Appendix S2: Growth and maintenance respiration
Autotrophic respiration Ra (Table 2) may be written Ra=Rm+Rg where Rm = plant maintenance respiration
(respiration used to drive anabolic reactions that maintain or replace existing structures and conditions for
cell viability, i.e. to keep existing phytomass in a healthy state) and Rg = plant growth/construction
respiration (respiration used to drive biosynthesis of new phytomass; in seasonal forests Rg=0 outside the
growing season) (Jarvis & Leverenz 1983; Ryan 1991; Amthor 2000; Mäkelä & Valentine 2001; Malhi et
al. 2009; Niinemets & Anten 2009; Landsberg & Sands 2011; Clark et al. 2011). It is a standard assumption
that Rg is a fixed fraction rg of carbon allocated to growth, i.e. net photosynthesis PSNnet where PSNnet=GPPRm (Ryan 1991; Cox 2001; Piao et al. 2010; Clark et al. 2011; reviewed in van Oijen et al. 2010) so
rg 
Rg
PSN net

Rg
GPP  Rm
 1
NPP
GPP  Rm
(i.e. NPP is a fixed 100 * 1  rg  % of PSNnet; in JULES rg is called the “growth respiration coefficient”,
Cox 2001; Clark et al. 2011). The “overhead cost of construction” cB of Mäkelä & Valentine (2001) is
related to rg by c B 
rg
1  rg

Rg
NPP
(i.e. cB g carbon of respiration is required to construct one g of new
material carbon). We can deduce that
 Rg


 Rm   Rm  R g

 1  rg 
NPP GPP  Rm  Rg  rg

CUE 



GPP
GPP
  rg
 Rg


 Rm 
r

 g

where γ=Rg/Rm is the ratio of growth to maintenance respiration, averaged over all parts of the vegetation (so
 

1  CUE  rg   % of R ).
and Rm is a fixed 100 *
a

1  rg 1  CUE 
1  CUE  rg

rg CUE
Robertson et al. (2010) measured stem Rg and Rm in the Kosñipata transect to be Rg,stem=0.000084a+0.269896 and Rm,stem=-0.000076a+0.832344 (where a is site elevation in m asl; both in μmol
CO2/m2s; corresponding to a reduction in Rg,stem/Rstem (=γ/(γ+1)) of ~9% every 1000 m increase in elevation,
compared to ~2% found by Zach et al. 2010 in Ecuador). Assuming that stem CO2 efflux is partitioned in
the same proportions as overall Ra, we can estimate
1
Rg
 
Rm

 0.000084a  0.269896
 0.000076a  0.832344
The elevation at which γ=0 is presumably related to the temperature at which production of new cells and
tissues becomes inhibited in higher plants, suggested by Körner (1998) to be in the 5.5-7.5°C range and may
partly control the treeline in the Andes. It follows that rg may be deduced from the values of γ and CUE:
 1  CUE
  CUE
rg 
JULES assumes rg=0.25 for all plant functional types (Cox 2001; Clark et al. 2011) and other estimates are
similar, e.g. Ryan (1991) who took cB=0.25 and therefore rg=0.20.
Following the derivation described in van Oijen et al. (2010) (and ignoring senescence) we can write
NPP as a sum:
NPP  G  S
where G is growth (production of structural biomass) and S is storage (the rate of increase of the plant
storage pool of labile carbon; S<0 represents remobilisation). Next, define

GPP  Rm  R g  G
S

GPP
GPP
and the ‘growth yield’ or ‘biosynthetic efficiency’ Yg (the amount of structural biomass in g dry mass
formed per g of photosynthate, van Oijen et al. 2010) is
Rg
Yg 
(from R g 
GPP  Rm  Rg  S
rg
G
NPP  S



Rg
G  R g NPP  S  R g
GPP  Rm  S
S
rg
1  Yg
Yg
Yg
1  Yg
1  rg 

1
rg S
Rg
rg S
Rg
G , van Oijen et al. 2010; for alternative definitions of Yg see below; note that this is
analogous to the definition of CUE, i.e. CUE 
G
 Rg  S
NPP
, but concentrating only on structural growth
NPP  Ra
R g ). Therefore:
2
NPP  GPP * CUE  G  S 
Yg R g
1  Yg
 1  Yg
so R g  GPP * CUE  S 
 Y
 g
so
 1  Yg
 CUE   
 Y
GPP
 g
Rg
S








and Ra  Rm  R g so
Rm  GPP  NPP  R g
so
Rg
Rm
 1  CUE  
GPP
GPP
from which we conclude four relationships, all of which can be evaluated given only knowledge of the
values of CUE, Yg and α (see van Oijen et al. 2010):
 1  Yg
 CUE   
 Y
GPP
 g
Rg




and
 1  Yg
Rg
Rm
 1  CUE  
 1  CUE   CUE   
 Y
GPP
GPP
 g

1  CUE Yg  CUE     CUE   Yg
Yg

1  CUE     11  Yg 
and
1 Y
Yg
Rg
Yg
G
CUE    g


GPP 1  Yg GPP 1  Yg
 Yg
and
S

GPP
(n.b.
Rg
GPP





Yg

  CUE  


Rm
G
S


 1). Finally, the same parameters may be used to calculate γ and rg:
GPP GPP GPP
 1  Yg 


Y
CUE   1  Yg 
R g / GPP
rg CUE
 g 

 


Rm / GPP 1  CUE     11  Yg  1  CUE     11  Yg  1  CUE  rg
Yg
CUE   

CUE   1  Yg  

1  CUE 
CUE   1  Yg 
 1  CUE   1  CUE     11  Yg  

and rg 

CUE   1  Yg 
  CUE

CUE   1  Yg  

 CUE
 1  CUE     11  Y  
g 

3
 CUE    1  Yg
(and c B  

 CUE  Yg

 ).


0.30
0
0.25
Early Succession
rg
0.20
0.25
0.15
0.5
0.10
Late Succession
0.05
0.75
0.00
0.0
0.2
0.4
0.6
0.8
1.0
CUE
Fig. A1: The theoretical variation of rg with CUE and for example values of Yg and α (see text for definitions).
Uncertainty in the value of Yg does affect rg (lines show values at Yg=0.75 and grey bands show values for the range
0.7<Yg<0.8), with higher values of Yg giving lower values of rg. The arrow shows the theoretical direction of forest
succession (Landsberg & Sands 2011 suggested that CUE decreases from ≈0.5 in young to ≈0.3 in mature forests, and
this may be combined with an increase in carbon storage from α≈0 in early successional stages to α≈CUE in mature
patches to give rg decreasing from 0.25 to 0). The rg=0.25 estmate of JULES (Cox 2001, Clark et al. 2011) may be
understood as a maximal value for vegetation with negligible storage (high growth), CUE<0.6 and Yg=0.75.
When S is negligible (e.g. in fast-growing vegetation after disturbance where   0 ), we have Yg  1  rg ,
 1  Yg
 CUE
 Y
GPP
 g
Rg
 
CUE 1  Yg 
Yg  CUE


 r
  CUE g

1 r
g


CUErg
1  rg  CUE

,


Yg  CUE 1  rg  CUE
Rm


,
GPP
Yg
1  rg
and rg 
CUE1  Yg 1  CUE 
CUE1  Yg   CUEYg  CUE 
(e.g. in mature vegetation where   CUE ), we have Yg  0 ,
Rg
GPP
G
 CUE ,
GPP
S
 0,
GPP
 1  Yg . When G is negligible
0,
Rm
G
0,
 1  CUE ,
GPP
GPP
S
 CUE ,   0 and rg  0 . Typical values of these quantities should lie between these two extremes,
GPP
e.g. if we assume that Yg=0.75 is a typical value during all growth phases independent of environmental
conditions
1  CUE 
(e.g.
van
Oijen
Rm
0.75  CUE
,

GPP
0.75
et
al.
2010)
0
G
 CUE ,
GPP
then
0
we
should
S
 CUE ,
GPP
expect
0 
0
Rg
GPP

CUE * 0.25
0.25  CUE
CUE
,
3
and
0  rg  0.25 over the course of forest successional cycles (Fig. A1). This analysis shows the crucial
importance of reliable estimates of CUE for the estimation of these important forest dynamical quantities.
4
Finally, note that we are here using the growth yield Yg of van Oijen et al. 2010, but others have
defined growth yield in relation to the increase in overall G+S rather than G alone, e.g. Yg 
'
G
GPP  Rm
 1  Yg ' 
Rg  S  and Rg   ' G   S )
(Amthor 2000, which leads to slightly different relationships G 
'
1  Yg
 Yg

Yg
and Yg 
''
'
NPP
(the “coefficient measuring the efficiency of conversion of assimilate into growth” of
GPP  Rm
''
 Y g ''

1  Yg
G  S  ) and others have
Jarvis & Leverenz 1983, which implies G  
R   S and R g 
''
 1  Y '' g 
Y
g
g


used definitions based on biomass rather than Mg C (e.g. Ryan 1991). However, for Yg’ or Yg’’ to be constant
when Yg is constant requires storage S to be either negligible or close to a constant fraction of G which can
only happen during periods of steady state growth without changes in the overall composition of biomass
(Amthor 2000).
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