Table 2). Experiment 615 (Appendix) had two such plots but the two-year period
from establishment until logging was too short to provide reliable increment data. The 66
plots which were logged twice had measurement records which commenced only after the
first harvest, and only one plot had a measurement record spanning the first harvest. However,

38 plots provided measurement data spanning the second harvest (Table 2). Only two plots
were logged three times, but these harvests differed from normal practice in that the first and
second harvests were only seven years apart (Appendix, Experiment 615). The majority of
plots (136) were in stands logged once, and had a measurement record which did not span any
logging activity.
A further problem was that these experiments were not well replicated through time - most
were first logged during the decade 1950-59, and were relogged during 1969-80 (Appendix).
Table 3 shows that the different harvesting histories were well sampled, but these plots were
not necessarily paired with suitable control plots. Thus differences detected during any given
period could be due to site or management differences, as well as to harvesting history.
Similarly, on any given plot, differences in increment between measurement periods could be
due to prevailing weather conditions, as well as due to harvesting. Thus although extensive,
the present database contained weaknesses which provided problems for the analysis and
interpretation of the results.
The severity of these problems may be gauged through a correlation matrix of plot variables
(Table 4). Ideally, the explanatory variables explored in an analysis should not be correlated,
although in practice this is rarely possible. When explanatory variables are correlated, the
ability to identify potentially causal relationships is reduced (explanatory variables do not
have a unique sum of squares), and the magnitude of possible effects may not be able to be
reliably determined (addition or subtraction of an explanatory variable may substantially
change parameter estimates for a model, standard errors of estimates may be inflated).
However, multicollinearity does not inhibit the ability to obtain a good fit, nor does it affect
inferences about responses or predictions within the region of observations (Neter and
Wasserman 1974:341). Correlations between explanatory variables considered in the present
analysis are not serious (Table 4). The high correlation between number of harvests and time
since logging (-0.64) is partly due to the encoding convention adopted (for unlogged plots,
time since logging = 99), and the correlation for logged plots is lower (-0.43).
Hypothesis and Analyses
The analyses test the hypothesis that selection logging leads to a reduction in productivity in
these rainforests and that this reduction may comprise two components, a transient and a
permanent loss of productivity. Figure 1 illustrates the pattern of productivity decline that the
analyses attempt to detect. The null hypothesis was that there is no reduction in productivity,
whilst the alternative hypothesis was that a reduction in productivity following logging can be
detected. The analyses endeavour to produce evidence to reject the null hypothesis.

Time
Figure 1. Hypothetical effect of logging on productivity.

Table 4. Correlation Matrix for Plot Variables:
Source
No of
harvests Time since
treatment
Time since
logging
Site
quality
Basal
Area
Mean
Residual
Year of measure 0.272* 0.071 0.088* -0.019 0.040 -0.092*
No of harvests 1.000 -0.252* -0.639* -0.084* -0.230* -0.079*
Time since treatment 1.000 0.473* 0.326* 0.741* -0.055
Time since logging 1.000 0.207* 0.588* 0.019
Site quality 1.000 0.615* 0.006
Stand basal area 1.000 0.101*
* indicates correlation significant at P<0.05
Unfortunately, a suitable measure of “productivity” is neither easy to define nor to measure.
Biomass production may seem a good measure of productivity, but has several weaknesses. It
cannot be measured directly, and is difficult to determine. Nett biomass production is near
zero in unlogged stands (any growth is offset by mortality) and increases following logging
due in part to a reduction in competition. Gross biomass production overcomes the problem of
mortality, but is dependent upon stocking, and a reduction in production following logging
could be due to the reduced occupancy of the site. This problem of distinguishing the effects
of site occupancy from the effects of logging is common to all stand level measures, including
volume and basal area increment per hectare. Thus we need to consider individual trees, and
could seek to monitor the growth of a “standard reference tree” in each plot. However,
suitable trees having the same species, size and competition do not exist in each plot. Even if
such trees could be found in a number of plots, logging would reduce competition and bias
comparisons with unlogged plots. One solution to this dilemma is to fit a regression equation
to the individual tree increments, and examine the residuals obtained from comparing the
observed and expected increments. This approach is widely used in many disciplines, most
commonly to derive seasonally adjusted figures (e.g. below average temperatures for June
take into account that it is winter; seasonally adjusted employment figures account for school-
leavers in December). Keenan and Candy (1983) used residuals about a height-age curve to
investigate site factors influencing Eucalyptus delegatensis regrowth.
Suitable residuals can be generated from published increment equations. Vanclay (1990)
presented 41 equations to predict the diameter increment of the 400 species occurring in the
database. These equations had the form:

where DI is diameter increment (cm y-1), D is dbh (cm), SQ is site quality (Vanclay 1989a),
BA is stand basal area (m2 ha-1) of trees exceeding 10 cm dbh, OBA is overtopping basal area
(m2 ha-1), defined as the basal area of stems whose diameter exceeds that of the subject tree,
TST is time (years) since silvicultural treatment, PS is a binary variable which takes the value
one if the species is growing on a “preferred soil parent material” and zero otherwise, and the
βs are parameters specific to each species group.
This equation does not include expressions of the number of harvests or of the time since
logging. Thus the residuals should indicate the effects of logging and other factors not
considered in Equation (1). Figure 2 illustrates these residuals (representing means of 8000,
4000, 3000 and 450 tree remeasurements for 0, 1, 2 and 3 harvests respectively). These
suggest some productivity change with time since logging, but little effect attributable to
number of harvests and little resemblance to Figure 1.

Figure 2. Difference between observed and predicted diameter increments for virgin stands (0)
and stands logged once (1), twice (2) or three times (3).
An analysis of variance of the residuals about Equation (1) enables a formal statistical test of
the hypothesis to be made. However, such an analysis of variance can be conducted in several
different ways, and can test several different factors. In compiling the analysis then, it is
essential to take account of the particular characteristics of the present data. In particular, we
have data from 62 372 remeasurements on individual trees to infer the effects of logging on
212 plots. These individual tree data may give an inflated estimate of precision and may place
undue emphasis on well stocked plots, so it is appropriate to calculate the mean residual for
each plot remeasurement and use that in further analyses. Not all plot remeasurements give
rise to a mean residual of equal precision, so it is appropriate to weight the analysis by the
inverse of the variance associated with the mean residual for each plot remeasurement. Such
weighting ensures that those plots which exhibit the most consistent growth patterns have
greater influence on the analysis. Some plot remeasurements exhibited very small variances
which would have given rise to inappropriately large weights. Thus 12 data with small
variances were assigned the value 0.1. Weights were adjusted so that the sum of the weights
equalled the number of data, and the final weights ranged from 0.1 to 4.2.
Table 5 reports several factors examined in an analysis of variance. Time since last logging
was represented as six intervals of five years (0-4, 5-9, ..., 25+ years), and other periodic
effects were taken into account through several approximately five year intervals (pre-1955,
1955-59, ..., 1980+). This analysis revealed that soil parent material, period of observation
and the interaction between soil and time since logging were significant (P < 0.05) in
influencing the differences between observed and expected diameter increments. The
significant factors could be due to management practices as well as to environmental effects.
Soil parent material influences topographic slope as well as soil type, and slope is a major
determinant of logging damage (Vanclay 1989b). A problem with multicollinear data is that
the explanatory variables do not have a unique sum of squares (Neter and Wasserman
1974:341), and that the significance associated with a variable may depend on the order in
which the variables were included in the model. One way to overcome this is to determine the
sum of squares for each variable by subtracting it from the maximal model. Whilst this
ensures unique sums of squares for each variable, an additional entry in the analysis of
variance table is required to reconcile the sums of squares (e.g. Table 5). This entry also
indicates the extent of multicollinearity.
Table 6 reports the changes in productivity estimated through the analysis of variance. None
of the estimates in Table 6 differ significantly from zero, and there is no suggestion of
productivity decline. Table 6 does not aid in the detection of long-term decline, as the
fluctuating response suggested does not enable forecasts. To detect a long term trend, we need
to reformulate the model with number of harvests as a linear variate rather than a factor. This
has the effect of estimating an equal and cumulative change in productivity following each

successive harvest, as is illustrated in Figure 1. Two linear transformations of time since
logging were also explored. One option is to use the inverse of time since logging, implying
the asymptotic trend illustrated in Figure 1. Another option is to use a transformation similar
to that used for the response to silvicultural treatment (te-t/α) which predicts a maximum
response in year a followed by an asymptotic return to zero. The present data support the
latter transformation (te-t) with a very short-lived response (α = 1). This linear transformation
provided a better fit with fewer degrees of freedom than the inclusion of time since logging as
a factor. However, the present data were derived from measurements over approximately 5-
year intervals and are not suited for determining the exact nature of this short-term response.
Including the number of harvests as a linear variate rather than a factor led to a slight increase
in the residual sum of squares (P = 0.13). The analysis of variance (Table 7) was not greatly
affected by the use of linear variates; time since logging was significant (P < 0.05) as a linear
variate whilst number of harvests remained non-significant (P > 0.05).
Table 5. Analysis of Variance of Mean Plot Residuals using four Factors with Interactions.
Source of
Variation
Degrees of
Freedom
Residual Sum
of Squares
Residual
Mean Square
Test Statistic:
F-ratio Probability Significance
MAIN EFFECTS
Soil parent material 5 1.920 0.3840 4.69 0.0005 ***
5-year period 6 1.357 0.2262 2.76 0.012 *
No. of harvests 3 0.411 0.1369 1.67 0.2
Time since logging 5 0.405 0.0811 0.99 0.6
Multicollinearity 0 0.981
INTERACTIONS
Soil-Time 15 2.470 0.1647 2.01 0.013 *
Soil-Harvests 4 0.343 0.0858 1.05 0.4
Period Time 27 2.196 0.0813 0.99 0.5
Period-Harvests 13 1.020 0.0785 0.96 0.5
Period-Soil 18 1.325 0.0736 0.90 0.6
Harvests-Time 5 0.304 0.0608 0.74 0.6
Multicollinearity 6 0.3671
Residual 65
9
53.967 0.0819
Total 76
6
67.066

Table 6. Productivity of Logged Forest relative to Virgin Forest..
Factors Considered Number of Harvests
Number of Harvests only, significant terms omitted +3% -5% +4%
All Main Effects except time since logging +5% -3% +20%
All Main Effects including time since logging +8% +2% +27%
All Main Effects & Significant Interactions +7% +5% +16%
N.B. None of these estimates is significantly different from zero.

A number of alternative approaches can be used to explore the proposed hypothesis. One
alternative is to perform an analysis of variance on the individual tree data, ignoring the
implications of the inflated degrees of freedom and unequal weighting of plots (Table 8,
Model 2). Another possibility is to fit Equation (1) simultaneously to all 41 species groups,
and to include additional variables for number of harvests, time since logging, time period
and soil parent material (Table 8, Model 3). Both these approaches indicated that both
number of harvests and time since logging were not significant (P > 0.2), whilst five-year
period and soil parent material remained significant (P < 0.001). .

Yet another technique is to identify comparable plots with different logging histories, and to
eliminate other factors which may confound the result. Selection of plots was based on
several objective criteria:
- Plots at least 0.2 hectares in area
- Established prior to 1960
- Maintained at least until 1980
- Measurement history spanning at least 30 years, and
- Plot site quality determined with variance not exceeding 0.1.
The majority of the plots satisfying these criteria were located on soils derived from coarse-
grained granites, so selection was further restricted to the 16 plots with this soil parent
material. This selection included (see Appendix) Experiments 591, 612, 613 (Plots 1& 3),
615, 616 and 619 (Plot 1). Analysis of variance and regression analysis indicated that none of
the factors considered (number of harvests, time since logging, 5-year period) were significant
(P > 0.05).
Table 7. Analysis of Variance of Mean Plot Residuals using Linear Variates.
Source of
Variation
Degrees of
Freedom
Sum of
Squares
Mean
Square
Test Statistic:
F-ratio Probability Significance
5-year period 6 1.923 0.321 3.87 0.0011 **
Soil parent material 5 1.740 0.348 4.20 0.0012 **
Time since last logged 1 0.524 0.524 6.32 0.012 *
No. of harvests 1 0.021 0.021 0.25 0.6
Multicollinearity 0 0.502
Residual 753 62.356 0.083
Total 766 67.066
The parameter estimates given in Table 8 enable the effects of time since logging and
logging history to be assessed. The test statistic (student's t) indicates the statistical
significance of the response, and parameter estimates enable the effect of logging to be
quantified. For example, the mean plot residuals (Table 8, Model 1) give rise to a parameter
estimate of -0.01308 for number of harvests which suggests that productivity will decrease
relative to the unlogged condition to e-0.01308 = 0.987 after the first harvest, to 0.974 after the
second, etc. Similarly, the transient response (time since logging) predicts a decrease of
e-0.3117t/e
t
= 0.892 in the first year after logging, 0.919 in the second year, and 0.990 in year 5.
Table 8. Parameter Estimates and Implied Productivity Change due to Selection Logging.
Number of Harvests (Permanent Change) Time since Logging (Transient Change)
Model
Parameter
Estimate
Standard
Error
Student's
t
Implied
Change
Parameter
Estimate
Standard
Error
Student's
t
Implied
Change
All available data:
1) Mean Residuals

-0.01308

0.02592

0.505 -1%

-0.3117

0.1239

2.516* -11%
2) Individual Trees -0.00111 0.00597 0.186 0% -0.0649 0.0390 1.664 -2%
3) Expanded Model +0.00165 0.00712 0.232 0% -0.0556 0.0406 1.369 -2%
Subset only:
4) Mean Residuals

-0.00856

0.03251

0.263 -1%

+0.0288

0.2289

0.126 +1%
5) Individual Trees +0.01108 0.01085 1.021 +1% +0.1050 0.0918 1.144 +4%
* indicates significantly different from zero at P< 0.05

Discussion
The analysis of variance of mean plot residuals reported in Table 7 provides no evidence to
reject the null hypothesis that harvesting causes no permanent decline in productivity. Model
1 provides evidence to support the existence of a transient decline in productivity during the
few years following logging. Other analyses of individual tree data, and of the selected subset
of data (Table 8) provided no evidence to reject the null hypothesis.
The parameter estimates for the terms reflecting the permanent impact of harvesting (number
of harvests) are always close to zero, never significantly different from zero, and do not differ
significantly from one another despite their different signs (Table 8). Because these
parameters are very close to zero, one should not place too much emphasis on this change of
sign, but it may be attributed, in part, to the non-orthogonal nature of the data. This weakness
is inevitable in opportunistic analyses of this sort, and can only be overcome by properly
designed and replicated experiments. Unfortunately, the large areas of virgin rainforest and
long time period required to conduct such a properly designed experiment probably render
such experimental results unattainable. In any case, such an experiment would not yield
useful results for several decades, so the present data provide the only means currently
available to assess the long term effects of repeated logging. Fortunately, multicollinearity
does not inhibit our ability to develop a good model from the data, or to make inferences from
that model (Neter and Wasserman 1974:341).
The parameter estimate for the transient decline in productivity (time since logging) from
Model 1 differs significantly those obtained from other approaches. This analyses of plot
mean residuals (Model 1) found a significant but short-lived transient decline in productivity.
It is beyond the scope of the present study to determine possible causes: it may be that
logging created an environment less favourable for growth; it may equally well be that trees
were directing photosynthates into canopy expansion rather than diameter increment. This
significant transient decline in productivity was not detected in Models 2-5, the parameter
estimates of which did not differ significantly from zero or from one another.

Figure 3. Predicted effects of logging on productivity. Models are indicated by numbers. Dotted
lines represent 95% confidence limits.
The implications of Models 1, 3, 4 and 5 of Table 8 are illustrated in Figure 3. Approximate
95% confidence intervals for Model 1 are also shown, and indicate that the illustrated models
do not differ significantly from the unlogged condition. Thus the principle of parsimony leads
us to accept the null hypothesis that logging has no permanent effect on productivity. There is
no evidence to reject the null hypothesis and support the alternate hypothesis, as any apparent
change in productivity is not significant and may be due to random variation.

Which is the most appropriate model? This question is largely academic as no model supports
the existence of a permanent decline in productivity. As previously argued, Models 1 and 4
which examine the plot mean residuals, are attractive. Model 3 estimates the logging effects
directly from the raw data rather from partial residuals and may be less subject to effects
multicollinearity, but has inflated degrees of freedom and may underestimate the standard
errors.
Tests so far have adopted the conventional parsimonious approach of accepting the null
hypothesis (that logging causes no decline in productivity) unless there is strong evidence to
the contrary. However, statistical tests can also be formulated to test the null hypothesis that
logging causes an x per cent decline in productivity, and to reject this only if there is strong
evidence that any decline is less than this specified amount. This places the burden of proof
on the forest manager. Suppose we have reason to suspect that each harvest causes a
permanent and cumulative five per cent decline in productivity (this assumes a parameter
estimate of -0.05130 for number of harvests). The data tabulated in Table 9 provide evidence
to reject this contention (P < 0.1 for Models 1& 4, P< 0.0001 for Models 2, 3 & 5). It is also
interesting to examine the critical values x which would just lead to the rejection of the null
hypothesis that logging led to a decline in productivity of (or exceeding) x per cent (Table 9).
The models based on plot mean residuals (Models 1& 4) are cautious models and allow the
possibility of a small productivity decline not admitted by models based on individual tree
data (Models 2, 3 & 5). This may be attributed in part to the inflated degrees of freedom and
underestimation of standard errors in the individual tree models (2, 3 & 5). However, the
multicollinearity evident in the data (Table 4) would lead to inflated estimates of standard
error (Neter and Wasserman 1974:341) with the result that the critical values for Models 1
and 4 (Table 9) may be unnecessarily cautious.
Table 9. Critical Values for Rejection of the Hypothesis that Logging Causes Productivity Decline.
Critical Values to Reject
Permanent Decline
Probability of Permanent
Decline
Model
P=0.05 P=0.01 P=0.01 2% 5%
1 -5.4% -7.1% -9.1% 0.4 0.07
2 -1.1% -1.5% -2.0% 0.001 < 0.0001
3 -1.0% -1.5% -2.1% 0.0013 < 0.0001
4 -6.0% -8.1% -10.6% 0.4 0.09
5 -0.7% -1.4% -2.3% 0.002 < 0.0001
It is appropriate to observe that no evidence exists of any long-term decline in productivity
following repeated harvesting. Whilst there is insufficient evidence to reject the possibility of
a small decline, there is evidence to support the assertion that any decline does not exceed six
per cent per harvest.
Conclusion
These analyses reveal no evidence to suggest any long-term decline in rainforest productivity
after three cycles of selection logging. Despite an extensive database incorporating over 200
plots, some established more than 40 years, the data are inadequate for conclusive studies on
the long term effects of rainforest harvesting. Continued monitoring and additional
harvesting of experimental plots will be necessary to conclusively demonstrate the long term
effects of logging.
However, the present analyses provide no evidence of any long-term decline in productivity
following three cycles of conservative polycyclic selection logging, and provide evidence
that any decline does not exceed six per cent per harvest. These results should not be
extrapolated to infer the sustainability of more intensive harvesting systems.

Acknowledgements
Many officers of the Queensland Department of Forestry have contributed to the
establishment and maintenance of experiments and the database. It is due to their diligence
that analyses such as these are possible. Special thanks are due to Greg Unwin for providing
data from the CSIRO EP series of plots, and to John Rudder for assistance with data
processing. Drs. H. C. Dawkins, D. Doley, D. Lamb and an anonymous referee provided
helpful comment on an earlier manuscript.


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Appendix
The following is a list of permanent sample plots in Queensland Forest Service rainforest database at the time this study was commenced. Only those plots with a valid site quality were used in
the present analyses. Geological types are Alluvial (AL), Acid Volcanic (AC), Basic Volcanic (BV), Coarse-grained Granite (CG), Sedimentary and Metamorphic (SM) and Tully fine-grained
Granite (TG). Rainforest structural types follow Tracey and Webb (1976). Brief descriptions of the origin of the various plot types are given below.
Expt
No
Plot
No
State
Forest
AMG Grid Ref. Area (ha) First
measure
Last
measure
Geol
type
Site qual Alt. (m) Aspect Slope
(deg)
Rain
(mm)
Struct
type
Years
logged
Years
treated
Plot type
69 1 185 55 349700 8101050 0.4047 48 59 SM 5.0 670 WSW 5 1320 6 1
77 1 185 55 348800 8101300 0.4047 48 57 SM 6.0 670 N 10 1320 6 43 1
77 2 185 55 348860 8101300 0.4047 48 57 SM 7.4 670 N 10 1320 6 43,52 52 1
78 1 185 55 349690 8100330 0.4047 48 87 BV 7.8 680 NNW 5 1320 6 43 1
78 2 185 55 349690 8100290 0.4047 48 87 SM 2.0 680 NNW 5 1320 6 43,49 49 1
79 1 185 55 349100 8101300 0.4047 49 57 SM 4.9 670 N 10 1320 6 43 51 1
79 2 185 55 349160 8101300 0.4047 49 57 SM 5.5 670 N 10 1320 6 43 51 1
89 1 191 55 340090 8082800 0.0405 51 64 BV 9.0 680 - 0 1400 27 51 2
89 2 191 55 340090 8082780 0.0405 53 64 B V - 680 0 1400 27 51 2
99 1 191 55 339030 8082560 0.1036 52 70 BV - 680 0 1400 28 53 2
99 2 191 55 339030 8082560 0.1036 52 70 BV - 680 SE 5 1400 28 53 2
99 3 191 55 339030 8082560 0.1012 52 70 BV - 680 0 1400 28 53 2
99 4 191 55 339030 8082560 0.1012 61 73 BV - 680 0 1400 28 53 2
99 5 191 55 339030 8082560 0.0838 52 70 BV - 680 SE 5 1400 28 53 2
99 6 191 55 341100 8082510 0.0979 52 87 BV - 680 0 1400 28 52 2
99 7 191 55 341190 8082580 0.1024 52 87 BV - 680 0 1400 28 52 2
110 2 310 55 361090 8086740 0.1012 52 68 BV 5.6 670 N 5 2000 30,68 30,53 3
111 1 185 55 350120 8099160 0.1578 52 68 SM 5.5 680 N 10 1320 6 39 4
111 2 185 55 350020 8099130 0.1348 52 68 SM - 670 W 10 1320 6 39 52 4
111 3 185 55 350200 8099090 0.1643 52 68 SM 7.6 680 SE 10 1320 39 52 4
137 1 194 55 331410 8086410 0.1060 54 77 CG 4.6 1080 W 5 1650 53,80 53,57 5
159 1 191 55 339670 8082920 0.1012 54 70 BV - 680 0 1400 5b 33 54,62 5
159 2 191 55 339580 8082900 0.1012 54 70 BV 1.4 680 0 1400 5b 33 54,62 5
159 3 191 55 339580 8082990 0.1012 54 70 BV 5.0 680 0 1400 5b 33 54,62 5
159 4 191 55 339660 8083000 0.1012 54 70 BV 3.0 680 0 1400 5b 33 54,62 5
159 5 191 55 339650 8083080 0.1012 55 70 BV 4.6 680 0 1400 5b 33 54,58,62 5
159 6 191 55 339610 8083070 0.1012 55 70 BV 2.0 680 - 0 1400 5b 33 54,58,62 5
159 7 191 55 339570 8083060 0.1012 55 70 BV - 680 - 0 1400 5b 40 54,58,62 5
166 1 251 55 347980 8038080 0.4047 69 83 BV 7.0 720 W 10 1800 55 56,57,62 5
166 2 251 55 347960 8038060 0.4047 69 83 BV 7.1 720 W 10 1800 55 56,57,62 5
167 1 194 55 331660 8086520 0.3541 54 63 CG 4.0 1060 - 0 1650 53 54 5
167 2 194 55 331640 8086570 0.2023 55 63 CG 7.2 1060 - 0 1650 53 54 5
174 1 310 55 361450 8086720 0.1010 54 68 BV 5.3 670 SSW 5 2000 29,68 29,54 3
174 2 310 55 361450 8086720 0.1008 54 68 BV 5.0 670 ESE 5 2000 29,68 29,54 3
178 1 1229 55 350960 8146940 0.0283 55 62 SM 0.2 440 - 0 2090 12c 50,78 55,62 5
178 2 1229 55 350980 8146940 0.0809 55 76 SM 3.2 440 N 5 2090 12c 50,78 55,62 5

178 3 1229 55 351060 8146940 0.0348 55 62 SM 3.7 440 - 0 2090 12c 50,78 55,62 5
180 1 1229 55 351300 8147000 0.0769 56 78 SM 5.7 440 - 0 2030 2a 51,77 56 5
184 1 310 55 357970 8090050 0.4047 55 68 BV 4.7 720 - 0 2030 1b 58 59 1
184 2 310 55 358100 8089950 0.4047 55 68 BV 6.2 720 - 0 2030 1b 58 59 1
207 1 194 55 332850 8087000 0.1012 56 68 CG 8.8 1130 N 5 1650 9 68 6
222 1 310 55 361180 8086730 0.1036 58 68 BV 6.2 670 NNW 5 2000 28 29 3
222 2 310 55 361130 8086680 0.1012 58 68 BV 5.8 670 NNW 5 2000 28 29,58 3
222 3 310 55 361060 8086610 0.1012 58 68 BV 5.8 670 NNW 5 2000 28 29,58 3
222 4 310 55 361110 8086680 0.1004 58 68 BV 5.9 670 NNW 10 2000 28 29,58 3
224 1 310 55 361470 8086320 0.1012 58 68 BV 7.4 670 SW 10 2000 28 29 3
224 2 310 55 361470 8086390 0.1000 58 68 BV 8.0 670 SW 10 2000 28 29,58 3
224 3 310 55 361560 8086360 0.1012 58 68 BV 6.1 670 SW 5 2000 28 29,58 3
224 4 310 55 361580 8086360 0.1012 58 68 BV 5.9 670 SW 5 2000 28 29,58 3
224 5 310 55 361330 8086390 0.1008 58 68 BV 6.0 670 NE 5 2000 28 29,58 3
224 6 310 55 361330 8086440 0.1020 58 68 BV 7.1 670 NE 5 2000 28 29,53 3
226 1 310 55 358520 8090320 0.0777 58 74 BV - 670 NNE 5 1800 57 58 5
241 1 310 55 358600 8090400 0.1267 59 75 BV 6.4 720 NE 25 2030 1b 58 59 5
242 1 194 55 331700 8084050 0.1117 59 74 AV 4.6 1035 N 25 1650 9 58 58 5
243 1 194 55 332870 8089170 0.2598 59 74 CG 3.8 980 W 10 1650 54 56,59 5
245 1 1229 55 349910 8147220 0.2068 59 72 SM 3.2 440 - 0 2030 2a 58 59 5
245 2 1229 55 349880 8147260 0.2262 59 72 SM 4.2 440 - 0 2030 2a 58 59 5
245 3 1229 55 349940 8147260 0.1941 59 72 SM 2.3 440 - 0 2030 2a 58 59 5
246 1 1229 55 351480 8146450 0.2582 59 79 SM 3.4 440 - 0 2030 12c 52 58 5
246 2 1229 55 351480 8146450 0.2145 59 79 SM 4.1 440 - 0 2030 12c 52 58 5
246 3 1229 55 351750 8146450 0.2307 59 79 SM 4.4 440 W 10 2030 12c 52 58 5
246 4 1229 55 351750 8146540 0.1959 59 79 SM 7.1 440 W 10 2030 12c 52 58 5
250 1 1229 55 352220 8145720 0.1214 60 75 SM 4.1 430 ESE 5 2030 2a 49 59,61,70 5
250 2 1229 55 352300 8145580 0.1012 60 75 SM 4.7 430 N S 2030 12c 49 59,61,70 5
282 1 194 55 331950 8084360 0.1068 61 74 AV 7.6 1040 W 15 1650 9 60 60,61 5
282 2 194 55 331950 8084460 0.1166 61 74 AV - 1040 W 15 1650 9 60 60,61 5
282 3 194 55 332040 8084460 0.1216 61 70 AV - 1040 W 15 1650 9 60 60,61 5
283 1 194 55 332750 8089530 0.1445 61 74 CG 9.6 1040 W 5 1650 9 57 57,61 5
283 2 194 55 332750 8089550 0.1538 61 74 CG 6.9 1040 W 5 1650 9 57 57,61 5
283 3 194 55 332750 8089590 0.1194 61 70 CG 7.4 1040 W 5 1650 9 57 57,61 5
310 1 310 55 358300 8090150 0.0911 55 75 BV 4.1 670 W 5 2030 1b 55 55,65 5
311 1 194 55 332200 8084450 0.1012 61 87 AV 9.2 1040 SW 15 1650 16c 60 60 5
317 1 185 55 349950 8101010 0.1012 62 67 SM - 730 - 0 1320 43,51 62 5
321 1 185 55 354030 8105410 0.1012 61 71 SM 5.0 730 NE 10 1650 45,60 60 5
322 1 1229 55 351060 8145760 0.1012 61 79 SM 7.2 488 WNW 15 2030 2a 56 61,75 5
324 1 1229 55 349920 8146860 0.0777 63 74 SM 5.4 460 E 5 2100 48 62 5
329 1 1137 55 400400 8026150 0.1590 63 82 SM 6.6 30 - 0 4000 2a 60 62,65 5
329 2 1137 55 400450 8026250 0.1348 63 82 SM - 30 SW 15 4000 2a 60 62,65 5
331' 1 185 55 352940 8105580 0.1012 61 71 CG - 730 SE 15 1650 58 62 5
332 1 1229 55 351630 8144880 0.1012 62 79 SM 7.0 560 W 10 2080 57 62,74 5
333 1 310 55 360510 8089250 0.1064 61 78 SM 2.5 670 SW 10 2090 58 61,73 5