Carbon use efficiency depends on growth respiration, maintenance respiration, and relative growth rate. A case study with lettuce

Authors

  • M. W. VAN IERSEL

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    1. Department of Horticulture, The University of Georgia, Athens, GA 30602, USA
      Marc van Iersel. Fax: + 1 706 542 0624; e-mail: mvanier@uga.edu
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Marc van Iersel. Fax: + 1 706 542 0624; e-mail: mvanier@uga.edu

ABSTRACT

Carbon use efficiency (CUE, the ratio between the amount of carbon incorporated into dry matter to the amount of carbon fixed in gross photosynthesis) is an important parameter in estimating growth rate from photosynthesis data or models. It previously has been found to be relatively constant among species and under different environmental conditions. Here it is shown that CUE can be expressed as a function of the relative growth rate (rGR) and the growth (gr) and maintenance respiration coefficients (mr): 1/CUE = 1 + gr + mr/rGR. Net daily carbon gain (Cdg), rGR, and CUE were estimated from whole-plant gas exchange measurements on lettuce (Lactuca sativa L.) ranging from 24 to 66 d old. Carbon use efficiency decreased from 0.6 to 0.2 with increasing dry mass, but there was no correlation between CUE and Cdg. The decrease in CUE with increasing dry mass was correlated with a simultaneous decrease in rGR. From the above equation, gr and mr were estimated to be 0.48 mol mol−1 and 0.039 g glucose g–1 dry matter d−1, respectively. Based on the gr estimate, the theoretical upper limit for CUE of these plants was 0.68. The importance of maintenance respiration in the carbon balance of the plants increased with increasing plant size. Maintenance accounted for 25% of total respiration in small plants and 90% in large plants.

INTRODUCTION

Photosynthesis is the basic process driving plant growth, but obtaining accurate estimates of plant growth from photosynthesis measurements can be difficult. To do so, one needs to know how efficiently carbohydrates are converted into structural dry matter (Amthor 1994). Convenient parameters in this regard are carbon use efficiency (CUE, the ratio between the amount of carbon incorporated into dry matter to the amount of carbon fixed in gross photosynthesis), and the ratio between daily respiration and daily gross photosynthesis (R : P = 1 − CUE). Cannell & Thornley (2000) suggested that CUE varies within a limited range (approximately 0.4–0.6), when averaged over weeks or longer and that mechanistic models should predict limited variation in CUE. This argument is based on reports that the CUE of various species and under different environmental conditions is relatively constant (Gifford 1994, 1995; Ryan, Lavigne & Gower 1996; Goetz & Prince 1998; Monje & Bugbee 1998; Reich et al. 1998a, b; Ziska & Bunce 1998). Probably the most convincing evidence for limited variation in CUE was presented by Gifford (1994), who reported that the CUE of plants was remarkably constant (about 0.6) among seven diverse species, with dry masses ranging over two orders of magnitude. Growing temperature (from 15 to 30 °C) affected CUE only slightly. Using a mechanistic model of short-term carbon dynamics, Dewar, Medlyn & McMurtrie (1998) found that CUE is approximately constant under variable light conditions, when averaged over days to weeks. A sudden change in temperature only has a short-term effect (2–3 d) on CUE (Gifford 1995).

However, others have shown that CUE can vary greatly, either among or within species. For example, Ryan et al. (1997) found that the CUE of pine (Pinus) stands can vary from 0.36 to 0.68. The CUE of wheat is relatively constant throughout much of the life cycle, but decreases rapidly near the end of the life cycle, as photosynthesis declines more rapidly than respiration after anthesis (Monje & Bugbee 1998). Similarly, Winzeler, Hunt & Mason (1976) found large ontogenetic changes in the CUE of barley (Hordeum vulgare L.), which increased early in the life cycle, and decreased again during the second half of the life cycle. Carbon use efficiency of vinca (Catharanthus roseus (L.) G. Don) was negative shortly after transplanting of bare-rooted seedlings, because of a sharp increase in dark respiration, but subsequently increased to 0.7 with increasing plant size and age (van Iersel 1999). Amthor (1989) argued that CUE should decline throughout the vegetative growth phase, because an increasing fraction of total respiration is associated with maintenance, leaving a smaller fraction for growth and growth respiration. Finally, Amthor (2000) showed in a literature review that there are large differences in CUE, both among and within species. Based on the respiratory needs for growth and maintenance, he estimated that CUE, averaged over long periods (i.e. a growing season), may vary from 0.2 to 0.65.

Although there is substantial evidence that changes in CUE are fairly small under some circumstances, it is not clear by which physiological mechanism plants would be able to maintain CUE at a specific level. A constant CUE suggests that plants always respire the same fraction of the carbohydrates fixed in gross photosynthesis (Pg). To get a better understanding of how CUE is determined, it is useful to separate respiration into growth (Rg) and maintenance respiration (Rm) (Cannell & Thornley 2000; see Amthor (2000) for an in-depth discussion of different growth and maintenance respiration paradigms). Growth and maintenance respiration cannot be clearly separated at the biochemical level, because they share certain biochemical pathways [i.e. for the production of ATP and NAD(P)H, Amthor (2000)]. Nonetheless, this concept has proven useful for modelling growth and respiratory processes in plants (Heuvelink 1995; Marcelis & Baan Hofman-Eijer 1995 , Amthor 2000, Thornley & Cannell 2000).

For CUE to remain constant throughout the life cycle of a plant, Rg and/or Rm would have to vary in some specific limited ways in response to changes in Pg. Although growth, and therefore Rg, clearly depends on the amount of carbohydrates fixed in Pg, there has not been a physiological explanation of how plants would maintain their CUE at a certain constant level. Based on the concept of growth and maintenance respiration, a constant CUE throughout plant development appears unlikely. Carbon use efficiency can be defined as:

CUE  =  Cdg/Pg,day(1)

where Cdg is the net daily carbon gain and Pg,day is the total gross photosynthesis of a plant during that same day. Since all carbon either remains in the plant (Cdg) or is respired, and respiration can be separated into Rg and Rm, Eqn 1 can be rewritten as:

CUE  =  Cdg/(Cdg  +  Rt)((2a))
 =  Cdg/(Cdg  +  Rg  +  Rm)((2b))

where Rt is the total daily respiration.

Growth respiration can be calculated as the product of the growth coefficient (gr) and the growth rate, and Rm equals the maintenance coefficient (mr) × plant size (Amthor 2000), where dry mass (Md) is a commonly used measure of plant size. Note that gr and mr do not necessarily have to be constant throughout plant development, although they often are assumed to be (e.g. McCree 1974; Hansen & Jensen 1977). Since Cdg can be used as a measure of the growth rate of a plant, it follows from Eqn 2b that:

CUE  =  Cdg/[Cdg  ×  (1  +  gr)  +  mr  ×  Md](3)

or

1/CUE  =  [Cdg  ×  (1  +  gr)  +  mr  ×  Md]/Cdg((4a))
 =  1  +  gr  +  mr  ×  Md/Cdg((4b))

since Cdg/Md is the relative growth rate [rGR, in moles of C per gram dry matter (DM) per day], this can be further simplified to:

1/CUE  =  1  +  gr  +  mr/rGR(5)

Note that the only assumption used in deriving Eqn 5 is that respiration can be divided into growth and maintenance components. No assumptions are made about which energy-requiring processes are related to growth and which are related to maintenance (see Cannell & Thornley 2000 for a review).

Equation 5 indicates that CUE depends on the ratio of growth rate to plant size (rGR), and thus on the ratio of Rg to Rm. To maintain a constant CUE throughout plant development or under different environmental conditions, either rGR has to be constant (i.e. exponential growth), or gr and/or mr have to change in accord with rGR. Although exponential growth can occur during the seedling stage, when there is no intra- or inter-plant competition for light, rGR decreases as plants get larger (Květ et al. 1971). Since gr and mr should be considered to be variables (Amthor 2000), they may change during plant development. The growth coefficient depends on which chemical compounds are produced (Penning de Vries, Brunsting & van Laar 1974), and therefore may change if the chemical composition of a plant changes during its development. Plant composition also affects mr, because certain plant compounds require little or no maintenance (e.g. lignin, cellulose), and other compounds (e.g. proteins) require a relatively large amount of maintenance (Penning de Vries 1975; Johnson 1990). If the ratio between these compounds changes (e.g. during secondary growth or lignification), mr will be affected as well. Thus, relatively constant CUE during plant development likely results from a decrease in rGR, accompanied by a simultaneous decrease in gr and/or mr.

The objective of this research was to determine how Pg, net photosynthesis (Pn), dark respiration (Rd), Rg, Rm, Cdg, and CUE change throughout plant development, and to determine how changes in CUE are related to these other physiological parameters. Lettuce (Lactuca sativa L.) was chosen as a model crop, because it grows relatively fast, has little lignification, and produces mainly leaves during the vegetative part of its life cycle. Thus, it seems unlikely that there would be large changes in gr and mr during its vegetative growth phase, which makes it an ideal crop to determine possible ontogenic changes in CUE. The hypothesis behind this research was that CUE of plants decreases as rGR decreases, because Rm will become a larger fraction of total respiration, thus reducing the amount of carbohydrates available for growth and Rg.

MATERIALS AND METHODS

Plant material

Seeds of lettuce (Lactuca sativa L.) ‘Grand Rapids’ were seeded in 1.5 L pots (15 cm diameter) filled with diatomaceous earth (Isolite CG-2; Sundine Enterprises, Arvada, CO, USA) every 3 to 5 d for 3 weeks. Seeding was done at six different times to assure that plants of different size and growth rate would be available for CO2 exchange measurements. Plants were drip-irrigated with a fertilizer solution containing nitrogen at 100 mg L−1. The fertilizer solution was made using a commercially available water-soluble fertilizer (Miracle-Gro Excel 15-5-15 Cal-Mag; The Scotts Co, Marysville, OH, USA). Plant density was approximately 15 plants m−2. Air temperature in the greenhouse averaged 25.0 °C, relative humidity averaged 73%, and daily photosynthetic photon flux averaged 10.5 mol m−2 d−1.

Gas exchange measurements

Gas exchange data were collected once a week for 4 weeks, starting 24 d after seeding of the last crop. On each measurement day, six groups of six plants each (one group of six plants from each seeding date) were measured, resulting in a total of 24 crops having ages ranging from 24 to 66 d during the 4 week measurement period. Younger seedlings were not included in the measurement, because of the difficulties associated with obtaining accurate measurements from very small plants. The six groups of six plants were placed in a whole-plant gas exchange system (van Iersel & Bugbee 2000), consisting of eight acrylic chambers (0.32 m × 0.50 m × 0.60 m; w × l × h), placed inside one of two growth chambers. Two empty chambers were used to check and correct for possible zero drift of the differential infra-red gas analyser (IRGA: model LI-6262; Li-Cor Inc., Lincoln, NE, USA). Ambient air, with a CO2 concentration of approximately 370 µmol mol−1, was blown into the gas exchange chambers with a rotary vane blower. The actual CO2 concentration inside the gas exchange chambers depended on the CO2 exchange rate of the plants, and ranged from 280 to 365 µmol mol−1 during the photosynthesis measurements. Although these differences in CO2 concentration may have affected the CO2 exchange rate, these effects probably were small, because the low photosynthetic photon flux (PPF) level during the measurements (200 µmol m−2 s−1) probably was the main factor limiting canopy photosynthesis. For example, Pn of Alstroemeria did not change appreciably with an increase in CO2 concentration from 280 to 365 µmol mol−1, when the PPF level was 200 µmol m−2 s−1, but increased by approximately 25% at a PPF level of 1200 µmol m−2 s−1 (Leonardos et al. 1994).

Flow rate through the chambers (approximately 0.6 L s−1) was measured continuously, and the difference in the CO2 concentration between the incoming and outgoing air of each chamber was measured with an IRGA for 30 s every 10 min. Water vapour was removed from the air before measuring the CO2 concentration by passing the air through a 4 °C condenser. The CO2 exchange rate (µmol s−1) was calculated as the product of mass flow of air through the chambers (mol s−1) and the difference in CO2 concentration between the incoming and outgoing air (µmol mol−1).

To minimize the effects of acclimation on the gas exchange measurements, environmental conditions in the gas exchange chambers were set to mimic greenhouse conditions. Temperature was controlled with resistance heaters mounted in each gas exchange chambers and maintained at 25 °C. Temperature fluctuations were within 0.5 °C of the set point. The PPF at the top of the canopies was 200 ± 5 µmol m−2 s−1, resulting in a total PPF of 10 mol for the entire 14 h photoperiod, similar to the average daily PPF in the greenhouse. Light was provided by a mixture of fluorescent and incandescent lights. During the next 10 h, Rd was measured. Gross photosynthesis (Pg) was calculated as the sum of the average values for Pn and Rd, based on the assumption that the respiration rates (excluding photorespiration) were similar in the light and dark. This assumption also was used to calculate total daily respiration (Rd,day).

After the gas exchange measurements, leaf area (LA) and dry mass (Md, shoots and roots) of the plants were determined. To adjust for differences in plant size, gas exchange rates not only are expressed on a whole plant basis (Pg, Pn, and Rd), but also per unit leaf area or Md (Pg,LA, Pn,LA and Rd,M). Both photosynthesis and respiration data are expressed as positive values, even though they represent CO2 fluxes in opposite directions.

Calculations and data analysis

The gas exchange measurements were used to calculate Cdg(g d−1), which is a direct measure of growth rate:

Cdg  =  (Pn,light  −  Rd,dark)  ×  12(6)

where Pn,light is the total net photosynthesis during the 14 h light period, Rd,dark is the total respiration during the 10 h dark period and 12 is the molecular mass of C.

Carbon use efficiency of the plants was calculated from Eqn 1 (with Cdg in units of mol d−1) and rGR of the plants was calculated as:

rGR  =  Cdg/Md(7)

Note that rGR is expressed in units of g C g−1 DM d−1, and not in the more traditional units of g DM g−1 DM d−1.

Gas exchange data also were used to estimate gr and mr using several different methods. Traditionally, gr and mr often have been estimated from the correlation between the specific respiration rate and rGR (Hesketh, Baker & Duncan 1971; Amthor 1984; Amthor & Cumming 1988 , Wullschleger & Norby 1992):

Rd,day/Md  =  mr  +  gr  ×  rGR(8)

where Rd,day is expressed in grams of glucose per day. Thus, gr is in units of grams of glucose respired per gram of carbon incorporated into plant dry matter and mr is in units of grams of glucose per gram DM per day. Similarly, gr and mr can be estimated directly from Rd,day, growth rate (Cdg) and Md (Amthor 1994):

Rd,day  =  mr  ×  Md  +  gr  ×  Cdg(9)

where gr and mr have the same units as in Eqn 8. Although Eqn 8 can be derived by dividing Eqn 9 by Md, they do not necessarily results in identical estimates of mr and gr, because the division by Md changes the distribution of the data points. One disadvantage of Eqn 9 is the lack of an intercept, which makes the calculation of an R2-value impossible. Finally, gr and mr were estimated from Eqn 5, which results in different units for gr (mol C respired mol−1 C incorporated) and mr (g C respired g−1 DM d−1). Estimates of mr and gr were obtained from Eqns 5, 8, and 9 by regression analysis across plants of different ages. Thus, these methods for estimating gr and mr assume that both are constant throughout plant development. Estimates of gr and mr subsequently were used to estimate Rg and Rm(g glucose d−1) as gr × Cdg and mr × Md, respectively. To determine the importance of Rm in the carbon balance of the plants, Rm as a fraction of total respiration (Rm/Rd,day) was calculated and plotted versus both Md and rGR. The dependence of Rm/Rd,day on rGR can be described as:

Rm/Rd,day  =  Rm/(Rm  +  Rg)  =  mr  ×  Md/(mr  ×  Md  +  gr  ×  Cdg)  =  mr/(mr  +  gr  ×  Cdg/Md)  =  mr/(mr  +  gr  ×  rGR)
 =  1/(1  +  rGR  ×  gr/mr)(10)

Relationships between other parameters of interest were determined using both linear and non-linear regression equations.

To determine whether the different atmospheric CO2 concentrations during the measurements may have affected the main conclusions from this research, its potential effect on the calculated rGR and CUE was estimated. For these calculations, it was assumed that for every 4 µmol mol−1 decrease in atmospheric CO2, Pn was reduced by 1%. This assumption was used to estimate what Pn would have been at an atmospheric CO2 concentration of 365 µmol mol−1, and rGR and CUE were recalculated accordingly. For these calculations, it was assumed that Rd would not have been affected by the higher, recalculated Pn. The assumptions of a strong dependence of Pn on atmospheric CO2 and independence between Pn and Rd, were used because they result in the largest possible effects on rGR and CUE, and thus represent a worst-case scenario.

RESULTS AND DISCUSSION

Gas exchange and plant growth

The response of photosynthesis to increasing leaf area depended greatly on whether it was expressed on a whole plant basis or per unit leaf area. Both Pg and Pn increased asymptotically with increasing leaf area (Fig. 1), presumably because of the asymptotic increase in canopy light interception with increasing leaf area (Monsi & Saeki 1953). In contrast, Pg,LA and Pn,LA decreased linearly with increasing leaf area (Fig. 2). Such a decrease is expected, due to increased intra- and inter-plant competition, which decreases the amount of light intercepted per unit leaf area. Whole-plant Rd also increased with increasing plant size (Fig. 1), whereas Rd,M initially decreased rapidly with an increase in Md from 0 to 5 g, but was similar (0.02 ± 0.005 µmol g−1 s−1) for plants with a Md of 5 g per plant or more (Fig. 2). Such a decrease in specific respiration with increasing mass has been reported previously, for example in barley (Hordeum vulgare L.) (Winzeler et al. 1976).

Figure 1.

Carbon exchange rate of lettuce as a function of plant size. Gross and net photosynthesis are plotted as a function of leaf area, whereas dark respiration is shown as a function of dry mass. All data are expressed on a per plant basis.

Figure 2.

Carbon exchange rate of lettuce as a function of plant size. Gross and net photosynthesis are expressed per unit leaf area, and plotted as a function of leaf area, whereas dark respiration is expressed per unit dry mass, and shown as a function of dry mass.

Daily carbon gain increased sharply as plant mass increased from 0 to approximately 5 g, whereas Cdg tended to decrease for plants with a mass> 5 g (Fig. 3). However, there was a poor correlation between Cdg and mass for plants with a mass> 5 g. The decrease in Cdg with increase in mass (>5 g) was the result of the increased importance of Rm in the carbon balance of the plants (see discussion of Rm/Rd,day below). Relative growth rate decreased exponentially with increasing plant size (Fig. 3). Such a decrease in rGR with increasing plant size is typical, and results from increasing inter- and intra-plant competition for light (Kvǩt et al. 1971).

Figure 3.

Relative growth rate and daily carbon gain of lettuce as function of plant dry mass. Daily carbon gain was calculated from 24 h gas exchange measurements, and relative growth rate was calculated as daily carbon gain divided by dry mass.

Carbon use efficiency, growth respiration and maintenance respiration

Carbon use efficiency of the plants decreased linearly with increasing Md, from 0.5 to 0.6 for small plants (Md of 0–3 g) to 0.2–0.3 for large plants (Md of 10–16 g, Fig. 4). Thus, the fraction of carbohydrates fixed in Pg that was lost through Rd increased with increasing plant size. There was no correlation between CUE and Cdg, whereas 1/CUE was closely correlated with 1/rGR (r = 0.97, Fig. 4). Based on this correlation, gr and mr were estimated to be 0.48 ± 0.08 mol mol−1 and 15.5 ± 0.7 mg C g−1 DM d−1 (estimate ± se) or 39 mg glucose g−1 DM d−1, respectively. A direct conversion of the gr estimate to the conventional units of grams of glucose per gram of new plant material is not possible, because it depends on the carbon content of the plant material. However, plants generally have a carbon content of approximately 0.4 g g−1 (Hadley & Causton 1984) as does glucose, and the value of gr therefore is similar when it is expressed in units of mol mol−1 or g g−1.

Figure 4.

Carbon use efficiency (CUE) as a function of daily carbon gain (Cdg, a measure of growth rate) and plant dry mass. Although there was a highly significant correlation between CUE and dry mass, there was a much better correlation between the inverse of CUE and the inverse of relative growth rate (dry mass divided by Cdg). The Y-intercept of this regression is an estimate of 1 + gr, while the slope of the regression estimates mr. The dashed line shows the estimated correlation between 1/CUE and 1/rGR (1/CUE = 1.44 + 1.24/rGR, r = 0.96), after recalculating the data based on the assumption that every 4 µmol mol−1 decrease in atmospheric CO2 decreased net photosynthesis by 1%.

As it cannot be ruled out that the collected Pn data were affected by differences in atmospheric CO2 concentrations among different groups of plants, the potential effect of atmospheric CO2 on CUE and rGR was estimated as outlined in the materials and methods. These calculations indicate that low CO2 concentrations may have resulted in underestimation of both CUE and rGR. Since both CUE and rGR would have been affected similarly, the basic relationship between these two parameters was only marginally affected by these recalculations (Fig. 4). Recalculated estimates for gr and mr were 0.44 mol mol−1 and 37 mg glucose g−1 DM d−1, respectively.

One of the most common methods to estimate gr and mr is by linear regression of specific respiration versus rGR (Eqn 8, Fig. 5; Chiariello, Mooney & Williams 1989), which resulted in estimates of 1.55 ± 0.15 g glucose g−1 C and 31 ± 5 mg glucose g−1 DM d−1 for gr and mr, respectively (r = 0.91). Assuming a carbon content of 0.4 g g−1, this estimate of gr is equivalent to 0.62 g glucose g−1 DM. Finally, gr and mr also were estimated by modelling them as a function of growth rate and plant size, respectively (Eqn 9), resulting in estimates of 1.00 ± 0.14 g glucose g−1 C incorporated (or 0.40 g glucose g−1 DM, assuming a carbon content of 0.4) for gr and 38.1 ± 1.7 mg glucose g−1 DM d−1 for mr.

Figure 5.

The correlation between the specific respiration rate and relative growth rate of lettuce. The Y-intercept of the regression line is an estimate of mr, while the slope is an estimate of gr.

The different methods for determining gr and mr resulted in different estimates, even though they were based on the same data. Estimates of gr ranged from 0.40 to 0.62 g g−1, while estimates for mr ranged from 31 to 39 mg g−1 d−1. These differences are due to differences in which data points have relatively more effect on the regression results. For example, plants with a high rGR (small plants) have a relatively strong effect on the slope of the regression (gr) of rGR versus specific respiration, whereas plants with a low rGR have a relatively strong effect on the estimate of the slope of the regression of 1/CUE versus 1/rGR (mr). These estimates are all based on the assumption that gr and mr were constant for plants of different size. Although this assumption resulted in a good fit of the data (especially in the case of 1/CUE versus 1/rGR), this does not necessarily mean that gr and mr were indeed constant in this trial. It cannot be ruled out that there were concomitant, and offsetting changes in gr and mr.

Other literature values for gr generally are close to 0.43 g g−1 (McCree 1982; Penning de Vries et al. 1989; Cannell & Thornley 2000; van Iersel & Seymour 2000). Thus, gr estimates from Eqn 5 (0.48 mol mol−1) and 9 (0.40 g glucose g−1 DM) are close to generally accepted values, while the estimate based on Eqn 8 (0.62 g g−1) may be unrealistically high. Literature values for mr are much more variable than those of gr, and generally range from 3 to 50 mg g−1 d−1 (Hesketh, Alberte & Jones 1980). The variability in estimates of mr is at least partly due to changes with plant age and environmental conditions (Walker & Thornley 1977; Mariko & Koizumi 1993). All estimates of mr of lettuce from the current data are well within the normal range.

Growth and maintenance respiration rates were estimated based on the gr and mr-values estimated from Eqn 5 (Fig. 4), since it had the best fit, and resulted in estimates consistent with other literature values. Since mr was assumed to be constant, Rm increased linearly with increasing plant size, whereas Rg increased with increasing plant size from 0 to 3 g, but there was no clear correlation between Rg and plant size for larger plants. Maintenance accounted for only 25% of total respiration in small plants, but for 90% in large plants (Fig. 6). This is consistent with the assertion that CUE should decrease with increasing plant size due to the increased importance of Rm (Amthor 1989). The increasing importance of Rm in the carbon balance of the plants explains the tendency for Cdg to decrease with increasing Md(> 3 g). For plants with a Md of more than 7 g, more carbon was lost in maintenance than was incorporated into the plants (Figs 3 & 6), indicating that the maintenance demand for carbon greatly reduced growth. As expected, Rm accounted for more of the total respiration with decreasing rGR, because rGR is the ratio between Cdg and Md and thus directly related to the ratio between Rg and Rm (Eqn 10; Fig. 6).

Figure 6.

Growth and maintenance respiration of lettuce as a function of dry mass (top). Maintenance as a fraction of total respiration increases with increasing plant dry mass (middle), but decreases with increasing relative growth rate (rGR).

Because gr is a measure of the biochemical efficiency with which plants convert carbohydrates into biomass, it can be used to calculate a theoretical upper limit for CUE (i.e. CUE when Rm accounts for a negligible fraction of the overall carbon balance) as 1/(1 + gr). Using an estimate of 0.48 mol mol−1 for gr of lettuce, this implies that the maximum possible CUE is 0.68 mol mol−1 and the difference between this theoretical maximum and the actual CUE is due to Rm.

Ontogenic changes in gr, mr, and CUE

Ontogenic changes in gr and mr have not been studied in much detail, at least partly because of the difficulty in estimating gr and mr without assuming that they are constant. Since gr depends on the chemical composition of the biomass that is being produced (Penning de Vries et al. 1974), changes in gr during plant development would be expected, especially in crops with an abrupt transition of vegetative to reproductive growth. For example, wheat produces roots, leaves and stems during its vegetative growth period, but a large amount of starch during seed fill. Since the production of starch is very energy efficient, gr would be expected to be low during seed fill. Similarly, many fruits contain large amounts of organic acids, whose production also requires little growth respiration (Penning de Vries et al. 1974). Thus, gr is likely to decline during periods of seed fill or fruit growth in such crops (in contrast to oil crops, which produce large amount amounts of fatty acids, which require relatively much growth respiration).

Despite these potential changes in gr, experimental estimates from a variety of studies suggest that gr is similar (generally differing by less than 10%) among plant parts, species, and growing conditions (Cannell & Thornley 2000). The growth yield (Yg, grams of dry matter produced per gram of glucose utilized for growth, thus excluding glucose used for maintenance needs) generally is close to 0.7 g g−1 (McCree 1982; Penning de Vries et al. 1989; Cannell & Thornley 2000). Since gr = 1/Yg − 1 (when both are expressed in units of g g−1, Johnson 1990), this corresponds to a gr of 0.43 g g−1 and a theoretical maximum CUE of 0.70.

Changes in mr during development likely are larger than changes in gr, especially if mr is expressed per unit total Md. For example, a linear relationship between Rm and Md did not describe the respiration of barley (Winzeler et al. 1976) or chrysanthemum (Dendranthema × grandiflorum Kitam.; Hughes 1973) adequately, especially early in the life cycle. This suggests that there were ontogenic changes in mr, which may be related to plant composition. Certain plant compounds require little or no maintenance (e.g. lignin, cellulose), whereas other compounds (e.g. proteins) require a relatively large amount of maintenance (Johnson 1990; Amthor 1994). In growth models, this can be accounted for by separating biomass into non-degradable and degradable fractions, with only the degradable fraction requiring maintenance (Thornley 1977). However, often it is simpler to not make this distinction, and plants that undergo a significant amount of lignification or wood formation during their development are likely to have a decrease in mr (per unit total Md). Since secondary growth alters the ratio of degradable to non-degradable biomass, large changes in mr are more likely in woody than in herbaceous plants. A decrease in mr during plant development will help to minimize changes in CUE, since it counteracts the effect of decreasing rGR on CUE. This may at least partly explain the relatively constant CUE during the life cycle of wheat (Monje & Bugbee 1998). Wheat straw has high concentrations of both lignin and cellulose (Rahn & Lillywhite 2002), and mr of wheat thus likely decreases during its life cycle. In addition, wheat produces mainly starch during grain fill, which requires little growth respiration (Penning de Vries et al. 1974) and thus reduces gr. The combined effects of decreasing gr and mr during plant development may explain the relatively small changes in CUE of wheat. Lettuce, on the other hand, does not have significant lignification or secondary growth, and its mr is likely to be much more stable than that of wheat, causing CUE to decrease throughout the growing period. Clearly, potential changes in CUE depend at least partly on changes in the chemical composition of plants throughout ontogeny and are likely to be species-specific.

Plants grown under near-optimal conditions (high light and CO2 concentrations, e.g. Monje & Bugbee 1998), likely will have smaller changes in CUE than plants grown under poor conditions (e.g. the low light intensity in this study), because rGR will be higher under near-optimal conditions, minimizing the effect of mr on CUE. Moreover, mr generally is decreased under high atmospheric CO2 (Gifford 1995; Wullschleger et al. 1997), further reducing its effect on CUE. For example, the CUE of lettuce decreases faster under low atmospheric CO2 (approximately 300 µmol mol−1) than under high CO2 (approximately 1200 µmol mol−1) (Frantz, van Iersel & Bugbee, unpublished results), presumably because of a combination of a lower rGR and higher mr at low CO2.

CONCLUSIONS

Carbon use efficiency can be expressed as a simple function of gr, mr and rGR. Based on this function it can be concluded that: (1) the decrease in CUE of lettuce from 0.6 to 0.2 during development could be explained based on the decrease in rGR and the resulting increase in importance of maintenance respiration in the carbon balance of the plants; (2) based on the respiratory requirements for growth, the theoretical upper limit for CUE of the lettuce in this experiment was 0.68; (3) ontogenic changes in CUE likely are more pronounced under poor growing conditions, because a low rGR increases the importance of mr in determining CUE; (4) a decrease in rGR will result in a decrease in CUE, unless gr and/or mr change concurrently with rGR. In many species, especially those with extensive lignification or secondary growth, changes in mr (expressed per unit total Md) are likely, because of changes in the ratio between degradable and non-degradable biomass. Large changes in gr appear to be less common, but may occur when the composition of newly produced biomass changes, e.g. during the transition from vegetative to reproductive growth.

ACKNOWLEDGMENTS

I thank Larry Freeman and Keven Calhoun for their technical assistance during this research and Jonathan Frantz, Krishna Nemali and two anonymous reviewers for their constructive comments.

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