Annals of Botany 85 : 55–67, 2000
Article No. anbo.1999.0997, available online at http:\\www.idealibrary.com on
Modelling the Components of Plant Respiration : Representation and Realism
J. H. M. T H O R N L E Y and M. G. R. C A N N E L L*
Institute of Terrestrial Ecology, Bush Estate, Penicuik, Midlothian EH26 0QB, UK
Received : 11 June 1999
Returned for revision : 28 July 1999
Accepted : 20 September 1999
This paper outlines the different ways in which plant respiration is modelled, with reference to the principles set out
in Cannell and Thornley (Annals of Botany 85 : 55–67, 2000), first in whole-plant ‘ toy ’ models, then within
ecosystem or crop models using the growth-maintenance paradigm, and finally representing many component
processes within the Hurley Pasture (HPM) and Edinburgh Forest Models (EFM), both of which separate C and N
substrates from structure. Whole-plant models can be formulated so that either maintenance or growth respiration
take priority for assimilates, or so that growth respiration is the difference between total respiration and maintenance
associated with the resynthesis of degraded tissues. All three schemes can be converted to dynamic models which give
similar, reasonable predictions of plant growth and respiration, but all have limiting assumptions and scope.
Ecosystem and crop models which use the growth-maintenance respiration paradigm without separating substrates
from structure, implicitly assume that maintenance respiration is a fixed cost, uncoupled to assimilate supply, and use
fixed rate coefficients chosen from a range of measured values. Separation of substrates in the HPM and EFM enables
estimates to be made of respiration associated with local growth, phloem loading, ammonium and nitrate N uptake,
nitrate reduction, N fixation and other mineral ion uptake, leaving a ‘ residual maintenance ’ term. The latter can be
#
explicitly related to C substrate supply. Simulated changes in grassland respiration over a season and forest
respiration over a rotation show that the ratio of total respiration to gross canopy photosynthesis varies within the
expected limited range, that residual maintenance accounts for 46–48 % of total respiration, growth 36–42 %, phloem
loading 10–12 % and the other components for the small remainder, with the ratios between components varying
during a season or forest rotation. It is concluded that the growth-maintenance approach to respiration, extended to
represent many of the component processes, has considerable merit. It can be connected to reality at many points,
it gives more information, it can be examined at the level of assumptions as well as at the level of predictions, and
it is open to modification as more knowledge emerges. However, currently, there are still parameters that require
adjustment so that the predictions of the model are acceptable.
# 2000 Annals of Botany Company
Key words : Respiration, photosynthesis, growth, maintenance, substrate, N uptake, mineral uptake, phloem loading,
model.
INTRODUCTION
In the previous paper (Cannell and Thornley, 2000) we
highlighted some of the principles to be considered when
modelling plant respiration. It was concluded that, in order
to be both mechanistic and realistic, models should separate
C substrate from structure, so that the dependence of
respiratory components on C substrate supply can be
represented, thereby coupling the respiration flux to
photosynthesis. Account should also be taken of the fact
that respiration in leaves can make a smaller demand on C
substrates than expected, principally because of excess ATP
and NAD(P)H produced in chloroplasts when illuminated.
Most importantly, it was suggested that, in addition to
direct growth respiration, it is desirable and now possible to
represent components of respiration associated with N
uptake, mineral uptake, nitrate reduction, phloem loading
and symbiotic N fixation (if appropriate) using known
#
average values of the specific unit respiratory costs. The
remaining respiration, associated with protein turnover,
maintaining ion gradients, the alternative pathway and
* For correspondence. Fax j44(0)131 4453943, e-mail mgrc!
ite.ac.uk
0305-7364\00\010055j13 $35.00\0
other types of wastage respiration, may be treated as
‘ residual maintenance ’ respiration and scaled with tissue N
content. This is a modification to the growth-maintenance
paradigm. Although it is usual to identify respiration and
its components under the two categories of ‘ growth ’
and ‘ maintenance ’, it was noted that energy-requiring
processes cannot be unambiguously separated into these
two categories.
Models should be capable of simulating variation in the
fractions of total plant respiration associated with different
processes during plant development, seasonally, and over
longer time periods. However, ratios between rates of
photosynthesis and respiration—and hence values of annual
net primary productivity per unit C assimilated—are
expected to vary within a limited range when averaged over
weeks or longer, because of the coupling between respiration
and C substrate supply. Realistic models should reflect this
inherent constraint as an unforced outcome of the dependence of respiration on C substrate concentrations.
In this paper, we review the different ways in which plant
respiration has actually been modelled. First, an outline is
given of three contrasting formulations of the growthmaintenance paradigm in simple whole-plant ‘ toy ’ models,
all of which can reproduce observed patterns of growth. We
# 2000 Annals of Botany Company
56
Thornley and Cannell—Modelling the Components of Plant Respiration
then point out the limitations of applying the growthmaintenance paradigm within comprehensive ecosystem
models which do not separate C substrate from structure.
This leads to an account of the ways in which individual
respiratory processes are now represented and parameterized within the Hurley Pasture Model (HPM) and Edinburgh
Forest Model (EFM) (Thornley and Cannell, 1996 ;
Thornley, 1998). Lastly follows a brief description of the
two models’ predictions of the magnitude of individual respiratory components relative to each other, over a season in
grassland and over the 60 years of a forest rotation.
A
Maintenance
respiration, Rm
Growth
respiration, RG
CO2
CO2
kmM
P
P – kmM
Supply of
substrate
from canopy
WHOLE-PLANT ‘TOY’ MODELS OF
GROWTH AND MAINTENANCE
RESPIRATION
YG(P – kmM)
Litter
Whole-plant models of plant respiration typically consider
only growth and maintenance respiration, and have simplified schemes of C flow with only one or two pools
representing plant tissue. They all assume that C substrates
are used in some fixed ratio or priority order between
growth and maintenance functions. Below, we outline three
different whole-plant schemes. All three schemes can be
converted to dynamic plant growth models, as outlined in
the Appendix. The models are capable of reproducing
observed patterns of whole-plant growth and have heuristic
value as ‘ toy ’ models, but they are clearly limited in scope.
The point to be made in this section is that the three
schemes, with very different assumptions, make very similar
predictions of plant growth and respiration.
(1 – YG)(P – kmM)
Senescence,
ksM
Plant
mass, M
B
Growth
respiration, RG
Maintenance
respiration, Rm
CO2
CO2
kmM
(1 – YG)P
YGP
P
Supply of
substrate
from canopy
Plant
mass, M
Senescence, ksM
Litter
C
(1) Maintenance respiration is giŠen priority oŠer growth
The earliest models, developed by McCree (1970) and
Thornley (1970) assume that a maintenance tax is subtracted
from the substrate supply rate (P) and that the residue is
used for growth with an efficiency YG. That is, maintenance
respiration is given priority. The basic model is drawn in
Fig. 1 A. The respiration rate, R (kg C d−"), is :
R l (1kYG) (Pkkm M )jkm M
Rm l km M,
Supply of
substrate
from canopy
Yd
(1 B)
R l RGjRm (2)
using eqn (1 A) (Fig. 1 A). Equation (1 B) shows that if
respiration R is regressed against photosynthesis P and
mass M, then the coefficients do not strictly define the
growth and maintenance components of respiration.
Nondegradable
mass, Mn
Degradable
mass, Md
Degradation, kdMd
where YG is the growth yield (units of C appearing in product
M per unit of C substrate utilized for growth), P is the
substrate supply rate (kg C d−"), M (kg C) is the dry mass
(DM) of the unit being considered (plant, organ, tissue, cell)
measured in C units, and km (d−") is the maintenance
coefficient. The growth and maintenance respiration rates,
RG and Rm (kg C d−"), are identified as :
RG l (1kYG) (Pkkm M),
P + kdMd
(1 A)
which is equivalent to
R l (1kYG) PjYG km M
P
Total respiration, R = RG + Rm
= (1 – YG)(P + kdMd)
CO2
(1 – YG)
YG
(1 – Yd)
Senescence, ksMn
Litter
F. 1. Three schemes for growth and maintenance respiration : A,
maintenance has priority ; B, growth has priority ; C, maintenance is
represented by a degradable fraction of dry matter, and a constant
fraction Yd of growth is input to this degradable pool.
Carbon conservation gives :
Pl
dM
jks MjR
dt
(3)
where ks (d−") is the senescence rate, and t is the time
variable (d). Eliminating P between eqns (1) and (3) leads
to :
1kYG dM
(4)
Rl
jks M jkm M
YG
dt
0
1
Thornley and Cannell—Modelling the Components of Plant Respiration
Here respiration has a growth component which is proportional to the gross growth rate of mass (dM\dtjks M ),
and a maintenance component which is proportional to the
dry mass (M ). Finally, the equation for the mass growth
rate is (directly from Fig. 1 A) :
dM
l YG(Pkkm M )kks M
dt
(5)
In this equation, a maintenance tax (km M ) is subtracted
from the gross substrate supply (P), and what is left is used
for tissue production.
Although this model separates growth and maintenance
functions and allows variable growth : maintenance respiration ratios, it is plainly unsatisfactory, as eqn (1) allows
the respiration : photosynthesis ratio R\P (and hence the
carbon use efficiency ; Cannell and Thornley, 2000) to have
any value between unity (if km M l P) and (1kYG) (if
M l 0).
Figure 2 A shows that the resulting dynamic model [eqn
(A 1) of the Appendix] leads to a typical sigmoidal growth
curve in plant mass (M ) and gross photosynthesis (P) ; the
growth (RG) and maintenance (Rm) components of respiration are of similar magnitude with growth respiration
first exceeding maintenance respiration, which becomes
reversed. The respiration to gross photosynthesis ratio
(R\P) begins at 0n33 and moves to 0n45.
(2) Growth respiration has priority ; maintenance
respiration consumes existing mass only, not substrate
A small but important change to the scheme of Fig. 1 A is
shown in Fig. 1 B. This leads to a change in interpretation
and to a changed prediction for allowed values of the
respiration : photosynthesis ratio. In Fig. 1 B, new substrate
(flux, P) is entirely used for growth. The maintenance
respiration occurs only at the expense of plant mass, M.
From Fig. 1 B, we can write :
dM
l YG Pk(kmjks) M
dt
(6)
R l (1kYG) Pjkm M l RGjRm
It is interesting to follow the fate of say 100 C atoms
through the system. A fraction YG of the 100 input atoms
enters the plant mass box, and 100 (1kYG) atoms are
respired in growth respiration. The 100 YG atoms which
enter the plant mass box will, eventually, exit from this box
either to maintenance respiration (the number being
proportional to km), or to senescence (net production,
defined here as the input to litter and soil, the number being
proportional to ks), which they do in the ratio of the rate
constants, km : ks. Note that if there are two linear rate
constants, k l 0n1 d−" and k l 0n2 d−", competing for C
"
#
atoms, then twice as many C atoms will take the k route
#
as take the k route. Important ratios are those of res"
piration : photosynthesis, and net production (NP) to gross
production (GP l photosynthesis). These can be deduced
57
for the steady state [dM\dt l 0 in eqn (6)], or by following
the 100 input C atoms right through the system. They are :
rR:P l
r
NP:GP
l
respiration
R
k
l l (1kYG)jYG m
ksjkm
photosynthesis P
net production
ks
l YG
ksjkm
gross production
(7)
where rR : P l 1krNP : GP
On the right-hand side of the first equation, the first term is
growth respiration and the second is maintenance respiration. In the second equation, the first factor YG gives the
fraction of the input C atoms which get into the plant mass
box, and the second factor [ks\(ksjkm)] gives the fraction of
these atoms which exit to litter. Note that the absolute value
of the maintenance coefficient is no longer of importance to
these ratios—it is the ratio of the maintenance rate to the
senescence rate that counts. Assuming, say, that the growth
efficiency YG l 0n75 and ks l 2km, then rR:P l 0n25j0n75i
km\(2kmjkm) l 0n5, and rNP:GP l 0n75iks\(ksj" ks) l 0n5.
#
This result is compatible with observations made by Gifford
(1994, 1995) and others (Cannell and Thornley, 2000, in the
discussion of carbon use efficiency). The interpretation of
the growth-maintenance model of Fig. 1 B shows that this
ratio will be the same over a wide range of tissue maintenance
coefficients and environmental conditions, so long as a
proportionality between maintenance and senescence rates
is preserved.
Figure 2 B shows that the dynamic model corresponding
to Fig. 1 B, ‘ growth has priority ’ [eqn (A 2) of the Appendix],
makes similar predictions to Fig. 2 A, corresponding to
Fig. 1 A, ‘ maintenance has priority ’. Thus, there is sigmoidal
asymptotic growth in mass and gross photosynthesis.
However, maintenance respiration is always less than growth
respiration, but approaches it as the asymptote is reached,
and the respiration : gross photosynthesis ratio increases
over the growth cycle.
However, the two notions that (a) the energy-requiring
maintenance processes of existing tissue occur entirely at the
expense of that tissue rather than making use of new
substrates, while (b) growth is the only process which uses
new substrates, are probably not sustainable as a general
principle, although it may be a useful approximation.
Generally, development, senescence and maintenance all
increase together at higher temperatures and there are
instances where the mass of tissues decreases with age, such
as conifer needles (reflected in an increase in specific leaf
area). On the other hand, senescence can be delayed by
warming, while maintenance respiration increases (Rosenthal and Camm, 1996) and in a particular situation,
senescence may be more related to nutrient shortage
stimulating nutrient salvage, rather than passively linked
to maintenance respiration (Nooden et al., 1997).
(3) Growth, degradation and resynthesis Šiew of
respiration
A third possible scheme divides plant tissue into nondegradable mass (cell walls etc.) and degradable mass
58
Thornley and Cannell—Modelling the Components of Plant Respiration
B Growth
has priority
C Constant fraction of
growth is degradable
2·5
2·0
M
M
M
1·5
1·0
0·5
0·0
0·20
0·15
Pg
Pg
Pg
0·10
0·05
Growth and maintenance
respiration (C units d–1)
0·00
0·05
Ratio of respiration
to gross photosynthesis
Gross photosynthesis
(C units d–1)
Plant mass (C units)
A Maintenance
has priority
0·5
Rm
0·04
RG
0·03
0·02
RG
Rm
RG
Rm
0·01
0·00
0·4
R/P
R/P
R/P
0·3
0·2
0·1
0
50
100
150
200
0
50
100
150
Time, t (d)
200
0
50
100
150
200
F. 2. Growth, photosynthesis and respiration predicted during the growth of a plant by the three whole-plant models depicted in Fig. 1. The
equations and parameter values for these simulations are given in the text and in the Appendix.
requiring maintenance (cell proteins etc.). There is a single
process of respiration associated with growth (Fig. 1 C), but
the component of this respiratory flux which can be
associated with the resynthesis of degrading tissue is deemed
to be maintenance respiration. Growth respiration is the
difference between the total respiratory flux and this
maintenance component.
The scheme was originally proposed by Thornley (1977)
(see also Loehle, 1982). In its simplest form, as depicted in
Fig. 1 C, growth leads to constant fractions of degradable
and non-degradable matter. In a modification of this
scheme, Dewar et al. (1998) separated growth respiration
and maintenance respiration by specifying different biosynthetic efficiencies for the two processes.
In Fig. 1 C, total respiration, in units of C per day, is a
fraction, (1kYG), of the C substrates supplied by photosynthesis (P) plus C recycled as a result of degradation :
R l (1kYG) (Pjkd Md)
l (1kYG) Pj(1kYG) kd Md l RGjRm
(8)
(see Fig. 1 C for definitions of the symbols). This equation
defines, rather arbitrarily, growth respiration as being the
component of the respiratory flux associated with photo-
Thornley and Cannell—Modelling the Components of Plant Respiration
synthesis, and maintenance respiration that is associated
with resynthesis using the recycled C flux. The R\P ratio
has a minimum value of 1kYG but can approach unity in
equilibrium if Yd l 1 so that all the structure is degradable
(no litter is produced, Md is constant, R l P).
Figure 2 C shows that this model predicts results [eqn
(A 3) of the Appendix] that are practically indistinguishable
from the predictions of the models of Fig. 1 A and B. The
recycling model of Fig. 1 C is valuable in that it demonstrates
that phenomenologically it does a similar job to the models
of Fig. 1 A and B, but the interpretation is quite different.
REPRESENTING RESPIRATION IN
COMPREHENSIVE ECOSYSTEM MODELS
In this section, we consider how respiration is represented at
the organ level (leaf, stem, root etc.) in more comprehensive
ecosystem and crop models. First, we comment on the
representation of respiration in models which do not
separate substrate from structure. We then describe how
respiration is represented in the current versions of our
grassland and forest ecosystem models, in which substrates
(C and N) are separated from structure so that substrates
can be transported to different organs, and local substrate
concentrations can be used to define the rates of the
different energy-requiring processes and thus the respiratory
costs specific to each process.
Models which do not separate substrate from structure
Thirteen grassland and forest ecosystem models were
compared by A/ gren et al. (1991) and Ryan et al. (1996)
(BACROS, BIOMASS, FORGRO, MAESTRO, FORESTBGC, BLUE-GRAMA, BIOME-BGC, CENTURY, MBLGEM, HYBRID, PnET-CN, Q) and other comprehensive
models are described by Spitters, van Kraalingen and van
Keulen (1989, SUCROS), Hunt et al. (1991, GEM), Schafer
and Krieger (1994, TREEDYN) and Chen and Coughenour
(1994, GEMT). Almost all these models separate growth
and maintenance respiration, but none distinguish any
components of maintenance respiration.
In all these models, maintenance respiration, Rm, is
calculated for each plant part as the product of a rate per
unit y, ry, where y is biomass, volume, surface area or N
content. Thus, Rm l ryiy. Nitrogen content is increasingly
favoured for y, especially for foliage (Ryan et al., 1966), but
for tree stems, surface area is preferred by some authors
(Stockfors and Linder, 1998).
Some authors assume that during the night maintenance
respiration in leaves is a function of Vc(max) [the apparent
maximum rate of carboxylation (Farquhar et al., 1980)],
which is closely correlated with leaf N content (e.g.
Reich et al., 1998), and that daytime respiration is about
half night respiration, recognizing the role of photosynthesis
in directly supplying ATP and NAD(P)H (e.g. Niinemets
and Tenhunen, 1997 ; Monje and Bugbee, 1998). In all
cases, the assimilate remaining after maintenance respiratory
costs are subtracted is allocated to increment plant parts
and growth respiration is subtracted as a construction cost.
59
These models have three basic weaknesses. First, maintenance respiration is a fixed cost, subtracted as a priority
tax from gross assimilation, as it was in the earliest wholeplant models, illustrated in Fig. 1 A. The problems given by
this approach were identified by de Wit, Brouwer and
Penning de Vries (1970, p. 61) who wrote : ‘ Simulation from
this viewpoint leads to inconsistent results. If it is assumed
that the respiration per unit plant material is low, it appears
that yield levels which are observed in the field may be
obtained, but then simulated respiration rates under
controlled conditions are far too small. If it is assumed that
the respiration rate per unit plant material is higher,
simulated respiration rates under controlled conditions may
be in the observed range, but then simulated ceiling yields in
the field are far too small ’. The unsatisfactory nature of the
fixed-cost assumption was recognized by Thornley (1971),
who discussed the possible substrate dependences of growth,
maintenance and wastage processes, and the potential to
separate them. This difficulty also led to the model
formulation in Fig. 1 C, which allows variable maintenance
respiration.
Second, maintenance rate coefficients are fixed and are
unrelated to C substrate supply, so that respiration is not
explicitly coupled to photosynthesis. If the rate of an
energy-requiring process is not linked to energy, so that it
can occur even if no energy is available, carbohydrate
concentrations can be driven negative, leading to nonsense
results. There is basically no control on maintenance
respiration, and the only way of preventing respiration from
overwhelming the C budget is to choose rate coefficients
(normally C cost per unit tissue N) which give a satisfactory
result—if that can be decided (see above quotation from De
Wit et al., 1970). Also, a single C cost per unit N makes no
allowance for the fact that substrate N (amino acids,
nitrate), protein N, or other forms of organic N, are likely
to incur different costs.
Third, grouping together many components of respiration
as maintenance, with a single rate coefficient, makes the
models particularly sensitive to the choice of rate coefficients.
The literature offers a wide range of possible coefficients (see
Cannell and Thornley, 2000).
The consequence is that the C cost of maintenance
respiration estimates of different models are highly variable.
This dramatically affects their estimates of net primary production and, when respiration is scaled according to tissue
N content, magnifies errors in the uncertain treatment of N
uptake and allocation (Ryan et al., 1996). Unreliable and
unrealistic predictions can result, undermining the often
precise treatment of photosynthesis.
Models which separate substrate from structure
The first comprehensive ecosystem model which separated
C and N substrates from structure was the Hurley Pasture
Model (HPM, Thornley and Verberne, 1989), described by
Thornley (1998) and developed by Riedo et al. (1998). The
equivalent forest model is the Edinburgh Forest Model
(EFM, Thornley, 1991 ; Thornley and Cannell, 1996).
Below, we describe how respiration is represented in the
latest versions of the HPM and EFM (Appendix, Figs A 1
60
Thornley and Cannell—Modelling the Components of Plant Respiration
and A 2). In both models, the transport-resistance mechanism of Thornley (1972) is employed to move C and N
substrates to each plant part, where their concentrations are
known and are used to calculate local growth and other
respiratory activities. Total plant respiration, R, is given by :
R l RG,ljRphloemjRNamm,uptjRNnit,uptjRNnit,red,rt
(9)
jRNnit,red,shjRNfixjRmin,uptj Rresidual
The summations refer to the tissue categories represented in
the model (shoot and root in the HPM ; foliage, branches,
stem, coarse roots and fine rootsjmycorrhiza in the EFM).
RG,l is local growth respiration. Rphloem is respiration
associated with phloem loading. RNamm,upt and RNnit,upt are
the respiratory fluxes associated with uptake of ammonia N
and nitrate N from the soil solution. Nitrate reduction can
be carried out in the shoot (RNnit,red,sh) and\or in the root
(RNnit,red,rt). RNfix is the total symbiotic N fixation costs
#
(where appropriate). Rmin,upt is respiration associated with
the uptake of minerals (other than N). Finally, Rresidual is a
‘ catch-all ’ category which includes, in addition to protein
turnover, uncertain items such as the maintenance of cell
ion gradients, any energy wasting or ‘ safety-valve ’ processes
such as alternative pathway respiration and futile (or
metabolic) cycles, and components of respiration such as
damage repair which are not included in this analysis.
Local growth respiration rate. RG,l is calculated for each
plant part using :
RG,l l
1kYG
G(C, N )
YG
(10)
where YG is the growth yield [as in eqn. (1)], and G(C, N ) is the
gross growth rate of plant tissue (units of C in plant tissue
per day), whose value depends on the local substrate C and
N concentrations, denoted by C and N, the mass of the
tissue (M ) and a growth constant (kG). At present YG is given
a single high value of 0n8 for all tissues (Thornley and
Johnson, 1990, p. 353) because (1) some growth costs
appear in other terms of eqn (9) (e.g. mineral uptake, N
uptake, NO − reduction, phloem loading ; cf. Poorter and
$
Villar, 1997, whose values are rather lower), (2) the HPM
and EFM models are vegetative only (vegetative tissues are
generally inexpensive), and (3) growth, whether occurring in
foliage, stem or root, leads first to young tissue, with,
arguably, similar energy requirements ; the processes of
differentiation and ageing may lead to tissues in foliage,
stem and roots which become different in chemical composition and energy costs, if they were synthesized directly,
which they are not.
Phloem loading respiration rate. Rphloem is given by :
Rphloem l cphloem OCS,sh4rt
(11)
where cphloem l 0n06 units C respired per unit C substrate
(e.g. sucrose) loaded into the phloem. This value is derived
from Bouma (1995), who gives a figure of 0n7 mol CO per
#
mol sucrose (0n06 l 0n7\12 for C H O ). OCS,sh4rt is the
"# ## ""
output flux from the shoot C substrate pool in the direction
of the root.
Ammonium uptake respiration rate. RNamm,upt, is given by :
RNamm,upt l cNamm,upt uNamm
(12)
where cNamm,upt l 0n17 kg C substrate respired per kg
ammonium N taken up. uNamm is the uptake rate of
ammonium N (kg N d−"). This uptake cost coefficient of
0n17 is half the value for nitrate uptake (see Cannell and
Thornley, 2000, and below).
Nitrate uptake respiration rate. RNnit,upt is given by :
RNnit,upt l cNnit,upt uNnit
(13)
where cNnit,upt l 0n34 kg C substrate respired per kg nitrate
N taken up. uNnit is the uptake rate of nitrate N (kg N d−").
The uptake cost coefficient of 0n34 assumes one NO −
$
requires 2H+ is equivalent to 2 ATP ; 1 C is equivalent to
5 ATP (C H O j6 O l 6 CO j6 H Oj30 ATP) ; 1 kg
' "# '
#
#
#
nitrate N requires (2 mole ATP\mole N)\(5 mole ATP\mole
C)i(12 kg C substrate\mole C)\(14 kg N\mole N) l
2\5i12\14 l 0n34 (Bouma, Broekhuysen and Veen, 1996).
Nitrate reduction-linked respiration. This occurs in the
root and shoot, RNnit,red,rt, RNnit,red,sh. It is assumed that
ammonium N, once taken up, is available for plant
metabolism without further respiratory costs, but that
nitrate N must be reduced to the ammonium level (assumed
to be equivalent to the plant amino acids). Nitrate reduction
in the shoot may require less energy and reducing power
than that in the root, because of the energy and reducing
power generated by photosynthesis. The two components of
nitrate reduction respiration are modelled in units of kg C
respired d−" as :
RNnit,red,rt l cNnit,red fuNnit,red,rt uNnit
RNnit,red,sh l fNnit,red,sh,CS cNnit,red fuNnit,red,sh uNnit
(14)
fuNnit,red,rtjfuNit,red,sh l 1
In this equation, the cost of nitrate reduction is cNnit,red l
1n7 kg substrate C (kg nitrate N)−". This is based simply on :
HNO j8 H l NH j3 H O and C H O j6 H O l
$
$
#
' "# '
#
6 CO j24 H. Thus 1 kg NO − N requires 8\14i(6i12)\24
#
$
l 1n71 kg substrate C. This number is comparable with
experimental estimates (e.g. cowpea ; Sasakawa and La Rue,
1986). fuNnit,red,rt and fuNnit,red,sh are the fractions of the
nitrate flux taken up (uNnit, kg nitrate N d−") which are
reduced in the root or in the shoot. These are both assumed
to be constant at 0n5, although in reality they should be
variables depending on environment and plant status. Also,
fNnit,red,sh,CS l 0n5 is taken to be the fraction of nitrate
reduced in the shoot using C substrate, rather than using
excess ATP and reducing power obtained directly from
photosynthesis.
N -fixation respiration. RNfix is given by :
#
RNfix l cNfix INfix,NSrt
(15)
where cNfix l 6 kg substrate C respired (kg N fixed)−" and
INfix,NSrt is the flux of fixed N into the root substrate N pool
(kg fixed N d−"). cNfix is the total respiratory cost of N
fixation by any leguminous component of the plant system,
including nodule growth and maintenance. Estimates of
61
cNfix are variable (depending on host species, bacterial
strain, plant development, plant age) but lie mostly in the
range 5 to 12 (same units) (see Marschner, 1997, p. 211).
The flux INfix,NSrt depends on root mass, root C and N
substrate status, and a temperature and water-status
dependent rate parameter which can be set to zero for plants
without symbiotic N fixation. The computation of INfix,NSrt
is similar to that of non-symbiotic N fixation in the soil (e.g.
see equation 5.4c, p. 92, of Thornley, 1998).
Mineral ion uptake-linked respiration. Rmin,upt takes account of minerals other than nitrogen. The uptake rate of
mineral ions into the plant, umin,pl (kg minerals d−"), is
calculated from the gross plant structural growth rate for
the plant and the ash content (0n05 kg minerals, excluding
N, per kg structural dry mass), less a fraction (0n5) of the
minerals in the litter fluxes which is internally recycled. The
respiratory flux is a drain on the root C substrate pool, given
by (kg C d−") :
Rmin,upt l cmin,upt umin,pl
(16)
The cost coefficient, cmin,upt, is assumed to have the value of
0n06 kg substrate C (kg ash)−". This value is based on eqn
12n21 g, slightly modified, of Thornley and Johnson (1990,
p. 349), where minerals are assumed to have an average
relative molecular mass (RMM) of 40 g mole−", the cost of
uptake and within-plant transport is 1 ATP per ion,
1 glucose with 6 C atoms of RMM l 12 gives 30 ATP.
Therefore 1 kg minerals requires 1\40i6\30i12 l 0n06 kg
substrate C.
‘ Residual maintenance ’ respiration. Rresidual is associated
with processes such as protein turnover, maintaining cell ion
gradients, futile cycles, and any use of the alternative
pathway of respiration (Cannell and Thornley, 2000). It is a
catch-all for contributions which have not been explicitly
recognized above and as yet unidentified processes. Mostly,
we regard this residual as fulfilling a ‘ maintenance ’ function.
Here we calculate it for each plant part as a function of the
weighted N components of biomass (MN,i) multiplied by a
maintenance coefficient (km), which is assumed to have a
Michaelis–Menten type of dependence on the local C
substrate concentration (C ) :
Rresidual l km,max
C
(f M jf M
KmjC NX NX NM NM
jfNS MNSjfNph MNph) (17)
Here, the dimensionless f factors can be varied, usually
between 0 and 1, to weight the different components of N
(default values : all 1). In order, the components of N are :
structural N, meristematic (structural) N, substrate N, and
photosynthetic N. The pasture model (HPM) does not
represent meristems. Photosynthetic N is only present in
leaves. This feature of the model enables C substrate
utilization for leaf residual maintenance respiration to be
adjusted to lower values in leaves than expected from their
N concentration (Cannell and Thornley, 2000). It is also, of
course, possible to choose different sets of f factors for
different plant parts, although this has not so far been
considered necessary in the HPM and EFM. Although eqn
Rate of utilizaton of C substrate
[kg C substrate (kg structural mass)–1 d–1]
Thornley and Cannell—Modelling the Components of Plant Respiration
0·4
kmax = 0·5
0·3
kmax = 0·25
Km = 0·01
0·2
Km = 0·2
0·1
0·0
0·0
0·1
0·2
0·3
0·4
C substrate concentration
–1
[kg C (kg structural mass) ]
0·5
F. 3. Illustration of competing processes of substrate utilization
represented by Michaelis–Menten equations used to give C substrate
dependence to residual maintenance respiration. The equation for the
responses is : C utilization l km,max (C\KmjC), where C is substrate
concentration, km,max is the maximum rate and Km is the Michaelis–
Menten constant (C substrate concentration at half the value of
km,max). The broken line, with a low Km, illustrates a reaction with a
higher affinity for substrate than the unbroken line, so that there is
priority use of substrates at low substrate concentrations. See text for
details.
(17) is N-based, we have not encountered problems using a
total dry mass or an area representation of maintenance
respiration, with pragmatically chosen coefficients and a
substrate-dependent turn-down mechanism.
km,max [kg substrate C (kg N)−" d−"] is the maximum value
of the maintenance constant when C is much greater than
Km, the Michaelis–Menten constant (C substrate concentration at half the value of km,max). Km has the same units as
the C substrate concentration, C, namely kg substrate C (kg
structural mass)−". The term C\(KmjC ) is a ‘ residual
maintenance reduction factor ’. The Michaelis–Menten factor in eqn (17) provides a ‘ turn-down ’ mechanism for
residual maintenance respiration, which is an essential
feature in the HPM, EFM and the model of Riedo et al.
(1998). Figure 3 illustrates two extreme examples of the
turn-down factor in operation. The broken line shows that,
when Km is small, substrates are utilized for respiration at
near the maximum rate (km,max) down to low substrate
concentrations, giving maintenance respiration a high
priority for substrates (i.e. a high substrate affinity). The
unbroken line shows that larger values of Km allow substrate
utilization to fall more gradually below its maximum rate as
substrate concentrations decrease, giving respiration a lower
priority for substrates when they are scarce. A high
maximum rate (km,max) means that substrate utilization is
high when substrate concentrations are high, despite a high
value of Km.
In the EFM and the HPM, residual maintenance respiration is calculated with the f factors of eqn (17) equal to unity,
and km,max (20 mC) l 0n1 (EFM), 0n3 (HPM) kg substrate C
(kg N)−" d−" and Km l 0n05 (EFM), 0n02 (HPM) kg substrate
C (kg structural mass)−". Note that the forest model uses a
lower value of the rate constant (km,max) and, for a given
substrate C concentration, a greater turn-down is achieved
62
Thornley and Cannell—Modelling the Components of Plant Respiration
by a higher value of Km (EFM). However, the most
important competing process is growth, which is differently
handled in the two models, using meristem activity in the
EFM, in contrast to a more aggregated growth parameter in
the HPM. The need for these residual maintenance
parameter differences in order to obtain satisfactory
outcomes is therefore not unexpected.
A strength of this approach is that it gives this large
component of respiration substrate dependence, thereby
coupling it to photosynthesis and also preventing numerical
failure due to substrate levels falling below zero. Values of
km,max (when respiration is not substrate limited) could be
assumed to be similar to measured rates of ‘ maintenance ’
respiration, but the values of km,max and Km are adjusted
together, pragmatically, to obtain acceptable values of
growth of dry mass and leaf area, respiration (in relation to
photosynthesis), net production, and C substrate values.
A weakness of the approach is that there are no measured
values of km,max and Km, although measurements of
components of maintenance respiration at this level of
sophistication are surely required. The values of these two
important conceptual parameters have to be chosen arbitrarily and adjusted until the model predicts acceptable
outcomes, as outlined in the previous paragraph.
RESPIRATION WITHIN THE HURLEY
PASTURE AND EDINBURGH FOREST
MODELS
The respiration components described above are embedded
within comprehensive models describing the flows of C, N
and water, with a sub-daily timestep (approx. 20 min),
within grazed grasslands in the Hurley Pasture Model
(HPM) and a plantation conifer forest, which is periodically
thinned and felled at age 60, in the Edinburgh Forest Model
(EFM). In both cases, the plant submodels are fully coupled
with the soil and water submodels. Flow diagrams for the
plant submodels, showing the location of the respiratory
fluxes, are given in the Appendix.
The purpose here is not to simulate observed respiration
rates, but to illustrate the predicted behaviour of the
component respiration fluxes, with reference to seasonal
changes in grasslands and changes over a forest rotation.
Model parameterization and enŠironments
The formulation and standard parameterization of the
HPM was fully described by Thornley (1998), and that of
the EFM by Thornley and Cannell (1996). The principal
subsequent changes are in respect of respiration, as described
above, and photosynthetic acclimation (Thornley, 1998), to
which has been added a simpler method of calculating
canopy photosynthesis.
The HPM was run in the average climate of southern
England (Hurley) simulating an unfertilized perennial
ryegrass pasture continuously grazed to a constant leaf area
index (LAI) of about 2. The EFM was run in the average
climate of southern Scotland (Eskdalemuir), simulating an
unfertilized, even-aged stand of Sitka spruce, thinned at
intervals and clear felled after 60 years. Initial values for the
simulations were equilibrium values obtained by applying
the average climate at the site for thousands of years.
Grassland and forest growth patterns
Both models predicted plant mass and leaf area index
(LAI) values within observed ranges. The grassland LAI
increased to about 2 in spring, but was then limited in
the model by grazing. Grass biomass increased to 1n0–
1n2 kg m−# in summer, peaking about a month later than
LAI (Fig. 4 A). The conifer forest plantation increased in
biomass to 6 kg m−# around the time of canopy closure at
about age 15 and to 23 kg m−# at the time of clearfelling,
equivalent to a ‘ yield class ’ of about 15 m$ ha$ y−" (final
stem volume divided by 60 years, including thinnings).
Forest LAI was restricted to 6–7 by light thinning every
5 years (giving the saw-tooth effect in Fig. 4 F).
Canopy photosynthesis and total plant respiration
Seasonal changes in grassland canopy photosynthesis
(Pcan) were modulated by temperature and LAI, but most
closely followed the seasonal change in solar radiation,
peaking in June (Fig. 4 B). Total plant respiration (Rpl)
followed a similar trend, so that the ratio Rpl : Pcan varied
within a narrow range of 0n35–0n45, reflecting the coupling
between C substrate supply and all respiratory processes
in the model. However, this ratio was not constant ; it was
smallest in spring and early summer, during the main
growth period, and was greatest in the autumn and winter.
There are several reasons why this occurs. One important
reason is that the inclusion of substrate pools decouples
substrate production from its subsequent utilization in
processes requiring respiration". The introduction of storage
pools gives rise to a lag between input and output, so that
the midsummer peak in canopy photosynthesis (Fig. 4 B)
gives rise to a delayed peak in respiratory outputs. The
representation of more storage pools with possibly slower
turnover times would accentuate this process. Note that the
age representation of tissue, with possible remobilization of
carbohydrates from senescing tissue, functions as a very
slow storage pool, giving a long time lag between the
vigorous growth in spring and early summer, and when that
now senescing material can provide a source of carbohydrate. The storage-pool induced lags occur in addition to
a lag which occurs because seasonal radiation which drives
photosynthesis leads seasonal temperature (Thornley, 1998,
p. 142), which is more important to respiration than to
photosynthesis. A further effect arises because the growth
component of respiration is somewhat suppressed by the
failure of mineralization rate to keep pace with plant growth
requirements ; we remember that growth and growth
respiration depend on both C and N substrates [eqn (10)]
whereas many other components of respiration are
" It may be noted that including substrate pools allows R : P to vary
because respiration R is decoupled from photosynthesis P, whereas in
the ‘ toy ’ models R : P varies because maintenance respiration depends
on dry mass which is a result of integrated photosynthesis.
63
Thornley and Cannell—Modelling the Components of Plant Respiration
0.9
1.9
0·8
1.8
Mpl
0·6
1.7
d
0·016
B
Rpl/Pcan
Pcan
0·012
0·47
0·44
0·008
0·41
Rpl
0·004
0·38
0·000
0·35
–2
0·0025
d
0·0020
0·0015
ΣRG,i
0·0010
Rphloem
5
0
0
kg C m
1·6
–2
y
–1
Rtree/Pcan
G
0·41
0·38
Pcan
Rtree
0·4
0·35
0·32
–2
y
–1
ΣRresidual
H
0·24
0·18
ΣRG,i
0·12
Rphloem
d
–1
kg C m
0·0200
D
Respiratory flux
Respiratory flux
RNmin,upt
–2
y
–1
I
RNmin,upt
0·0150
0·0100
Rmin,upt
0·0050
Rmin,upt
0·6
0·5
0·4
0·015
0·3
0·010
0·005
0
1 Jan
0·2
0·1
CS,pl
73
146
219
Time, t (d)
292
0·0
365
31 Dec
Tree C substrate concn, CS,tree
–1
kg C substrate (kg structural DM)
CS,pl
(CS,pl + K )
E
0·020
0·0000
Residual maintenance
respiration turn-down factor
Plant C substrate concn, CS,pl
–1
kg C substrate (kg structural DM)
RNnit,red
RNnit,red
0·0000
0·03
0·4
J
CS,tree
0·3
0·02
CS,tree
(CS,tree + K)
0·01
0
10
20
30
40
50
0·2
0·1
0·0
60
Residual maintenance
respiration turn-down factor
–2
RNfix
0·025
0·44
1·2
0·8
10
0·00
0·0000
0·0001
Tree dry mass
2
0·06
0·0005
kg C m
15
4
kg C m
0·30
ΣRresidual
C
20
LAI
6
0·0
–1
Respiratory flux
kg C m
–2
–2
2
–1
Gross photosynthesis, Pcan
Tree respiration, Rtree
–2
Ratio: Rpl/Pcan
Gross photosynthesis, Pcan
Plant respiration, Rpl
kg C m
Respiratory flux
0·7
25
F
Tree dry mass (kg m )
1.0
8
Ratio: Rtree/Pcan
2.0
Leaf area index, LAI (m m )
1.1
–2
LAI
A
Plant dry mass, Mpl (kg m )
EFM
1.2
2
–2
Leaf area index, LAI (m m )
HPM
2.1
Years
F. 4. Predictions of the Hurley Pasture and Edinburgh Forest Models (HPM, EFM) using standard parameterizations in environments
simulating that in the English lowlands and Scottish uplands, respectively. Both models are in equilibrium. The HPM is simulated over 1 year ;
the EFM over a rotation of 60 years. Leaf area index and total plant mass (A, F) ; canopy gross photosynthesis, plant respiration, and their ratio
(B, G) ; growth respiration (RG,l), residual maintenance respiration (Rresidual), and phloem loading respiration (Rphloem) (C, H) ; respiration
associated with mineral N uptake, uptake of other minerals, nitrate reduction, N fixation (HPM only) (D, I) ; mean substrate C concentration
in the plant and the ‘ pragmatically ’ adjusted residual respiration turn-down factor [eqn (17) ; Fig. 3] (E, J).
dependent on C substrate alone (Fig. 4 C). There is a marked
depression in midsummer N substrate levels in the plant
which mirrors inversely the C substrate seasonal dependence
shown in Fig. 4 E but with a time lag. The seasonally
changing levels of the substrate pools, which, because they
are small pools with high turnover, can vary quite subtly,
are important in driving respiration in total and its various
components.
Annual canopy photosynthesis during a forest rotation
was determined mainly by light interception, and so rose to
a maximum (1n0–1n2 kg C m−# y−") when LAI exceeded
about 4 and then remained quite constant. Total tree
64
Thornley and Cannell—Modelling the Components of Plant Respiration
respiration (Rtree) followed a similar trend (Fig. 4 G). The
ratio Rtree : Pcan varied within the same range as grassland
(0n35–0n45), and like the grassland was smallest when the
forest was growing fastest—in this case during the first 10
years after planting. Note that the ratio remained in the
range 0n40–0n42 after canopy development despite a large
increase in forest biomass—again reflecting the coupling
between photosynthesis and respiration in the model. It is
noteworthy that canopy photosynthesis increased after each
thinning, despite a decrease in LAI, because of decreased
transpiration, decreased water stress and stomatal closure,
increased litter input to the soil and N mineralization,
improving N nutrition which increased light-saturated
photosynthesis. Total tree respiration was less affected by
thinning (Fig. 4 G), owing to opposing trends in local
growth (RG,l) and residual maintenance respiration (Rresidual,
Fig. 4 H), so that Rtree : Pcan decreased after each thinning and
then recovered, giving the saw-tooth effect in Fig. 4 G.
IndiŠidual respiration processes
In the grassland model, the fractions of total annual plant
respiration in the different categories (ignoring N fixation)
were about 0n46 residual maintenance, 0n42 local growth,
0n10 phloem loading (Rphloem), 0n01 N uptake (RNmin,upt) and
0n01 for other mineral ion uptake plus N reduction (Rmin,upt,
RNnit,red) (Fig. 4 C and D). These fractions were very similar
for the forest, averaged over the rotation, namely 0n48
residual maintenance, 0n36 local growth, 0n12 phloem
loading, 0n03 N uptake and 0n01 for other mineral ion
uptake plus N reduction (Fig. 4 H and I). Thus, accounting
for individual respiration processes reduced the fraction of
‘ maintenance ’ (i.e. all non-growth) respiration from 0n58–
0n64 to a ‘ residual maintenance ’ fraction of 0n46–0n48,
largely due to the representation of respiration associated
with phloem loading.
Clearly, the energy required for N and other mineral ion
uptake was very small compared to that needed for growth
and residual maintenance functions. Also, little energy was
required for nitrate reduction, because most N was taken
from the soil as ammonium rather than as nitrate. Other
simulations showed that changing the ammonium\nitrate
ratio in the soil had little effect on the system C budget. In
the grassland, mineral-uptake linked respiration was actually zero for much of the season, because sufficient
minerals were obtained from senescing tissue.
As expected, the proportions of total respiration attributable to the different processes changed during the year
in grassland and during the forest rotation. In grassland,
growth and phloem loading respiration peaked earlier in the
year than residual maintenance respiration (Fig. 4 C). Also,
mineral uptake respiration peaked early (with subsequent
retranslocation) and N fixation respiration peaked later
than N uptake respiration (Fig. 4 D). Similarly, in the forest,
growth and phloem loading respiration rose towards their
maximum values earlier in the rotation than residual
maintenance respiration (Fig. 4 H) and respiration associated with N uptake increased throughout the rotation while
that associated with mineral uptake did not (Fig. 4 I).
Residual maintenance turn-down factor
The concentration of C substrates in grass varied almost
ten-fold from low values in winter to high values in summer
(CS,pl, Fig. 4 E). The maximum residual maintenance
respiration rate was modulated accordingly, with the turndown factor varying from about 0n1 in winter to 0n5 in
midsummer (Fig. 4 E). In the forest, the C substrate
concentration was greatest during the period of rapid
growth before canopy closure, when the annual mean turndown factor was about 0n35, compared with 0n20–0n25 for
the rest of the rotation (Fig. 4 J).
DISCUSSION
The simple growth-maintenance respiration paradigm provides a useful approximate view of plant respiration which
has endured for 30 years. However, it is limited. This was
illustrated here by the fact that, in whole-plant ‘ toy ’ models,
similar predictions could be made of plant growth and
respiration with three completely different interpretations of
the growth-maintenance paradigm (Figs 1 and 2). When the
paradigm is used within more comprehensive plant models
which do not separate C and N substrates from structure,
unreliable and unrealistic predictions can be obtained. This
occurs because maintenance respiration is subtracted as a
fixed cost, is unrelated to assimilate supply and is scaled by
unvarying coefficients per unit tissue N content, mass,
volume or surface area, which have to be chosen
pragmatically from a wide range of possible values in the
literature. Consequently, maintenance respiration is not
coupled to photosynthesis nor to the varying rates of
energy-requiring processes and so cannot be expected to
reliably simulate changes in respiration occurring over
seasons or the lifetime of a forest.
By separating C and N substrates from structure, the
Hurley Pasture and Edinburgh Forest Models make it
possible to follow most of the principles identified in the first
paper (Cannell and Thornley, 2000) and offer greater
realism. Maintenance respiration rates can be related to C
substrate supply as well as tissue N content. It is possible to
separate some of the components of maintenance respiration, which can vary independently, while maintaining
the observed coupling between total plant photosynthesis
and respiration.
By representing component processes, the models can be
connected to reality at many points, give more information,
can be examined at the level of assumptions as well as at the
level of predictions and are open to modification as more
knowledge accumulates. However, even when the quantifiable components of maintenance respiration are accounted
for, a large ‘ residual maintenance ’ term remains, and this
term has to be tuned pragmatically to give dependence on
C substrate supply (Fig. 3). In order to give realistic
behaviour—preventing excessive respiration—this turndown factor rises (giving less turn-down) with increasing C
substrate concentration to 0n5 during the summer in grassland and varies from annual means of about 0n1 to 0n3 over a
forest rotation (Fig. 4 E and J). The need for such large
Thornley and Cannell—Modelling the Components of Plant Respiration
variation in this turn-down factor underlines the need to
couple maintenance respiration to C substrate supply in a
dynamic way. There is, however, no escaping the fact that
this coupling has to be achieved by tuning parameters which
are not yet measurable, and some may regard this as less
acceptable than choosing maintenance rate coefficients from
the range of measured values. At some level, pragmatism
is inescapable : in our view, the coupling of respiration to
substrate concentrations in the HPM and EFM, like the
transport-resistance approach to C and N allocation, offers
greater realism than choosing fixed coefficients.
Respiration measurements are notoriously difficult, and
for present purposes they are usually incomplete or
inadequate. If we are to proceed beyond description towards
understanding, then it seems essential that measurements of
respiratory fluxes are accompanied by measurements of
other processes (fluxes), and of the status of the tissue being
investigated (e.g. nutrient status, sugar concentration, N
content and categories).
It would be valuable to have more detailed measurements
of the turnover rates of specific proteins in different tissues
of various ages, of the operation of futile cycles and different
metabolic pathways, and studies of the existence and
importance of ion gradients within and between cells. Just
as plant models which ignore shoot : root partitioning are
of very limited value because of the great plasticity of the
plant’s responses, so respiratory submodels which ignore
substrates and the categorization of plant mass into e.g.
structure, storage, and recyclable\degradable components,
seem to have a limited future. Experimentalists and
modellers may have to accept and work with a degree of
complexity which, however unwelcome, cannot be wished
away, or usefully simplified.
A C K N O W L E D G E M E N TS
This work has been supported by the European Union
MEGARICH project. We thank an anonymous referee for
suggesting many improvements to the original manuscript.
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of growth and maintenance respiration in stems of Norway spruce
trees. Tree Physiology 18 : 155–166.
Thornley JHM. 1970. Respiration, growth and maintenance in plants.
Nature 227 : 304–305.
Thornley JHM. 1971. Energy respiration and growth in plants. Annals
of Botany 35 : 721–728.
66
Thornley and Cannell—Modelling the Components of Plant Respiration
Thornley, JHM. 1972. A balanced quantitative model for root : shoot
ratios in vegetative plants. Annals of Botany 36 : 431–441.
Thornley JHM. 1977. Growth, maintenance and respiration : a reinterpretation. Annals of Botany 41 : 1191–1203.
Thornley JHM. 1991. A transport-resistance model of forest growth
and partitioning. Annals of Botany 68 : 211–226.
Thornley JHM. 1998. Grassland dynamics. Wallingford : CAB
International.
APPENDIX
Equations for the simple plant growth models using the
different respiration schemes of Fig. 1
In order to make the schemes of Fig. 1 into dynamic growth
models, an equation is needed to calculate the rate of supply
of substrate, P, from the state variables. For a small plant,
this rate must be proportional to plant size giving
autocatalytic growth. When the plant is large, self-shading
will asymptotically limit P. The same basic negative
exponential equation is used for all three models, except
that for Model C, P is also proportional to degradable
(protein) content. The parameter Mss defines the onset of
self-shading.
Model A. Maintenance respiration has priority (Fig. 1 A).
The equations for plant dry mass growth are :
Thornley JHM, Cannell MGR. 1996. Forest responses to elevated [CO ],
#
temperature and nitrogen supply, including water dynamics :
model-generated hypotheses compared with observations. Plant,
Cell and EnŠironment 19 : 1131–1138.
Thornley JHM, Johnson IR. 1990. Plant and crop modelling. Oxford :
Oxford University Press.
Thornley JHM, Verberne ELJ. 1989. A model of nitrogen flows in
grassland. Plant, Cell and EnŠironment 12 : 863–886.
dM
l YG(Pkkm M )kks M
dt
P l kP Mss(1ke−M/Mss)
(A 1)
YG l 0n75, km l 0n02 d−", ks l 0n04 d−"
kP l 0n2 d−", Mss l 1 kg DM, M(t l 0 d) l 0n01 kg DM
Model B. Growth respiration has priority (Fig. 1 B). The
differential equation for plant dry mass growth is :
dM
l YG Pk(kmjks) M
dt
(A 2)
The equation for substrate supply rate P, and all parameters
and the initial value are as in eqn (A 1).
Plant Submodel (Hurley Pasture Model)
Harvesting
Removal of shoot structure and substrates
Animal grazing
Animal submodel
SHOOT
Lamina area
Lamina mass
Sheath + stem mass
Four age categories:
i=1
2
3
4
Senescence
Soil
Grazing/degradation by other fauna
and litter
Senescence
submodel
Photosynthesis
Light
Recycling of C and N
Shoot C
substrate
Photosynthetic
N
Shoot N
substrate
Growth
CO2
CO2
Residual
maintenance
respiration
Transport
Respiration:
loading,
nitrate
reduction
Transport
CO2
Local growth
respiration
Degradation
NH3
absorption/
emission
(atmosphere)
Symbiotic
nitrogen
fixation
Growth
CO2
Respiration:
N uptake,
mineral uptake,
nitrate reduction,
N2 fixation
Root C
substrate
Root N
substrate
Recycling of C and N
N
uptake
Soil
and
Senescence
CO2
Exudation
i=1
2
3
4:
four age categories of
root mass
Root density
ROOT
Senescence
litter
Exudation
Grazing/degradation by other fauna
submodel
F. A 1. The Hurley Pasture Model, plant submodel, showing the flows of carbon and nitrogen and the location of the respiratory fluxes
(Thornley, 1998).
67
Thornley and Cannell—Modelling the Components of Plant Respiration
Tree Submodel (Edinburgh Forest Model)
A
Compartments of tree
Thinning, pruning
Products
Photosynthesis
Litter
Foliage
le
Branches
br
Stem
st
Coarse roots
co
Fine roots,
mycorrhizas
fi
Structure, X
Meristem, M
C substrate, C
N substrate, N
Photosynthetic
N, Nph
Structure, X
Meristem, M
C substrate, C
N substrate, N
Structure, X
Meristem, M
C substrate, C
N substrate, N
Height, h
Diameter, d
Stem number
per m2
Structure, X
Meristem, M
C substrate, C
N substrate, N
Structure, X
Meristem, M
C substrate, C
N substrate, N
Area, A
CO2
Respiration: loading,
nitrate reduction
NH3
absorption/emission
Regeneration
Self-thinning
Foliage and fine roots have four age categories for structure and foliage area
B
Processes for a single compartment (not foliage)
Residual maintenance respiration, CO2
Litter
Structure
X
Growth
Meristem
M
N uptake
Soil mineral nitrogen
NH4+, NO3–
CO2
Respiration:
N uptake,
mineral uptake,
nitrate
reduction
Transport processes
Carbon
substrate, C
Nitrogen
substrate, N
C and N
exudates
Growth
Recycled C and
N to substrate
pools
Growth
CO2, local growth respiration
F. A 2. The Edinburgh Forest Model, tree submodel, showing the flows of carbon and nitrogen and the location of the respiratory fluxes
(Thornley, 1991 ; Thornley and Cannell, 1996).
Model C. Constant fraction (Yd) of growth becomes
degradable (maintainable) mass (Fig. 1 C). This is a twostate variable problem with two pools which allows a
variable degradable (protein) fraction, in comparison with
cases A and B above, which are both single pool problems.
The equations defining the system are :
dMd
l Yd YG(Pjkd Md)kkd Md
dt
dMn
l (1kYd) YG(Pjkd Md)kks Mn
dt
P l kP fd Mss(1ke−M/Mss) ; fd l
Md
MdjMn
(A 3)
Yd l 0n5, YG l 0n75, km l 0n02 d−", kd l ks l 0n05 d−",
kP l 0n5 d−", Mss l 1 kg DM, Md(t l 0 d)
l Mn(t l 0 d) l 0n01 kg DM
Modelling respiration in two plant ecosystem models
The way in which respiration is modelled is shown in Figs
A 1 and A 2. ‘ Residual maintenance respiration ’ is a catchall category, representing components of respiration which
are not explicitly calculated. With the present formulation
[eqn (9)], which does not explicitly model protein recycling
and ion gradient\leakage processes, this residual is identified
principally with maintenance, although it may contain
components associated with aspects of growth, recycling in
general, and wastage.
The current versions of the two ACSL programs (ACSL,
1995) are highly structured and extensively annotated. They
are available by anonymous ftp (username : anonymous ;
password : email address) to budbase.nbu.ac.uk. The HPM
source program is PASTURE.CSL in \pub\tree\Pasture\.
The EFM source program is FOREST.CSL in \pub\tree\
Forest\. These define state variables, input and output
variables and flux calculations, with units.