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Influence of light on the growth of young tomato, cucumber and sweet pepper plants in the greenhouse: Calculating the effect of differences in light integral
Scientia Horticulturae, 31 (1987) 175-183
175
Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands
Influence of Light on the Growth of Young Tomato, Cucumber and Sweet Pepper Plants in the Greenhouse: Calculating the Effect of Differences in Light Integral G.T. BRUGGINK
Agricultural University, Department of Horticulture, P.O. Box 30, 6700 AA Wageningen (The Netherlands) Publication No. 527 (Accepted for publication 23 October 1986)
ABSTRACT Bruggink, G.T., 1987. Influence of light on the growth of young tomato, cucumber and sweet pepper plants in the greenhouse: calculating the effect of differences in light integral. Scientia Hortic., 31: 175-183. A method is presented to calculate the effect of different levels of mean daily light integral (PAR incoming per unit ground area) on the growth of young tomato, cucumber and sweet pepper plants. The relative sensitivity of the growth parameters RGR and NAR to a difference in light integral was determined, as well as the relative sensitivity of LAR to a difference in NAR. Differences between the three species were small. At higher values of mean daily light integral, LAR appeared to have a strong compensating effect on changes in NAR. This is expressed as the flexibility index of LAR. Levels of light integral differing by 1% caused values for RGR to differ by 0.6% in wintertime and 0.4% in spring. Using the relationship between light integral and RGR, calculations are presented on the effect of different light transmission values of the greenhouse and different intensities of artificial light on the time needed for plants to double in dry weight. Keywords: cucumber; growth analysis; light; sweet pepper; tomato; young plants. Abbreviations: B, C=coefficients in the linear relationship between 1/LAR and NAR; K], K2=Michaelis-Menten constants; L A R = l e a f area ratio; N A R = n e t assimilation rate; NAl~ax = maximum value for NAR at light saturation; PAR = photosynthetically active radiation (400-700 nm); R=mean daily light integral (PAR incoming per unit ground area); RGR = relative growth rate; RGRmAx= maximum value for RGR at light saturation; Td = time needed to double in dry weight (In2/RGR); % Y/%X = relative sensitivity of Y to a 1% difference in X.
0304-4238/87/$03.50
© 1987 Elsevier Science Publishers B.V.
176 INTRODUCTION Bruggink and Heuvelink (1987) determined relationships between R and RGR for young tomato, cucumber and sweet pepper plants. From a practical horticultural point of view, it is not only absolute values of RGR which are interesting. It is also important to know the relative sensitivity of RGR to differences in the amount of light received by the plant. Light integrals may be altered as a result of energy conservation measures in a greenhouse which result in a lower light transmission, or as a result of the use of additional artificial light, a common practice in wintertime for the first stages of growth of vegetable plants. In the first case, R is altered by a certain percentage; in the second case, by a certain amount. Information on plant reactions to light is essential if an economic evaluation is to be made between, e.g., energy conservation and growth reduction. The principles of these effects may also be important from a botanical or ecological point of view, e.g. in order to understand why certain species are able to adapt to conditions of very low light intensities while other species are not. In this context, it may also be useful to explain the effects of light on growth by the effects on photosynthesis and morphology. In terms of growth analysis, this means the effects on NAR and LAR. Calculations on the effect of differences in light integral on plant growth were presented by Challa and Schapendonk (1984), but their data concerned cucumber plants grown under controlled environmental conditions. In this study, we will use data from plants grown under normal greenhouse conditions and plants grown in a double-layer system (Bruggink and Heuvelink, 1987). MATERIALSAND METHODS The relationships and parameter values used in this study are those found by Bruggink and Heuvelink (1987) for young tomato (Lycopersicon lycopersicum L. 'Moneymaker'), cucumber ( Cucumis sativus L. 'Uniflora' ) and sweet pepper ( Capsicum annuum L. 'Propa Rumba' ) plants. They determined average values for RGR, NAR and LAR over a certain interval of plant dry weight at different values of R. R signifies mean daily light integral (J (PAR) cm-2 day-1 ) received by the plants during the growing period considered. A range of values for R was realised by growing in different seasons and by using a double-layer system with additional artificial light, as well as a normal greenhouse situation. Values for RGR and NAR were related to R and values for LAR were related to NAR by the following functions: NAR = NARmax "R R + K1
(1)
LAR=I/(B+C.NAR)
(2)
177 TABLEI Parameter values used in the relationshipsbetween R G R and R (eqn. (I)),N A R and R (eqn. (2) ) and between L A R and N A R (eqn. (3) ).Values were obtainedby Bruggink and Heuvelink (1987) forplantsin the range 220-740 nag dry weight RGR
RGRmax (day ') Tomato 0.29 Cucumber 0.31 Sweetpepper 0.22
NAR
LAR
/(2 (Jcm -2 day-')
NARma~ (mgcm -2 day-')
K1 (Jcm -2 day-')
B (mgcm -2)
C (days)
50.8 88.1 68.1
0.75 0.74 0.59
108.7 155.8 128.3
1.22 1.33 1.48
1.76 1.48 1.93
Multiplying eqns. (1) and (2) gives RGR=
RGR~ax .R
B'K1
(3)
)
R -F B + C" N A R ~ x RGRmax .R
R+K2
(4)
Bruggink and Heuvelink (1987) used these equations for data from plants in the dry-weight intervals 20-67, 67-220, 220-740 and 740-2460 mg. Unless otherwise specified, the parameter values used here are those for the weight-interval 220-740 mg plant dry weight. These values are listed in Table I.
Calculations. - In order to calculate the relative sensitivity of the growth parameters to a difference in R (in the case of LAR, the relative sensitivity to a difference in N A R ) , the following equation was used:
% Y/%X= ( dY/dX) / ( X/Y)
(5)
Evaluation of this equation for RGR, NAR and LAR results in
%RGR/%R= K2/ ( K2 + R )
(6)
%NAR/%R=K1/(K1 + R)
(7)
%LAR/%NAR= - C-NAR/(B + C.NAR)
(8)
The effects of light on growth are also presented in a way better related to practical circumstances t h a n the method described above. In this case,
178 .....
1.0. i,
Cucumber Sweet Pepper Tomato
~ 0.8. 0.6.
0.~..
\'~,, 'N " " -
0.2.
o
i
100
i
200
i
300
#
i
400 500 R (J cm"2 d-1)
Fig. 1. Calculated relative sensitivity of RGR to differences in R, expressed as %RGR/%R and plotted as a function of R. Values were calculated for young cucumber, sweet pepper and tomato plants in the dry-weight interval 220-740 mg.
in 2/RGR rather than RGR was taken as the relevant parameter. This is also denoted as Td, the time needed for the plants to double in dry weight. In this case, average radiation values for Wageningen (De Vries, 1955) were related to time of year by a polynomial function. With this function, the light integral for every day of the year was calculated, and from this the actual light integral reaching the plant as a result of greenhouse transmission for natural light or the use of additional artificial light. With this light integral, Td was calculated using eqn. (4). RESULTS AND DISCUSSION
Effects of a proportional difference in R on RGR. - Figure 1 shows the calculated
percentage differences in RGR when values for R differ by 1%. At low values for R, RGR reacts almost proportional to the difference in R, but with increasing R, this effect diminishes strongly. Above approximately 300 J cm -2 day-1 there is little effect of R on RGR. This confirms the observations by Klapwijk (1981) and Klapwijk and Tooze (1982), who found a constant value for RGR of tomato and cucumber from March to September. During this period, R inside the greenhouse is above approximately 300 J cm -2 day-1 in The Netherlands. When we compare our data with those of Challa and Schapendonk (1984) for young cucumber plants in a growth-chamber experiment, there appears to be a stronger reaction to light for the growth of their plants, but the shape of their curves is similar to ours. For the plants in our experiment, it may be concluded that the effect of a 1% reduction in R is a 0.6% reduction in RGR in wintertime, when R is around 50 J cm -2 day -1 and a 0.4% reduction in spring, when R is
179
around 100 J cm-2 day-1. There is little difference between the three species, although tomato appears to be least sensitive to differences in R and cucumber most sensitive. For all three species, the sensitivity decreases further towards summer. Explaining light effects on RGR by effects on N A R and LAR. - On an instantaneous basis, RGR is the product of NAR and LAR. When averaging over longer periods this is not necessarily true ( Hunt, 1982 ), but calculations showed that in our case it was a good approximation. Therefore the effect of R on RGR was separated into effects on NAR and LAR. This was done by substituting NAR" LAR for Y and R for X in eqn. ( 5 ), which results in
%RGR/%R = %LAR/%R + %NAR/%R
(9)
This means that the relative sensitivity of RGR to a difference in R may be considered as the sum of the relative sensitivities of NAR and LAR. As we did not describe LAR as a function of R but as a function of NAR (eqn. ( 2 ) ), the separation in eqn. (9) is not very useful, because %LAR/%R will result in a formula including both the relationship between LAR and NAR and the relationship between NAR and R. Therefore it is useful to separate %LAR/%R into %LAR/%R = %LAR/%NAR" %NAR/%R
(10)
A combination of eqns. (9) and (10) yields %RGR/%R = (1 + %LAR/%NAR) • (%NAR/%R)
(11)
Equation (11) describes differenees in RGR due to differences in R as the result of a difference in NAR, and the difference in LAR due to this difference in NAR. We cannot prove that the differences in LAR are in fact the result of differences in NAR and not the direct result of a difference in R. However, Thornley and Hurd (1974) made this assumption likely. This is further discussed by Bruggink and Heuvelink (1987). The value of %NAR/%LAR may be considered as a measure for the ability of LAR to eompensate for differences in NAR. In other words, if %LAR/%NAR equals - 1, then a difference in NAR is fully compensated by an opposite difference in LAR, and thus RGR remains unchanged. However, if %LAR/%NAR equals 0, then a difference in NAR will be fully reflected in a difference in RGR. Calculation of %NAR/%R proceeds according to eqn. ( 7 ). Figure 2 shows the calculated values for the three species. The differences between the three species appear to be small. The shape of the curves is similar to those of Fig. 1. %LAR/%NAR can be calculated from eqn. (8). Because B and C have positive values, the value of %LAR/%NAR will always be negative or zero. Extreme values for %LAR/%NAR can be calculated by substituting the value for NARma~ in eqn. (8). This results in the values -0.52, -0.45 and -0.43 for
180 1.0-
....... ....
~t ~,,
Cucumber Sweet Pepper Tomato
0.8x
0.6
"~'x',~..
0.~.,
0.2.
0 0
I 100
I 200
I 300
I I ~,00 500 R (J cm-2 d-l)
Fig. 2. Calculated relative sensitivity of N A R to differences in R, expressed as %NAR/%R and plotted as a function of R. Values were calculated for young cucumber, sweet pepper and tomato plants in the dry-weight interval 220-740 rag.
tomato, cucumber and sweet pepper, respectively. Figure 3 shows %LAR/%NAR as a function of NAR. Three conclusions result from this analysis. (1) The relative sensitivity of NAR to differences in R decreases with increasing R. ( 2 ) This reaction is partly compensated by an opposite effect on LAR which increases with increasing NAR and thus with increasing R. (3) The flexibility of LAR for tomato is higher than for cucumber and sweet pepper.
Effect of plant weight. Figure 4 shows a comparison of the four weight inter-
vals over which Bruggink and Heuvelink {1987) calculated average values for -0.5
-o.4
i
N
-a3
j J/- .-"
-Q2
• ~" ----
Tomato . 9 , ~ Pt~oW
......
Cucun¢~
-0.1 I
I
0.1
0.2
I
0.3
O.t,
I
I
0.5 O~ NAR (mg cr 2 d -1)
Fig. 3. Calculated relative sensitivity of LAR to differences in NAR, expressed as %LAR/%NAR and plotted as a function of NAR. Values were calculated for young tomato, sweet pepper and cucumber plants in the dry-weight interval 220-740 rag.
181 1.0,
Weight intervals 20-
o~ ~'
67rag
220rag ------220740m9 __.-"/z,O- 2z+60 mg
,~
......
0.8 I",~ ~,i'~
67-
\i~",~x
0.6
0
I 100
I
200
I 300
I
I
z,O0 500 R (Jcm-2c1-1)
Fig. 4. Calculated relative sensitivity of RGR to differences in R, expressed as %RGR/%R and plotted as a function of R. Valueswere calculatedfor youngtomato plants in different dry-weight intervals, as given in the figure. the growth parameters. Only the results for RGR of tomato are shown; those for the other species are more or less similar. There appears to be a tendency for less sensitivity to light with increasing plant weight. This contrasts with experiments on the effect of a change in R for a closed canopy. These showed an almost exact proportionality between R and yield for cucumber and tomato (Drews et al., 1980; Drews and Heisner, 1982). Calculations based on a simulation model of plant growth indicate that yield should react even more t h a n just in proportion to R in the case of a closed canopy (Challa and Schapendonk, 1984). Evidently the plants in our experiment do not yet show a tendency to a more proportional reaction to light integral with increasing plant weight. Effects of light integral on Td. - Figure 5 shows the time needed for tomato plants to double in dry weight (Td) plotted over the year. The reference condition chosen is a greenhouse situation with a light transmission of 65%; average values of global radiation for The Netherlands are assumed. This is compared to situations with (a) different light transmission values and (b) different amounts of additional light given during 10 h per day. The strong effect of greenhouse transmission on Td in winter is clearly demonstrated in Fig. 5a. From Fig. 5b, it appears that intensities of artificial light over 10 W m -2 have little promoting effect on RGR. Furthermore, this effect is only appreciable from the middle of November to the middle of February.
CONCLUSION The methods described here add more value to the initial data that were used by extending these data for use in a practical situation. In conjunction with an
182 7
Transmission
a
...... -
50%
-
65%
80%
------
..,~ ..,\ / !
\
/
\
!
\
!
\
/
\
z
,
,
J
J
~
~
. 0
\
.
. N
. D
.
. J
. F
. M
A
M
months
Light intensity b
- -
°wlm2 SW/m2
...... .
.
.
.
10W/m 2 --.--
15Wire 2
i
i
i
i
i
i
i
i
i
i
i
i
J
J
A
S
0
N
O
J
F
M
A
M
months
Fig. 5. Calculated time needed for young tomato plants (220-740 mg dry weight) to double in dry weight, expressed as Ta, plotted as a function of time of year. The lines drawn in (a) and (b) represent a reference situation with a greenhouse light transmission of 65%. The broken lines in (a) represent situations with a light transmission of 50 and 80%, respectively. The broken lines in (b) represent situations with different intensities of artificial light, given during 10 h per day.
183
economic model, the methods can be used to evaluate the effect on plant growth of energy conservation methods which reduce the light transmission in a greenhouse. In this way, the effect of the use of additional light can also be evaluated. The value %LAR/%NAR could be termed a flexibility index of the leaf area ratio. Together with the reaction of net assimilation rate, this index determines the reaction of relative growth rate to differences in light integral. It will be interesting to see if this flexibility is of the same order of magnitude for other species. ACKNOWLEDGEMENTS
The author wishes to thank E. Heuvelink for his assistance and cooperation in calculating the results. He is also much indebted to the late Prof. J.F. Bierhuizen for advice and criticism.
REFERENCES Bruggink, G.T. and Heuvelink, E., 1987. Influence of light on the growth of young tomato, cucumber and sweet pepper plants in the greenhouse: effects on relative growth rate, net assimilation rate and leaf area ratio. Scientia Hortic., 31:161-174. Challa, H. and Schapendonk, A.H.C.M., 1984. Quantification of the effects of light reduction in greenhouses on yield. Acta Hortic., 148: 501-510. De Vries, D.A., 1955. Solar radiation at Wageningen. Mededelingen Landbouwhogeschool, Wageningen, 55, 28 pp. Drews, M. and Heisner, A., 1982. Die Ertragsbildung der Gewaechshaustomate beim Fruehanbau in Abhaengigkeit v o n d e r Temperatur und der Beleuchtungsstaerke. Arch. Gartenbau, 30: 387-404. Drews, M., Heisner, A. and Augustin, P., 1980. Die Ertragsbildung der Gewaechshausgurke beim Fruehanbau in Abhaengigkeit vonder Temperatur und Bestrahlungsstaerke. Arch. Gartenbau, 28: 17-30. Hunt, R., 1982. Plant Growth Curves. The Functional Approach to Plant Growth Analysis. Edward Arnold, London, 248 pp. Klapwijk, D., 1981. Effect of season on early tomato growth and development rates. Neth. J. Agric. Sci., 29: 179-188. Klapwijk, D. and Tooze, S.A., 1982. The effect of season on the growth and development of young cucumbers. Internal Rep. No. 43, Glasshouse Crops Research and Experiment Station Naaldwijk, The Netherlands, 4 pp. Thornley, J.H.M. and Hurd, R.G., 1974. An analysis of the growth of young tomato plants in water culture at different light integrals and CO2 concentrations. II. A mathematical model. Ann. Bot., 38: 389-400.
175
Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands
Influence of Light on the Growth of Young Tomato, Cucumber and Sweet Pepper Plants in the Greenhouse: Calculating the Effect of Differences in Light Integral G.T. BRUGGINK
Agricultural University, Department of Horticulture, P.O. Box 30, 6700 AA Wageningen (The Netherlands) Publication No. 527 (Accepted for publication 23 October 1986)
ABSTRACT Bruggink, G.T., 1987. Influence of light on the growth of young tomato, cucumber and sweet pepper plants in the greenhouse: calculating the effect of differences in light integral. Scientia Hortic., 31: 175-183. A method is presented to calculate the effect of different levels of mean daily light integral (PAR incoming per unit ground area) on the growth of young tomato, cucumber and sweet pepper plants. The relative sensitivity of the growth parameters RGR and NAR to a difference in light integral was determined, as well as the relative sensitivity of LAR to a difference in NAR. Differences between the three species were small. At higher values of mean daily light integral, LAR appeared to have a strong compensating effect on changes in NAR. This is expressed as the flexibility index of LAR. Levels of light integral differing by 1% caused values for RGR to differ by 0.6% in wintertime and 0.4% in spring. Using the relationship between light integral and RGR, calculations are presented on the effect of different light transmission values of the greenhouse and different intensities of artificial light on the time needed for plants to double in dry weight. Keywords: cucumber; growth analysis; light; sweet pepper; tomato; young plants. Abbreviations: B, C=coefficients in the linear relationship between 1/LAR and NAR; K], K2=Michaelis-Menten constants; L A R = l e a f area ratio; N A R = n e t assimilation rate; NAl~ax = maximum value for NAR at light saturation; PAR = photosynthetically active radiation (400-700 nm); R=mean daily light integral (PAR incoming per unit ground area); RGR = relative growth rate; RGRmAx= maximum value for RGR at light saturation; Td = time needed to double in dry weight (In2/RGR); % Y/%X = relative sensitivity of Y to a 1% difference in X.
0304-4238/87/$03.50
© 1987 Elsevier Science Publishers B.V.
176 INTRODUCTION Bruggink and Heuvelink (1987) determined relationships between R and RGR for young tomato, cucumber and sweet pepper plants. From a practical horticultural point of view, it is not only absolute values of RGR which are interesting. It is also important to know the relative sensitivity of RGR to differences in the amount of light received by the plant. Light integrals may be altered as a result of energy conservation measures in a greenhouse which result in a lower light transmission, or as a result of the use of additional artificial light, a common practice in wintertime for the first stages of growth of vegetable plants. In the first case, R is altered by a certain percentage; in the second case, by a certain amount. Information on plant reactions to light is essential if an economic evaluation is to be made between, e.g., energy conservation and growth reduction. The principles of these effects may also be important from a botanical or ecological point of view, e.g. in order to understand why certain species are able to adapt to conditions of very low light intensities while other species are not. In this context, it may also be useful to explain the effects of light on growth by the effects on photosynthesis and morphology. In terms of growth analysis, this means the effects on NAR and LAR. Calculations on the effect of differences in light integral on plant growth were presented by Challa and Schapendonk (1984), but their data concerned cucumber plants grown under controlled environmental conditions. In this study, we will use data from plants grown under normal greenhouse conditions and plants grown in a double-layer system (Bruggink and Heuvelink, 1987). MATERIALSAND METHODS The relationships and parameter values used in this study are those found by Bruggink and Heuvelink (1987) for young tomato (Lycopersicon lycopersicum L. 'Moneymaker'), cucumber ( Cucumis sativus L. 'Uniflora' ) and sweet pepper ( Capsicum annuum L. 'Propa Rumba' ) plants. They determined average values for RGR, NAR and LAR over a certain interval of plant dry weight at different values of R. R signifies mean daily light integral (J (PAR) cm-2 day-1 ) received by the plants during the growing period considered. A range of values for R was realised by growing in different seasons and by using a double-layer system with additional artificial light, as well as a normal greenhouse situation. Values for RGR and NAR were related to R and values for LAR were related to NAR by the following functions: NAR = NARmax "R R + K1
(1)
LAR=I/(B+C.NAR)
(2)
177 TABLEI Parameter values used in the relationshipsbetween R G R and R (eqn. (I)),N A R and R (eqn. (2) ) and between L A R and N A R (eqn. (3) ).Values were obtainedby Bruggink and Heuvelink (1987) forplantsin the range 220-740 nag dry weight RGR
RGRmax (day ') Tomato 0.29 Cucumber 0.31 Sweetpepper 0.22
NAR
LAR
/(2 (Jcm -2 day-')
NARma~ (mgcm -2 day-')
K1 (Jcm -2 day-')
B (mgcm -2)
C (days)
50.8 88.1 68.1
0.75 0.74 0.59
108.7 155.8 128.3
1.22 1.33 1.48
1.76 1.48 1.93
Multiplying eqns. (1) and (2) gives RGR=
RGR~ax .R
B'K1
(3)
)
R -F B + C" N A R ~ x RGRmax .R
R+K2
(4)
Bruggink and Heuvelink (1987) used these equations for data from plants in the dry-weight intervals 20-67, 67-220, 220-740 and 740-2460 mg. Unless otherwise specified, the parameter values used here are those for the weight-interval 220-740 mg plant dry weight. These values are listed in Table I.
Calculations. - In order to calculate the relative sensitivity of the growth parameters to a difference in R (in the case of LAR, the relative sensitivity to a difference in N A R ) , the following equation was used:
% Y/%X= ( dY/dX) / ( X/Y)
(5)
Evaluation of this equation for RGR, NAR and LAR results in
%RGR/%R= K2/ ( K2 + R )
(6)
%NAR/%R=K1/(K1 + R)
(7)
%LAR/%NAR= - C-NAR/(B + C.NAR)
(8)
The effects of light on growth are also presented in a way better related to practical circumstances t h a n the method described above. In this case,
178 .....
1.0. i,
Cucumber Sweet Pepper Tomato
~ 0.8. 0.6.
0.~..
\'~,, 'N " " -
0.2.
o
i
100
i
200
i
300
#
i
400 500 R (J cm"2 d-1)
Fig. 1. Calculated relative sensitivity of RGR to differences in R, expressed as %RGR/%R and plotted as a function of R. Values were calculated for young cucumber, sweet pepper and tomato plants in the dry-weight interval 220-740 mg.
in 2/RGR rather than RGR was taken as the relevant parameter. This is also denoted as Td, the time needed for the plants to double in dry weight. In this case, average radiation values for Wageningen (De Vries, 1955) were related to time of year by a polynomial function. With this function, the light integral for every day of the year was calculated, and from this the actual light integral reaching the plant as a result of greenhouse transmission for natural light or the use of additional artificial light. With this light integral, Td was calculated using eqn. (4). RESULTS AND DISCUSSION
Effects of a proportional difference in R on RGR. - Figure 1 shows the calculated
percentage differences in RGR when values for R differ by 1%. At low values for R, RGR reacts almost proportional to the difference in R, but with increasing R, this effect diminishes strongly. Above approximately 300 J cm -2 day-1 there is little effect of R on RGR. This confirms the observations by Klapwijk (1981) and Klapwijk and Tooze (1982), who found a constant value for RGR of tomato and cucumber from March to September. During this period, R inside the greenhouse is above approximately 300 J cm -2 day-1 in The Netherlands. When we compare our data with those of Challa and Schapendonk (1984) for young cucumber plants in a growth-chamber experiment, there appears to be a stronger reaction to light for the growth of their plants, but the shape of their curves is similar to ours. For the plants in our experiment, it may be concluded that the effect of a 1% reduction in R is a 0.6% reduction in RGR in wintertime, when R is around 50 J cm -2 day -1 and a 0.4% reduction in spring, when R is
179
around 100 J cm-2 day-1. There is little difference between the three species, although tomato appears to be least sensitive to differences in R and cucumber most sensitive. For all three species, the sensitivity decreases further towards summer. Explaining light effects on RGR by effects on N A R and LAR. - On an instantaneous basis, RGR is the product of NAR and LAR. When averaging over longer periods this is not necessarily true ( Hunt, 1982 ), but calculations showed that in our case it was a good approximation. Therefore the effect of R on RGR was separated into effects on NAR and LAR. This was done by substituting NAR" LAR for Y and R for X in eqn. ( 5 ), which results in
%RGR/%R = %LAR/%R + %NAR/%R
(9)
This means that the relative sensitivity of RGR to a difference in R may be considered as the sum of the relative sensitivities of NAR and LAR. As we did not describe LAR as a function of R but as a function of NAR (eqn. ( 2 ) ), the separation in eqn. (9) is not very useful, because %LAR/%R will result in a formula including both the relationship between LAR and NAR and the relationship between NAR and R. Therefore it is useful to separate %LAR/%R into %LAR/%R = %LAR/%NAR" %NAR/%R
(10)
A combination of eqns. (9) and (10) yields %RGR/%R = (1 + %LAR/%NAR) • (%NAR/%R)
(11)
Equation (11) describes differenees in RGR due to differences in R as the result of a difference in NAR, and the difference in LAR due to this difference in NAR. We cannot prove that the differences in LAR are in fact the result of differences in NAR and not the direct result of a difference in R. However, Thornley and Hurd (1974) made this assumption likely. This is further discussed by Bruggink and Heuvelink (1987). The value of %NAR/%LAR may be considered as a measure for the ability of LAR to eompensate for differences in NAR. In other words, if %LAR/%NAR equals - 1, then a difference in NAR is fully compensated by an opposite difference in LAR, and thus RGR remains unchanged. However, if %LAR/%NAR equals 0, then a difference in NAR will be fully reflected in a difference in RGR. Calculation of %NAR/%R proceeds according to eqn. ( 7 ). Figure 2 shows the calculated values for the three species. The differences between the three species appear to be small. The shape of the curves is similar to those of Fig. 1. %LAR/%NAR can be calculated from eqn. (8). Because B and C have positive values, the value of %LAR/%NAR will always be negative or zero. Extreme values for %LAR/%NAR can be calculated by substituting the value for NARma~ in eqn. (8). This results in the values -0.52, -0.45 and -0.43 for
180 1.0-
....... ....
~t ~,,
Cucumber Sweet Pepper Tomato
0.8x
0.6
"~'x',~..
0.~.,
0.2.
0 0
I 100
I 200
I 300
I I ~,00 500 R (J cm-2 d-l)
Fig. 2. Calculated relative sensitivity of N A R to differences in R, expressed as %NAR/%R and plotted as a function of R. Values were calculated for young cucumber, sweet pepper and tomato plants in the dry-weight interval 220-740 rag.
tomato, cucumber and sweet pepper, respectively. Figure 3 shows %LAR/%NAR as a function of NAR. Three conclusions result from this analysis. (1) The relative sensitivity of NAR to differences in R decreases with increasing R. ( 2 ) This reaction is partly compensated by an opposite effect on LAR which increases with increasing NAR and thus with increasing R. (3) The flexibility of LAR for tomato is higher than for cucumber and sweet pepper.
Effect of plant weight. Figure 4 shows a comparison of the four weight inter-
vals over which Bruggink and Heuvelink {1987) calculated average values for -0.5
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Fig. 3. Calculated relative sensitivity of LAR to differences in NAR, expressed as %LAR/%NAR and plotted as a function of NAR. Values were calculated for young tomato, sweet pepper and cucumber plants in the dry-weight interval 220-740 rag.
181 1.0,
Weight intervals 20-
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Fig. 4. Calculated relative sensitivity of RGR to differences in R, expressed as %RGR/%R and plotted as a function of R. Valueswere calculatedfor youngtomato plants in different dry-weight intervals, as given in the figure. the growth parameters. Only the results for RGR of tomato are shown; those for the other species are more or less similar. There appears to be a tendency for less sensitivity to light with increasing plant weight. This contrasts with experiments on the effect of a change in R for a closed canopy. These showed an almost exact proportionality between R and yield for cucumber and tomato (Drews et al., 1980; Drews and Heisner, 1982). Calculations based on a simulation model of plant growth indicate that yield should react even more t h a n just in proportion to R in the case of a closed canopy (Challa and Schapendonk, 1984). Evidently the plants in our experiment do not yet show a tendency to a more proportional reaction to light integral with increasing plant weight. Effects of light integral on Td. - Figure 5 shows the time needed for tomato plants to double in dry weight (Td) plotted over the year. The reference condition chosen is a greenhouse situation with a light transmission of 65%; average values of global radiation for The Netherlands are assumed. This is compared to situations with (a) different light transmission values and (b) different amounts of additional light given during 10 h per day. The strong effect of greenhouse transmission on Td in winter is clearly demonstrated in Fig. 5a. From Fig. 5b, it appears that intensities of artificial light over 10 W m -2 have little promoting effect on RGR. Furthermore, this effect is only appreciable from the middle of November to the middle of February.
CONCLUSION The methods described here add more value to the initial data that were used by extending these data for use in a practical situation. In conjunction with an
182 7
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Fig. 5. Calculated time needed for young tomato plants (220-740 mg dry weight) to double in dry weight, expressed as Ta, plotted as a function of time of year. The lines drawn in (a) and (b) represent a reference situation with a greenhouse light transmission of 65%. The broken lines in (a) represent situations with a light transmission of 50 and 80%, respectively. The broken lines in (b) represent situations with different intensities of artificial light, given during 10 h per day.
183
economic model, the methods can be used to evaluate the effect on plant growth of energy conservation methods which reduce the light transmission in a greenhouse. In this way, the effect of the use of additional light can also be evaluated. The value %LAR/%NAR could be termed a flexibility index of the leaf area ratio. Together with the reaction of net assimilation rate, this index determines the reaction of relative growth rate to differences in light integral. It will be interesting to see if this flexibility is of the same order of magnitude for other species. ACKNOWLEDGEMENTS
The author wishes to thank E. Heuvelink for his assistance and cooperation in calculating the results. He is also much indebted to the late Prof. J.F. Bierhuizen for advice and criticism.
REFERENCES Bruggink, G.T. and Heuvelink, E., 1987. Influence of light on the growth of young tomato, cucumber and sweet pepper plants in the greenhouse: effects on relative growth rate, net assimilation rate and leaf area ratio. Scientia Hortic., 31:161-174. Challa, H. and Schapendonk, A.H.C.M., 1984. Quantification of the effects of light reduction in greenhouses on yield. Acta Hortic., 148: 501-510. De Vries, D.A., 1955. Solar radiation at Wageningen. Mededelingen Landbouwhogeschool, Wageningen, 55, 28 pp. Drews, M. and Heisner, A., 1982. Die Ertragsbildung der Gewaechshaustomate beim Fruehanbau in Abhaengigkeit v o n d e r Temperatur und der Beleuchtungsstaerke. Arch. Gartenbau, 30: 387-404. Drews, M., Heisner, A. and Augustin, P., 1980. Die Ertragsbildung der Gewaechshausgurke beim Fruehanbau in Abhaengigkeit vonder Temperatur und Bestrahlungsstaerke. Arch. Gartenbau, 28: 17-30. Hunt, R., 1982. Plant Growth Curves. The Functional Approach to Plant Growth Analysis. Edward Arnold, London, 248 pp. Klapwijk, D., 1981. Effect of season on early tomato growth and development rates. Neth. J. Agric. Sci., 29: 179-188. Klapwijk, D. and Tooze, S.A., 1982. The effect of season on the growth and development of young cucumbers. Internal Rep. No. 43, Glasshouse Crops Research and Experiment Station Naaldwijk, The Netherlands, 4 pp. Thornley, J.H.M. and Hurd, R.G., 1974. An analysis of the growth of young tomato plants in water culture at different light integrals and CO2 concentrations. II. A mathematical model. Ann. Bot., 38: 389-400.