2000 EcolModel.pdf

Ecological Modelling 134 (2000) 185–205
The decline of forest productivity as stands age: a
model-based method for analysing causes for the decline
Danuse Murty *, Ross E. McMurtrie
School of Biological Science, Uni6ersity of New South Wales, Sydney, NSW 2052, Australia
Received 23 March 1999; received in revised form 30 May 2000; accepted 6 June 2000
Abstract
For closed canopy forests, both above-ground net primary productivity (ANPP) and wood yield decline as stands
age. However the physiological mechanisms responsible for the decline are not well understood. Understanding of the
causes of the decline and incorporation of aging mechanisms into models of forest production are essential both for
sound forest management and for reliable prediction of changes in terrestrial carbon storage under altered climates.
To investigate causes for declining net primary productivity (NPP) an ecosystem model G’DAY was modified to
include aging mechanisms associated with three main current hypotheses for NPP decline. These hypotheses are: (1)
sapwood maintenance respiration increases as stands age, reducing the availability of carbon to support growth; (2)
stomatal conductance and hence photosynthetic rates decline; and (3) soil nitrogen availability declines due to
nitrogen (N) accumulation in woody litter. A model-based method was developed for determining the relative
importance of three mechanisms for NPP decline in forest stands. The method involves a decomposition of simulated
model output into three components, each related to one aging mechanism. The method is illustrated by parameter-
izing G’DAY for young (40 year-old) and mature (245 year-old) stands of Pinus contorta in Colorado USA. Results
from this method of analysis indicate that:
1. The G’DAY model without aging mechanisms cannot reproduce the observed changes in NPP as stands age.
When the above three aging mechanisms are switched off, G’DAY shows only transient changes in NPP lasting
less than 20 years. When the aging mechanisms are incorporated in G’DAY, the model simulates declining NPP
on a scale similar to that observed in the field.
2. The gradual decline in NPP following canopy closure is sensitive to assumptions about aging mechanisms and is
particularly sensitive to assumptions about soil N availability and declining photosynthetic rates.
We identified key areas of model uncertainty requiring further experimental clarification. Here we highlight two
inadequately understood processes: soil N immobilization associated with woody litter accumulation and changes in
carbon allocation as stands develop. © 2000 Elsevier Science B.V. All rights reserved.
Keywords: Forest model; Forest aging; Net primary production; Nitrogen availability; Photosynthetic efficiency
www.elsevier.com/locate/ecolmodel
* Corresponding author. Tel.: +61-2-9385-2213; fax: +61-2-9385-1558.
E-mail address: d.murty@unsw.edu.au (D. Murty).
0304-3800/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved.
PII: S0304-3800(00)00345-8

D. Murty, R.E. McMurtrie / Ecological Modelling 134 (2000) 185–205
186
1. Introduction
In even-aged forests both above-ground net
primary production (ANPP) and wood yield are
observed to increase from the seedling stage until
canopy closure and then gradually decline as
stands age (Forrest and Ovington, 1970; Turner
and Long, 1975; Attiwill, 1979; Peet, 1980; War-
ing and Schlesinger, 1985; Turner and Lambert,
1986; Attiwill and Leeper, 1987; Kozlowski et al.,
1991; Long and Smith, 1992; Ryan and Waring,
1992; Gower et al., 1996; Ryan et al., 1997). For
11 tree species from contrasting climates the re-
ported percentage decline in ANPP varied widely
from 0% to 65%, depending upon species and age
range considered (Gower et al., 1996). For exam-
ple, measured ANPP of Pseudotsuga menziesii
declined by 45% from age 22 to 73 years, whereas
ANPP of Populus tremuloides declined merely by
4% over a similar age interval (from age 8 to 63
years) and ANPP of Pinus caribaea also declined
by 4% but over a shorter time interval (from age
5 to 15 years). Comparing two Alaskan stands of
Picea sitchensis, aged 50 and 160 years, Borman
and Siddle (Borman and Siddle, 1990) found that
ANPP was 50% lower in the older stand. In a
study of two adjacent lodgepole pine (Pinus con-
torta) stands in Colorado, aged 40 and 245 years,
Ryan and Waring (Ryan and Waring, 1992)
found that gross primary production (GPP) and
ANPP were 37% and 65% lower, respectively, in
the older stand. Comparing young and mature
Abies amabilis stands (25 and 180 years old)
Meier et al. (1985) reported that ANPP and net
primary production (NPP) were 44% and 23%
lower, respectively, in the older stand. In two
Picea sitchensis–Tsuga heterophylla stands, 85 and
138 years old, bolewood production was found to
be 45% lower in the older stand (Harcombe et al.,
1990). Wood production of South Australian Pi-
nus radiata plantations decreased by up to 50%
over a 40-year period following canopy closure
(Lewis et al., 1976) and mean annual biomass
increment in native Eucalyptus forests in Victoria,
Australia, declined by more than 50% as forests
aged (Grierson et al., 1992).
The above studies indicate that the decline in
forest production with age can be large. Hence
this decline is of major importance to both forest
management and to global climate change re-
search. In the forest management context, the
decline is important because the extent and rate of
productivity decrease with age will determine op-
timal forest rotation length and maximum sus-
tainable yields. In the global context, the decline
is important because forests are thought to con-
tribute 35% of global and 65% of terrestrial NPP
(Waring and Schlesinger, 1985; Gower et al.,
1996).
Although this age-related decline of forest
ANPP is a seemingly universal phenomenon, its
physiological mechanisms are not well under-
stood. Most commonly the decline has been at-
tributed to increases in respiring woody tissue (i.e.
sapwood) in older stands (Hellmers, 1964; Kira
and Shidei, 1967; Whittaker and Woodwell, 1967;
Peet, 1980; Waring and Schlesinger, 1985; Ko-
zlowski et al., 1991; Hunt et al., 1999). Several
recent studies have identified other possible causes
for declining NPP (Borman and Siddle, 1990;
Ryan and Waring, 1992; Yoder et al., 1994; Bink-
ley et al., 1995; McMurtrie et al., 1995; Gower et
al., 1996; Murty et al., 1996; Ryan et al., 1997;
Magnani and Grace, 2000; Magnani et al., 2000).
The most commonly-reported causes are decreas-
ing leaf biomass, decreasing stomatal conduc-
tance, altered pattern of carbon allocation and
decreasing nutrient availability (Turner, 1977;
Grier et al., 1981; McMurtrie et al., 1995; Vanni-
nen et al., 1996; Ryan et al., 1997; Prescott, 1999;
Magnani and Grace, 2000; Magnani et al., 2000).
Most forest models developed over the last
decade incorporate at least one mechanism for
NPP decline during stand development, usually
increased plant respiration (e.g. Keane et al.,
1990; Leersnijder, 1992; Comins and McMurtrie,
1993; Melillo et al., 1993; Potter et al., 1993;
Ruimy et al., 1994; Tiktak and Van Grinsven,
1995; Loehle and LeBlanc, 1996; Kellomäki and
Väisänen, 1997; Cao and Woodward, 1998;
Larocque, 1999; Linder, 2000; Sands et al., 2000).
But few encapsulate more than one aging mecha-
nism (Ryan and Waring, 1992; Gower et al., 1996;
Murty et al., 1996; Ryan et al., 1996a,b; Lands-
berg and Waring, 1997; Hunt et al., 1999; Valen-
tine, 1999; Magnani et al., 2000). Of the above

D. Murty, R.E. McMurtrie / Ecological Modelling 134 (2000) 185–205 187
models, even fewer incorporate all the commonly
reported mechanisms of aging, and use simple
simulations to resolve the relative contribution of
each mechanism to NPP decline (Gower et al.,
1996; Murty et al., 1996). For example, the
FOREST-BGC model used by Ryan and Waring
(Ryan and Waring, 1992) focusses on respiration
and stomatal conductance, but does not include
nutrient availability mechanisms. The 3-PG model
of Landsberg and Waring (Landsberg and War-
ing, 1997) includes the C-allocation and respira-
tion mechanisms, but omits coarse litter dynamics
and soil nutrient feedbacks. The Pipestem model
of Valentine (Valentine, 1999) focusses primarily
on C-allocation, and Magnani et al.’s (Magnani et
al., 2000) model on hydraulic conductance and
respiration. The BGC+ + model used by Hunt
et al. (Hunt et al., 1999) does contain all major
aging mechanisms, but does not provide a simple
method to resolve the relative contribution of
each to NPP decline.
The original contribution of this paper is that it
both represents the key aging mechanisms and
describes a method for quantifying their contribu-
tion to NPP decline.
In this paper the decline of production with age
will be analysed using the ecosystem model
G’DAY (Generic Decomposition And Yield,
Comins and McMurtrie, 1993) which has been
modified to incorporate aging effects. Aims of the
paper are:
1. to show how G’DAY can be used as a tool to
test three alternative hypotheses for the decline
of NPP over time;
2. to demonstrate a new method of model-based
analysis — a decomposition of simulated NPP
into three components each representing one
hypothesis for NPP decline; and
3. to investigate how aging mechanisms influence
NPP during stand development.
The three hypotheses under consideration here
are:
1. sapwood maintenance respiration rate in-
creases, reducing C availability to support
plant growth;
2. stomatal conductance (represented by maxi-
mum PAR utilization efficiency o0) declines,
leading to reduced canopy photosynthetic
rates; and
3. nitrogen (N) immobilization in decomposing
woody litter increases, reducing N-availability
to support tree growth, and altering biomass
allocation in trees.
Declining foliage biomass is not treated as a
separate hypothesis. Rather it is assumed that the
decline in foliage mass is a consequence of the
reduced NPP brought about by the aging pro-
cesses associated with the above three hypotheses.
To achieve the above aims, the full G’DAY
model was parameterized using available data for
two adjacent stands of lodgepole pine (Pinus con-
torta) in Colorado, described by Ryan and War-
ing (Ryan and Waring, 1992). We have chosen
these two stands to parameterize our model and
to demonstrate a new method of analysing NPP
declines with age because several of the most
important papers on the topic of NPP decline
were based on this site (including Ryan and War-
ing, 1992; Yoder et al., 1994; Murty et al., 1996;
Gower et al., 1996). For these stands, aged 40 and
245 years, Ryan and Waring (Ryan and Waring,
1992) found that gross primary production (GPP)
and ANPP were 37% and 65% lower, respectively,
in the older stand. Measured GPP of the 40-year-
old and 245-year-old stands was 0.915 and 0.577
kg C m−2
per year, respectively, and measured
ANPP was 0.242 and 0.085 kg C m−2
per year,
respectively, while sapwood maintenance respira-
tion was only 0.018 kg C m−2
per year higher in
the older stand. This relatively small increase in
respiratory load could not account for the large
decline of measured GPP and ANPP.
Ryan and Waring (Ryan and Waring, 1992)
used a process-based model (Forest-BGC, Run-
ning and Coughlan, 1988) to compare alternative
explanations for the lower productivity of the
older lodgepole pine stand. The model estimated
only a 13% decline in GPP, which they attributed
mainly to reduced foliage biomass; modelled sap-
wood respiration contributed only 7% and 13% to
the total C budget in the young and old stands,
respectively. They argued that if photosynthetic
rates were approximately 18% lower in the old
stand, then the model could fully explain the 65%
decline in ANPP. Subsequent measurements re-
vealed that photosynthetic rates were 14–19%
lower in the old stand, and that stomatal conduc-

188
tance was also lower (Yoder et al., 1994). However
Ryan and Waring (Ryan and Waring, 1992) did not
simulate nutrient cycling and therefore did not
address its importance.
Ryan and Waring (Ryan and Waring, 1992) did
not attribute lower NPP in the older lodgepole pine
stands to lower N-availability in the older stands.
They measured total N on ion exchange resins
(IER) in both the young and old stands and found
that soil N-availability was similar in both stands.
The IER technique, however, does not indicate how
much of the available N is taken up by the plants
and how much is utilized by woody litter decom-
posers (Binkley, 1984). While they also estimated
total C allocated below-ground (below-ground
GPP, BGPP), they made no estimates of fine root
biomass or fraction of NPP allocated to fine roots.
However, measurements of GPP and BGPP sug-
gest that in the old stand a greater proportion of
NPP is allocated below-ground than in the young
stand (Table 1). Ratios of BGPP/GPP in the young
and old stands are 0.36 and 0.45 (Ryan M.G.,
personal communication), indicating a 25% in-
crease in the fraction of the total C allocated
below-ground from the young to the old stand. This
observation of increased below-ground C alloca-
tion in older stand is consistent with other recent
studies (Santantonio, 1989; Vanninen et al., 1996;
Magnani and Grace, 2000).
The paper begins with a description of how
G’DAY has been modified to incorporate aging
mechanisms. This is followed by descriptions of
modelling methods we used to achieve our objec-
tives, and details of the simulated values for NPP
and the decomposition variables. Finally the paper
concludes with discussion of the model results and
recommendations for further research.
2. Model description
2.1. The G’DAY model of Comins and
McMurtrie
The G’DAY model (Comins and McMurtrie,
1993), hereafter referred to as CM) is based on
Table 1
Values of some variables estimated from field data for 40 and 245-year-old stands of P. contorta
Variable Old stand
Young stand
Units
Definition References
Age – years 40 245 (1) Ryan and Waring, 1992.
Gross primary production kg C m−2
per (2) Ryan, M., unpublished data.
GPP 0.915 0.577
year
Below-ground GPP
BGPP (2)
kg C m−2
per 0.257
0.333
year
(total C allocated (3) Raich and Nadelhoffer, 1989.
below-ground)
Net primary production 0.475
NPP 0.254
kg C m−2
per (4) Derived from unpublished data.
year
0.085
0.242 (2)
ANPP kg C m−2
per
Above-ground NPP
year
C in foliage kg C m−2
0.65 0.41 (2)
Cf
C in fine roots
Cr (4)
kg C m−2
0.15
0.2
nf (5) Schoettle, 1989; Yoder et al.,
0.017
0.0175
–
Foliar N:C ratio
1994.
kg C m−2
C in wood 5.5 8.5 (2)
Cw
Foliar respiration rate kg C m−2
per (2)
Rmf 0.21 0.132
year
Rmsw Sapwood respiration rate: kg C m−2
per (2)
year
0.065
0.051
stem wood
branches 0.010 0.014
coarse roots 0.010 0.019

Fig. 1. Carbon (C) and nitrogen (N) cycling in the G’DAY model, adapted to simulate aging. Fast pools are indicated by clear boxes
and slow pools by gray boxes: (a) C cycling and C sequestration coefficients. C respired is indicated by short upward-pointed arrows;
(b) N cycling. Solid lines with arrows indicate one-directional flows and dashed lines without arrows indicate two-directional flows;
(c) C sequestration coefficients for woody litter and associated active, slow and passive soil organic matter (SOM). The C
sequestration coefficient bij represents the fraction of C decomposition from pool j partitioned to pool i. Values of bij were obtained
from Parton et al. (Parton et al., 1987). Subscripts are f (foliage), r (fine roots), u (surface structural litter), 6 (soil structural litter),
m (surface metabolic litter), n (soil metabolic litter), w (woody litter), a (active SOM), s (slow SOM) and p (passive SOM).
the plant production models of McMurtrie and
Wolf (McMurtrie and Wolf, 1983) and McMurtrie
(McMurtrie, 1985, 1991) and the soil carbon and
nutrient cycling model CENTURY of Parton et al.
(Parton et al., 1987). It consists of a set of 10
differential equations describing C and N dynamics
of various tree and soil pools. The model’s structure
is illustrated schematically in Fig. 1. Tree biomass
components are foliage, wood and fine roots. The
wood pool consists of stemwood, branches and
coarse roots. Decomposing litter is partitioned into
four pools (surface and soil structural litter pools
and surface and soil metabolic litter pools) and soil
organic matter (SOM) into three pools (active, slow
and passive; Parton et al., 1987). Growth and
decomposition processes depend on soil
characteristics and on several environmental
variables: incident photosynthetically active
radiation (PAR), air and soil temperatures,
precipitation, and N inputs from atmospheric
deposition and N fixation.
G’DAY assumes that annual net primary pro-
duction NPP (kg C m−2
per year) is proportional
to absorbed photosynthetically active radiation
APAR (Monteith, 1977):
NPP=oE(nf) APAR (1)
where o is maximum net PAR utilization effi-
ciency, and E(nf) represents its dependence on
foliar N:C ratio (nf):

190
Fig. 1. (Continued)
E(nf)=
1.84nf −0.01
0.017+nf
,1.84ncrit −0.01
0.017+ncrit
if nf Bncrit, (2a)
E(nf)=1 if nf ]ncrit, (2b)
where ncrit(=0.035) represents the foliar N:C ra-
tio below which production is N-limited
(Kirschbaum et al., 1994).
APAR is calculated from Beer’s law (Jarvis and
Leverenz, 1983):
APAR=I0 (1−exp(−ksCf)), (3)
where I0 is incident PAR, k is the light extinction
coefficient, s is leaf area per unit carbon and Cf is
foliar carbon mass. (See Appendix 1 for definition
of all symbols.)

Carbon acquired through photosynthesis is dis-
tributed to foliage, fine roots and woody tissue in
fixed proportions, af:ar:aw, respectively. Senescence
rates of each biomass component are also fixed.
Plant litter is sub-divided into four pools: above
and below-ground structural and metabolic frac-
tions, using equations given by Parton et al. (Parton
et al., 1987).
Carbon from decomposing litter enters three soil
organic matter pools: active, slow and passive, with
decay time constants of order 1–5, 20–50 and
200–2000 years, respectively (Parton et al., 1987).
Decomposition rates are functions of soil moisture
and air temperature. G’DAY simulates fluxes of N
corresponding to each C flux, and N fluxes associ-
ated with atmospheric deposi-tion, biological fixa-
tion, soil mineralization, nutrient uptake, soil
gaseous emission and leaching. Complete descrip-
tions of the equations describing the plant and soil
C and N pools in this model can be found in
Appendix A of Comins and McMurtrie (Comins
and McMurtrie, 1993).
2.2. The G’DAY model incorporating aging
mechanisms
CM’s model does not incorporate the mecha-
nisms necessary to represent the hypotheses posed
in the Section 1 as possible explanations for the
decline of NPP with age. There is no explicit
representation of plant respiration (hypothesis 1),
no representation of effects of age on stomatal
conductance (hypothesis 2) or on C allocation and
there is no separate woody litter pool (hypothesis
3). We will now show how G’DAY has been
modified to incorporate these aging mechanisms
(cf. Murty et al., 1996).
2.2.1. Plant respiration
CM’s expression for NPP (Eq. (1)) does not
explicitly represent the C sinks associated with
respiration; maintenance and construction respira-
tion are readily incorporated in Eq. (1):
NPP=GPP−(Rc +Rm), (4a)
where GPP is gross primary production and Rc and
Rm are construction and maintenance respiration
rates, respectively. GPP is defined here as net
daytime carbon gain and is proportional to APAR:
GPP=o0E(nf)APAR, (4b)
where o0 is maximum gross PAR utilization
efficiency.
We assume that total construction respiration
represents 25% of NPP (Ryan, 1991a):
Rc =0.25NPP. (5a)
Following Ryan (Ryan, 1991b), Ryan and War-
ing (Ryan and Waring, 1992) and Murty et al.
(Murty et al., 1996), maintenance respiration is
modelled as the sum of three components:
Rm =Rmf +Rmr +Rmsw, (5b)
where Rm is total annual maintenance respiration
and Rmf, Rmr and Rmsw are annual maintenance
respiration rates of foliage (dark period only), fine
roots and sapwood, respectively. Both foliage and
fine root respiration rates are functions of mean
annual air temperature (Ta) and their nitrogen
contents (Nf and Nr, respectively):
Rmf =0.5R0NfQ10
Ta/10
, (5c)
Rmr =R0NrQ10
Ta/10
, (5d)
where the value of R0, the respiration rate per unit
nitrogen content corresponding to a temperature of
0°C, is derived from Ryan (Ryan, 1991a,b) and Q10
is 2.0 (Ryan, 1991a). The factor of 0.5 included in
Eq. (5c) is included because GPP, given by Eq. (4b),
is assumed to be net of daytime foliar respiration,
so that Rmf represents night respiration only.
Sapwood respiration is assumed to depend on
mean air temperature and sapwood volume (Ryan,
1990; Ryan and Waring, 1992; Ryan et al., 1995).
Assuming constant mean sapwood density (Ryan,
1991b), Ryan and Waring’s equation for sapwood
respiration (Ryan and Waring, 1992) can be con-
verted to a function of temperature and sapwood
C content (Csw):
Rmsw =0.00876CswQ10
’Ta/10
, (5e)
where Q%
10 =1.94. An empirical equation for sap-
wood C is derived from measurements of woody
biomass for three lodgepole pine stands aged 40, 65
and 245 years and assuming that branches and
coarse roots are composed entirely of sapwood
(Ryan and Waring, 1992):
Csw =1.11Cw
0.77
. (6)

192
Thus, given values of Nf, Nr and Cw, maintenance
respiration can be calculated from Eq. (5) and Eq.
(6).
2.2.2. Age-dependent stomatal conductance and
maximum gross PAR utilization efficiency
Yoder et al. (Yoder et al., 1994) observed that
photosynthetic rates were 14–19% lower in the
245-year-old lodgepole pine stand than in the
40-year-old stand and hypothesized that the reduc-
tion is an effect of altered canopy architecture on
hydraulic resistance and hence on stomatal conduc-
tance. Measured stomatal conductance of the older
trees was similar to the young trees in early
morning, but was lower during the day when
evaporative demand was at its peak.
Stomatal conductance is not explicitly repre-
sented in CM’s model because G’DAY is a daily
time step model, whereas stomatal conductance
varies on timescales of minutes. Nor are canopy
architecture and hydraulic resistance. However
Yoder et al.’s hypothesis can be incorporated in
G’DAY by assuming that maximum gross PAR
utilization efficiency o0 declines with age; the im-
plicit assumption here is that photosynthesis corre-
lates with stomatal conductance (Wong et al.,
1979). The link between PAR utilization efficiency
and stomatal conductance can be understood by
observing that PAR utilization efficiency depends
on inter-cellular CO2 concentration (ci) (McMur-
trie et al., 1992; McMurtrie and Wang, 1993), and
that declining stomatal conductance leads to re-
duced ci. In all the simulations that follow we will
consider the consequences if o0 is 16% lower in the
older stand. Since the pattern of o0 decline is not
known and we are primarily interested in the
relative change in NPP between the young and old
stands, for simplicity we assume that o0 declines
linearly with age of the stand:
o0 =oyoung if t5t1,
o0 =oold if t]t2,
o0 =oyoung −(oyoung −oold)
t−t1
t2 −t1
if t1 BtBt2,
(7)
where oyoung and oold are maximum gross PAR
utilization efficiency of the young and old stands,
respectively, t is age of the stand, t1 is the age after
which o0 begins to decline and t2 is the age at which
o0 reaches a minimum.
2.2.3. New wood N:C ratio and woody litter
decay
Based on evidence (Jeffreys, 1999) that N:C ratio
of new wood increases with foliar N:C ratio, the
new wood N:C ratio (nw) is modelled as a linear
function of foliar N:C (nf):
nw =0.08nf. (8a)
CM considered the senescence and decay of
leaves and fine roots, but not of wood. We incor-
porate wood senescence into equations for wood C
and N:
dCw
dt
=awNPP−swCw, (8b)
dNw
dt
=awnwNPP(1−rw)−swnwlwCw,
where Cw and Nw are wood carbon and nitrogen,
sw is wood senescence rate, nw is N:C ratio of new
wood, rw is the fraction of N in new wood derived
through retranslocation from existing wood, and
lw is a ratio of N:C of woody litter to new wood.
To simulate woody litter accumulation and de-
cay, woody litter C and N pools have been added
to CM’s original model. Equations describing these
new pools have a similar form to the equations used
to describe the structural litter pools in CM’s
model. The rate of change of woody litter C and
N are given by:
dCwl
dt
=swCw −dwlCwl, (8c)
dNwl
dt
=nwlwswCw −dwlNwl,
where Cwl and Nwl are woody litter carbon and
nitrogen, and dwl is intrinsic woody litter decompo-
sition rate. This decomposition rate is given by:
dwl =d%
wl
exp(−3Lw)A(Ts), (8d)
where Lw is the lignin fraction of wood, Ts is soil
temperature, A(Ts) represents the temperature de-
pendence of decomposition rate, and d%
wl is a
decomposition rate that can be estimated using
measured decomposition rates (dwl) at known val-

ues of Lw and Ts. The dependence on lignin content
is based on experimental studies showing that both
foliage and woody litter decay rates decline with
increasing litter lignin content (Meentenmeyer,
1978; Harmon et al., 1986; Taylor et al., 1989; Aber
et al., 1990). Eq. (8d) is analogous to equations for
decomposition of structural litter used in the CEN-
TURY model (Parton et al., 1987; Comins and
McMurtrie, 1993). The soil temperature function
A(Ts) is identical to that defined in Appendix A of
CM (Comins and McMurtrie, 1993):
A(Ts)=0.0326+0.00351Ts
1.652
−(Ts/41.748)7.19
.
(8e)
2.2.4. C allocation
There is evidence that below-ground C allocation
increases in response to declining N-availability
(Linder and Axelsson, 1982; Cannell, 1985; Santan-
tonio, 1989; Lambers and Poorter, 1992; A
, gren and
Wikstrom, 1993; Pongracic, 1993; Gower et al.,
1994; Ruess et al., 1996; Vanninen et al., 1996).
However, mechanisms for the change in C alloca-
tion with N-availability and stand age are poorly
understood (Ryan et al., 1997).
Some modellers have used the ‘Pipe model’
(which assumes a linear relationship between fo-
liage area and sapwood cross-sectional area) to
simulate C-allocated to wood (Shinozaki et al.,
1964; Mäkela, 1986). However, Cannell and Dewar
(Cannell and Dewar, 1994) who reviewed published
information on C allocation in trees pointed out
that ‘‘one of the limitations of the pipe model
hypothesis is that the sapwood area-foliage area
relationship is empirical and differs greatly among
species, among trees that differ in size within
species, within individual trees and in differing
environments.’’ Hence we chose to model C-alloca-
tion using allocation coefficients. This approach
has been used successfully by McMurtrie (McMur-
trie, 1991), Comins and McMurtrie (Comins and
McMurtrie, 1993), Kirschbaum et al. (Kirschbaum
et al., 1994, 1998), and Murty et al. (Murty et al.,
1996).
As in the case of o0, for simplicity we assume a
linear change in allocation parameters with age of
the stand:
ai =ai,young if t5t1,
ai =ai,old if t]t2,
ai =ai,young −(ai,young −ai,old)
t−t1
t2 −t1
if t1 BtBt2,
(9)
where ai represents the fraction of C allocated to
foliage (i=f), fine roots (i=r) and wood (i=w),
and ai,young and ai,old are allocation coefficients to
component i in young stands (aged t1) and old
stands (aged t2), respectively. The allocation coeffi-
cients are constrained so that af +ar +aw =1.
2.3. Decomposition of simulated NPP into three
components
To investigate contributions of the three aging
hypotheses to the NPP decline, simulated NPP was
expressed as a product of three terms, each repre-
senting one hypothesis for NPP decline:
NPP=
NPP
GPP
GPP
U
U. (10)
U represents modelled plant N uptake, which is
simulated using equation given in McMurtrie et al.
(McMurtrie et al., 2000).
In Eq. (10) the ratio NPP/GPP (sometimes called
carbon use efficiency) incorporates the effect of
altered maintenance respiration on NPP (associ-
ated with hypothesis 1), the ratio GPP/U is photo-
synthetic N-use efficiency which incorporates
changes in maximum gross PAR utilization effi-
ciency o0 (hypothesis 2), and the simulated value of
U describes changes in N-availability (hypothesis
3).
3. Modelling methods
To evaluate G’DAY as a model for simulating
the age-related decline in NPP, data from two
adjacent even-aged stands (aged 40 and 245 years)
of lodgepole pine (P. contorta) are used. The model
is parameterized using data from the younger stand
and model outputs are compared with data from
both stands.
The stands grow in Frazer Experimental Forest
near Winter Park, Colorado, USA. The forest lies

194
in a subalpine region (39°54% N, 105°52% W, 2800
m a.s.l.) with a 3-month growing season, mean
annual air temperature of 3.8°C, mean growing
season air temperature of 14.5°C and mean grow-
ing season incident photosynthetically active radia-
tion (PAR) of 1.164 GJ m−2
(averaged over 10
years). Stands were aged 40 and 245 years at the
time of measurement by Ryan and Waring (Ryan
and Waring, 1992). The methods used by them to
estimate tree biomass components, above-ground
NPP, below-ground C allocation and respiration
rates are described by Ryan (Ryan, 1991b) and
Ryan and Waring (Ryan and Waring, 1992). Esti-
mated stand properties and parameter values for
both stands, with references, are listed in Table 1
and Appendix 1.
3.1. Parameterization
Values of several parameters listed in Appendix
1 were estimated indirectly:
1. Maximum gross PAR utilization efficiency
(o0), defined in Eq. (4b), was inferred for the
young stand from estimated GPP and APAR
(Table 1), and a knowledge of the foliar N:C
ratio. It is assumed to be 16% lower for the
older stand (Yoder et al., 1994).
2. Foliar senescence rate (sf) was estimated from
the fraction of the total foliar C present in
1-year-old foliage (Schoettle, 1989).
3. Fractions of carbon allocated to foliage and
fine roots (af, aw and ar, respectively) were
derived using available data on GPP, total C
allocated below-ground (or below-ground
GPP, BGPP), C respired and C content of
foliage and fine roots. Values were derived
assuming foliage and fine roots are at equi-
librium, where rates of change of C in foliage
and fine roots are zero.
Stemwood allocation was estimated from
aw =1−af −ar. Calculations give lower aw in
the older stand which is consistent with other
studies. For instance, Cannell (Cannell, 1985)
investigated effects of tree age and size on
fraction of current net above-ground dry
matter increment (ANPP) partitioned to
wood in broadleaf and coniferous forests. On
reviewing many studies he concluded that the
fraction of above-ground C allocated to
wood was usually constant, or declined, with
age after canopy closure.
4. Wood senescence rate (sw) was assumed to be
the same in the old and young stands. Its
value was based on the assumption that
woody biomass has reached equilibrium in
the old lodgepole pine stand (i.e. that aw
NPP=sw Cw). It was calculated by substitut-
ing the measured value of wood C (Cw) and
derived values of NPP and C allocated to
wood (aw) for the old stand into the above
equilibrium equation. This gives sw =0.0069
per year.
5. Intrinsic woody litter decomposition rate
(dwl) was evaluated in Fahey’s (Fahey, 1983)
study of lodgepole pine in the Rocky Moun-
tains, USA. He obtained a value of dwl =
0.016 per year, which is comparable to rates
found in other cold temperate forests (Har-
mon et al., 1986). This value was used to
estimate the equilibrium value of decomposi-
tion rate d%
wl in Eq. (8d). It should be noted
that dwl was not measured for either of the
stands of lodgepole pine used here.
6. The N:C ratio of new wood (nw) was derived
using relative values of sapwood and heart-
wood N:C given by Pearson et al. (Pearson et
al., 1987).
7. Values of soil C partitioning coefficients and
decomposition rates di (i=a, p, s, u, 6, m, n)
for active, passive and slow soil pools, sur-
face and soil structural litter, and surface and
soil metabolic litter, respectively, were
derived from the CENTURY model of Par-
ton et al. (Parton et al., 1987).
8. Gaseous N emission fraction was set to 1% of
net N mineralisation (Kirschbaum et al.,
1994).
9. N:C ratios of surface and soil structural litter
pools were assumed constant and were taken
from CM. N:C ratios of surface and soil
metabolic pools vary with foliar and fine root
litter N:C ratios, respectively (Parton et al.,
1987).
10. Because of uncertainty about variability in
soil N:C ratios, we ran simulations with both
fixed and variable N:C ratios of SOM (cf.
Murty et al., 1996). Firstly, N:C ratios of

active, slow and passive soil pools were as-
sumed to be constant, with the N:C ratios of
active and passive SOM taken from CM and
Parton et al. (Parton et al., 1992), respectively.
The N:C ratio of slow SOM (ns) was estimated
using known values of SOM and N-content of
the soil (Ryan and Waring, 1992). In a second
set of simulations, N:C ratios of SOM were
assumed to be linear functions of inorganic soil
N (Parton et al., 1993; McMurtrie et al., 2000).
Specifically, the N:C ratios of substrate enter-
ing active, slow and passive SOM were as-
sumed to in-crease linearly between minimum
and maximum values estimated for forests by
Parton et al. (Parton et al. 1993) as inorganic
soil N increased from zero to a critical value
of 2 g N m−2
.
3.2. Initialization
To simulate NPP using the full G’DAY model,
we require initial values of C in foliage (Cf), fine
roots (Cr), and wood (Cw) (Table 1), and initial
values of C in woody, structural (foliar and fine
root) and metabolic (foliar and fine root) litter
pools and in active, slow and passive soil pools.
Both C in foliage and GPP are 37% lower in the
older than in the younger stand (Table 1). C in fine
roots has been estimated using values of C allocated
below-ground, coarse root maintenance respira-
tion, fine root senescence rate and N:C ratios of
foliage and fine roots. Woody biomass of the
younger stand is 35% less than that of the older
stand (5.5 versus 8.5 kg C m−2
, Ryan and Waring,
1992).
The initial value of C in woody litter was
estimated indirectly. Field work indicated that
forest floor woody litter (Cwl) was low in the young
and somewhat higher in the old stand, though
actual values were not available (Ryan M., personal
communication). Because of the uncertainty in the
values of Cwl, we assume that woody litter pool is
negligible in the young stand (i.e. Cwl =0) and has
reached equilibrium in the old stand.
Estimates of structural and metabolic litter and
active, slow and passive SOM are required to
evaluate net release of N from the structural,
metabolic, active, slow and passive pools, respec-
tively. Some estimates of foliar litter were available
but not of fine root litter. Measurements of total
SOM were available (8.0 kg C m−2
), but not of its
separate components in active, slow and passive
pools. We assume that passive SOM is constant for
both stands (Cp =4 kg C m−2
; Scott, N., personal
communication) Thus only the estimates of the
surface and soil structural litter (Cu and C6, respec-
tively), surface and soil metabolic litter (Cm and Cn,
respectively), and active (Ca) and slow (Cs) SOM
in the young stand are required to initialize the
model. Rather than guessing the values of these
variables we assume that the young stand had been
re-established on an old forest site which had
equilibrated litter and soil pools). However it would
also be defensible to assume that a proportion of
slow SOM is lost during stand establishment (John-
son, 1992).
Uncertainty about some key parameters and
initial values would be a serious concern if our
objective were to accurately predict NPP. However,
our main objectives are rather to show the general
capability of the model to simulate NPP decline
with age and to show a new method for evaluating
the contribution of aging mechanisms to the simu-
lated NPP decline.
3.3. Modelling strategy
To demonstrate the effect of the aging hypothe-
ses on NPP decline, we modified the G’DAY model
(as described in Section 2.2) to incorporate the
following processes: increased sapwood respiration
(Rmsw), declining leaf stomatal conductance (incor-
porated by reducing PAR utilization efficiency, o0),
altered C allocation to foliage (af), fine roots (ar)
and wood (aw), and immobilization of soil N
associated with woody litter decay (Dwl). When the
age-related variables are held constant this model
will be referred to as G’DAY without aging mech-
anisms, and when the age-related variables are
allowed to vary this model will be referred to as
G’DAY with aging mechanisms.
The model was simulated first with the above six
age-related variables constant and subsequently
with aging variables varying. For all simulations
the model was first parameterized for the young
stand with estimated C values for the slow, active,

196
Fig. 2. NPP simulated by the G’DAY model when soil N:C
ratios are assumed constant. The model was parameterized for
the young P. contorta stand (40 years old, Cf =0.65 kg C
m−2
, Cr =0.2 kg C m−2
and Cw =5.5 kg C m−2
). Four
simulations are shown: with aging mechanisms not included
(curve ‘0’) (where o0 =1.25 g C MJ−1
, af:ar:aw =0.16:0.42:0.42
and Cwl =0.0); with respiration hypothesis included (curve
‘1’), with respiration and stomatal conductance hypotheses
included (curve ‘2’); and with all three aging hypotheses incor-
porated into the model (curve ‘3’). o0 and C allocation begin to
change when stands are 40 years old and change linearly from
young to old values over a period of 205 years (o0 declines
from 1.25 to 1.05 kg C GJ−1
and af:ar:aw changes from
0.16:0.42:0.42 to 0.19:0.58:0.23).
pools (plant, soil and litter) is modelled to an
accuracy of two decimal places; i.e. we assume that
if none of the simulated pools changes by more than
0.005 units per 1000 years, then modelled C values
at long-term equilibrium are accurate to two deci-
mal places. At long-term equilibrium so defined,
NPP and foliar N:C ratios are accurate to three and
four decimal places, respectively.
4. Results
4.1. Model with fixed soil N:C ratios
Without the aging mechanisms, the G’DAY
model simulates only a transient increase and
decline in NPP followed by a long-lasting ‘stable’
phase (Fig. 2). When G’DAY is initialized at 40
years, NPP declines within less than 10 years to
below its long-term equilibrium value and reaches
a value that is within 5% of the equilibrium value
by the time the stand is 50 years old. This change
is not consistent with experimental data from a
variety of stands, which show a large (40% or more)
gradual NPP decline extending over several
decades. The simulated NPP of the 40-year-old
stand (0.425 kg C m−2
per year) is 10% lower than
that estimated from the data (0.475 kg C m−2
per
year, Table 1). This discrepancy occurs because
simulated NPP was obtained using Eq. (4), whereas
the NPP value derived from data was obtained
using given values of GPP and respiration (Table
1). The model simulates at most a 9% decline in
NPP, occurring over a period of less than 10 years.
When all aging mechanisms are included in
G’DAY (i.e. when sapwood respiration, o0, woody
litter decay rate and C allocation to plant parts vary
with stand age), the simulated NPP curve shows
three phases: (1) an initial phase with a sharp
increase in NPP to a maximum, over a period of
less than 10 years; (2) an intermediate phase char-
acterized by a gradual decline in NPP to a mini-
mum at an age of approximately 250 years and; (3)
a long-term phase characterized by a slow increase
in NPP over a period of more than 500 years (Fig.
2) to a long-term equilibrium. At this long-term
equilibrium all pools are equilibrated and cease to
change. The modelled long-term equilibrium NPP
metabolic litter and structural litter pools, and then
run to long-term equilibrium to obtain the long-
term equilibrium C and N in these soil pools. Next,
for simulations of NPP decline with age, the model
was again parameterized for the young stand but
assuming that the above soil pools were initially at
long-term equilibrium (i.e. they were parameterized
using the long-term equilibrium values), and NPP
was simulated. In all simulations NPP was evalu-
ated from Eq. (4a), which replaces CM’s Eq. (1).
Thus, in the simulations with age-related vari-
ables constant Rmsw, o0, af, ar and aw correspond to
the young P. contorta stand and woody litter decay
Dwl (=dwl Cwl, Eq. (8c)) is zero throughout the
simulations. On the other hand, in the simulations
with age-related variables varying Rmsw, o0, af, ar
and aw change from their initial values (correspond-
ing to the young P. contorta stand) to their long-
term equilibrium values, and Dwl is initially zero but
increases during stand development.
Since simulations to long-term equilibrium for P.
contorta can take simulation periods of several
thousand years, a criterion is required to determine
that long-term equilibrium has been achieved. In
this paper, long-term equilibrium of the simulated

is 0.294 kg C m−2
per year. The simulated NPP of
the young stands is approximately 10% lower than
that estimated from data. The simulated NPP of the
old stand (0.270 kg C m−2
per year) is 6% higher
than that estimated from data (Tables 1 and 2).
Fig. 2 also shows simulations when G’DAY
includes only the first aging hypothesis (respiration)
and the first two hypotheses (respiration and stom-
atal conductance). In these two simulations, curves
1 and 2, respectively, there is a small short-term
NPP decline lasting less than 10 years, but there is
no long-term NPP decline. When only the sapwood
respiration hypothesis is included in the model
simulated NPP declines by 11% from the young
(40-year-old) to the old (245-year-old) stand (Table
2). When both sapwood respiration and stomatal
conductance hypotheses are included the modelled
NPP decreases by 18%, while when all three hy-
potheses are included the NPP declines by 36%
from the young to the old stand (Table 2).
Fig. 2 shows that the NPP decline cannot be
explained unless aging mechanisms are invoked. In
the simulation with all three aging mechanisms
there is a gradual decline over a period of 250 years,
whereas in the other three simulations the decline
of NPP occurs mainly in the first 20 years. Thus
Fig. 2 suggests that the gradual decline in NPP
following canopy closure (after the stands are more
than 40 years old) cannot be explained by increas-
ing sapwood respiration and declining stomatal
conductance alone, but it can be explained when
the model also incorporates declining N uptake by
plants (U).
Causes for the simulated NPP decline can also
be explained from graphs of the four variables in
Eq. (10). For example, when all aging mechanisms
are included in the model (Fig. 3) the ratio (NPP/
GPP) declines by 9% between ages 50 and 245
years. This decline, which is associated with in-
creasing maintenance respiration, is much smaller
than the decline associated with N-availability (U).
For the simulation incorporating all aging mech-
anisms, normalized values of NPP, NPP/GPP,
GPP/U and U at 245 years are 0.56, 0.91, 1.02 and
0.6, respectively (Table 3). Thus the decline of
simulated NPP between ages 50 and 245 years is
associated with a small decrease in NPP/GPP, a
slight increase in GPP/U and a large decrease in U.
Thus, increasing respiration has relatively little
effect on NPP decline while N-availability (U)
contributes most to NPP decline.
Table 2
Simulated values of NPP (kg C m−2
per year) for 245-year-old
P. contorta standa
Yes
Yes
Yes
Sapwood respiration No
varies
Yes
No Yes
Stomatal conductance No
varies
No Yes
No
No
Woody litter varies
No Yes
C allocation varies No No
0.392
NPP when soil N:C is 0.377 0.349 0.270
fixed
0.327
0.339 0.303
NPP when soil N:C varies 0.230
a
Simulated NPP for the young (40-year-old) P. contorta is
0.425 kg C m−2
per year in all simulations.
Fig. 3. Simulated normalized values of the decomposition
variables, NPP, NPP/GPP ratio, N uptake rate U (kg N m−2
per year) and photosynthetic nitrogen-use efficiency GPP/U
(kg C/ kg N), for the P. contorta stand when all 3 aging
hypotheses are included in the model and soil N:C ratios are
kept constant (curve ‘3’ in Fig. 2). All variables are normalized
relative to their values at age 50 years.
Table 3
Simulated normalized values of NPP and its decomposition
variables for 245-year-old P.contorta standa
Fixed
Soil N:C ratio Variable
NPP 0.56 0.63
0.60
U 0.87
NPP/GPP 0.91 0.90
GPP/U 1.02 0.80
a
Values have been normalized relative to the simulated
values for the 50-year-old P. contorta.

198
Fig. 4. NPP simulated by the G’DAY model when soil N:C
ratios are assumed to vary. For the description of the four
curves displayed in this figure, see caption of Fig. 2.
hypotheses are incorporated NPP declines by 29%
between 40 and 245 years and there is a gradual NPP
decline through the simulation. When all three
mechanisms are included in G’DAY, the NPP
decline is largest (46% between 40 and 245 years).
These results suggest that NPP decline can be
explained if all three mechanisms are invoked.
For the simulation incorporating all three aging
mechanisms, the curves in Fig. 5 indicate that the
ratio NPP/GPP (hypothesis 1) declines by 10%
between 50 and 245 years, GPP/U (hypothesis 2)
declines by 20% and N uptake (hypothesis 3)
declines by 13% (Table 3). The curves in Fig. 5 also
suggest that NPP decline prior to age 70 is associ-
ated with declining GPP/U (hypothesis 2) and is not
strongly linked with hypotheses 1 and 3. After the
age 70 years all three hypotheses contribute to NPP
decline, with hypothesis 3 being most important.
5. Discussion
The G’DAY model without aging mechanisms
cannot reproduce observed changes in NPP as
stands age. It shows only transient changes in NPP
which occur over a short time interval lasting less
than 20 years (Figs. 2 and 4). However the G’DAY
model with aging mechanisms can both reliably
simulate the magnitude of NPP decline observed for
P. contorta in the field and can represent the three
forest development stages commonly described in
the literature (Attiwill, 1979; Miller, 1981; Turner
and Lambert, 1986; Attiwill and Leeper, 1987;
Miller, 1995) (Fig. 2). The early transient phase of
our simulations is characterized by canopy develop-
ment, rapid changes in NPP (Fig. 2) and reliance
on soil N reserves. The modelled second phase of
growth (lasting more than 100 years) is character-
ized by development of heartwood, increasing N
retranslocation, accumulation of woody litter and
increasing immobilization of soil N during woody
litter decay. The third phase is characterized by low
NPP, low rates of change in both plant and soil
pools and reliance on N retranslocation and recy-
cling of litter N (Miller, 1981).
Conclusions drawn here are broadly consistent
with the modelling results reported by Murty et al.
(Murty et al., 1996) who concluded that: (1) when
Fig. 5. Simulated normalized values of the decomposition
variables, NPP, NPP/GPP ratio, N uptake rate U (kg N m−2
per year) and photosynthetic nitrogen-use efficiency GPP/U
(kg C/ kg N), for the P. contorta stand when all three aging
hypotheses are included in the model and soil N:C ratios vary
(curve ‘3’ in Fig. 4). All variables are normalized relative to
their values at age 50 years.
4.2. Model with 6ariable soil N:C ratios
One uncertainty in the above simulations is the
assumption that soil N:C ratios are constant during
stand development. This assumption is question-
able because coarse woody litter accumulates dur-
ing stand development leading to enhanced input
of low N:C substrate into soils. It is uncertain
whether input of low N litter will tend to reduce N:C
ratios of SOM. If so, then less soil N will be
immobilized in aging stands than if soil N:C ratios
are fixed.
Simulations with variable soil N:C ratios are
shown in Fig. 4. For the simulation without aging
mechanisms there is some decline of NPP (20%), but
it occurs entirely in the first 20 years of the
simulation. Thus this simulation does not show a
gradual NPP decline. With the respiration mecha-
nism only incorporated into G’DAY, there is a
small gradual decline with NPP falling by 23%
between 40 and 245 years (Fig. 4). When both
respiration and reduced photosynthetic efficiency

soil N:C ratios are fixed, declining N-availability
alone can explain the decline in NPP; (2) when soil
N:C ratios are allowed to vary, increasing sapwood
respiration contributes little to NPP decline, but the
NPP decline can be explained as a combined effect
of declining photosynthetic efficiency and declining
N-availability to trees.
The decomposition analysis presented in this
paper represents a simple and very useful means to
analyse causes for the decline in forest production.
This method is particularly useful when we wish to
understand the patterns of change in NPP from
canopy closure until old age. The NPP decomposi-
tion into three components representing the three
aging hypotheses (Fig. 5) suggests that the NPP
decline observed in these lodgepole pine stands is
not caused by increasing respiratory load; this result
is consistent with experimental evidence from these
stands (Ryan and Waring, 1992). According to
G’DAY, the observed NPP decline can be explained
if all three aging mechanisms are invoked, but
declining N availability (U) and reduced photosyn-
thetic efficiency (stomatal conductance) are the
most important mechanisms. The decline in U is
caused by increasing N immobilization in woody
litter.
The simulation with variable soil N:C suggests
that declining photosynthetic efficiency is the dom-
inant mechanism for NPP decline for several
decades, but that reduced N availability is more
important in the older stands. In our simulations
the N-availability hypothesis contributed more
than 50% and 37% to the NPP decline (between ages
40 and 245 years) simulated under fixed and variable
soil N:C ratios, respectively (Table 2). However
Ryan and Waring (Ryan and Waring, 1992) did not
attribute lower NPP in the older lodgepole pine
stands to lower N-availability in the older stands.
They measured total N on ion exchange resins (IER)
in both the young and old stands and found that
soil N-availability was similar in both stands.
Similar results were obtained by Olsson et al.
(Olsson et al., 1998) who found that N availability,
measured using the IER technique, did not differ
among the lodgepole pine stands aged 50, 100 and
200 years (though N availability was higher in a
30-year-old stand). Net N mineralization has been
measured in the field using incubations of soil cores
at the young and old lodgepole pine stands (Stump
and Binkley, 1993); low rates of N mineralization
(approximately 2 and 6 kg ha−1
, respectively)
indicate that both sites may be N-limited, but N
availability was higher in the old stand.
Thus experimental evidence does not support our
model-based conclusion that N availability declines
as stands age. The IER technique, however, does
not indicate how much of the available N is taken
up by the plants (U) and how much is utilized by
woody litter decomposers (Binkley, 1984).
In order to resolve this disparity between model
and data, and in view of our model’s sensitivity to
assumptions concerning variability in soil N:C
during stand development, we believe that further
research is required into woody litter dynamics and
N fluxes associated with its decomposition, includ-
ing differences related to litter particle size. Another
area for future research is C allocation. We have
assumed that age-related changes in C allocation
are related to altered N availability. However an
alternative view has been proposed that C alloca-
tion is dictated by hydraulic constraints as tree
height increases (Magnani et al., 2000; West et al.,
2000).
Although G’DAY results indicate that the three
aging mechanisms (increased sapwood respiration,
decreased stomatal conductance and decreased N-
availability) when combined can explain the re-
duced NPP of the 245-year-old lodgepole pine
stand, we do not claim that these three factors are
the true causes of the decline in this old stand.
Rather our results show that it is important to
include these age-related mechanisms in models.
Acknowledgements
We thank Dr Mike Ryan for providing the data
and to all members of the UNSW-CSIRO research
team for valuable advice. This work was supported
by the National Greenhouse Advisory Committee
and the Australian Research Council. This research
contributes to the Global Change and Terrestrial
Ecosystems (GCTE) Core Project of the Interna-
tional Geosphere–Biosphere Programme (IGBP)
and DeCAF Project supported by the National
Center for Ecological Analysis and Synthesis
(NCEAS).

200
Appendix 1. Model variables and parameters
Abbreviations: APAR; absorbed photosynthetically active radiation; C, carbon; GPP, gross primary
production; N, nitrogen; NPP, net primary production; PAR, photosynthetically active radiation; SOM,
soil organic matter; T, temperature. Subscripts: f, foliage; p, passive; r, fine roots; s, slow; w, wood; wl,
woody litter.
A1.1. Variables
Units
Symbol Definition
bsi, bpi (i=f, r) Fractions of leaf and fine root litterfall C which are –
sequestered in slow and passive SOM
C content of foliage, fine roots, wood, sapwood, woody kg C m−2
Cf, Cr, Cw, Csw, Cwl, Cs
litter and slow SOM
Cin, Cout kg C m−2
per year
C fluxes into, out of aggregated fast pools
C fluxes into slow SOM from decomposing foliage, fine
Csf, Csr, Cswl, Csp kg C m−2
per year
root, woody litter and passive SOM
CRs Net C release from slow SOM decay kg C m−2
per year
per year
Inrinsic decomposition rates of slow and passive SOM
ds, dp
dwl Intrinsic decomposition rate of woody litter per year
Function for N-dependence of PAR utilization –
E
efficiency
GPP, NPP kg C m−2
per year
Gross and net primary production
kg N m−2
per year
N fluxes into, out of aggregated fast pools
Nin, Nout
NRp, NRs, NRwl Net rates of N release from passive and slow soil and kg N m−2
per year
woody litter pools
Rates of N sequestration in passive and slow SOM and
NSp, NSs, NSw kg N m−2
per year
wood
Nf, Nr N contents of foliage and fine roots kg N m−2
Nmin Rate of N mineralization kg N m−2
per year
nf, nr, nfl, nrl N:C ratio of foliage, fine roots, foliage litter and fine –
root litter
–
N:C ratio of new slow SOM
nso
–
nw, nwl N:C ratio of wood and woody litter
kg C m−2
per year
Rates of construction and maintenance respiration
Rc, Rm
kg N m−2
per year
U Rate of N uptake by plants
A1.2. Parameters
Value Units References
Symbol Definition
Fraction of NPP allocated to fo-
af, ar, aw – (1) Derived using available
liage, fine roots and wood in the: data on GPP, ANPP and
BGPP.

0.16, 0.42,
young stand
0.42
0.19, 0.58,
old stand
0.23
Fraction of C released from
bps (2) Comins and McMur-
0.032 –
trie, 1993; Parton et
slow SOM entering passive
SOM al., 1987.
Fraction of C released from 0.16 –
bsp (2)
passive SOM entering slow
SOM
(2)
bss Fraction of C released from 0.15 –
slow SOM which re-enters
slow SOM
(2)
0.32, 0.0017
Fraction of C released from –
bsw, bpw
woody litter pool entering
slow and passive SOM
4.0
Cp kg C m−2
Carbon content of passive SOM (3) Scott, N., personal
communication.
0.2378
d%
wl – (4) Derived using value
Woody litter decay coefficient
for Lw, Pinus contorta
data for dwl and Ts
and Eq. (8d).
0.0 −– (5) Ryan, M.G., unpub-
Woody litter decay rate in the
Dwl
young stand lished data.
0.3
Fine –
Fine soil fraction (2)
Incident PAR over active
I0 1.164 GJ m−2
(5)
growing season
0.5
k kg C m−2
PAR extinction coefficient (5)
(6) Pierce and Running,
1988.
(7) Ryan and Waring,
1992.
Lignin to biomass ratio of
Lf 0.25 – (2)
foliage and fine roots
Lignin to biomass ratio of 0.25
Lw – (2)
wood
M0 Fraction of N going to 0.85 – (2)
metabolic pool for zero lignin
M1 Decrease in metabolic fraction 0.018 – (2)
per lignin per N
Rate of atmospheric N deposi- 0.00021
NA kg N m−2
(2)
per year
tion
(8) Stottlemyer and
Troendle, 1987.
NF 0.0
Rate of N fixation kg N m−2
(9) See Section 3.2.
per year
Foliar N:C ratio below which 0.034 – (2)
ncrit
photosynthesis is N limited

202
0.1
npo –
N:C ratios of new passive SOM (2)
N:C ratios of slow and passive
ns, np 0.034, 0.1 – (2), (7)
SOM
Temperature dependence of 2.0, 1.94
Q10, Q%
10 – (7)
maintenance respiration
(10) Ryan, 1991a, Ryan,
1991b.
Fraction of N in new wood
rw (5)
0.56 –
obtained through retransloca-
tion from existing wood
Respiration rate corresponding 27.0
R0 kg C kg N−1
(10)
per year
to 0°C
Intrinsic senescence rates of
sf, sr 0.12, 1.0 per year (11) Schoettle, 1989
Schoettle and Fahey,
foliage and fine roots
1994.
0.0069
Intrinsic senescence rate of per year
sw (12) See Section 3.1.
wood
Mean annual air and soil
Ta, Ts 3.8, 4.0 °C (5)
temperatures
0.01 –
x (2), (5), (8)
Gaseous N emission fraction
(13) Yoder et al., 1994.
1.25, 1.05
Maximum gross PAR utiliza- g C MJ−1
o0
tion efficiency in young and
old stands
s Leaf area per unit carbon 7.6 m2
kg C−1
(5)
(14) Kaufmann et al.,
1982.
Ratio of leaf and root litter 0.5, 1.0
lf, lr – (5)
N:C to N:C of live tissue
lw Ratio of wood litter N:C to 0.44 (5)
N:C of new wood
Root N:C as a fraction of leaf 0.33 –
r (5)
N:C
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