designing rice for the 21st century: the three laws of maximum yield

7/28/2019 Designing rice for the 21st century: the three laws of maximum yield

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Designing rice for the 21st century:

the three laws of maximum yieldJohn E. Sheehy and P.L. Mitchell

2013

Discussion Paper Series No. 48


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Suggested citation:Sheehy JE, Mitchell PL. 2013. Designing rice for the 21st century: the three laws of

maximum yield. Discussion Paper Series 48. Los Baos (Philippines): International Rice Research Institute.

19 p.

Editing: Bill Hardy

Design and layout: Grant Leceta


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Contents

Abstract ............................................................................................................................................................................................1

Introduction .............................................................................................................................................................................2

Assumptions ............................................................................................................................................................................3

Canopy architecture and the distribution o solar irradiance ................................................................................3

Lea photosynthesis, lea angle, and solar irradiance ...............................................................................................4

Canopy architecture and canopy photosynthesis .....................................................................................................6

Mass conservation: the link between photosynthesis and yield or the ideal crop .................. .................... .8

Maximum yield o biomass ..............................................................................................................................................10

The law o maximum grain yield .................. .................... ................... .................... .................... ................... ...............11

Radiation use efciency ....................................................................................................................................................12

Discussion ..............................................................................................................................................................................13

Concluding remarks ...........................................................................................................................................................16

Acknowledgments ..............................................................................................................................................................16

Appendix ................................................................................................................................................................................16

Reerences ..............................................................................................................................................................................18

About the authors ...............................................................................................................................................................19


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Designing rice for the 21st century:the three laws of maximum yield

John E. Sheehy and P.L. Mitchell

Abstract

Designing high-yielding rice plants

When trying to design high-yielding rice plants, several questions arise. What sets the limit to the maximum yield

o a crop? What are those limits? To what extent does photosynthesis shape yield? What is the importance o

canopy architecture in yield ormation? Why are high yields achieved in one region not achievable in another?

Below, we describe tools that allow us to answer those questions and, using them, we propose that breeders

should aim or an advanced type o rice, dierent rom the traditional or semidwar or new plant type (NPT)

varieties currently available. Furthermore, we believe that an advanced type with very erect leaves and a large

lea area index (Vela) would increase the maximum yield o C3

rice to about 13 t ha1 (at a moisture content o

14%).

The results show that in the tropics a Vela variety would increase maximum yield by 11% (rom 11.7 to 13.0t ha1). Yields in the subtropics are about 38% higher than in the tropics largely owing to the lower average daily

temperatures, which reduce the coecient o maintenance respiration and increase the quantum yield o C3

photosynthesis. The C4

syndrome could increase yields by about 40% above the yields o semidwar cultivars in

the tropics and by about 24% above the predicted yields or C3

rice in the subtropics.

Tools for designing high-yielding plants: the laws of maximum yield

A major aim o this work is to provide simple tools to obtain a better understanding o how solar energy can be

used most eciently or growth and what sets the limit to the maximum yield o a crop. In the spirit o simplication

to describe ideal gases, we set the challenge o deriving three simple expressions linking maximum daily crop

photosynthesis (Pgdmax

) and maximum aboveground biomass and grain yield (Wsmax

,W

gmax) to the driving variables

radiation (Iday

) and temperature (T):

Pgdmax = TfIday (A1)W

smax= c

TP

gdmax(A2)

Wgmax

= HWsmax

(A3)

The term Iday

is the photosynthetically active solar radiation (PAR) incident on a crop in a day (MJ m2 d1).The term

f is the ractional interception o PAR by the crop; in theory, the maximum value of (fmax

) is 1 but, in practice, ull

interception is achieved whenf= 0.95. Solar energy (PAR) is converted into the energy contained in carbohydrate

by T, the quantum use eciency o PAR intercepted by the crop. The term

Tis temperature dependent or C

3

(Tmax

= 6.6 g CH2O MJ1 at 30 C), but not or C

4crops (

Tmax= 8.0 g CH

2O MJ1). We explore how

Tis aected by

canopy architecture and lea photosynthesis. Maximum aboveground biomass (Wsmax

) depends on maximum

crop photosynthesis and a conversion actor (cT

), which is crop and temperature dependent. We show that cT

depends on major losses o carbohydrate rom shoot biomass in respiration and allocation to roots. In addition,

it is infuenced by the decline in maximum canopy photosynthesis toward nal yield owing to nitrogen recycling

rom vegetative to reproductive sinks. Maximum grain yield (Wgmax) is simply the product o harvest index andmaximum shoot biomass; we describe the relationship between the raction o biomass supporting grain yield

and harvest index. Our analysis gave us an opportunity to derive a theoretical expression or the radiation use

coecient, rue

:

rue

= Sr(1 )

T(A4)

where Sris the shoot weight ratio and is the raction o gross photosynthesis lost as respiration. The theoretical

estimates or rice and maize were 2.5 and 3.4 g MJ1 (aboveground biomass, intercepted PAR), respectively. We

tested the equations or a contrasting crop (orage grass) grown in an environment very dierent rom that o

rice (Appendix).

Keywords: photosynthesis, biomass, yield, source-sink,radiation use eciency, respiration, models.


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Introduction

The world population is predicted to reach a plateauof 9.3 billion in 2050, with the population of Asiarising by about 27% to 5.2 billion and that of Africaalmost doubling to nearly 2 billion. Asia and Africaare continents where most of the worlds existingpoverty is concentrated. More than 850 million

people are hungry and each day about 25,000 peopledie from hunger-related causes. Sheehy and Mitchell(2011a, b) discussed these global concerns from theperspective of the research in rice required to preventpotentially catastrophic consequences of risingpopulations and climate change. Of all the problemsfacing the human race, food and energy, with manylinks between them, must be the largest. And, rice,wheat, maize, millet, and sorghum provide 70% ofthe food energy of the world.

How do we design a very high yielding rice typefor the 21st century? Have the semidwarf varieties

of the Green Revolution reached a source-sinkboleneck set by their dwarng genes? What setsthe limit to the maximum yield of a crop? What arethose limits? To what extent does photosynthesisshape yield? What is the importance of canopyarchitecture in yield formation? Why are high yieldsachieved in one region not achievable in another?What is the role of crop management? It is easy toask such questions, but answering them is alwaysmore dicult. In order to do so, we trace the routefrom solar energy via photosynthesis to crop yieldin a simple and quantitative manner. The ultimate

aim of that journey is to gain a beer understandingofthe core characteristics of rice plants capable ofdelivering substantially higher yields. Each part ofthe yield puzzle needs a name and a number; in thispaper, we aempt to provide tools to supply them.The work described grew out of an aempt to usesimple models to describe the relationship betweencrop photosynthesis and yield. We noticed thatpredicted daily crop photosynthesis ploed againstfractional interception of PAR could be described

by a straight line. This suggested that, even in thetropics, the irradiance of leaves inside a canopywas suciently low that the relationship betweenphotosynthesis for such leaves and irradiance could,to a good approximation, be described by a straightline. We decided to investigate the consequencesof making that assumption and whether suchsimplications could be extended to produce a set ofsimple equations describing maximum crop yield.

Our previous analyses of limitations to riceyields (Sheehy et al 2000a, Mitchell and Sheehy2000, Sheehy et al 2007b) led to the C4 Rice Projectat IRRI (von Caemmerer et al 2012; and see C

4Rice

Project at www.irri.org). What has become clear isthat the supercharged engine (C4 photosynthesis)will need a fuel supply (light) to match its capacity,and transmission and suspension (structure andproportions of the rice plant) that use the increasedpower (more xed carbon) in the way required(increased grain yield). To this end, we propose that

breeders aim for an advanced type of rice, dierentfrom traditional or semidwarf or new plant type(NPT) varieties currently available. Furthermore, we

believe that an advanced type with very erect leavesand a large leaf area index (Vela) would increase theyield of C

3rice signicantly.

Assumptions

Several assumptions have to be made to achievethe comparative simplicity of equations describingcanopy photosynthesis and yield. The principal ones

are sketched below. Values for the parameters aregiven in Table 1.1. The carbon content of biomass is taken as 40% so

that carbohydrate (CH2O) and dry maer can beused interchangeably (Latshaw and Miller 1924,

Jimenez and Ladha 1993).2. Respiration is divided into two components: one

associated with synthesis of new biomass, a cost of25% of the carbohydrate available, and the otherassociated with the maintenance of biomass andthus varying with the amount of biomass at anyone time and also sensitive to temperature (see

Appendix).3. Roots are taken as 0.15 of total crop biomass (rootsand shoots combined), and are accounted forthrough a parameter so that aention is solely onaboveground biomass.

4. The crop exhibits a logistic growth paern inwhich maximum rate of growth occurs halfwaythrough the growth duration and then decreasesto zero as maximum biomass is reached at the endof growth duration.

5. The maximum rate of crop photosynthesis isachieved at owering, about halfway through crop

duration.6. Although the shape of the curve relating leaf

photosynthesis to PAR incident on the leaf ishyperbolic, in practice, with erect canopies andthe angular distribution of PAR through the day,the leaf is never receiving an amount of PARthat would take it beyond the more or less linearportion of the curve.

7. Canopy photosynthesis when maximum biomassis achieved is less than its maximum value by thefraction f. This allows for changes in the canopy


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Table 1. Values or the driving variables (Iday

, TPS

, Tmean

) and parameters (T, c, , mT, , , kd, H, pg) or a well-ertilized and irrigated rice crop. (The

driving variables or temperature do not appear in the nal equations but control the values or T and mT.) The equations consider 1 m2 o

ground and use values or a day, averaged over the second hal o crop duration. This is the period when the canopy is complete, interception o

PAR is maximal, the rate o canopy photosynthesis is near maximum, and biomass is near maximum so that the maximum amount o maintenance

respiration is occurring.

Variable or parameter (units) Meaning Value, typical Value, alternative

Iday

Daily total o PAR incident

on the crop (MJ m2 d1)

Main driving variable: energy source or

photosynthesis.

10 or tropics, subtropics,

and unusually sunny

temperate growth season

TPS Temperature duringdaylight (C)

Controls quantum yield (T) o C3 plants: changingit by 0.14 g CH

2O MJ1 C1 rom value o 5.9 g CH

2O

MJ1 at base temperature o 30 C.

30 C tropics; 25 Csubtropics and warm

temperate

Tmean

Mean daily temperature

(C)

Controls rate o maintenance respiration (mT):

using Q10

= 2 rom a value o 0.007 g g1 d1 at base

temperature o 20 C.

28 C tropics; 23 C

subtropics and warm

temperate

T Apparent quantum yield

o lea photosynthesis

(g CH2O MJ1) at daylight

temperature

Maximum amount o photosynthesis or unit

increment in PAR incident on crop.

For C3, 5.9 at 30 C; 6.6 at

25 C

For C4, 7.2 (invariant

with temperature)

c

Canopy eciency actor

(dimensionless)

Allows or the eect o the canopy architecture

and maximum rate o lea photosynthesis on the

eective quantum yield o a canopy.

For C3, 0.87 For C

4, 0.97

Fraction o PAR transmitted

by a lea (dimensionless)

Allows or lea photosynthesis inside the canopy. 0.1

kd

Fraction o dead matter in

aboveground dry matter

(dimensionless)

Reduces the amount o biomass needing

maintenance respiration.

0.15

mT The rate o maintenance

respiration (g g1 d1) at

mean daily temperature

Main variable source o losses o fxed carbon,

depending on crop biomass and mean daily

temperature.

0.012 (at 28 C);

0.0086 (at 23 C)

Coecient representing

losses rom gross

photosynthesis

(dimensionless)

Allows or synthetic (growth) respiration, losses as

exudates rom roots, and in legumes the respiratory

cost o nitrogen fxation; also allocation to roots (in

perennial grasses, the weight o stubble).

0.59 0.38 (legumes);

0.3 (perennial grasses)

Factor representing

gross daily canopy

photosynthesis as a raction

o its maximum value

(dimensionless)

Allows or the decline in photosynthetic activity

o the canopy at crop maturity, rom its maximum

value earlier in crop duration; particularly when

nitrogen is transerred rom senescing lower leaves

to flling grain.

0.7

H Harvest index Fraction o crop biomass (aboveground) or harvest. 0.5

pg

Maximum rate o lea

photosynthesis (mol CO2

m2 s1)

At 2,000 mol quanta m2 s1. 32.5 rice (C3) 56 maize (C

4)

and changes in leaf photosynthesis characteristicsthat occur during the second half of growthduration.

8. The driving variables of PAR and temperature areeach supplied as a single average value for thesecond half of growth duration. This assumptionis reasonable in the tropics and subtropics wherevariations in solar angle and in temperature arerelatively small across a period of 2 or 3 months.In temperate regions where solar angle andtemperature change greatly during the growing

season, this assumptionof linear averagingacross a period of monthsworks less well.

Canopy architecture and the distribution osolar irradiance

Photosynthetically active radiation (PAR,wavelengths 400700 nm) at Earths surface isabout 50% of the total shortwave incident solarradiation, with the other 50% being shortwave


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infrared radiation. On a clear day, the amount ofPAR incident on a horizontal surface varies in anapproximately sinusoidal manner with a typicalmaximum daily irradiance in the tropics of about10 MJ m2 d1, giving 1,673 mol m2 s1 at midday.Erect leaves do not experience full midday solarirradiance. To illustrate the principle, contrast thePAR incident on a horizontal leaf at midday with thesun overhead with the irradiance of a leaf inclinedat 80 to the horizontal. The horizontal leaf wouldreceive 1,673 mol m2 s1, whereas the inclinedleaf would receive 334 mol m2 s1. In order tointercept the entire energy incident on its horizontalcounterpart, the area of the erect leaf would have to

be ve times that of the horizontal leaf. Many leaveswithin the canopy receive PAR after transmissionthrough other leaves. Monsi and Saeki (1953)demonstrated that the decline in solar irradianceinside a canopy can be described by the BouguerLambert Law:

IL

= I0 exp(kL) (1)

where IL is the irradiance (on a horizontal surface)beneath leaf area index L of a canopy, I

0 is theirradiance incident on the canopy, and k is theextinction coecient for PAR (m2 ground m2 leaf).Canopies with erect leaves have values of k 0.20.3and canopies with more prostrate leaves have valuesof k 0.60.8.The fraction of incident PAR that isintercepted by the canopy, ,can be wrien as

= [1 exp(kL)] (2)

At a given value of L, the PAR incident on a leaf(I

l) is given by

Il= kI

0exp(kL)/(1 ) (3)

where is the fractional transmission of PARthrough a leaf. The fractional distribution ofirradiance incident on leaves of a prostrate canopy(k = 0.6) and an erect canopy (k = 0.2) is shown inFigure 1. At the top of the canopy (less than 3 LAI

units downward), it can be seen that the leaves of theerect canopy receive lower irradiance than the leavesof a prostrate canopy. Overall, the erect canopydistributes the irradiance more uniformly throughthe canopy than the prostrate canopy.

From the perspective of nitrogen recyclingfrom leaves during reproductive growth, it issometimes convenient to divide the leaf area intodierent categories. In this respect, a model of lightdistribution derived by Monteith (1965) is valuable.The interception and distribution of irradiance in a

Monteithian canopy are dened by a parameter, s,

where s denes the fraction of irradiance that passesthrough unit LAI without interception. The modeldivides the LAI according to the irradiance received

by leaves: there are sunlit, once-shaded, and twice-shaded categories of LAI. Twice-shaded leaves exist

just above the light compensation point and areunimportant photosynthetically, but important as anitrogen store (Sinclair and Sheehy 1999). The sunlit,once-shaded, and twice-shaded fractions of the LAIapproach an asymptotic value of (1 s)1.

The values of k, s, mean leaf angle, sunlit leafarea index, and the LAI required to intercept 95%

of the PAR incident on the canopy are shown inTable 2. The smaller the extinction coecient, themore erect are the leaves and the greater the LAIrequired for full interception of PAR. Improvementsin the erectness of leaves must be accompanied byincreases in LAI to ensure the full interception ofPAR. Such high LAIs are probably key to nitrogenreservoirs and high rates of canopy photosynthesis atcrop maturity.

Lea photosynthesis, lea angle, and solar

irradiance

The simplest model of leaf photosynthesis is denedin terms of limiting factors (Fig. 2A) and goes back toBlackman (1905). At rst, photosynthesis is limited

by light and then, at high irradiance, by other factorssuch as CO2, temperature, and intrinsic anatomicaland biochemical factors (Farquhar et al 1980).Therelationship between leaf photosynthesis (p

g) and

irradiance (Il) incident on a leaf (Fig. 2B) is oftendescribed using a simple rectangular hyperbola:

Fig. 1. Fractional irradiance on a lea in a canopy as a unction o leaarea index above the lea, or prostrate leaves (k = 0.6) and erect leaves(k = 0.2). Fractional irradiance is computed as I

l/I

0rom equation 3; it is

the amount o PAR received by a lea as a raction o what is availableat the top o the canopy.

Fractional irradiance on a lea

k = 0.6 prostrate

k = 0.2 erect

0.8

0.6

0.4

0.2

0.0

0 4 8 12 16

Lea area index above lea


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pg

= T

Ilp

max/(

TI

l+ p

max) (4)

where T is the quantum yield, T is temperature, and

pmax is the theoretical rate of leaf photosynthesis asI . The practical maximum rate of leafphotosynthesis (32.5 mol CO

2m2 s1 for rice and

52.0 mol CO2 m2 s1 for maize at an irradiance

of 2,000 mol m2 s1) depends linearly on thenitrogen content of the leaf as described by Peng(2000) and Evans and von Caemmerer (2000). Itshould be noted that the greater the maximumrate of leaf photosynthesis, the greater the range ofirradiance values over which photosynthesis can

be described in terms of the light-limited portionof the relationship.This can be seen in Figure 2B,

where noticeable curvature occurs at lower valuesof incident PAR looking from the uppermost curvedownward.

The quantum yield, T, is the initial slope ofthe hyperbola ed to leaf photosynthesis ploedagainst PAR incident on the leaf and it represents themaximum amount of carbon dioxide xed by unitamount of PAR. It is sometimes called photochemicaleciency and general values for C

3 and C4photosynthesis can be estimated from measurements.Ehleringer and Pearcy (1983) found that measuredquantum yields (at 30 C leaf temperature and 330ppm carbon dioxide concentration) varied lileamong C3 species and averaged 0.053 mol CO2mol1 quanta, absorbed PAR. In C4 plants with theNADPME pathway, which is the group includingmaize and sorghum, the measured quantum yieldwas 0.065 mol CO2 mol

1 quanta, absorbed PAR.Converting units (1 mol CO2 produces 1 mol CH2O;30 g CH2O mol

1; 4.6 mol quanta MJ1 PAR) gives7.314 and 8.970 g CH2O MJ

1, absorbed PAR, for C3and C4 plants, respectively. To adjust the basis ofexpression from absorbed PAR to PAR incident on

A

Rate o lea photosynthesis

Imax

Pmax

Irradiance

B

Rate o lea photosynthesis (mmol CO2

m2 s1)


m2 s1)

60

40

20

0

0 500 1,000 1,500 2,000

C4

C3

C3 Low P/S

Fig. 2. (A) Diagram o the Blackman (1905) representation o leaphotosynthesis as a unction o irradiance. The quantum yield ()is the slope o the line given by P

maxdivided by I

max(which is the

tangent o angle a). (B) Lea photosynthesis as a unction o irradiancerepresented by simple hyperbolic curves or C

3and C

4photosynthesis

(quantum yields 0.042 and 0.052 mol CO2

mol1 quanta, respectively,where quanta are incident PAR). The curves are calculated to providerates o photosynthesis at 2,000 mol m2 s1 PAR o 56, 32.5, and 16.25mol CO

2m2 s1 or C

4, C

3, and C

3with low photosynthesis, respectively

The asymptotes or the curves are 121.3, 53.0, and 20.1 mol CO2

m2s1 in the order used above.

Table 2. Properties o rice canopies or dierent architectures. The our canopy types are

dened by approximate extinction coecients and values o Monteiths parameter s, which

was computed using s = (exp(k) )/(1 ) (Sheehy and Johnson 1988), with = 0.1. Using

the extinction coecient (two signicant gures as tabulated), the LAI or 95% interception

o PAR was derived. In turn, the s value was used to calculate the sunlit LAI with the ormula

(1 sL)/(1 s) rom Monteith (1965); the lea angle was also estimated using the approach

described in that paper. The advanced canopy architecture described by very erect leaves and

large LAI is called Vela.

Item Canopy type

Traditional Semidwar Erect Vela

Monteiths parameter, s 0.5 0.6 0.7 0.8

Extinction coecient, k 0.60 0.45 0.31 0.20

LAI or 95% interception, LAI95

5.0 6.7 9.7 15.0

Sunlit LAI 1.9 2.4 3.2 5.2

Lea angle (degrees rom horizontal) 60 66 73 79

a


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the leaf, we take general values for the fractions ofincident PAR that are reected or transmied ( inthe equations above) each as 0.1, averaged across thePAR waveband and across all angles of incidence(Monteith and Unsworth 1990, p 86). Then measuredquantum yields for one unit of absorbed PAR are for1/0.8 = 1.25 units of incident PAR so they must bedivided by 1.25 to express them on the incident basis,producing 5.8512 and 7.176, rounding to 5.9 and7.2 g CH2O MJ1, incident PAR, for C3 and C4 plants,respectively. Quantum yield for C4 plants does notvary with temperature but for C3 plants the amountof photorespiration increases with temperature andchanges the quantum yield by 0.0013 mol CO2 mol

1quanta, absorbed PAR, for each 1 C increase in leaftemperature (measurements in the range of 1638 C;Ehleringer and Pearcy 1983). Converting units andadjusting the basis gives a temperature coecientof 0.14 g CH2O MJ

1 C1, incident PAR. This can besummarized as

T

= 30 0.14(TPS 30) (5)

where T is the quantum yield at temperature TPS(C), which is the mean leaf temperature duringphotosynthesis, that is, during daylight, taken forconvenience as sunrise to sunset; 30 is the quantumyield at 30 C (leaf temperature during daylight);0.14 g CH2O MJ

1 C1 is the temperature coecient;and 30 C is the base temperature of the leaf duringdaylight.

For crops with sucient water for maximal

photosynthesis, as considered here, transpirationwill be sucient to maintain leaf temperature closeto that of the air. The mean air temperature duringdaylight can be taken as the mean of maximumand mean daily temperatures, where mean dailytemperature is the mean of maximum and minimumtemperatures. This can be calculated from thesetemperatures as

TPS = (3 Tmax + Tmin)/4 (6)

If only mean temperature is available, then an

alternative approach is to estimate the span betweenminimum and maximum temperatures, Tspan, and use

TPS

= Tmean

+ 0.25 Tspan

(7)

In the tropics, Tspan can be as low as 5 C so

that TPS is only about 1 C higher than mean dailytemperature; in temperate climates, where Tspan could

be 10 C, then TPS

would be 23 C higher than Tmean

.

Canopy architecture and canopyphotosynthesis

Models of canopy photosynthesis are the result ofcombining models of the distribution of irradiancewith a model of leaf photosynthesis as a function ofirradiance (Thornley and Johnson 1990). The diurnalpaern of incident solar irradiance is assumed to

vary sinusoidally (Monteith 1965). The classicalequation for canopy photosynthesis is the outcome ofcombining the rectangular hyperbolic function of leafphotosynthesis and irradiance with the BouguerLambert Law description of PAR distribution in thecanopy. This equation linking canopy photosynthesisand irradiance (Verhagen et al 1963, Sheehy and

Johnson 1988) can be wrien as

Pg(I) = (pmax/k) ln {[TkI + pmax(1 )]/[TkI exp(kL) +pmax(1 )]} (8)

where Pg(I) is gross canopy photosynthesis (g CH2Om2 ground) at irradiance I, which is the irradianceincident on the canopy (PAR, MJ m2 ground), is thefraction of PAR transmied by a leaf, and L is the leafarea index (m2 leaf m2 ground).

We used this equation to make a series ofpredictions of daily canopy photosynthesis for clearconditions (PAR = 10 MJ m2 d1). We observed that,for high rates of individual leaf photosynthesisand erect canopies, the relationship betweenpredicted canopy photosynthesis and fractional lightinterception was to a good approximation linear. The

predictions for erect C4 (y = 80.8x, r2 = 0.99) and C3 (y= 61.5x, r2 = 0.99) canopies are shown in Figure 3A.To ensure that the result was not a quirk of equation8, we used the Monteith model to conrm thisobservation.

The leaf irradiance data shown abovesuggest that the photosynthetic rate of leavesin a canopy could, to a good approximation, berepresented by the light-limited linear portion ofthe leaf photosynthesis irradiance relationship.Consequently, we assumed that the constant ofproportionality linking leaf photosynthesis and

irradiance was cT, where c is a canopy eciencyfactor representing the eect of canopy architectureand maximum leaf photosynthesis on the eectivequantum yield of a leaf over the range of irradiancesexperienced by leaves in a canopy during the day.

The linear approximation to the relationshipbetween leaf photosynthesis (Fig. 3B) and irradiance(instantaneous rate of receipt of PAR) can be wrienas

pg = cT Il (9)


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(MJ m2 d1). It is convenient to write the quantumyield of the canopy as T =cT/(1 ), and canopyphotosynthesis as the product of the fraction of dailyPAR intercepted by the canopy, , multiplied by thequantum yield of the canopy:

Pgd = TIday (12)

where = [1 exp(kL)] and it is the fractionalinterception of PAR by the crop. Mathematically,the maximum value of is 1, but, in practice,full interception is achieved when = 0.95. Themaximum rate of canopy photosynthesis is

Pgdmax = 0.95 TIday (13)

The quantum yield of the canopy T = cT /(1 ) has as units g CH

2O MJ1, and

cis a canopy

eciency factor (dimensionless) governing the eectof the canopy architecture and maximum rate of

leaf photosynthesis on the eective quantum yieldof leaves in a canopy. The fractional transmission ofPAR by a leaf, , is assumed to be 0.1. The magnitudeof c was calculatedby comparing the predictions ofcanopy photosynthesis models using the hyperbolicand linear descriptions of leaf photosynthesis asa function of irradiance (Table 3). The value of cfor C

3crops increases with canopy erectness from

0.83 to 0.98. For a C4 crop, c = 1.0. At the otherextreme, the lowest value of c, 0.75, was obtainedfor the assumption that the maximum rate of leafphotosynthesis was limited to 50% of its normal

value. The values of canopy photosynthesis for thescenarios considered in this paper are shown in Table3, with semidwarf canopies having a rate of 55.2 gCH2O m

2 d1, which rises to 61.5 g CH2O m2 d1 for a

Vela canopy.Canopy photosynthesis is rarely measured in

a direct way but, when data have been obtained,they support the assertion above that canopyphotosynthesis is linearly related to intercepted PAR.For example, the relationship between measuredcanopy photosynthesis (y) and fractional interceptionof PAR (x) for data obtained for lucerne and sainfoin

by Sheehy and Popple (1981) is y = 38.1x, r2 = 0.93(Fig. 4). The daily total of PAR close to harvest was 7.3MJ m2 d1, the average daylight temperature, TPS, was18.6 C, and the mean daily temperature was 16.1 CFrom equation 5, we estimate the quantum yield to

be 7.5 g CH2O MJ1; both lucerne and sainfoin have

prostrate canopies and, by comparing equation 12and the regression equation, we estimated the meanvalue of their canopy factor, c, as 0.63.

Canopy photosynthesis increases as LAIincreases but at a decreasing rate and so approaches

A

Rate o canopy photosynthesis (g CH2O m2 d1)

Fractional interception o PAR

90

60

30

00.4 0.6 0.8 1.00.2

C4

C3

Quantum yield

Photosynthesis

B


m2 s1)

PAR (mmol m2 s1)

20

15

10

5

00 100 200 300 400 500

Fig. 3. (A) The relationship between canopy photosynthesis predictedby equation 8 and ractional interception o PAR when PAR (variableI) is set at 10 MJ m2 d1. The points come rom calculation with various

values o lea area index (variable L) to cover a range o ractionalinterception o PAR. Values o parameters are in Table 1. The equationso the tted lines are y = 61.5x (r2 = 0.99) or C

3rice and y = 80.8x (r2 =

0.99) or C4

maize.(B) The rate o lea photosynthesis (solid curve) calculated withequation 4 up to 500 mol m2 s1 PAR, the range o values experiencedinside the rice canopy. The straight lines are the quantum yield (dashedline; the initial slope o the curve, 0.042 mol CO

2mol1 quanta) and the

linear approximation (dotted line; slope 0.036 mol CO2

mol1 quanta).The linear approximation is within 10% o photosynthesis given bythe curve or the range 0350 mol m 2 s1 PAR.

and, if we substitute for Il from equation 3 and

integrate it over the leaf area index L, canopy

photosynthesis is given by

Pg(I) = cT I[1 exp(kL)]/(1 ) (10)

Canopy photosynthesis over a day can beobtained by integrating irradiance over a day to give

Pgd = cT Iday[1 exp(kL)]/(1 ) (11)

where Iday

is the total photosynthetically activesolar radiation (PAR) incident on a crop in a day


11/228

an asymptote (Fig. 5) at full PAR interception. Inrice, the maximum value of LAI is achieved nearowering, thus imposing a maximum rate of canopyphotosynthesis. Usually, the live LAI declines toward

maturity as nitrogen is withdrawn from leaves andthey become senescent. It is interesting to note thatthe loss of the once-shaded leaves results in a declineof only 2227% in canopy photosynthesis (Sheehy2000). This emphasizes the point that, in a maturecanopy, nitrogen and carbohydrates can be recycledfrom approximately 70% of the leaves without aproportionate loss in canopy photosynthesis. Growthand leaf area data for a high-yielding rice crop ofIR72 (Sheehy et al 2000b) are shown in Table 4.

Mass conservation: the link betweenphotosynthesis and yield or the ideal crop

The mass balance of the whole crop (shoots plusroots) at time t can be wrien as

dW/dt = Fci(t) + Fmi(t) Fco(t) Feo(t) Fdo(t) (14)

where W is the total weight of the crop (shootsplus roots), Fci(t) is the input of carbon-basedmaer associated with the instantaneous rate ofcanopy gross photosynthesis, Fmi(t) is the rate ofinput of mineral elements, Fco(t) represents thelosses from the system as respiration in the same

Table 3. The eect o extinction coecient (k) and maximum rate o lea photosynthesis

(at 2,000 mol m2 s1 PAR and 390 ppm CO2) on the canopy eciency actor and maximum

daily canopy photosynthesis. The our canopy types o rice were dened in Table 2. The extra

subtypes o erect canopy are or a C4

rice and or C3

with low photosynthesis (hal the usual

maximum rate o lea photosynthesis o 32.5 mol CO2

m2 s1). Note the dierent units or lea

and canopy photosynthesis, including that lea photosynthesis is or unit lea area and canopy

photosynthesis is or unit ground area.

Item Canopy type


Extinction coecient, k 0.60 0.45 0.31 0.20Lea photosynthesis, P

gmax

(mol CO2

m2 s1)

32.5 32.5 32.5

(C4, 56.0)

(low, 16.3)

32.5

Canopy eciency actor, c

0.83 0.88 0.93

(C4, 1.00)

(low, 0.75)

0.98

Canopy photosynthesis, Pgdmax

(g CH2O

m2 d1)

52.1 55.2 58.3

(C4, 76.0)

(low, 47.0)

61.5


Fractional interception o PAR

40

30

20

10

00.4 0.6 0.8 1.00.20.0

Fig. 4. The relationship between canopy photosynthesis and ractionalinterception o PAR using experimental data or lucerne and sainoin(Sheehy and Popple 1981). The equation o the tted line is y = 38.1x(r2 = 0.93).


Lea area index

90

60

30

06 9 12 1530

C4

C3

Fig. 5. The relationship between canopy photosynthesis and leaarea index as predicted by equation 8 using values or variables andparameters rom Table 1.


12/229

units as photosynthesis, Feo

(t) is the rate of loss ofcarbohydrate through root exudation, and Fdo(t)

is the rate of loss of dead maer by detachment. Itis recognized that age and crop composition willaect the variablesused in evaluating equation 14.However, to fully represent the crop throughout itslife would require a complex model and our aim is tokeep things simple and to evaluate the consequencesof this approach later.

The units throughout are g m2 for the timeinterval being considered, typically 1 day. The carboncontent of crop plants is approximately 40% so thatcalculating the mass balance of a plant in terms ofcarbohydrates gives an acceptable prediction of

weight change. This occurs because the proportionof dry maer that is mineral elements more or lesscompensates for the higher proportion of carbon inlipids and other substances than in carbohydrates. Ifgreater precision is required, the fraction of carbon inthe dry weight, fc, needs to be known for each organand the amount of carbohydrate is multiplied by 0.4/fc to obtain dry maer.

Using daily time steps, equation 14 can now bewrien in units of carbohydrate (g m2) as

dW/dt = (1 )Pg(t) R

s(t) R

m(t) D(t) (15)

where Pg is gross photosynthesis (shoot netphotosynthesis plus shoot respiration for thedaylight hours), is the fraction of grossphotosynthesis exuded through the roots and lostthrough nodule respiration in legumes, Rs is the cropsynthetic respiration (shoots plus roots), Rm is thecrop maintenance respiration, and D is the daily lossof maer through detachment.

If it is assumed that synthetic respiration isequivalent to 0.25 Pg and maintenance respiration(see below and Appendix) can be wrien as theproduct of a maintenance coecient and live crop

weight (McCree 1970, Penning deVries et al 1983,Thornley and Johnson 1990, Amthor 2000), k

d(t) is

the fraction of dead maer in total abovegrounddry maer, and, if root exudates account for 5% ofdaily photosynthesis (Marschner 1995) and nodulerespiration is zero, equation 15 can be rewrien as

dW/dt = 0.70 Pg(t) mTW(t) (1 kd(t)) D(t) (16)

Table 4. Measurements o a high-yielding crop o indica rice (Sheehy et al 2000b) at dierent stages o

growth. Components o shoot weight and o LAI are oset in the table. Stem is culm (the true stem) plus

lea sheaths surrounding it. Photosynthetic LAI is dened as the sunlit and once-shaded ractions o LAI,

given here as a percentage o total LAI. Useul LAI is dened as the sunlit, once-shaded, and twice-shaded

ractions o LAI, given here as a percentage o total LAI; these leaves are alive and, i not photosynthetic

(twice-shaded), acting as a store o nitrogen, which can be moved later to the maturing grain. At nal

harvest, live leaves are present only at the top o the canopy and hence all are sunlit. This crop yielded

11.6 t ha1 (14% moisture content).

Measurement Stage o growth (days ater transplanting)

Panicle initiation

(43)

Flowering

(61)

Maximum LAI

(67)

Final harvest

(102)

Shoot dry weight (t ha1) 3.9 9.2 11.8 21.8

Lea dry weight (t ha1) 1.7 3.2 4.0 1.9

Stem dry weight (t ha1) 2.1 4.5 5.2 4.5

Panicle dry weight (t ha1) 0 1.2 2.2 12.2

Dead dry weight (t ha1) 0.1 0.3 0.4 3.2

Lea area index 3.0 5.9 7.0 2.8

Sunlit area index 2.2 2.9 3.1 2.8

Once-shaded area index 0.7 1.9 2.2

Twice-shaded area index 0.1 0.9 1.2

More than twice-shaded 0 0.2 0.5

Photosynthetic LAI (%) 97 81 76

Useul LAI (%) 100 97 93

Intercepted PAR (%) 61 84 89

Canopy photosynthesis

(g CH2O m2 d1)

40 56 59


13/2210

where mT is the maintenance respiration coecient(g carbohydrate g1 DM d1; Table 1) assumed to havea Q

10of 2 from a base temperature of 20 C (Ryle et al

1976). The value of mT at any time is calculated froma value at the base temperature and the temperatureat the time, T(t), as

mT

= m20

2(T(t) 20)/10 (17)

where m20 (g g1 d1) is the maintenance respirationcoecient at 20 C and T(t) is the mean dailytemperature (C).

Maintenance respiration declines with age(Loomis and Connor 1992, Liu et al 2011) andpublished values for mT vary (McCree 1970, Thornleyand Hesketh 1972, Ryle et al 1976, Thornley and

Johnson 1990). In the absence of data for rice, wehave used a base value of 0.007 g g1 d1 estimatedusing the approach described in the Appendix.

Roots account for a comparatively small fraction

of crop dry maer (measured as root weight ratio)for most of crop duration, typically declining atharvest to 0.1 in irrigated rice (Sheehy et al 2000b) or0.3 in wheat (Siddique et al 1990). To make progress,we assume a general value of 0.15 for root weightratio so that total crop dry maer is 1/0.85 = 1.18times larger than aboveground dry maer (Sheehy2000).Substituting in equation 16 and assumingproportional detachment of dead material, we obtain

1.18 dWs/dt = 0.70 Pg(t) 1.18 mT(t)Ws(t) (1 kd(t))

1.18 Ds(t) (18)

where Ws is aboveground dry maer and Ds(t) isdetached dead aboveground dry maer. Dividingthroughout by 1.18 and assuming that Ds(t) isnegligibly small in a rapidly growing crop gives

dWs/dt = 0.59 Pg(t) mT(t)Ws(t) (1 kd(t)) (19)

More generally, the relationship between cropgrowth rate and crop photosynthesis can be wrienas

dWs/dt = Pgd(t) mTWs(t)(1 kd(t)) (20)

where is a coefficient whose value is derived asshown in the Appendix (0.59 in general). Whenrespiration is dened as a biphasic process (seeAppendix), maintenance respiration (mT) is denedas the second phase associated with the maintenanceof metabolic activity (Ryle et al 1976).

Maximum yield o biomass

To fully understand the dynamics of internal trans-fers of nitrogen between vegetative and reproductivestructures, Sheehy et al (2007a) described the growthof rice in terms of three phases. For simplication, weassume here that aboveground dry maer accumula-tion follows the classical logistic paern (Williams

1964) as shown in Figure 6. At maturity, we can writedWs/dt 0, as W

sW

smaxand P

gdf P

gdmax, largely

owing to a recycling of nitrogen associated withsenescence (the loss of leaves shaded once or twice),and, associated with that process, kd (t) kdmax. Set-ting dW

s/dt to zero in equation 20 gives

Wsmax = f Pgdmax/(mT(1 kdmax)) (21)

where Wsmax is the maximum crop aboveground

dry maer (g m2) and f is Pgd as a fraction of itsmaximum value, P

gdmax. As described by Sheehy

(2000) in a canopy with a high LAI, leaves that areshaded once or twice can become senescent for a lossof less than 30% of canopy photosynthesis (f 0.7).For convenience, we rewrite equation 21 as

Wsmax = cT Pgdmax (22)

wherecT = f /(mT(1 kdmax)) (23)

Amount o biomass, W (g m2)

Asymptote

dW/dt 0

Time ater sowing or planting, t (days)

Maximum

dW/dt

1,000

1,500

2,000

500

00 4020 60 12010080

Fig. 6. The classical S-shaped curve or accumulation o crop biomass(aboveground dry matter) with time or an annual crop (Williams1964). It is represented here using a logistic equation; the numbersare plausible values or illustration and do not relate to any particularcrop. Maximum growth rate occurs at the steepest point on the curve,the point o infection, which is taken to be the time o maximum rateo canopy photosynthesis. As biomass approaches the asymptote(W

max), the growth rate (dW/dt) approaches zero.


14/2211

so that cT is a temperature-dependent parametergoverning the conversion of photosynthate intoaboveground biomass.

We can now combine equations 13 and 22 toobtain maximum crop biomass (abovegrounddry maer) from the main driving variable,I

day, and several parameters. Canopy quantumeciency,

T, is a combination of the parameters

c

, T

, and . Parameter cT

accounts for majorlosses of carbohydrate from shoot biomass ingrowth respiration, maintenance respiration(mT), and allocation to root growth. Parameter flargely represents the consequences for canopyphotosynthesis of nitrogen transfer from leavesto panicles. Temperature is also a driving variable

because during daylight it acts through the values for

T (equation 5), and the mean daily temperature actsthroughout 24 hours on m

T(equation 17).

For a semidwarf crop that recycles nitrogenfrom once-shaded and twice-shaded leaves, but

retains nitrogen in sunlit photosynthetically activeleaves, f 0.7 (Sheehy 2000). The value of f will bestrongly inuenced by nitrogen management andthe demand for nitrogen from the reproductiveorgans. The data in Table 4 give the value of kdmax as0.15 and we assume that this value remains constantin the calculations made in this paper. It is likelythat f and (1 k

dmax) are related although we do

not explore that here. The maintenance respirationcoecient (see Appendix) for rice in the tropics is0.012 (g g1 d1, T = 28 C) and for subtropical ortemperate rice (T = 23 C) it is 0.0086 (g g1 d1) when

the applicable temperatures are for the period ofowering to maturity (Sheehy et al 1998). We discussthe factors inuencing the value of the conversionfactor cT below. Using the data in Tables 1 and 4,we calculated values of cT for a range of values of f(Table 5): for f = 0.7, then c

Tis 40.5 for the tropics and

56.5 for the subtropics (units g DW g1 CH2O d, i.e.,the inverse of the units for mT).

The law o maximum grain yield

The maximum grain yield is obtained by multiplyingequation 22 by the harvest index to give

Wgmax = HcTPgdmax (24)

where H is the harvest index dened as the

harvested part of the crop, which is grain, as afraction of crop aboveground dry maer (Hay 1995).Substituting for Pgdmax from equation 13 in equation24 gives

Wgmax = 0.95 H T cT Iday (25)

Harvest indexThe analysis of canopy structure in relation to theinterception of PAR suggests that, as canopies

become more erect, a larger LAI is required for fullinterception. It follows that leaf weight and stem

weight must both increase and this also has theconsequence of increasing the size of the nitrogenreservoir and the amount of structural biomassavailable to support increased yield. The balance

between the investment of resources in grain andsupport structures can be examined by consideringthe equation for calculating harvest index. Harvestindex (H) can be wrien as

H = Y/(Wsst

+ Y) (26)

where Y is grain dry weight, Wsst is the weight of

the leaves and stems,which for convenience wecall support structure, describes the weight of thepanicle relative to grain weight, and, from the data inTable 4, we can write 1.25.

We can make another useful simplication byassuming W

sst =Y so that

H = Y/(Y + Y) (27)

where describes the weight of the biomass (leaves,stems, and dead maer) invested in support of grainproduction relative to grain weight. By rearranging

equation 27, we get

= (1/H) 1.25 (28)

Figure 7 shows the relationship between andH and it can be seen that, when H = 0.5, the weightof the support structures is 75% of the weight ofthe grain; when H = 0.45, the weight of the support

Table 5. Values o the photoassimilate conversion parameter cT (cT =

/(mT(1 kdmax))) or tropics and subtropics or various values o the

actor governing the decline rom maximum canopy photosynthesis

by crop maturity, assuming mT or the tropics = 0.012 g g1d1 and0.0086 g g1 d1 or the subtropics; is assumed to be 0.59 and k

dmax=

0.15.

cT tropics cT subtropics

(g g1 d) (g g1 d)

0.8 46.3 64.6

0.7 40.5 56.5

0.6 34.7 48.4


15/2212

structures and grain is equal; and, when H = 0.4,

the weight of the support structures is equal to theweight of the panicle. Equation 28 shows, as has longbeen known, that, for a given biomass, a higher grainyield is obtained by reducing the amount of supportstructures. There are limits: thus, H = 0.8 gives themathematically correct, but biologically ridiculous,conclusion of unsupported grain weight.

Predicting yieldGrain yields of rice are stated at a nominal moisturecontent (fresh weight basis) of 14% (for wheat, it is15%). To convert yield as dry maer in g m2 to t

ha1

, divide by 100; then divide by 0.86 to allow formoisture content.Table 2 shows that a Vela variety would have

to increase LAI by 50% to 100% above that of asemidwarf variety to intercept the available PAR.At constant specic leaf area, this means that leafweight and stem weight would have to increaseproportionally. The ratio of weight to LAI atmaximum LAI (Wsst/LAI = 1.37) from the data inTable 4 combined with the predicted LAIs in Table2 suggest that, for an erect NPT-like canopy, W

sst 13.3and, for the Vela canopy, Wsst 20.6. It is

clear that erect canopies achieve higher rates ofcanopy photosynthesis than the more semidwarfcanopies. In order to do so, they have to investheavily in the support structures that the dwarnggenes limit, suggesting that H may decrease in themore erect canopies. One consequence of this extrainvestment would be an increase in the size of thenitrogen reservoir available for grain growth and thefractional decline in canopy photosynthesis towardmaturity might be reduced, for example, f 0.8.The eect of increasing f to 0.8 and reducing H to

0.4 increases the biomass of the Vela type to 28.4 tha1, the grain yield to 13.2 t ha1 (14% m.c.), and thesupport biomass (stem, leaves, and dead maer) to14.2 t ha1. At the moment, uncertainty exists aboutthe values of f and H for a Vela type; however, thechanges in f and H aect the predicted supportweight but not the grain yield.

Values for the driving variables (Iday

, TPS, T

mean)

and parameters (T

, c

, , mT

, f, , H, pg

) are listed inTable 1 for a well-fertilized and irrigated rice crop.Achievable values of c and canopy photosynthesisfor various combinations of leaf architecture and leafphotosynthesis are given in Table 3, and values of c

T

are shown in Table 5. We used the above equations topredict maximum yield as shown in Table 6.

The results show that, in the tropics, a Velavariety would increase maximum yield by 11%(from 11.7 to 13.0 t ha1). Yields in the subtropics areabout 40% higher than in the tropics owing to thelower average daily temperatures, which reduce the

coecient of maintenance respiration (mT). The C4syndrome in the erect canopy type could increaseyields by about 38% in the tropics or subtropicscompared with the semidwarf type.

Radiation use eciency

Although radiation use eciency is a valuableagronomic parameter, it is not an ideal trait foruse in breeding. It requires careful measurementthroughout the growing season and, because of its

low precision, small dierences between breedinglines cannot be reliably distinguished. Here, weprovide a theoretical derivation of the coecient thatprovides insight into the factors shaping its value.

If we assume that, over the growingperiod, respiration is some fraction () of grossphotosynthesis, the accumulated crop biomass(including roots), W

cum, can be wrien as

Wcum = (1 )Pgd (29)

Substituting for Pgd from equation 12 and

integrating equation 29 over the growing season gives

Wcum = (1 ) cT Rcum/(1 ) (30)

where Rcum is the total PAR intercepted over thegrowing period, that is, I

day. The constant ofproportionality between accumulated biomassand accumulated intercepted PAR (W

cum/Rcum) wasdened by Monteith (1977) to be the radiation useeciency (r). Thus, equation 30 denes radiationuse eciency for total crop biomass as

Relative weight o support biomass, h

Harvest index, H

0

1

2

3

4

0.2 0.4 0.80.6

Fig. 7. The weight o the biomass (leaves, stems, and dead matter)invested in support o grain production relative to grain weight (h)decreases nonlinearly as the harvest index (H) increases (rom theequationh = (1/H) 1.25).


16/2213

r = (1 ) cT/(1 ) (31)

which can be wrien as

r = (1 )T (32)

The more usual form of the coecient (rue

) is

calculated for shoot biomass and, if we dene theshoot weight ratio as Sr, it can be wrien as

rue = Sr (1 ) T (33)

Ryle et al (1976) suggested that total respirationcould amount to 50% of gross photosynthesis,that is, = 0.5. Several of the terms in equation 33could be inuenced by temperature, but possiblyin opposite directions, giving an expression that isoften regarded as describing a conservative entityand one independent of location (Russell et al 1989,Mitchell et al 1998). Using Ryles suggestion ( =0.5), = 0.1, and the parameters for semidwarf rice(

c= 0.88,

T= 5.9 g CH

2O MJ1) and maize (

c= 1.0,

T = 7.2 g CH2O MJ1) at a daytime temperature

of 30 C, the r of rice and maize computed usingequation 33 would be 2.9 and 4.0 g total biomassMJ1 intercepted PAR, respectively. Converting tothe more familiar basis of aboveground biomass, bymultiplying by shoot weight ratio, for example, 0.85for a cereal crop, we obtain values for rue of 2.5 and3.4 g MJ1 (aboveground biomass, intercepted PAR),

in moderate (rice) or good (maize) agreement withgeneral values of RUE for these crops (Mitchell et al1998).

Given that PAR is about half of solar radiation,and the peak growth rate above would be aained

by a crop intercepting 95% of incident PAR, thenthe maximum growth rate for rice in the tropics isgiven by I

day

rue, which would be 10 0.95 2.5

= 23.8 g d1

(for C4 rice, it would be 32.3 g d1

). Acrude estimation of crop duration can be obtainedby dividing total biomass by the radiation usecoecient and dividing that by the average dailyincident PAR. The ratio of W

smaxand

ruegives the

total radiation intercepted, which, if used with theenergy balance equation (see Appendix), can be usedto calculate the total amount of water transpired bythe crop.

Discussion

As canopies become increasingly erect, the LAIrequired for full light interception increases (Table2). Maximum rice yields in irrigated systems areobtained in the clear sunny conditions of the dryseasons in the tropics and subtropics. The relation-ship between daily total canopy photosynthesis andirradiance was calculated using a model based onthe BouguerLambert Law of PAR distribution in acanopy and a hyperbolic description of the relation-ship between leaf photosynthesis and PAR. For erect

Table 6. The calculated grain yields (14% moisture content) o rice in the tropics and

subtropics or the our canopy types o rice as dened in Table 2. The extra subtypes o erect

canopy are or a C4

rice and or C3

with low photosynthesis (hal the usual maximum rate o

lea photosynthesis o 32.5 mol CO2

m2 s1). Canopy photosynthesis is calculated or 95%

interception o PAR; values o cT are 40.5 or the tropics and 56.5 or the subtropics (units g

DW g1 CH2O d); biomass yields are dry weights; and the harvest index is 0.45.

Item Canopy type


Extinction coecient, k 0.60 0.45 0.31 0.20

Canopy photosynthesis, Pgdmax (g CH2Om2 d1)

52.1 55.2 58.3(C

4, 76.0)

(low, 47.0)

61.5

Tropics, grain yield (t ha1, 14% m.c.) 11.0 11.7 12.3

(C4, 16.1)

(low, 9.9)

13.0

Tropics, biomass (t ha1) 21.1 22.3 23.6

(C4, 30.8)

(low, 19.0)

24.9

Subtropics, grain yield (t ha1,

14% m.c.)

15.4 16.2 17.3

(C4, 22.5)

(low, 13.9)

18.1

Subtropics, biomass (t ha1) 29.4 31.1 33.0

(C4

, 42.9)

(low, 26.6)

34.7


17/2214

canopies, the total daily rate of canopy photosyn-thesis was shown to be linearly related to fractionalinterception of PAR (Fig. 3). The leaves of modernerect varieties receive only a fraction of full sunlight,so, to a good approximation, their photosynthesiscan also be described by the linear part of the leafphotosynthesis versus irradiance curve. Conse-quently, a model of daily canopy photosynthesis

was derived assuming that the relationship betweenleaf photosynthesis and PAR was linear, with a slopeproportional to the quantum yield of photosynthesis.The model described the relationship between dailycanopy photosynthesis and daily irradiance as beingproportional to the fraction of the irradiance inter-cepted () and the quantum yield of the canopy (T),which was shown to be the product of leaf quantumyield (T) and a canopy eciency factor, c/(1 ).The factor c is a measure of the eective quantumyield of leaves in a crop, which approaches unityfor erect canopies with high maximum rates of leaf

photosynthesis. Thus, daily canopy photosynthesiscan be described as the product of the interception ofdaily PAR and canopy quantum yield (TIday) andat full interception of PAR for modern crop canopieswith erect leaves and when = 0.1 is approximately0.95

TI

day. Consequently, for modern canopies with

erect leaves, the only way to improve canopy photo-synthesis is by increasing the quantum yield (T) andremoving its temperature sensitivity by introducingthe C4 syndrome into rice.

A simple growth analysis based on the massbalance of a crop showed that maximum grain

yield depends on canopy photosynthesis, theability to convert photoassimilate into biomass (cT),and the harvest index (H). The conversion factorc

T(which is the group of parameters f /(m

T(1

kdmax)) collected together) is inversely related tothe coecient of maintenance respiration. Carbonxed by photosynthesis that did not contribute tocrop aboveground biomass was used in allocationto roots, in synthetic respiration, and by exudationfrom roots. All of those factors were combined intoa dimensionless parameter, . For cereals in general, is about 0.59 but will vary between crops; for

example, in legumes it is likely to be less becauseof additional expenditure of carbon in symbioticnitrogen xation. The parameter f allows forcanopy photosynthesis declining from its maximumvalue toward maturity. Maintaining canopyphotosynthesis close to its maximum value by goodfertilizer and crop management (Table 5) as the cropapproaches maturity is important for maximizing

biomass and yield (equations 2225).The grand simplication of crop growth that

we sought is represented by equations 22 and 25.

We tested our equations for a contrasting crop in acontrasting environment, forage grasses growingin the autumn of a temperate climate, and wefound them to work well (see Appendix). It may befortuitous that plausible gures for rice biomass andyield can be calculated from equations 22 and 25unrealistic results can easily be obtained using othervalues for the parametersbut we believe that thegeneral principles represented in the equations aresound.

The largest uncertainties are in the base rates formaintenance respiration and quantum yield, and theeects of temperature on respiration and quantumyield. Good data for rice, for example, are largelyabsent from the literature. Work by Hogewoning etal (2012) suggests that the spectral composition of thehigh-pressure sodium lamps used by Ehleringer andPearcy (1983) may have led to an incorrect estimateof the value of quantum yield in daylight. Whenmore quantitative information concerning such

spectral eects becomes available, it will be a simplemaer to estimate their impact on the calculationof photosynthesis and yield. A further uncertaintyis that values for all driving variables andparameters are being averaged over crop durationor over the period of closed canopy and maximumphotosynthesis. These values are hard to obtainexactly even if linearity does hold over the relevantperiod so that an average value can be meaningful.

Equations 22 and 25 highlight the importance ofboth photosynthesis and maintenance respiration.(The coecient of maintenance respiration, m

T,

occurs within cT in equations 22 and 25 and issensitive to temperaturesee Figure 8.) We hope thatthe prominent eect of maintenance respiration indetermining yield dierences between climatic zoneswill encourage more research aimed at answeringthe various questions about respiration raised byAmthor (2000), especially for rice. Meanwhile, theconclusion must be that photosynthesis(throughquantum yield) and maintenance respirationare the prime drivers of crop biomass and yield.Improvements in photosynthesis will be essential forproductive and sustainable agriculture.

Both theory (Table 2) and practice (Table 4)give a maximum LAI of around 7 for semidwarfindicas. The predictions for erect and Vela canopyarchitectures (Table 2) show that leaf area wouldhave to increase by 50100% to intercept all of theavailable PAR. The changed canopy architecture hastwo eects: (1) it improves canopy photosynthesisand (2) it probably increases the size of the vegetativereservoir of nitrogen, which is required for increasedgrain yield. In the tropics, a Vela variety wouldincrease maximum yield by 11% (from 11.7 to 13.0 t


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and elsewhere.) The C4 syndrome could increaserice yields to 16.1 t ha1 in the tropics and to 22.5 tha1 in the subtropics, about 38% above the yields ofsemidwarf cultivars (Table 6).

Links between photosynthesis and crop yieldwere discussed by Long et al (2006) and in Sheehy etal (2000b). From the results above, we suggest thatyield increases of 50% resulting from improvementsin photosynthesis wanted by Long et al (2006) could

be achieved, in rice, only by increasing the quantumyield to the value achieved by the C4 syndrome andimproving canopy architecture and sink capacityduring vegetative growth. The possibility ofconverting rice from a C3 pathway to a C4 pathwaywas discussed in Sheehy et al (2007b) and in vonCaemmerer et al (2012) and research is in progress(see www.irri.org/c4rice).

We hypothesize that semidwarf indicamaterials may not be suitable platforms for furtherimprovements in C3 or C4 rice owing to insucient

sink capacity (leaves and stems) in the vegetativephase of development. Culm length declined fromabout 128 cm in the rice types before the GreenRevolution to about 53 cm afterward. This changeprevented lodging in crops receiving large amountsof fertilizer nitrogen. However, the importance ofthe vegetative component of the crop acting as areservoir for nitrogen in support of reproductivegrowth also needs to be borne in mind whendesigning high-yielding crops. In contrast to thevegetative stage of growth, the reproductive stageof rice has unused sink capacitythere are many

more spikelets (orets) initiated than nally developas grains at harvest (Sheehy et al 2001)thusenabling observed increases in yield in response toelevated CO2 up to about 500 ppm although not athigher concentrations (Rowland-Bamford et al 1990,1991). It is worth noting that rice varieties adaptedto deep water can produce elongation growth upto about 25 cm per day, and successful cultivarsfor those environments have been developed fromsubmergence-tolerant landraces (Catling 1992,Bailey-Serres and Voesenek 2008, Sheehy andMitchell 2011b). It would seem that there is a limit to

the amount of CO2 that the semidwarf indica typesof rice can use and it may be set by the strength ofvegetative sinks.

The large amounts of mineral nutrients requiredin high-yielding crops far exceed the capacity ofthe soil to supply them without the application offertilizers (Table 7). The proportion of an appliedfertilizer nutrient that appears in the crop (fertilizeruse eciency for each nutrient) is highly variabledepending on soil type and other environmentalfactors. Thus, site-specic nutrient management

Fig. 8. The eect o temperature (considered constant across 24 h) onthe model parameters (graphs A and B) and predicted grain yields(graph C). Yields (14% moisture content) were calculated with harvestindex o 0.45, PAR o 10 MJ m2 d1. For C

3crops, the value o lea

quantum yield (T) varies as shown in (A); or C

4crops, the value o

lea quantum yield is constant at 7.2 g CH2O MJ1. The value oe

cor

calculating T

was taken as 1.0. The lines or yield o C3

and C4

cropscross over at about 20 C and 28 t ha1. The dotted portions o the linesindicate temperature ranges (below 20 C and above 35 C) where

harvest index or rice tends toward zero.

Value oaT orT (g CH2O MJ1)

4

6

8

10

T

aT

A

0.03 120

80

40

0

0.02

0.01

0.00

mT

cT

B

Coecient o maintenancerespiration, m

T(g g1 d1) Value o c

T(g g1 d)

ha1). Yields in the subtropics are about 40% higherthan in the tropics owing to the lower averagedaily temperatures, which reduce the coecient ofmaintenance respiration (mT). (The simplicationused here removes crop growth duration as a factorinuencing maximum yield, which we have usedin other analyses (Mitchell and Sheehy 2000) toexplain the dierences between yields in the tropics

Temperature (C)

50

40

15 20 25 30 35 40

30

20

10

0

C

Yield (t ha1)

C4

C3


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is recommended for increasing yield (Cassmanet al 1996, Olk et al 1999, Dobermann et al 2004).Retaining canopy photosynthesis close to itsmaximum value (f 0.7 to f 0.8) through good cropmanagement (Greenwood et al 1990, Sheehy et al1998) while enabling nitrogen to be transferred tothe grain as the crop matures is important (Sheehy etal 2004). Shaded leaf areas contribute about 25% oftotal canopy photosynthesis (Sheehy 2000) and theirinuence is partly governed by the parameter f. Theequations in this paper suggest that improvements

in the quantum yield of photosynthesis of the sameorder as the change that occurs in the change fromthe C3 to C4 syndrome of photosynthesis wouldprobably take yields to their upper limit achievablewith current biological technologies (Allen et al2003).

Our work in this paper was not designed to dealwith the problems surrounding climate change,water, or high temperature (Prasad et al 2006), butrather the immediate consequences for crop yieldof improving the photosynthetic system underconditions that might exist in the rst half of this

century. Nonetheless, the equations derived canbe used to examine the consequences of changesin temperature. The eects of temperature areimplemented in equation 17 for mT and equation 5for T; each works in the same direction to decrease

biomass and yield as temperature rises (Fig. 8). It isclear that changes in cT dominate yield responses totemperature in both C

3and C

4crops. Below 30 C,

predicted C3 yields increase more rapidly than thosepredicted for C4 crops and above 30 C theyfallmore rapidly.Cooler, high-radiation conditions favorhigh yields but temperature and irradiance tend to

be inversely related. Moreover, riceyields approachzero outside the temperature range of 20 to 35C.A rising concentration of CO2 could increase theapparent quantum yield of rice up to a concentrationof about 500 ppm, although the work on high-CO2eects on rice suggests that rice cultivars capable of

being more responsive to CO2 than the semidwarfindicas would be needed to fully exploit suchincreases.

Concluding remarks

The overall conclusions in this paper are that(1) improvements in yield can be made withimprovements in canopy photosynthesis, (2)those improvements need to focus on improvingcanopy architecture and the quantum yield ofphotosynthesis, (3) improvements in canopyarchitecture should focus on Vela plants withsucient vegetative and productive sink capacity torealize the benets of improved carbon capture, and

(4) crop management cannot be ignored in the drivefor enhanced crop yields.The negative aspects of the law of unintended

consequences should not inhibit research aimed atincreasing yield in all rice ecosystems nor shouldit, like history, be ignored. Good research is aboutideas and the testing of hypotheses, with empiricism

becoming increasingly important as the productsof research are measured against theoreticalpredictions.

Acknowledgments

J.E.S. thanks IRRI for the use of facilities and M.Barrios for technical assistance. The use of facilitiesat the Department of Animal and Plant Sciences andsupport from Professor F.I. Woodward are gratefullyacknowledged by P.L.M.

Appendix

Dening maintenance respirationRyle et al (1976), using labeled CO2, showed thatthe respiratory ux of CO2 from plants could bedened in terms of two phases. The rst phase wasan intense eux having a half-life of 48 h and wasassociated with biosynthesis in meristems. Thesecond phase was less intense, with a half-life of26120 h and associated with the maintenance ofmetabolic activity. The rst phase amounted to 25%to 35% of the labeled assimilate; the second phasetotaled from 12% to 27% of the labeled assimilate.The maintenance eux showed a temperature

Table 7. The mineral element content (kg ha1) o a rice crop yielding 12 t ha1 grain (14% moisture content) with a harvest index o 0.43 and total

aboveground biomass o 24.2 t ha1 (ater Sheehy et al 2000b). Latshaw and Miller (1924) showed that carbon, oxygen, and hydrogen made up

about 95% o the dry weight o corn (maize). The carbon content o rice plants is approximately 40%; rice straw = 38% (Jimenez and Ladha 1993),

rice grain = 39.8% (Ladha pers. comm., IRRI 2000), and mineral elements comprise about 8%.

N P K Ca Mg S Cl Si Fe Mn B Zn Cu

234 56 377 33.3 42.5 18 119 1,086 6 1.6 0.8 0.43 0.04


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response with a Q10 2, and is dened in this paperas the cumulative second phase of respirationdivided by the weight of the crop. Given that everyunit of carbon assimilated is associated with a

biphasic loss of carbon in respiration, associatingthe cumulative second phase of respiration withweight gives a convenient method of describingmaintenance respiration. Sheehy et al (1979, 1980)used the concept of two phases of respiration tomodel the growth of a grass crop; crop weight wasdened in terms of the fraction of carbon capturedduring photosynthesis that remained in the cropafter respiration. We use their approach and dene aweight-related maintenance coecient of respirationas the ratio of the cumulative second phase ofrespiration divided by the weight of the crop, wrienhere for day d as

mT(d) = d 1P (d t) G(t)/d 1P(d t) f(t) (1a)

where G is the fractional amount of previouslyacquired photoassimilate P(d t) respired on dayd and f(t) is the fraction of P(d t) remaining afterrespiration. This approach gives estimates of mT

broadly consistent with published values.

Testing the equations or a contrasting cropThe various equations can be compared with themean data for eight forage grass species covering arange of canopy structures growing in the eld inSeptember to October (Sheehy and Peacock 1975).The average radiation use eciency of the grasses,

rue, for the growth rate data is calculated to be 2.2 gDM MJ1, the same value as the general one for rice(Mitchell et al 1998). The average temperature fordaylight was 12.25 C, just outside the temperaturerange of equation 5, which predicts T to be 8.4 gCH

2O MJ1 if extrapolated. Agreement was good

between the predicted maximum daily rate ofcanopy photosynthesis from equation 12, 36.7 gCH2O m

2 d1, and the average of the measuredvalues, 33.5 g CH2O m

2 d1, so that c = 0.91. Therewas a large mass of roots relative to shoots (137%;root weight ratio 0.58), which might be expected of

a perennial crop measured in autumn when largeamounts of stubble were left after the harvest ofshoots, so that was estimated to be 0.3. Equation 20can be used with the data to calculate m

Tas 0.0048

g g1 d1 at the mean temperature of 10.5 C. Usinga Q10 of 2, this gives a value at 20 C of 0.0093 g g

1d1, a value in good agreement with values reported

by McCree (1970) and others above. The value of ffor forage grass canopies is likely to approach 0.5

because canopy photosynthesis declines once fulllight interception is approached owing to the decline

in the maximum rate of photosynthesis of successiveleaves (Sheehy 1977).

Solar energy use by cropsUltimately, the bioenergetics of crops are driven

by solar radiation and it is useful to set this outquantitatively. The energy balance of a crop,considering 1 m2 of ground for a period of time suchas a day, can be wrien as

aRs = Rl + H + LE + Pe (2a)

where a is the fraction of solar radiation absorbedby the crop; Rs is solar (shortwave, wavelengths3003,000 nm) radiation received (MJ m2); Rl is thenet longwave (thermal, over 3,000 nm wavelength)radiation (MJ m2); H is the exchange of sensibleheat (MJ m2); LE is the loss of latent heat (MJ m2),from multiplying the latent heat of vaporization ofwater (L, MJ kg1) by the amount of water lost by

evapotranspiration (E, kg m2

); and Pe is the energystored in photosynthesis (MJ m2).On a sunny day, a typical total of solar radiation

received would be 20 MJ m2. Allowing for longwaveradiation exchanges, the net absorption of radiantenergy would be about 13.3 MJ m2 d1 (Woodwardand Sheehy 1983). The sensible heat loss is zero whencrop and air temperatures are the same. The latentheat of vaporization of water is 2.43 MJ kg1 (at 30 C)so the daily solar radiation absorbed is equivalentto evaporation of about 5.5 kg H2O m

2 or 55 t H2Oha1 or 5.5 mm of water, a value often observed for

the evapotranspiration of irrigated rice in the tropics.The energy content of biomass is about 15.5 MJ kg1;therefore, the daily net energy receipt (13.3 MJ m2)is equivalent to about 8.6 t DM ha1 (DM is oven-drymaer of biomass), far higher than ever observed forcrops. As an example of solar energy conversion into

biomass, the maximum growth rate of a rice crop ina day was estimated to be about 24 g DM m2 (0.24 tDM ha1), thus equivalent to 0.37 MJ m2 d1 (Sheehyet al 2007a). Relative to incident solar radiation (20MJ m2 d1), this is a maximum daily eciency of1.9%; relative to 10 MJ m2 d1 PAR, it is 3.7%, which

is more realistic since photosynthesis cannot usewavelengths longer than 700 nm.

We have two conclusions from this briefanalysis. First, much of the solar energy absorbed

by crops is used for transpiration, an unavoidableloss of water if stomata are open for photosynthesisto occur. Second, the eciencies of energy use inphotosynthesis and the synthesis of crop biomassare low so there is much scope for improvement,albeit those improvements may be beyond currenttechnologies.

1 0


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