There continues to be considerable discussion of respiration. This is focused partly on how to handle maintenance respiration (MR) when working within the ‘growth respiration/maintenance respiration paradigm’ (GMRP) (Amthor, 2000
) and partly on the ratio (r
) of respiration (R
) to gross photosynthesis (Pg
) in plant ecosystems, defined as rR:Pg
. There is concern as to whether rR:Pg
is constant or variable. The topic is important in addressing some climate change issues, such as short-
term and long-term contributions of plant ecosystems to carbon (C) sequestration. On one hand are simplifying and perhaps optimistic holists, who would like to assume that rR:Pg
is approximately constant over a range of species and conditions (e.g. Gifford, 2003
). This might permit construction of simple ecosystem models applicable to climate problems. A recent example of this is Van Oijen et al. (2010)
, who, working within GMRP, with some assumptions, demonstrate that a more or less constant value of the ratio is to be expected, partly as a result of conservation of matter (stoichiometry). On the other are reductionists who might also consider themselves as realists. The latter, to which group I mostly adhere, make efforts to understand the detailed mechanisms of respiration which cause rR:Pg
to fall below unity and, possibly, be rather variable (Cannell and Thornley, 2000
; Thornley and Cannell, 2000
). Amthor (2000)
gives an excellent review of plant respiration, supplying a valuable historical perspective and also the current state of the art – there have been no substantive advances in the past decade.
Mainteneance respiration is often considered to be a distinct portion of respiration, but it has long been regarded sceptically. Wohl and James (1942)
, remarked that ‘It is a facile assumption that the energy change revealed by the continuous liberation of heat from mature tissues which are neither doing external work nor synthesizing appreciably, is a measure of the energy of maintenance. The assumption will not stand closer inspection …’.
The construction and analysis of simple models can sometimes be employed to illuminate important problems; this is what is attempted below. A simple model without a maintenance component is described. Solutions are obtained, focusing on two important phases in the growth dynamics: exponential growth and the steady state. The first phase, exponential growth, is transient, but it often lasts sufficiently long to be characterizable, and it is amenable to experimentation. The second phase, the steady state, is important because many plant ecosystems may be approximately in a steady state, although it can be less accessible to experimentation.
We define the specific MR rate (ρm; d−1) as being the specific respiration rate when the growth rate is zero, i.e. when the status quo is maintained. The growth rate can be zero in two cases: when the plant is in the exponential growth (eg) phase but is growing at zero rate; and when the plant is in the steady state (ss) (its mass has reached an asymptote). In both cases, the same expression is obtained for the specific MR rate, depending on three parameters of the model (Fig. ). This permits a re-parameterization of the model, which can, with assumptions, be simplified to a form perhaps more acceptable to the holists.
Fig. 1. Plant growth model for respiration. The two state variables are substrate mass, MCS, and structural mass, MCX. There are four key parameters: YG, growth efficiency – fraction of substrate C utilized for growth which appears in structure – (more ...)
Current understanding of plant respiration was given impetus and direction by the findings of McCree (1970)
, and his famous equation:
is 24 h respiration (kg CO2
is daily gross photosynthesis (kg CO2
is plant mass (kg CO2
is a constant (dimensionless), and c
is has units of d−1
. McCree applied a 12 h light period during a 24 h day. Details of how R
are obtained from the measurements are given by McCree (1970)
, a procedure which could be affected by daylength. McCree's estimate of the parameters was k
= 0·25 and c
= 0·015 d−1
. Dividing through by dry mass W
This equation relates a specific 24 h respiration rate to a specific daily gross photosynthetic rate. The simplicity and intuitiveness of these equations has contributed greatly to the appeal of the GMRP paradigm, with c
being interpreted as a maintenance coefficient.
The situation here may be compared with micro-organisms in a chemostat (Pirt, 1965
), where it is possible, in a true steady state without diurnality, to measure directly the gross rate of supply of substrate, respiration rate and also growth rate. This leads to a similar equation.
The meaning of eqns (1
) and (2
) has been much discussed over the years (Amthor, 2000
). A common interpretation is that respiration is viewed as having two components: one results from growth of the organism [growth respiration (GR)]; the other (MR) is attributed to the organism maintaining its status quo
; Thornley, 1970
Two objections can be raised against GMRP. The first is on scientific grounds: the biochemical and other processes occurring in a growing organism are qualitatively the same as those which occur in an organism which is maintaining the status quo. This especially applies to the metabolic processes which give rise to respiration and yield ATP and reducing power, but also those anabolic processes which are synthesizing compounds which in some cases are replacing compounds that have recently been catabolized. In general, there is not a distinct set of processes which can be said to belong to ‘maintenance’, and another set which belongs to ‘growth’, although catabolic processes (such as protein breakdown) may lead to a growth-associated process (protein synthesis) maintaining the status quo of the plant and giving a respiratory flux which can be dubbed maintenance.
The second objection is a practical matter: many authors have used the paradigm when constructing models of plant growth, crop growth and plant ecosystems. Again and again unacceptable behaviour of the model has occurred, and the maintenance component has to be arbitrarily ‘fixed’. For example, de Wit et al. (1970
, p. 61) remarked ‘Simulation of 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 respiration per unit of 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.’ Loomis (1970
, p. 140, 141) states ‘The McCree equation R
summarizes well certain data … but it would be a mistake to assume it holds a priori
for other situations, …’, and ‘The big difficulty is, of course, in accounting for ‘maintenance’ respiration …’. The impasse is resolved (typically) by making the maintenance coefficient variable, e.g. Seginer (2003)
assumes that the maintenance coefficient depends asymptotically on plant structural mass. Van Oijen et al. (2010)
assume that MR equals GR, an assumption tantamount to jettisoning GMRP in favour of a growth-only respiration model. Others assume that the MR rate coefficient depends on the availability of substrates (e.g. Thornley, 1998
, p. 38), as in the growth process. The problems revolve around issues such as: a common substrate (carbohydrate) is used for both growth and maintenance; priorities (more explicitly, utilization rate constants) have to be assigned between growth and maintenance; and these priorities need to change according to substrate supply and utilization (which determine substrate fraction). There is no straightforward way of dealing with growth and maintenance separately because the pools and anabolic processes are the same for both growth and maintenance. Many modellers do not like to represent substrates because their representation is perceived to be difficult (which it can be), although consideration of the differences between sub-arctic and semi-tropical plant ecosystems, and the diurnality of many plant variables including substrate pools might suggest that their representation is essential for realism.
Here a two-state variable model (structure and substrate; Warren Wilson, 1967
) is described. ‘Substrate’ includes storage (easily remobilizable) components. The model is a simplification and extension of a model proposed some years ago (Thornley, 1977
; see also Loehle, 1982
, who expanded on the 1977 model and provided a reconciliation of it with the more traditional view of respiration). The simplification is that non-degradable structure is omitted so that steady-state solutions can be derived, providing the insights that can be obtained from analytical expressions. The extension is that senescence is included, again so that steady-state solutions can be obtained. The significant processes are photosynthesis, growth with GR, senescence and recycling to the substrate pool. Respiration is an output of the growth process alone. Maintenance is not a feature. The model is simple enough (with three significant constants) to permit a thorough exploration of its properties, for both exponential growth and the steady state. My first objective is to demonstrate that its predictions are reasonably compatible with McCree's equation [our eqn (1
)] (McCree, 1970
), and therefore provides an alternative to the GMRP. My second objective is to define and extract a specific MR rate for a non-growing plant (which can occur in two ways). My last objective is to show that the model gives explicit expressions and acceptable and conservative predictions for the respiration:photosynthesis ratio (rR:Pg
), which for plant ecosystems is often in the range 0·4–0·5. Approximate expressions for the parameters of McCree's equation can be derived in terms of the significant parameters of the current model.