D. H. ZHAO ET AL.
for some work of Kanazawa et al. (1985, 1990).
Previous studies (Harrison & Kane, 2008; Zhao et al., 2008)
indicated that the CR declining trend over time is significantly
influenced by initial density and management intensity. The CR
decrease rate increases with increasing initial density and man-
agement intensity. Tree CR models for estimating CR from tree
and/or stand attributes have been developed for several species
(Dyer & Burkhart, 1987; Hasenauer & Monserud, 1996; Te-
mesgen et al., 2005), but there is no model developed for di-
rectly describing the CR change through time. The RS devel-
opment through time has been modeled for loblolly pine planta-
tions in the southern United States (Zhao et al., 2010). The
resulting models indicated significant effects of initial density,
site index and management intensity on the RS trend. The in-
tensively managed plots have lower CR and RS than operation-
ally managed plots planted at the same density; with the same
management intensity, both the CR and RS decline with in-
creasing initial density (Zhao et al., 2009, 2010). Therefore, if
there is a predictable relationship between CR and RS, this rela-
tionship is expected to be influenced by initial density, site
index and management intensity.
With data from two loblolly pine culture and density studies
across the southeastern United States, the objective of the pre-
sent study is to test the hypothesis that there is a predictable
relationship between the CR and RS. Moreover, the effects of
initial planting density, site quality, and management intensity
on this relationship are investigated with a nonlinear mixed-
effects modeling approach.
Materials and Methods
Study Description
The data came from two well-designed loblolly pine culture
and density studies initiated by the Plantation Management Re-
search Cooperative (PMRC) of the University of Georgia. The
Lower Coastal Plain (LCP) Culture/Density Study was estab-
lished in 1995/96, with seventeen installations in Georgia,
Florida and South Carolina across five broad soil groups. The
Piedmont and Upper Coastal Plain (PUCP) Culture/Density stu-
dy was established in 1997/98, with twenty-three installations
in Georgia, Alabama, Florida, Mississippi and South Carolina,
stratified over seven broad soil classes.
In both Culture/Density studies, site preparation and subse-
quent silvicultural treatments were designed to represent two
levels of management intensity: operational and intensive cul-
ture. In the LCP study, the operational treatment consisted of
bedding in the spring followed by a fall banded chemical site
preparation; the intensive cultural treatment included bedding
in the spring followed by a fall broadcast chemical site prepara-
tion. The intensive cultural treatment plots also received tip
moth control through the first two growing seasons and re-
peated herbicide applications to achieve complete vegetation
control throughout their rotation. At planting, 561 kg/ha of 10-
10-10 fertilizer was applied on all plots. The operation treat-
ment plots were fertilized with the equivalent of 224 kg/ha of N
and 28 kg/ha of P in the spring of the eighth and twelfth grow-
ing seasons. The intensive cultural treatment plots also received
673 kg/ha of 10-10-10 plus micronutrients and 131 kg/ha of
NH4NO3 in the spring of the third growing season, 131 kg/ha
NH4NO3 in the spring of the fourth growing season, 336 kg/ha
NH4NO3 in the spring of the sixth growing season, and 224
kg/ha of N and 28 kg/ha of P in the spring of the eighth, tenth,
and twelfth growing seasons.
In the PUCP study, any tillage treatments included in site
preparation were carried out on all treatment plots. Both the
operational and intensive treatments included a broadcast chem-
ical site preparation. The operational treatment included a first-
year banded weed control. The intensive cultural treatment
plots received additional herbicide treatments to keep them as
completely free of competing vegetation as possible throughout
their rotation and received tip moth control through the first two
growing seasons. The same fertilizer treatments in the opera-
tional and intensive cultural treatment regimes as the LCP study
were applied.
Within both the intensive and operational treatments, six lob-
lolly pine subplots with densities of 741, 1483, 2224, 2965,
3706 and 4448 trees/ha were randomly located and established
in each installation. To ensure the targeted initial density, each
planting spot was double-planted and reduced to a single sur-
viving seedling after the first growing season. For detailed in-
formation on these two studies such as soils and treatments
carried out for each management level, please refer to Harrison
and Kane (2008) and Zhao et al. (2008, 2010).
Beginning after the second growing season, biennial meas-
urements of diameters at breast height (DBH) for all trees and
heights (H) on every other tree were made. Heights to the base o f
the live crown were measured on all trees that were measured
for total height. Total heights of unmeasured trees were esti-
mated using a height-diameter equation,
01
ln HbbDBH ,
fitted to each plot at each measurement age. A tree was consid-
ered a dominant tree if it was in the upper 50percent of diame-
ters on the plot. Mean live crown ratio was calculated by plot
from trees with height measurements, and relative spacing in-
dex was also calculated by plot.
Base age 25 years site index values were estimated for each
installation using the dominant height of the operational treat-
ment plot with 1483 trees/ha planting density at the age of the
most recent measurement. Site index was calculated using the
site index equations developed by Borders et al. (2004) for
second rotation loblolly pine plantations. Site indices ranged
from 22.8 to 31.3 m for the LCP Culture/Density Study and
from 22.4 to 28.1 m for the PUCP Culture/Density Study.
After 12 growth seasons 14 of the original 17 installations in
the LCP culture/density study were viable; and all 23 installa-
tions in the PUCP culture/density study remained after 10
growth seasons. Data from these active installations were used
for the analysis reported.
Model Development
Plot examination of the CR versus RS indicated that CR is
positively correlated with RS. While CR more closely approaches
1 in early ages, the RS is larger. With stand development both the
RS and CR become smaller, approaching to their different mini-
mum values. To constrain CR predictions between 0 and 1, the
following general equation was used to describe the relationship
between the CR and RS:
2
1
CR RSRS
2
(1)
where 12
and
are the paramet ers.
Preliminary analysis indicated that both parameters 1
and
2
varied across installations and plots. These between-in-
stallation and between-plot variations may be accounted in the
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