ArticlePDF Available

Data requirements for developing growth models for tropical moist forests

Authors:

Abstract

Permanent sample plots provide the basis for growth modelling, yield prediction and sustained yield management, and the reliability of the data is crucial to these and many other aspects of forest management. To obtain reliable data, it is necessary to ensure consistent standards and that a wide range of stand and site conditions are sampled using both passive monitoring and experimental plots. Individual trees should be numbered, marked and mapped. Remeasurement frequency should be determined to facilitate plot relocation and ensure that growth is greater than measurement errors. Measurement records should be unambiguous and secure.
248
DATA
REQUIREMENTS
FOR
DEVELOPING
GROWTH
(9
Commonwealth Forestry Association
REVIEW:
DATA
REQUIREMENTS
FOR
DEVELOPING
GROWTH
MODELS
FOR
TROPICAL
MOIST FORESTS
Jerome
K.
Vanclay*
Summary
Permanent sample plots provide the basis for growth modelling,
yield prediction and sustained yield management, and the reli-
ability
of
the data
is
crucial to these
and
many
other
aspects
of
forest management.
To
obtain reliable data, it
is
necessary
to
ensure consistent standards
and
that
awide range
of
stand and site
conditions are sampled using
both
passive monitoring and experi-
mental plots. Individual trees should
be
numbered,
marked
and
mapped. Remeasurement frequency should
be
determined to facili-
tate
plot relocation
and
ensure
that
growth
is
greater
than
measure-
ment
errors. Measurement records should
be
unambiguous and
secure.
Resume
Revue: Conditions prealables
pour
l'evolution de modeles de crois-
sance
pour
les forets tropicales humides.
Les terrains
de
tests permanents fournissent la base de modeles
de croissance,
de
la prediction
du
rendement
et
de
l'organisation du
rendement continuo
La
precision des donnees est indispensable
pour
ces derniers
et
pour
beaucoup d'autres aspects de l'exploita-
tion des forets.
Pour
obtenir des donnees precises il faut que des
normes uniformes soient garanties
et
que les experiences consistent
d'une
ample serie d'echantillons quant aux conditions de situation
ou
de
site,
en
utilisant l'observation passive
et
des terrains experi-
mentaux
en
me
me temps. Les arbres particuliers doivent etre
numerotes
et
clairement indiques sur un plan.
La
frequence des
controles
de
mesure doit
etre
determinee afin de faciliter les
changements
de
terrain
et
d'assurer que la croissance soit plus
grande
que
les erreurs de mesure. Les registres de mesure doivent
etre
clairs
et
surs.
*Department of Economics and Natural Resources, Royal Veterinary and Agricultural
University, Thorvaldsensvej
57,
DK-1871 Frederiksberg C, Denmark.
DATA
REQUIREMENTS
FOR
DEVELOPING
GROWTH
249
Resumen
Las parcelas
de muestreo dan la base para los mode-
los de crecimiento, la predicci6n de rendimiento ymanejo para un
rendimiento sostenible, yla confiabilidad en los datos es impre-
scindible tanto para estos prop6sitos como para otros aspectos del
manejo forestal. Para obtener datos confiables, es necesario asegu-
rar normas constantes yque se muestrean una gama amplia de
condiciones de sitio yde rodal utilisando metodos pasivos de moni-
toreo yparcelas experimentales. Los arboles individuales deben ser
numerados, marcados ymapeados. La frecuencia de remedici6n
debe fijarse para facilitar la reubicaci6n de las parcelas yasegurar
que el crecimiento es mayor que los errores de medici6n. Los
archivos de medici6n deben ser inequlvocos yasegurados.
Introduction
One
way to assist the continued survival of the tropical moist forest
is
to
manage it for commercial production of timber and other forest prod-
ucts, so that it becomes valuable in the eyes of local communities. Two
conditions are essential, but not sufficient for its survival. Firstly to
ensure that harvesting leaves the forest in an ecologically and silvicul-
turally "good" condition
(VANCLA
Y,
199Gb).
Secondly, to eke out the
resource so that harvesting provides acontinuing supply
of
timber and
other benefits (VANCLAY, 1991a). Growth models, when combined with
inventory, provide areliable way to examine harvesting options, to
determine the sustainable timber yield, and to examine the impacts
on
other values ofthe forest.
The first step in constructing agrowth model
is
to obtain suitable
data. All too often, the modelling approach
is
dictated by limitations
of
the data.
Data
requirements of many modelling approaches are similar
and allow aset of minimum procedures to be established. The proce-
dures discussed here relate to the requirements for development of
growth and yield models. Additional details may be necessary if plots
are to serve other uses such as ecological studies.
Although directed
at
tropical moist forests, this review
is
applicable
to data requirements of growth models generally. Stem analyses do not
provide reliable growth data for many tree species in the tropical moist
forest, so data must be obtained from remeasurements
on
permanent
sample plots (PSPs).
KRAMER
and KOZLOWSKI (1979:27) reported some
of the anomalies
of
growth rings in tropical tree species. Some ever-
green trees (e.g. Swietenia spp.) may form rings while deciduous trees
250
DATA
REQUIREMENTS
FOR
DEVELOPING
GROWTH
(e.g. some Ficus spp.) may not. Some species (e.g. Hevea braziliensis)
may form several growth rings each year, while other species (e.g.
Shorea robusta) may form only one ring
but
not necessarily in the same
month each year.
MARIAUX
(1981) presented adetailed review of the
possibilities and problems of stem analysis in tropical tree species.
Permanent plots can never be completely replaced by temporary
plots even for species amenable to stem analysis, because only PSPs
allow satisfactory statistical comparisons within and between plots to
check the adequacy of models
(STRAND,
1970), and only PSPs can pro-
vide reliable and consistent data on mortality, crown dynamics and
stand level variables (MCQUILLAN, 1984).
DEADMAN
(1979) recorded anumber of observations concerning data
for growth modelling: permanent plots must cover extremes of site and
treatment; periodic reviews of data collection policy are necessary;
quality of data collected
is
of extreme importance; and documentation
should be complete, consistent and accurate.
ADLARD
(1990) empha-
sized three factors: relevance, reliability and relationships. vANCLAY
(1990a) stressed standardization of procedures, accurate measurements,
specific location (description and map coordinates), clear objectives and
sufficient resources (funds and trained staff). CURTIS (1983) provided a
comprehensive reference manual for PSP establishment and main-
tenance in temperate regions, most of which
is
relevant to the tropical
moist forest.
Data
used for growth research must be of ahigher quality than that
used for point-in-time inventories. For example, adiameter measure-
ment of
50
±
0.5
cm may seem precise, but if aremeasure indicates
51
±
0.5
cm, the growth estimate will be 1±0.7 cm which
is
not very precise.
Differing Data Needs
Sample plots serve many purposes, but different procedures are
required to satisfy efficiently various needs ofresource managers. Some
information needs and corresponding sample plot procedures include:
Resource Inventory ("What
is
the present nature and extent
of
the
resource?"): Typically alarge number of plots (or point samples)
will
be
required to achieve the desired precision. Precision can be
gained by orienting plots across environmental gradients to maxi-
mize within plot variation and thus reduce between plot variance.
Cost considerations usually dictate that temporary inventory plots
(or
point samples) are most efficient for resource inventory (e.g.
MATIS et al. 1984,
SCHREUDER
et
ale
1987). Specialized techniques
DATA
REQUIREMENTS
FOR
DEVELOPING
GROWTH
251
for timber cruising offer great efficiencies (e.g. 3-P sampling), but
may not provide data suitable for input to yield forecasting sys-
tems.
Continuous Forest Inventory for yield control: If yield regulation
is
by volume control, it
is
important that permanent plots be repre-
sentative and established in various forest types and stand condi-
tions in proportion to their area (this system
is
often called Contin-
uous Forest Inventory). As with resource inventory, precision
is
gained by minimising between plot variance. Plots should be
marked so that they can be relocated for remeasurement, but
should remain inconspicuous so that they receive unbiased man-
agement.
Growth Modelling: The development of growth models requires
data obtained from the remeasurement
of
PSPs. The most reliable
and flexible modelling techniques require data in which the indi-
vidual trees are identified. This requires that all trees
on
the PSP
are permanently tagged and uniquely numbered. Irrespective of
the modelling approach, unique numbering and tagging of trees
is
the only sure way of detecting measurement errors. Growth mod-
elling also requires homogeneous plots, and this means minimising
within plot variance: the ability of the PSPs to quantify the present
resource
is
irrelevant. Thus the same plot series cannot be efficient-
ly
used for both resource inventory and growth model develop-
ment. If the growth model
is
to be used to investigate silvicultural
and management alternatives, the database must include experi-
mental data with paired treatment and control plots, both with ade-
quate isolation.
In
contrast to continuous forest inventory plots, it
is
not necessary for PSPs to be representative
or
numerically pro-
portional to forest type areas, but it
is
essential that they sample
the full range ofstand conditions.
Long
Term Monitoring
of
Environmental Change: DAWKINS and
FIELD
(1978) describe aseries of plots to monitor subtle long term
changes in aforest. Whilst such studies are desirable, few organiza-
tions have the resources
or
need to establish such plots
on
the same
scale as required for growth studies. Such detailed plots should be
reserved for special studies. For growth modelling, it
is
better to
sample the full range with conventional PSPs than to have afew
detailed "Dawkins" plots. However, quantity
is
no substitute for
quality. ,
Permanent sample plots established to provide data for growth
modelling should be designed to satisfy this primary need, and should
252
DATA
REQUIREMENTS
FOR
DEVELOPING GROWTH
not be compromised in order to satisfy secondary needs. They need not
provide efficient resource inventory data, as alternative sampling proce-
dures can better fulfil that need.
Model Development
The initial and most obvious requirement for data
is
during model
development when they are required for the construction of the basic
functions comprising the model.
---ts-
Optimal
sampling
...
·0·····
Suboptimal
sampling
FIG
1:
Polynomial approximation of afunction with optimal and sub-optimal
sampling
It can be shown mathematically, that the relationship between two
variables given by aseries of points known without error, can be
described by polynomials most accurately if the sample points are locat-
ed along the trend line with intensity increasing towards the limits of
the region of interest. Figure 1illustrates acubic polynomial fitted to
seven points selected from adiameter increment function
(VANCLA
Y,
1991b, species group 1). The ticks on the horizontal axis indicate anear
optimal sampling
which produced avery good approximation (solid
line) to the original function. Amore arbitrary sampling (0) resulted in
apoor approximation (dotted line in Figure 1). In establishing astatisti-
cal relationship, these points are not known with certainty, but with
some error, and the sampling intensity should reflect the variance.
Extending this concept to amulti-dimensional space, it can be seen that
sampling should be carried out across the entire response surface, with
DATA
REQUIREMENTS
FOR
DEVELOPING
GROWTH
253
agreater intensity at the extremities, and in accordance with the vari-
ance. Limited but reliable data
at
each extreme and at the mean are
more useful than copious' data clustered about the mean (KIRKLAND,
1985).
Such data should not only sample arange
of
stand and tree condi-
tions, but must also include remeasurements to enable detection of
change, and must include asufficient time period to average any climat-
ic variations, and to ensure that growth patterns are not obscured by
measurement error.
Validation and Monitoring
To provide aconvincing demonstration, data used to validate amodel
should be excluded from its development and may comprise data drawn
from adifferent population. This ideal
is
not always attainable, and it
is
common to partition the available data into two subsets, one to be used
for development and the other for validation.
It
is
important that the
subset used for validation should contain at least some data collected
over very long periods to allow detection of possible subtle
but
cumula-
tive errors in the model. Where the model
is
used to estimate some
optimum stand condition, it
is
advisable to obtain data to ascertain the
production from this estimated optimum condition.
Monitoring may be viewed as continuing validation of amodel by
checking its operational predictions. It involves comparing projected
and realised yields to identify any discrepancies. Such discrepancies
may arise due to changes in management regime (especially logging
practices), decline in site productivity, inaccurate resource data,
or
cor-
ruption of the validated growth model. Monitoring the performance of
models
is
often neglected, but
is
necessary to ensure reliable forecasts.
Applications Data
Applications data may comprise basic resource information used in
conjunction with the growth model to estimate future yields. Most oper-
ational resource inventory provides suitable data. Such data should
detail areas of each homogeneous forest unit, the species composition,
stand condition, and the site productivity of each unit.
MEAD
(1982)
discussed how to gauge the value of data of this type. vANCLAyand
PRESTON (1989) gave an example of the integration
of
inventory data
and agrowth model to predict yields in tropical moist forest in north
Queensland.
254
DATA
REQUIREMENTS
FOR
DEVELOPING
GROWTH
Integration
of
Data
Resource data have been integrated since inventories began,
but
recently attempts have been made to define principles and procedures
for efficient integration (e.g.
LUND,
1986). Integration simply implies
combining data obtained in different places, for different reasons, by
different agencies
or
at different times (VANCLAY, 1990a). This may
involve combining regional inventories to provide national
or
global
statistics, finding correlations between timber inventory and soil
or
fauna survey data,
or
using growth models derived from PSP data to
extrapolate data from temporary inventory plots to estimate sustainable
yields (e.g. VANCLAY and PRESTON, 1989).
Integrated inventory designs enable data from different inventories
to be meaningfully combined. This does not necessarily mean that
everything in every inventory must be measured.
On
the contrary, it
is
better to do afew things well than to do alot inadequately (VANCLAY,
1990a). However, in designing aPSP system, it
is
necessary to be aware
of the information requirements of other researchers and other disci-
plines, and to consider how these requirements can be efficiently
accommodated in PSP design. It
is
not necessary that all these require-
ments
be
satisfied immediately, but rather that the design accommo-
dates these needs so that they can be phased in as required and when
feasible.
Plot Selection and Establishment
Ideally, PSPs should sample the geographic range of the forest, and
encompass abroad range offorest types, site quality and topography. A
broad range
of
stand basal area and tree sizes should be sampled for
each tree species. Plots should include stands which have been sub-
jected to arange of silvicultural management, including extremes of
logging and treatment.
Growth of forests varies from year to year, fluctuations can be
extreme, and mortality tends to be clustered in both time and space
(CURTIS, 1983). Thus short time periods can give rise to biased growth
estimates. Reliable growth models require PSPs with long measurement
histories and adequate geographical distributions. Some of the plots
should
be
left unlogged over long periods to ensure the most exacting
validation.
CURTIS and HYINK (1984) recommended that new PSP installations
should be established only as part of acarefully planned series designed
DATA
REQUIREMENTS
FOR
DEVELOPING
GROWTH
255
to give reasonable coverage of some defined range of site, geography,
stand condition and treatment. The primary objective should be to pro-
vide data for defining response surfaces; thus studies should involve
many locations with minimal replication at each location. Satisfactory
growth models are dependent upon the availability of high-quality data
from awide range of stand conditions and treatments. Both "passive
monitoring" data (i.e. survey data in undisturbed forest) and "treatment
response" data (i.e. from paired treatment and control plots) from
designed experiments are necessary.
Subjective location ofPSPs may give rise to bias in the database if the
environment cannot be completely quantified. It
is
preferable to locate
PSPs randomly within adefined stratum of interest. This stratum may
be defined on the basis of standing volume, species composition, soil
type
or
any other objective means. Care needs to be taken when estab-
lishing plots at the forest edge
or
along roads and firebreaks, to avoid
bias (RENNOLLS, 1978;
FOWLER
and ARVANITIS, 1979).
BRUCE
(1977)
gave anumber of reasons why research plots may give higher yields
than managed forests. Although some bias may be due to plot demarca-
tion and management, much of this bias arises from subjective location
of plots. The need for random location based
on
athoughtful stratifica-
tion cannot be overemphasized.
There
is
some evidence that gains in precision can be achieved by
sampling more large trees (e.g.
GERTNER,
1987), and it may be desirable
to establish some plots around subjectively selected large trees. Such
subjective selection of plots may introduce bias, but this may be an
acceptable trade-off to reduce the variance associated with growth pre-
dictions from large trees. To minimize bias, these plots should consti-
tute asmall proportion of the total, and should be selected within strata
based on site quality and stand density (e.g. stand basal area).
Plots which are intended to be left unmanaged, for example to allow
expression of density-dependent mortality and natural basal area in
dense stands, should be clearly marked and excluded from any logging
operations. Such plots which receive special management (no logging
or
more intensive treatment), should have adequate buffers to eliminate
edge effects. The appropriate size of the buffer depends
on
tree size,
but should be wider than the mature tree height.
Other
plots intended
to receive routine management, should
be
marked in such away as to
be invisible to forest workers so as to ensure representative treatment.
SYNNOTT (1979) argued that aplot should be "difficult to recognize for
those who do not know where it is, and easy to recognise for those who
do and are looking for it". Plots must have unambiguous addresses
256
DATA
REQUIREMENTS
FOR
DEVELOPING
GROWTH
(DAWKINS and
FIELD,
1978). In some areas, plots may suffer excessive
trampling through high visitation. DAWKINS and
FIELD
(1978) marked
plot locations clearly, but
50
maway from the plot, and used invisible
steel markers at all four plot corners.
Experiments
Although experimental data are extensively used in developing planta-
tion growth models, it
is
more common to develop growth models for
mixed forests solely from passive monitoring data. Although logging
and treatment of these forest stands
is
likely to influence stand density,
other unknown factors may also determine stand density and composi-
tion in these plots.
There
is
avery real danger that attempts to describe the behaviour of
the stand as afunction of stand density, for instance, will be confounded
by the effects of site, pest and disease occurrence, and past history.
BOX
(1966) warned that to find out what happens to asystem when you
interfere with it, you have to interfere with it, not just passively observe
it.
SNEDECOR
and
COCHRAN
(1980:356) discussed astudy in which asur-
vey revealed the unexpected result that the application of farmyard
manure reduced the yield of potatoes by half atonne per hectare.
In
contrast, in controlled, randomized experiments, manure increased the
yield by three to six tonnes
per
hectare. The difference may be due to
the fact that those who had manure were livestock farmers with little
interest in growing potatoes, and those who were most skilful at grow-
ing potatoes had no manure. Can we be sure that asimilar problem in
our PSP data
is
not troubling our attempts to develop growth models
(e.g. stand density and site quality interaction)?
Passive monitoring data may indicate greatest growth on the best
sites with high standing basal areas, and little growth on poorer sites
with little basal area. Agrowth model constructed from such data could
suggest that greater increments accrue in stands with greater competi-
tion, as the effects of site quality and stand density would be confound-
ed. Thus amodel constructed from such passive monitoring data would
predict areduction in diameter increments following thinning, whilst a
model from experimental data (e.g. thinning studies) would show an
increase in diameter increment.
Consideration should be given to establishing aseries of plots in
homogeneous tracts
of
each forest type. Some should
be
left at maxi-
mum stocking to allow expression
of
density-dependent mortality and
natural basal area, some should
be
logged and treated as amanaged
DATA
REQUIREMENTS
FOR
DEVELOPING
GROWTH
257
stand, and others should be heavily thinned to allow expression of
open-grown development,and regeneration.
It
does not matter that
extreme treatments may never be applied in practice; they remain
essential to define properly the response surface for growth models.
Number
of
Plots
The number of plots
is
usually determined by available resources.
There
is
little point establishing more plots than can be maintained. It
is
better to have few plots providing reliable data, than many plots with
inadequate management. The number of plots will also be determined
by the variability of the forest estate, and the need to sample the full
range of forest conditions.
SYNNOTI
(1979) recommended 50 to 100
randomly located plots for each forest type.
Adatabase comprising afew plots each with many remeasurements
violates statistical assumptions of independence, and may require spe-
cial analysis techniques
(WEST
et
ale
1984, 1986). This violation becomes
significant when the number of remeasures
is
large relative to the num-
ber
of plots.
An
alternative
is
to use partial replacement, abandoning
plots after several remeasures and establishing new ones
(TENNENT
1988). However, some plots must be retained for long periods with
many remeasures to allow convincing validation.
Size and Shape
of
Plots
Ageneral guide to the choice of plot shape
is
to minimize the plot edge
to area ratio, and the number of corners. This leads to the choice of
point samples,
or
circular, triangular,
or
four-sided plots according to
the emphasis attached to corners and edges. Triangular plots are rarely
used, perhaps because of the high edge to area ratio, and four-sided
plots are generally rectangular (or square) to facilitate relocation of
corners and boundaries.
Point samples
(BEERS
and MILLER, 1964) have an advantage in being
defined by asingle point and abasal area factor (BAF),
but
they are
inconvenient when dealing with recruitment, and create difficulties for
the development of distance-dependent models. Circular plots are also
defined by asingle point' and aradius,
but
the plot boundary becomes
more difficult to define as the plot becomes large, as unlike polygonal
plots, sight lines cahnot
be
established along boundaries. As these plots
are defined by asingle marker (the centre), they may be more difficult
to relocate if the marker is damaged
or
removed. Rectangular plots are
258
DATA
REQUIREMENTS
FOR
DEVELOPING
GROWTH
more versatile. Plots marked by four corner pegs may be less likely to
be lost than circular plots marked by only one peg. However, amore
important reason for the choice of rectangular plots
is
their straight
edges, few corners, and convenience. Square plots offer atheoretical
advantage ofminimum edge to area ratio.
Ideally, the plot size should be sufficiently small for the plot to be
homogeneous, at least with respect to forest type and site productivity,
and sufficiently large to provide arepresentative sample of the forest
stand. If adistance-dependent model
is
contemplated, the plot should
be sufficiently large to allow estimates of competition to be determined
for several trees on the plot. This leads to the conclusion that larger
plots offer greater flexibility, and the author's experience suggests that
plots up to one hectare should be considered for growth modelling
studies in the tropical moist forest. Ecological studies may warrant even
larger plots.
CURTIS and
POPE
(1972) suggested that small plots may result in errat-
ic
estimates of stand attributes because of within stand clumping, and
recommended the use of large plots.
PAYANDEH
(1974) examined the
distribution of trees within north American forests, and reported that
unlike plantations, natural forests rarely exhibit aregular spacing, but
tend to have arandom (in hardwoods)
or
slightly clustered (conifers)
spatial distribution. HANN (1980) used plots varying in size from
0.3
to
0.5
hectares in even-aged stands, and 0.8 to 1.2 hectares in uneven-aged
stands. Plots smaller than 0.8 hectares were available for the uneven-
aged stands, but were discarded by
HANN
(1980) to avoid problems
arising from within stand clumping. SYNNOTT (1979) recommended
square plots one hectare in area, subdivided into
25
subplots. WEST et
ale
(1988) found that
0.5
ha was the practical upper limit in tropical moist
forest for homogeneous plots,
as
physical and floristic discontinuities
hampered the establishment oflarger plots.
Unless circular plots or point samples are adopted, the orientation of
the plots needs to be considered. This may be inconsequential for
square plots, but may be significant with elongated rectangular plots.
Three possibilities exist. The plots may be randomly oriented, may be
oriented according to the cardinal direction (e.g. long axis north-south),
or
may be oriented according to topography.
In
view of the need for
plots which are homogeneous with regard to site productivity, the last
of
these
is
likely to be preferable.
It
is
suggested that wherever possible,
plots should be oriented with their long axis perpendicular to the slope,
or
any other perceived gradient of site productivity to minimize within
plot variation. In contrast, for temporary inventory plots, it
is
desirable
DATA
REQUIREMENTS
FOR
DEVELOPING
GROWTH
259
to maximize within plot variation so
as
to reduce the between plot vari-
ation and thus the sampling error. PSPs for growth model development
have adifferent goal, and thus within plot variation should be
minimized.
Measurement Procedures
Providing that PSPs continue to provide useful information, existing
standards and procedure should be maintained to ensure uniformity.
The continuity of standards
is
critical. However, when new plots are
established
or
procedures for existing plots are revised, the