Ecological Modelling, 23 (1984) 227-241
Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
227
THE PREDICTION OF FOREST PRODUCTION FROM INVENTORY
AND CLIMATIC DATA
JOHN A. DOWNING
Departement de Sciences Biologiques, Universite de Montreal, C.P. 6128, Succursale 'A
Montreal, Que. H3C 3J7 (Canada)
LAURA A. WEBER *
College of Forestry, University of Minnesota, 110 Green Hall, St. Paul, MN 55108 (U.S.A.)
(Accepted for publication 30 November 1983)
ABSTRACT
Downing, J.A. and Weber, L.A., 1984. The prediction of forest production from inventory
and climatic data. Ecol Modelling, 23: 227-241.
Published data are analyzed to produce equations that predict rates of net production and
net harvestable production of forests. These equations can be applied between the latitudes of
31° and 65° N and S, and use common biotic and abiotic site descriptors as independent
variables. Forest biomass (or basal area) and age are of primary importance, while climatic
conditions perform a significant role. The equations are shown to make more accurate
predictions of forest production than the Miami Model, which is based on climatic conditions
alone. Example applications are presented that examine the effects of forest age and biomass
on production to biomass ratios, and the effects of climate on the energy fixation and storage
efficiency of forests.
INTRODUCTION
A major purpose of ecological research is to explain (Elton, 1927;
Andrewartha and Birch, 1954) or predict (Rigler, 1982) the distribution and
abundance of plants and animals in nature. The importance of models or
theories that predict the production of various parts of ecosystems is central
to this goal. Although compendia of production data are now being pub
lished (e.g. DeAngelis et al., 1980; Westlake, 1980; Cannell, 1982), only a
* Present address: Veterans Administration, Eduard Hines, Jr. Hospital, Hines, IL 60141,
U.S.A.
0304-3800/84/$03.00
© 1984 Elsevier Science Publishers B.V.
228
few attempts to produce models from these data have been made (e.g.
O'Neill and De Angelis, 1980; Webb et alM 1983). This is especially surpris
ing for resources of economic importance such as forests. A few general
models have been produced (e.g. Rosenzweig, 1968; Lieth and Box, 1972;
Lieth, 1975). These models have been built for all plant communities and are
probably of little use for predicting the production of individual forests.
Many stand-specific models exist for growing individual trees mathemati
cally (Reed, 1980), but such models lack generality (Koerper and Richard
son, 1980).
Predictions of forest production are difficult to make because many
factors affect rates of forest production. Ecologists have found that the most
influential abiotic variables are temperature (Rosenzweig, 1968; Lieth and
Box,
1972;
Lieth,
1975;
Whittaker
and
Marks,
1975),
precipitation
(Rosenzweig, 1968; Lieth and Box, 1972; Lieth, 1975; Whittaker and Marks,
1975),
intensity
of
solar
radiation
(Whittaker
and
Marks,
1975),
evapotranspiration (Rosenzweig, 1968; Lieth and Box, 1972; Lieth, 1975),
length of growing season (Paterson, 1956, cited by Spurr, 1964), and nutrient
availability (Cole and Rapp, 1980). Biotic factors such as standing biomass
(Whittaker, 1966; Sharpe, 1975), age of stand (Clawson, 1979), and tree
density (Whittaker and Marks, 1975) are stand-specific factors that regulate
production. Taxonomic composition of forests also influences production
(Whittaker, 1966), and plantations are generally thought to be more produc
tive than natural forests (Tillman, 1978). These variables can combine in a
variety of ways. It is no wonder, therefore, that few accurate general models
of forest production have been developed (O'Neill and DeAngelis, 1980).
The purpose of this report is to use statistical analysis to summarize
general trends in published net forest production data and to produce
general models to predict the net production of forests from easily collected
data. Further, we test these models with respect to the Miami model (Lieth
and Box, 1972; Lieth, 1975) which predicts the productivity of terrestrial
vegetation as a two-tiered positive function of mean annual temperature and
total annual precipitation (see applications in: Johnson and Miller, 1973;
Odum, 1976). The new equations are then used to examine general world
patterns in production to biomass ratios and solar energy fixation efficiency.
METHODS
Data collection
Regression analysis of published data was used to derive equations to
predict rates of net forest production. The data are too extensive to be listed
here, but sources are marked with an asterisk (*) in the References section. A
229
full listing of the data is available at a nominal charge from the Depository
of Unpublished Data, CISTI, National Research Council of Canada, Ottawa, Ont. K1A 0S2, Canada. The data represent measurements made in a
wide variety of forest types in many regions around the world between the
latitudes of 31° and 65°N and S. The measurements of production (g dry wt.
m~2 yr"1) collected were net aboveground annual biomass increment (P),
and net harvestable aboveground annual biomass increment (PH)- Net
aboveground annual biomass increment is the net annual biomass increment
including bole, branches, leaves, and seeds of plants with stems greater than
2 cm DBH. Harvestable production is the net annual biomass increment of
all aboveground parts excluding leaves and seeds.
Descriptors of biotic and abiotic conditions were also collected from the
literature. Variables that were available frequently enough to allow inclusion
in the analysis were: aboveground biomass (B; g dry wt. m"2), latitude (L),
mean annual daily temperature (T;°C), mean total annual precipitation (R;
cm yr."1), mean age of stand (.4; years), mean tree diameter at breast height
(DBH;
cm), mean stem density (D), and average basal area (BA).
Aboveground biomass includes all tree parts except roots. The mean diame
ter breast high (DBH) is the average stem diameter at approximately 4.5 feet
(1.3 m) from the ground. The mean tree density is the average number of
stems (DBH> 2 cm) per hectare. Basal area (m2 ha"1) is the cross-sectional
area of stems at breast height.
Three classification variables that describe whether the stand represents
plantation or natural growth (Z), and whether the stand is composed
primarily of evergreen (£), or deciduous (W) growth, were also collected.
The variable Z was given the value 1 if the stand was a plantation. The
variables E and W are two designations of a three-level dummy variable, so
that the effect of forest composition can be assessed without prior ranking of
effects (Gujarati, 1978). Evergreen stands were assigned values of E = 1 and
W= 0, deciduous stands were given values of E = 0 and W=l, and mixed
stands were designated as E = 0 and W = 0.
Data analysis
Models were fitted to the observations using multiple regression analysis
(Draper and Smith, 1966; Helwig and Council, 1979). First, some of the
variables were transformed logarithmically (base 10) to linearize responses
and stabilize the variance where necessary. The necessity for transformation
was determined using bivariate plots of the data, and eventually verified by
detailed analysis of the residuals. Second, the regression models were fitted
using all the independent variables except those few that were collinear in
their transformed form (r > 0.7; Gujarati, 1978). Finally, backwards elimina-
230
tion (Hocking, 1976; Park, 1977) was used to delete insignificant indepen
dent variables until only the variables with significant (P < 0.05) partial
F-values were retained, or the error mean-square of the multiple regression
was minimal. Although the original data set contained over 200 observations,
half of these could not be used in the final equations because of missing site
descriptors. No attempt was made to infer missing values using statistical
techniques. The residuals were plotted against all the independent variables
to make sure that the linear models of transformed variables fitted the
responses well, and that no significant lack of fit remained after analysis
(Draper and Smith, 1966). The residuals were also examined with respect to
production measurement techniques. This fitting procedure is designed to
yield the most accurate equations without retaining undue complexity.
A useful model is one that is both accurate and easy to apply. Most
independent variables are either easily measured by survey sampling tech
niques (viz. DBH, D, BA, Z, E,
W) or are obtainable from published
weather and geographic records (viz. T, R, L). Because biomass (B) is
difficult to estimate (Parde, 1980), we offer an alternative. Basal area is, in
general, an excellent correlate of biomass, so we derive and analyze four
equations below: one each to predict P and PH using estimates of either
forest biomass or basal area in conjunction with all the other independent
variables.
RESULTS AND DISCUSSION
Multivariate equations
Equations to characterize general world trends in P and PH are presented
in Table I. All four equations are statistically significant and account for a
range of variation many times the size of residual error (Suich and Derringer,
1977). F-statistics range from 30 to 59, while multiple coefficients of de
termination (R2) range from 0.63 to 0.81. Equations to predict P and
equations using measures of B as independent variables have the highest R2
values. Table I lists the variables in order of their relative importance (most
influential first). The sign and significance of all the independent variables
are listed in Table II.
Biomass, or its correlate, basal area, is the most powerful predictor of P
and PH. Production increases, but decelerates with increased B. This quanti
fies the compensatory growth assumption behind most renewable resource
management models (Schaefer, 1968; Clark, 1976). The second most power
ful predictor of P and PH is forest age. The partial effect of mean age was to
decrease rates of net and net harvestable forest production in all cases (Table
II). This supports the common practice of culling old trees to increase
production rates (Stoddard, 1978).
231
The relative power of the other independent variables varies among
equations. The effect of DBH on P and PH is consistently positive (Table II).
This shows that forests with large diameter trees yield the highest rates of
production for a given biomass and age. Annual precipitation has a positive
effect in most equations, while the effect of temperature varies (Table II).
Latitude accounts for significant variation in forest production in eq. II,
where it replaces both R and T as the best descriptor of climatic conditions.
Forest type also has a significant effect on P and PH. Given the effect of
other site descriptors, plantations and natural stands yielded rates of produc
tion that were usually not significantly different (Table II). Equation I shows
that plantations might even yield lower rates of production than natural
stands. Thus, not all plantations have yielded the high rates of production
TABLE I
Multivariate equations for the prediction of net aboveground annual biomass increment (P; g
dry wt. m~2 yr~\), and net aboveground harvestable biomass annual increment (PH\ g dry
wt. m~2 yr"1) as functions of aboveground biomass (2?; g m~2), mean age of stand (A\
years), mean stem diameter at breast height (DBH; cm), mean stem density (D; number
ha~l), average basal area (BA; m2 ha"1), average total annual precipitation (R; cm), annual
mean daily temperature (T; °C), latitude (L; decimal degrees), and two dummy variables
describing whether or not the stand represented plantation or natural growth (Z), or whether
the stand was made up primarily of evergreen trees (£) (see text for explanation of dummy
variables). These equations were derived by regression analysis of published data. Multiple
coefficients of determination are abbreviated to "R2", F-values: "F", and number of
observations: "«". Partial F-values of all regression coefficients are significant (P<0.05).
Variables are listed in decreasing order of partial F which measures the role each variable
plays in predicting P or PH. R2 indicates the proportion of the variation in the dependent
variable accounted for by the regression equation. Ranges (and means) of independent
variables over which these equations are valid are: B = 560-78300 (15261), A = 5-321 (53),
DBH= 3.9-61.3 (16.0), D =112-14000 (3050), BA = 2-118 (36), R = 64-240 (100), and
T= 3.6-18.8 (8.6). The table shows that significant variation in both aboveground forest
production and net aboveground harvestable forest production is predictable from a variety
of biotic and abiotic variables.
Ia
log P = 0.40 + 0.60 log fl-0.64 log/4-0.24 Z + 0.42 log DBH + 0.U F.+2X10"5 D
II b
log PH = 0.20 + 0.59 log B -4X10"3 A -0.11 L +0.53 log DBH + 3X10"5 D
+ 0.27 log/?
+ 0.08 £
IIIc
log P = 0.86 + 0.53 log BA + 0.69 log R - 0.29 log A + 0.12 E + 0.27 log DBH
IV d
-ixio-2r
log PH = 0.09 + 0.78 log BA - 3 X10 ~3 A + 0.44 log DBH + 0.47 log R + 0.01 T
a R2
b /?2
c *2
d/?2
=
=
=
=
0.Sl,
0.67,
0.66,
0.63,
F=59,
F=32,
F=30,
F=33,
« =101.
n=102.
n=101.
n=102.
232
TABLE II
Sign and significance of effects of independent variables in Table I. " + " signifies that the
variable has a significant positive effect on forest production, "-" a significant negative
effect, and "0" no significant effect (P > 0.05). Equations marked with an "*" are those that
predict net aboveground annual harvestable biomass increment, others predict net
aboveground annual biomass increment of all tree parts. NA signifies that the variable was
not included in the regression model.
Variable
Equations
I
Biomass
+
II*
III
IV*
+
NA
NA
Basal area
NA
NA
Age
~
~
Diameter
Density
Precipitation
0
Latitude
0
Evergreen?
+
0
0
0
Temperature
Plantation?
+
-
+
0
0
0
0
0
0
+
+
0
attained by natural forests with otherwise similar stand and climatic condi
tions. Data were insufficient to determine whether managed "natural"
forests, or those receiving nutrient subsidies, yielded greater rates of produc
tion than unmanaged stands. The analyses provided consistent corroborative
evidence, however, that pure evergreen forests produced more dry matter
than deciduous and mixed stands (cf. Whittaker, 1966; Cole and Rapp,
1980).
The large F-statistics (legend, Table I) and lack of pattern in the residuals
suggest that the equations accurately mimic the annual biomass increment
measurments that we drew from the literature. The top two panels of Fig. 1
compare our predictions of forest production with the observed values, using
the most and least accurate equations (F=59 and 30). There is residual
scatter, but the data, with some exceptions, cluster around a 1:1 correspon
dence. The most notable outlier (star) in both cases is an estimate made on a
seven-year old plantation stand of Pinus radiata (Forrest and Ovington,
1970). This discrepancy may be due to the estimation technique used in this
study, since production was inferred from biomass differences between
stands of differing age.
Comparison with the Miami model
Because we suggest that eqs. I-IV can be used to make accurate predict
ions of forest production, they should be compared with existing general
233
models. As an example, we compare predictions of forest production made
by the Miami model with those actually observed in many forests around the
world (lower panel, Fig. 1). Examination shows that the Miami model yields
positively biased predictions that are much less accurate than those obtained
using our equations. Application of the Friedman Test (Conover, 1971) to
the residuals shows that our equations yielded test statistics ranging from 25
to 66 (critical value = 7.8 at P < 0.05), thus showing that our equations make
significantly smaller errors than does the Miami model.
0.0
o:o
0:5
1:0
1:5
2:0
2.5
OBSERVED PRODUCTIVITY
Fig. 1. Comparison of predicted and observed rates of net forest production (P; kg dry wt.
m"2 yr."1). Predictions are from eqs. I (F= 59) and HI (F= 30) in Table I, and the Miami
model (Lieth 1975). The observation marked with a star is an estimate made on a seven-year
old plantation stand of Pinus radiata (Forrest and Ovington, 1970; see text). The figure shows
that equations presented in Table I provide accurate predictions, on average, while the Miami
model makes consistent overestimates of forest production.
234
Example applications
The ratio of production to standing biomass has an important place in
ecology. It has been used to indicate qualities ranging from the production
/
efficiencies of plant communities (Smith, 1974) to the suitability of plant
material for consumption by heterotrophs (Ricklefs, 1979). The ratio is also
used as a constant to make indirect production estimates (e.g. Winberg et al.,
>
1971; Banse and Mosher, 1980). Equations I and II (Table I) show that the
ratios P: B and PH: B are not constant in forests. Figure 2A shows a
contour plot of P/B as a function of biomass and mean age of stand (from
eq. I). The annual rate of forest production varies from < 2% to > 30% of
total aboveground biomass. P/B declines as biomass accumulates, and as
forests age. The average P: B in Fig. 2A is about 0.05, or 5% of standing
biomass produced per year. If the average P: B were used to estimate P from
5, then the production of old, high biomass forests would be overestimated
five-fold, and the production of young, low biomass forests would be
underestimated ten-fold. Equations I and II also show that P: B varies with
average size, density, species composition of trees, and climatic conditions.
The conversion of solar energy to non-heat forms (e.g. electricity) is
limited by collector and storage cost, and by inefficiency (Bolton, 1978;
Evtuhov, 1979). Biomass fuels may be a means of inexpensive and efficient
solar energy fixation and storage (Burgess, 1978; Burwell, 1978). Using our
equations, we can predict forest energy fixation rates under differing en
vironmental and biological conditions, by assuming that wood has an
average energy content of 20,000 joules g"1 dry wt. (Tillman, 1978). The
energy fixation efficiency of forests is the ratio of net annual energy fixation
(eqs. I-IV) to net annual insolation. To predict fixation efficiency here, we
use a simple equation to predict solar radiation from average annual daily
temperature (T; °C) and total annual precipitation (R; cm). Data are
primarily from Liu and Jordan (1963), and additional published data (De
Barry, 1960; El Sabban and Elnesr, 1960; Canham and Golding 1963;
Quraishee, 1969; Hirschmann, 1973; Moni and Chacko, 1973) were used to
test the model. The least squares equation is:
S = 1452.25 + 37.45r- 0.324*
where S is the annual average daily total radiation on a horizontal surface (J
cm"2 day"1) collected with standard pyrheliometric equipment (R2 = 0.76;
n = 61; F= 92; P «: 0.01). Figure 2B shows predicted forest energy fixation
efficiency as a function of temperature and precipitation. Solar energy
fixation efficiencies of forests range between 0.06 and 0.60%. Highest ef-
*
ficiencies occur in cool, wet climates. These predictions compare well with
estimates of whole forest fixation efficiency (Kira, 1975) but are much lower
than the 2-13% efficiency attained by photovoltaic cells (Kelly, 1978).
)
235
FIXATION EFFICIENCY
PR0DUCTI0N/810MASS
300-
A.
2.5
3.0
3.5
4.0
4.5
5.0
LOG. BIOMASS (G M")
._
100
150
200
250
% CONVERSION EFFICIENCY
o
LU
CC
50
PRECIPITATION (CM)
15-
\\ ( \ \
\ \
\
D
10-
Oa05
T\
CC
LU
Q.
0.04
5 ■
LU
I-
0.03
0-
\
50
100
\
150
\
200
250
PRECIPITATION (CM)
Fig. 2. Example applications of predictions from equations in Table I. (A) Relationship
between production and biomass ratio (P/B)t aboveground biomass (B\ g dry wt. m"2), and
mean age of stand (A; years) predicted from eq. I assuming a natural, mixed or deciduous
forest and holding all variables other than A and B constant at their mean values (Table I);
(B) Efficiency of energy fixation by forests (%) under various climatic conditions (from eq.
HI); and (C) efficiency of solar energy conversion through forests to electricity, considering
losses due to harvest and conversion to electricity (from eq. IV). Figures 2B and 2C assume a
mixed or deciduous forest with all variables other than mean annual temperature (T; °C) and
total annual precipitation (R; cm yr"1) held constant near their mean values (Table I). Dry
weight production was converted to energy fixation using a mean value for North American
hardwoods and softwoods of 20,000 J g"1 dry wt. (Tillman, 1978; n = 7, SE= 240). Energy
conversion values assume harvest loss plus a further 75% energy loss on conversion to
electricity (Pimentel et al., 1981). Predicted energy fixation and conversion rates were
converted to efficiency predictions by division by the predicted average rate of insolation (see
text).
236
The actual solar energy conversion efficiencies may be even lower, because
foliage cannot always be harvested and energy is lost on conversion of
biomass to other energy forms. Harvest loss can be accounted for by using
eq. IV (Table I) to predict aboveground harvestable production, and biomass
can be converted to electricity with about 25% efficiency (Pimentel et al.,
1981). Figure 2C shows the predicted conversion efficiency of solar radia
tion, through forests, to electricity, as a function of climatic variables.
Conversion efficiencies range between 0.02 and 0.08%. Highest efficiencies
occur in warm, wet climates, and lowest efficiencies occur in all dry areas.
Solar conversion efficiency is relatively insensitive to variation in tempera
ture, probably because of the high correlation between solar radiation and
temperature (see above). The harvest technique or utility of tree parts will
influence the regional practicality of using forests as solar collectors. If all
aboveground production can be harvested, then the highest efficiencies occur
in cool, moist climates (Fig. 2B). If only boles and branches can be
harvested, then the highest efficiencies occur in warm, moist climates (Fig.
2C). Variations in any of the independent variables in Table I will alter the
predicted efficiencies because forest production is a function of many
factors.
This analysis should not be construed to suggest that forest fixation of
solar energy cannot be energetically or economically favorable. Forests fix
and store energy, unlike their photovoltaic counterparts. In addition, the
high cost of photovoltaic collectors discourages their use. "Target costs" for
thin-film solar cells are between $30 and $50 m~2 (roughly $120,000 to
$200,000 per acre) (Bolton, 1978; Evtuhov, 1979). The availability of forests
may compensate for their low fixation efficiency, rendering their use eco
nomically attractive for energy fixation and storage. The development of
these equations will allow a rational economic assessment of forest energy
use to be made.
CONCLUSION
We have suggested that previous general models of forest production may
be too simple to yield adequate predictions of net aboveground or net
aboveground harvestable production. The simple regression equations pre
sented here show that much variation in the rates of forest production is
predictable and that many physical and biological variables affect local rates
of forest production and energy fixation. In addition, the new equations
yield more accurate predictions than the Miami model. Koerper and
Richardson, 1980 (cf. Smith and Williams, 1980) have suggested that these
sorts of models might even facilitate contemporary forest management.
Examples illustrate that there are many possible uses for these new equa-
237
tions. These models yield better predictions than could have been made
before, as well as a multivariate understanding of the factors regulating
forest production on a world scale. We are thus one step closer to explaining
and predicting the distribution and abundance of plants in nature.
ACKNOWLEDGEMENTS
This research was supported by a Natural Sciences and Engineering
Research Council of Canada Research Fellowship to JAD. Computing funds
were granted by the McGill University Computer Centre and le Centre de
Calcul, Universite de Montreal. Additional support was received from the
Lake Memphremagog Project. We also thank N. Ursel, E. McCauley, M.
Hansen, A.R. Ek, C.A.S. Hall, M.R. Anderson and an anonymous reviewer.
NOMENCLATURE
Variable Definition
Units
P
Net aboveground annual biomass increment (bole, branches,
g dry wt.
leaves, and seeds)
yr *
Net harvestable aboveground annual biomass increment (bole
g dry wt.
and branches)
yr"1
PH
B
Above ground biomass (bole, branches, leaves, and seeds)
L
Latitude
m-2
m"2
gdry wt.
°Nor S
T
Mean annual daily temperature
°C
R
Mean total annual precipitation
cm yr
A
Mean age of stand
years
DBH
Mean tree diameter at breast height (approximately 1.3 m
cm
-l
from ground)
D
•l
Mean density of stems > 2 cm DBH
stems
ha"
BA
Basal area: cross-sectional area of stems at breast height
m2 ha
-i
Z
Plantation (Z = 1) or natural growth (Z = 0)
E, W
Evergreen (£ = 1, W = 0), deciduous (E = 0, W = 1), or mixed
(£ = 0, W=0)
REFERENCES
*Andersson, F., 1970. Ecological studies in a Scanian woodland and meadow area, southern
Sweden. II. Plant biomass, primary production and turnover of organic matter. Bot. Not.,
123: 8-51.
Andrewartha, H.G. and Birch, L.C., 1954. The Distribution and Abundance of Animals.
Univ. of Chicago Press, Chicago, IL, 782 pp.
*Art, H.W. and Marks, P.L., 1971. A summary table of biomass and net annual production in
forest ecosystems of the world, in: H.E. Young (Editor), Forest Biomass Studies. 15th
IUFRO Congress, University of Maine Press, Orono, ME, pp. 3-34.
238
Banse, K. and Mosher, S., 1980. Adult body mass and annual production/biomass relation
ships of field populations. Ecol. Monogr., 50: 355-379.
*Baskerville, G.L., 1965a. Dry matter production in immature fir stands. For. Sci. Monogr.,
Number 9.
*Baskerville, G.L., 1965b. Estimation of dry weight of tree components and total standing
crop in conifer stands. Ecology, 46: 867-869.
Bolton, J.R., 1978. Solar fuels. Science, 202: 705-711.
*Bray, J.R. and Dudkiewicz, L.A., 1963. The composition, biomass, and productivity of
Populus forests. Bull. Torrey Bot. Club, 90: 298-308.
Burgess, R.L., 1978. Potential of forest fuels for producing electrical energy. J. For., 76:
154-157.
Burwell, C.C., 1978. Solar biomass energy: an overview of U.S. potential. Science, 199:
1041-1048.
Canham, A.E. and Golding, E.W., 1963. Solar radiation and horticulture in Britain. Sol.
Energy, 7: 34-38.
Cannell, M.G.R., 1982. World Forest Biomass and Primary Production Data. Academic
Press, New York, NY, 391 pp.
Clark, C.W., 1976. Mathematical Bioeconomics. Wiley and Sons, New York, NY, 352 pp.
Clawson, M., 1979. Forests in the long sweep of American history. Science, 204: 1168-1174.
Cole, D.W. and Rapp, M., 1980. Elemental cycling in forest ecosystems, in: D.E. Reichle
(Editor), Dynamic Properties of Forest Ecosystems. IBP 23, Cambridge University Press,
Malta, pp. 341-409.
*Cole, D.W., Gessel, S.P. and Dice, S.F., 1967. Distribution and cycling of nitrogen,
phosphorus, potassium, and calcium in a second-growth Douglas-fir ecosystem. In:
Symposium on Primary Productivity and Mineral cycling in Natural Ecosystems. Univer
sity of Maine Press, Orono, ME, pp. 197-232.
Conover, W.J., 1971. Practical Non-Parametric Statistics. Wiley and Sons, New York, NY,
462 pp.
DeAngelis, D.L., Gardner, R.H. and Shugart, H.H., 1980. Productivity of forest ecosystems
studied during the IBP: the woodlands data set. In: D.E. Reichle (Editor), Dynamic
Properties of Forest Ecosystems. IBP 23, Cambridge University Press, Malta, pp. 567-672.
De Barry, E., 1960. Examples of statistical representation of radiation data. Sol. Energy, 4:
2-7.
*Doucet, R., Berglund, J.V. and Farnsworth, C.E., 1976. Dry matter production in 40-year-old
Pinus banksiana stands in Quebec. Can. J. For. Res., 6: 357-367.
Draper, N.R. and Smith, H., 1966. Applied Regression Analysis. Wiley and Sons, New
York, NY, 407 pp.
*Duvigneaud, P. and Denaeyer, S., 1967. Biomass, productivity and mineral cycling in
deciduous mixed forests in Belgium. In: Symposium on Primary Productivity and Mineral
Cycling in Natural Ecosystems. University of Maine Press, Orono, ME, pp. 167-186.
*Duvigneaud, P. and Denaeyer-DeSmet, S., 1970. Biological cycling of minerals in temperate
deciduous forests. In D.E. Reichle (Editor), Analysis of Temperate Forest Ecosystems.
Springer-Verlag, New York, NY, pp. 199-225.
El Sabban, A.F. and Elnesr, M.K., 1960. A note on the solar radiation pattern for the
United Arab Republic. Sol. Energy, 4(1): 48.
Elton, C, 1927. Animal Ecology. Sedgwick and Jackson, London, 209 pp.
♦Environment Canada, 1975a. Canadian normals, 1-SI. Downsview, Ont., Canada.
♦Environment Canada, 1975b. Canadian normals, 2-SI. Downsview, Ont., Canada.
Evtuhov, V., 1979. Parametric cost-analysis of photo-voltaic systems. Sol. Energy, 22:
427-433.
239
*Federer, C.A., 1973. U.S. Department of Agriculture Research Note NE-167. U.S. Govern
ment Printing Office 1973-711-162/507.
♦Forrest, W.G. and Ovington, J.D., 1970. Organic matter changes in an age series of Pinus
radiata plantations. J. Appl. Ecol., 7: 177-186.
Gujarati, D., 1978. Basic Econometrics. McGraw Hill, New York, NY, 462 pp.
Helwig, J.T. and Council, K.A., 1979. The SAS user's guide. SAS Institute Inc., Raleigh, NC.
Hirschmann, J., 1973. Records of solar radiation in Chile. Sol. Energy, 14: 129-138.
Hocking, R.R., 1976. The analysis and selection of variables in linear regression. Biometrics,
32: 1-49.
Johnson, A.W. and Miller, P.C., 1973. Dynamic Ecology. Prentice-Hall, Englewood Cliffs,
NJ.
*Johnson, F.L. and Risser, P.G., 1974. Biomass, annual net primary production and dynamics
of six mineral elements in a post oak-blackjack forest. Ecology, 55: 1246-1258.
*Kan, M., Saito, H. and Shidei, T., 1965. Studies of the productivity of evergreen broad
leaved forests. Bull. Kyoto Univ. For., 34: 55-75.
*Keay, J. and Turton, A.G., 1970. Distribution of biomass and major nutrients in a maritime
pine plantation. Aust. For., 34: 39-48.
Kelly, H., 1978. Photovoltaic power systems: a tour through the alternatives. Science, 199:
634-643.
*Kestemont, P., 1971a. Aerial biomass and productivity of an oak-and-birch copse rich in
Stetiaria and weed violets in Rope (Orchimont). Bull. Soc. R. Bot Belg., 104: 91-102.
*Kestemont, P., 1971b. Aerial productivity and biomass of an oak-and-birch copse rich in
brier on Robiet Plateau (Vresse). Bull. Soc. R. Bot. Belg., 104: 103-113.
*Kimura, M., 1960. Primary production of the warm temperate laurel forest in the southern
part of the Osumi Peninsula, Kyushu, Japan. Misc. Rep. Res. Inst. Nat. Resour. (Tokyo),
52: 36-47.
Kira, T., 1975. Primary production of forests. In: J.P. Cooper (Editor), Photosynthesis and
productivity in different environments. IBP 3, Cambridge University Press, Cambridge,
England, pp. 5-40.
Koerper, G.J. and Richardson, C.J., 1980. Biomass and net annual primary production
regressions for Populus grandidentata on three sites in northern lower Michigan. Can. J.
For. Res., 10: 92-101.
Lieth, H., 1975. Modeling the primary productivity of the world, in: H. Lieth and R.H.
Whittaker (Editors), Primary Productivity of the Biosphere. Springer-Verlag", New York,
NY, pp. 237-263.
Lieth,
H.
and
Box,
E.,
1972.
Evapotranspiration
and
primary
productivity.
C.W.
Thornthwaite Memorial Model. Publ. Climatol., 25: 37-46.
Liu, B.Y.H. and Jordan, R.C., 1963. The long-term average performance of flat-plate solar
energy collectors. Sol. Energy, 7(2): 53-74.
Moni, A. and Chacko, O., 1973. Solar radiation and climate of India. Sol. Energy, 14:
139-156.
*Monk, CD., Child, G.I. and Nicholson, S.A., 1970. Biomass, litter and leaf surface area
estimates of an oak-hickory forest. Oikos, 21: 138-141.
Odum, E.P., 1976. Fundamentals of Ecology. W.B. Saunders Co., Philadelphia, PA, 574 pp.
O'Neill, R.V. and DeAngelis, D.L., 1980. Comparative productivity and biomass relations of
forest ecosystems. In: D.E. Reichle (Editor), Dynamic properties of forest ecosystems. IBP
23. Cambridge University Press, Malta, pp. 411-449.
*Ovington, J.D., 1956. The form, weights and productivity of three species grown in close
stands. New Phytol., 55: 289-304.
240
*Ovington, J.D., Heitkamp, D. and Lawrence, D.B., 1963. Plant biomass and productivity of
prairie, savanna, oakwood, and maize field ecosystems in central Minnesota. Ecology, 44:
52-63.
Parde, J., 1980. Forest biomass. For. Abstr., 41: 343-362.
Park, S.H., 1977. Selection of polynomial terms for response surface experiments. Biomet
rics, 33: 225-229.
Paterson, S.S., 1956. The forest area of the world and its potential productivity. Department
of Geography, Royal University of Goteberg.
*Peterken, G.F. and Newbould, P.S., 1966. Dry matter production by Ilex aquifolium L. in
the New Forest. J. Ecol., 54: 143-150.
Pimentel, D.M., Moran, M.A., Fast, S., Weber, G., Bukantis, R., Balliett, L., Boveng, P.,
Cleveland, C, Hindman, S. and Young, M., 1981. Biomass energy from crop and forest
residues. Science, 212: 1110-1115.
*Post, L.J., 1970. Dry matter production of mountain maple and balsam fir in northwestern
New Brunswick. Ecology, 51: 548-550.
Quraishee, M.M., 1969. Global solar radiation measurements at Kabul, Afghanistan. Sol.
Energy., 12: 387-390.
Reed, K.L., 1980. An ecological approach to modeling growth of forest trees. For. Sci., 26:
33-50.
*Reiners, W.A., 1972. Structure and energetics of three Minnesota forests. Ecol. Monogr., 42:
71-94.
Ricklefs, R.E., 1979. Ecology. Chiron Press Ltd., New York, NY, 966 pp.
Rigler, F.H., 1982. Recognition of the possible: an advantage of empiricism in ecology. Can.
J. Fish. Aquat. Sci., 39: 1323-1331.
*Rodin, L.E. and Bazilevich, N.I., 1967. Production and Mineral Cycling in Terrestrial
Vegetation. Oliver and Boyd, Edinburgh, 288 pp.
Rosenzweig, M.L., 1968. Net primary productivity of terrestrial communities: prediction
from climatological data. Am. Nat., 102: 67-74.
*Saito, H. and Kira, T., 1965. Dry matter production by Camellia japonica stands. Jpn. J.
Ecol., 15: 131-138.
*Satoo, T., 1967. Primary production relations in woodlands of Pinus demiflora In: Sym
posium on primary productivity and mineral cycling in natural ecosystems. University of
Maine Press, Orono, ME, pp. 52-80.
Schaefer, M.B., 1968. Methods of estimating effects of fishing on fish populations. Trans.
Am. Fish. Soc., 97: 231-241.
*Schlesinger, W.H., 1978. Community structure dynamics and nutrient cycling in the
Okefenokee cypress swamp forest. Ecol. Monogr., 42: 71-94.
*Shanks, R.E., 1954. Climates of the Great Smoky Mountains. Ecology, 35: 354-361.
Sharpe, D.M., 1975. Methods of assessing the primary production of regions. In: H. Lieth
and R.H. Whittaker (Editors), Primary Productivity of the Biosphere. Springer-Verlag,
New York, pp. 147-166.
Smith, J.H.G. and Williams, D.H., 1980. A proposal to develop a comprehensive forest
biomass growth model. ENFOR Project P-64, Supply and Services Canada, Ottawa, Ont.,
47 pp.
Smith, R.L., 1974. Ecology and Field Biology. Harper and Row, New York, NY, 686 pp.
Spurr, S.H., 1964. Forest Ecology. Ronald Press, New York, NY, 687 pp.
Stoddard, C.H., 1978. Essentials of Forestry Practice. Wiley and Sons, New York, NY, 387
pp.
Suich, It. and Derringer, G.C., 1977. Is the regression equation adequate? — One criterion.
Technometrics, 19: 213-216.
241
Tadaki, Y., 1965. Studies on production structure of forests (VII). The primary production
of a young stand of Castanopsis cuspidate. Jpn. J. Ecol., 15: 142-147.
Tadaki, Y. and Kawasaki, Y., 1966. Studies on the production structure of forests. IX.
Primary productivity of a young Cryptomeria plantation with excessively high stand
density. J. Jpn. For. Soc, 48: 55-61.
Tadaki, Y., Ogata, N. and Takagi, T., 1962. Studies on production structure of forest. III.
Estimation of standing crop and some analyses on productivity of young stands of
Castanopsis cuspidata. J. Jpn. For. Soc, 44: 350-359.
*Tadaki, Y., Ogata, N. and Nagatomo, Y., 1963. Studies on production structure of forest
(V). Some analyses on productivities of artificial stand of Acacia mollissima. J Jpn For
Soc, 45: 293-301.
♦Tadaki, Y., Ogata, N. and Nagatomo, Y., 1965. The dry matter productivity in several
stands of Cryptomeria japonica in Kyushu. Bull. Gov. For. Exp. Stn., Meguro Tokyo 173*
45-66.
Tillman, D.A., 1978. Wood as an energy resource. Academic Press, New York, NY, 252 pp.
Turner, J. and Long, J.N., 1975. Accumulation of organic matter in a series of Douglas-fir
stands. Can. J. For. Res., 5: 681-690.
Webb, W.L., Lauenroth, W.K., Szarek, S.R. and Kinerson, R.S., 1983. Primary production
and abiotic controls in forests, grasslands, and desert ecosystems in the United States.
Ecology, 64: 134-151.
*Weetman, G.F. and Harland, R., 1964. Foliage and wood production in unthinned black
spruce in northern Quebec. For. Sci., 10: 80-88.
*Wernstedt, F.L., 1972. World Climatic Data. Climatic Data Press, Lemont, PA.
Westlake, D.F., 1980. Primary production. In: E.D. LeCren and R.H. Lowe-McConnell
(Editors), The Functioning of Freshwater Ecosystems. IBP 22, Cambridge University
Press, Cambridge, pp. 141-246.
*Whittaker, R.H., 1963. Net production of heath balds and forest heaths in the Great Smoky
Mountains. Ecology, 44: 176-182.
*Whittaker, R.H., 1966. Forest dimension and production in the Great Smoky Mountains.
Ecology, 47: 103-121.
Whittaker, R.H. and Marks, P.L., 1975. Methods of assessing terrestrial productivity. In: H.
Lieth and R.H. Whittaker (Editors), Primary Productivity of the Biosphere. SpringerVerlag, New York, pp. 55-118.
*Whittaker, R.H., Bormann, F.H., Likens, G.E. and Siccama, T.G., 1974. The Hubbard
Brook ecosystem study: forest biomass and production. Ecol. Monogr., 44: 233-254.
♦Whittaker, R.H. and Niering, W.A., 1975. Vegetation of the Santa Catalina Mountains,
Arizona. V. Biomass, production, and diversity along the elevation gradient. Ecology 56771-790.
* Whittaker, R.H. and Woodwell, G.M., 1969. Structure, production and diversity of the
oak-pine forest at Brookhaven, New York. J. Ecol., 57: 157-174.
Winberg, G.G., Patalas, K., Wright, J.C., Hillbright-Ilkowska, A., Cooper, W.E. and Mann,
K.H., 1971. A manual on methods for the assessment of secondary productivity in fresh
waters. In: IBP Handbook Number 17, Blackwell Scientific Publications, Oxford, pp.
296-317.