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Limits to plant production
J. theor. Biol. (1985) 113, 89-92
L i m i t s to P l a n t P r o d u c t i o n GORAN I. ~GREN
Department of Ecology and Environmental Research, Swedish University of Agricultural Sciences, S-750 07 Uppsala, Sweden (Received 14 June 1984, and in revised form 3 September 1984)
Of the factors limiting plant growth some are more fundamental than others in the sense that they are not easily or not at all available for manipulations either by the plant itself or by man. Among these are physical limitations like incoming solar radiation and evolutionary ones like basic biochemical functions, whereas e.g. nutrient or water availability sets the limits to the realization o f this potential. In this note I will, with some rough calculations, estimate which of four (carbon, light, water, and nitrogen) o f these more fundamental factors is likely to be the first in limiting growth. It is worth noticing the different characters of the limitations set by these factors. In the case o f carbon, light and water the plant is dependent on a continuous flux, while with nitrogen it is the current amount that matters because the nitrogenous compounds can be reutilized. These estimates indicate that the utilization efficiency of nitrogenous compounds is likely to be the most critical limiting factor.
1. Carbon Dioxide The major chemical component in plant biomass is carbon, constituting approximately 50% of dry weight. The supply of carbon in the form of carbon dioxide is therefore one possibly critical rate limiting step. Let me assume that what limits carbon supply rate is the diffusion over a boundary layer at the leaf surface; once at the leaf surface the carbon dioxide is under the control of the plant. The thickness o f the boundary layer will, among other things, depend on the wind speed, u, and leaf width, d. Thorn (1968) showed that boundary layer thickness (in cm) = 0.27(d/u) -~/2. Thus, already at wind speeds of 1 m s -~ and a leaf width o f 5 cm the boundary layer thickness is less than 1 mm. Hence, with a carbon dioxide concentration o f 350 ppm on one side of the boundary layer of a 1 mm (corresponding to a boundary layer resistance of 0.7 s cm -~) and 0 at the other, the flow of 89 0022-5193/85/050089+04 $03.00/0
(~) 1985 Academic Press Inc. (London) Ltd
90
G.I.A.GREN
carbon is ( D = 0-14 cm 2 s -l) 2-4 10 -7 gC (cm 2 leaf area) -~ s - l = 17 g dw (m 2 leaf area) -~ h -t. Evergreen broad-leaved forest trees have specific leaf areas of around 20-25 m 2 kg -~ (cf. Cannell, 1982) implying that if only diffusion of carbon dioxide were limiting, plants should be able to attain relative growth rates as high as 35-40% h -~, which is well above any observation. Experimentally it is, however, often found that elevated carbon dioxide concentrations increase plant production (e.g. Rogers et al., 1984). One possible explanation for this is that these experiments are conducted in greenhouses where the wind speed is very low with consequently much larger boundary resistances.
2. Light Maximal incoming light intensity is 700 W m -2 (1 cal cm -2 min-t). About half of this light falls within the photosynthetically active range (400700 nm) which gives approximately 2 IxE j - t The maximal yield with only light as a limiting factor (8 quanta per atom of carbon) is therefore 15 g dw m -2 h -t. This is a high estimate in that it assumes a total absorbance of incoming light, ideally efficient chemical conversion, and neglects all respiratory losses. On an energy basis, where also the difference between energy in the incoming photon and the absorbed energy is accounted for, Radmer & Kok (1977) estimated that 10% of the solar radiation could at best be converted into chemically bound energy. Their estimate o f maximal production, assuming 6000 kcal m -2 of radiation per day therefore amounts to 1 2 0 g d w m - 2 d -I ( 1 2 g d w m - 2 h - I ) .
3. Water Water is ubiquitous in living biomass, but even the very high production rate of 15 g dw m -2 h -~ and a water content of 85% in living biomass (e.g. Ingestad & L u n d , 1979) leads only to a requirement of 85 g water m -2 h -t (equivalent to 0.085 mm of precipitation per hour) to preserve the water balance of a plant under growth. Another important function of water for plants is in maintaining the heat balance. Under the most extreme conditions a plant may receive 2.52 MJ m -: h -~ of insolation. I f a reasonable operating temperature of the plant is 20°C, the plant can dissipate 1.57 MJ m -2 h -t as long-wave radiation and the rest, neglecting heat conduction, must be through transpiration, implying a transpiration rate of 0.4 kg m -2 h -~. Such a transpiration rate is certainly high, but should easily be sustainable even over longer time periods.
LIMITS
TO PLANT
PRODUCTION
91
4. Mineral Nutrients
I will only look at nitrogen of the different essential mineral nutrients, because nitrogen is generally considered the major limiting mineral nutrient and it also has a fairly well defined role in the plant's biochemistry with about 85% of the nitrogen in green plant material bound in proteins (Mengel & Kirkby, 1979). My assumption is therefore that the growth limitation from lack of nitrogen is expressed in lack of proteins. Evolution should have resulted in a balanced distribution of proteins such that overall protein use is optimized. It should therefore be possible to consider any protein with a well specified function. I have chosen as model protein ribulose diphosphate carboxylase, which is an enzyme with a molecular weight of 557 000 capable of catalyzing in vitro (fixing CO2) 1300 moles of D-ribulose 1,5-diphosphate/min per mole of enzyme (Paulsen & Lane, 1966) at pH 7.9 and 30°C. Paulsen & Lane also Found that ribulose diphosphate carboxylase constituted about 16% of the protein in spinach leaves, which allows me to estimate a nitrogen productivity (amount of biomass produced per unit of nitrogen and unit of time, see ~gren, 1983, 1985) of 1.8 g dw (gN) -l h -l at 20°C (assuming a Qi0 of 2), and with whole plant nitrogen as base. To make this value comparable to the other estimates I use the relation between leaf area and nitrogen content of 85 dm 2 (gN) -l found for Salix by Linder, McDonald & Lohammar ( 1981) giving 2.1 g dw (m 2 leaf area)-l h-i. Other Factors, such as temperature, are less easily quantified in similar ways, but are probably not as critical as the ones just discussed. Of the four factors studied nitrogen appears to be the most important one allowing production rates an order of magnitude less than either light or carbon dioxide. The maximal nitrogen productivity estimated above compares well with what can be estimated from expected maximal plant growth rates (e.g. a relative growth rate of 100% d -I) and internal nitrogen concentrations (5% of dry weight) giving 20 g dw (gN) -I d -l, as well as observed ones ( 1 4 g d w ( g N ) - l d -l or 0-6gdw(gN) - I h -l) for Lemnaminor, Ericsson, Larsson & Tiltberg (1982). In real situations a plant has to cope with a number of external constraints simultaneously and the growth form of the plant is therefore a compromise in resource allocation such that several factors become growth limiting. However, the intention with the present note has been to point to some ultimate limitations to plant growth under ideal conditions and not to answer which factor (or factors) is, in a practical situation, likely to be the most limiting. I wish to thank T. Fagerstr/Sm for valuable comments on the manuscript. This work was supported by the Swedish National Council for Forestry and Agricultural Research.
92
G.I.
,~GREN
REFERENCES ~GREN, G. 1, (1983). Can. J. For. Res. 13, 494. ,~,GREN, G. I. (1985). Physiol. Plant. (In press). CANNELL, M. G. R. (1982). World Forest Biomass and Primary Production Data. London: Academic Press. ERICSSON, T., LARSSON, C. M. & TILLBERG, E. (1982). Z. Planzenphysiot. 105, 331. INGESTAD, T. & LUND, A. B. (1979). PhysioL Plant. 45, 137. LINDER, S., McDONALD, J. & LOHAMMAR,T. (1981). ESO Tech. Rep. vol. IZ MENGEL, K. & KIRKBY, E. A. (1979). Principles of Plant Nutrition (2nd edition) Berne: International Potash Institute. PAULSEN, J. M. & LANE, M. D. (1966). Biochemistry 5, 2350. RADMER, R. & KOK, B. (1977). BioScience 27, 599. ROGERS, H. H., CURE, J. D~, THOMAS, J. F. & SMITH, J. M. (1984). Crop. Sci. 24, 361. THOM, A. S. (1968). Quart. J. R. Soc. 94, 44.
L i m i t s to P l a n t P r o d u c t i o n GORAN I. ~GREN
Department of Ecology and Environmental Research, Swedish University of Agricultural Sciences, S-750 07 Uppsala, Sweden (Received 14 June 1984, and in revised form 3 September 1984)
Of the factors limiting plant growth some are more fundamental than others in the sense that they are not easily or not at all available for manipulations either by the plant itself or by man. Among these are physical limitations like incoming solar radiation and evolutionary ones like basic biochemical functions, whereas e.g. nutrient or water availability sets the limits to the realization o f this potential. In this note I will, with some rough calculations, estimate which of four (carbon, light, water, and nitrogen) o f these more fundamental factors is likely to be the first in limiting growth. It is worth noticing the different characters of the limitations set by these factors. In the case o f carbon, light and water the plant is dependent on a continuous flux, while with nitrogen it is the current amount that matters because the nitrogenous compounds can be reutilized. These estimates indicate that the utilization efficiency of nitrogenous compounds is likely to be the most critical limiting factor.
1. Carbon Dioxide The major chemical component in plant biomass is carbon, constituting approximately 50% of dry weight. The supply of carbon in the form of carbon dioxide is therefore one possibly critical rate limiting step. Let me assume that what limits carbon supply rate is the diffusion over a boundary layer at the leaf surface; once at the leaf surface the carbon dioxide is under the control of the plant. The thickness o f the boundary layer will, among other things, depend on the wind speed, u, and leaf width, d. Thorn (1968) showed that boundary layer thickness (in cm) = 0.27(d/u) -~/2. Thus, already at wind speeds of 1 m s -~ and a leaf width o f 5 cm the boundary layer thickness is less than 1 mm. Hence, with a carbon dioxide concentration o f 350 ppm on one side of the boundary layer of a 1 mm (corresponding to a boundary layer resistance of 0.7 s cm -~) and 0 at the other, the flow of 89 0022-5193/85/050089+04 $03.00/0
(~) 1985 Academic Press Inc. (London) Ltd
90
G.I.A.GREN
carbon is ( D = 0-14 cm 2 s -l) 2-4 10 -7 gC (cm 2 leaf area) -~ s - l = 17 g dw (m 2 leaf area) -~ h -t. Evergreen broad-leaved forest trees have specific leaf areas of around 20-25 m 2 kg -~ (cf. Cannell, 1982) implying that if only diffusion of carbon dioxide were limiting, plants should be able to attain relative growth rates as high as 35-40% h -~, which is well above any observation. Experimentally it is, however, often found that elevated carbon dioxide concentrations increase plant production (e.g. Rogers et al., 1984). One possible explanation for this is that these experiments are conducted in greenhouses where the wind speed is very low with consequently much larger boundary resistances.
2. Light Maximal incoming light intensity is 700 W m -2 (1 cal cm -2 min-t). About half of this light falls within the photosynthetically active range (400700 nm) which gives approximately 2 IxE j - t The maximal yield with only light as a limiting factor (8 quanta per atom of carbon) is therefore 15 g dw m -2 h -t. This is a high estimate in that it assumes a total absorbance of incoming light, ideally efficient chemical conversion, and neglects all respiratory losses. On an energy basis, where also the difference between energy in the incoming photon and the absorbed energy is accounted for, Radmer & Kok (1977) estimated that 10% of the solar radiation could at best be converted into chemically bound energy. Their estimate o f maximal production, assuming 6000 kcal m -2 of radiation per day therefore amounts to 1 2 0 g d w m - 2 d -I ( 1 2 g d w m - 2 h - I ) .
3. Water Water is ubiquitous in living biomass, but even the very high production rate of 15 g dw m -2 h -~ and a water content of 85% in living biomass (e.g. Ingestad & L u n d , 1979) leads only to a requirement of 85 g water m -2 h -t (equivalent to 0.085 mm of precipitation per hour) to preserve the water balance of a plant under growth. Another important function of water for plants is in maintaining the heat balance. Under the most extreme conditions a plant may receive 2.52 MJ m -: h -~ of insolation. I f a reasonable operating temperature of the plant is 20°C, the plant can dissipate 1.57 MJ m -2 h -t as long-wave radiation and the rest, neglecting heat conduction, must be through transpiration, implying a transpiration rate of 0.4 kg m -2 h -~. Such a transpiration rate is certainly high, but should easily be sustainable even over longer time periods.
LIMITS
TO PLANT
PRODUCTION
91
4. Mineral Nutrients
I will only look at nitrogen of the different essential mineral nutrients, because nitrogen is generally considered the major limiting mineral nutrient and it also has a fairly well defined role in the plant's biochemistry with about 85% of the nitrogen in green plant material bound in proteins (Mengel & Kirkby, 1979). My assumption is therefore that the growth limitation from lack of nitrogen is expressed in lack of proteins. Evolution should have resulted in a balanced distribution of proteins such that overall protein use is optimized. It should therefore be possible to consider any protein with a well specified function. I have chosen as model protein ribulose diphosphate carboxylase, which is an enzyme with a molecular weight of 557 000 capable of catalyzing in vitro (fixing CO2) 1300 moles of D-ribulose 1,5-diphosphate/min per mole of enzyme (Paulsen & Lane, 1966) at pH 7.9 and 30°C. Paulsen & Lane also Found that ribulose diphosphate carboxylase constituted about 16% of the protein in spinach leaves, which allows me to estimate a nitrogen productivity (amount of biomass produced per unit of nitrogen and unit of time, see ~gren, 1983, 1985) of 1.8 g dw (gN) -l h -l at 20°C (assuming a Qi0 of 2), and with whole plant nitrogen as base. To make this value comparable to the other estimates I use the relation between leaf area and nitrogen content of 85 dm 2 (gN) -l found for Salix by Linder, McDonald & Lohammar ( 1981) giving 2.1 g dw (m 2 leaf area)-l h-i. Other Factors, such as temperature, are less easily quantified in similar ways, but are probably not as critical as the ones just discussed. Of the four factors studied nitrogen appears to be the most important one allowing production rates an order of magnitude less than either light or carbon dioxide. The maximal nitrogen productivity estimated above compares well with what can be estimated from expected maximal plant growth rates (e.g. a relative growth rate of 100% d -I) and internal nitrogen concentrations (5% of dry weight) giving 20 g dw (gN) -I d -l, as well as observed ones ( 1 4 g d w ( g N ) - l d -l or 0-6gdw(gN) - I h -l) for Lemnaminor, Ericsson, Larsson & Tiltberg (1982). In real situations a plant has to cope with a number of external constraints simultaneously and the growth form of the plant is therefore a compromise in resource allocation such that several factors become growth limiting. However, the intention with the present note has been to point to some ultimate limitations to plant growth under ideal conditions and not to answer which factor (or factors) is, in a practical situation, likely to be the most limiting. I wish to thank T. Fagerstr/Sm for valuable comments on the manuscript. This work was supported by the Swedish National Council for Forestry and Agricultural Research.
92
G.I.
,~GREN
REFERENCES ~GREN, G. 1, (1983). Can. J. For. Res. 13, 494. ,~,GREN, G. I. (1985). Physiol. Plant. (In press). CANNELL, M. G. R. (1982). World Forest Biomass and Primary Production Data. London: Academic Press. ERICSSON, T., LARSSON, C. M. & TILLBERG, E. (1982). Z. Planzenphysiot. 105, 331. INGESTAD, T. & LUND, A. B. (1979). PhysioL Plant. 45, 137. LINDER, S., McDONALD, J. & LOHAMMAR,T. (1981). ESO Tech. Rep. vol. IZ MENGEL, K. & KIRKBY, E. A. (1979). Principles of Plant Nutrition (2nd edition) Berne: International Potash Institute. PAULSEN, J. M. & LANE, M. D. (1966). Biochemistry 5, 2350. RADMER, R. & KOK, B. (1977). BioScience 27, 599. ROGERS, H. H., CURE, J. D~, THOMAS, J. F. & SMITH, J. M. (1984). Crop. Sci. 24, 361. THOM, A. S. (1968). Quart. J. R. Soc. 94, 44.