A mathematical model of carbon acquisition and utilisation by kiwifruit vines

Ecological Modelling, 57 (1991) 43-64

43

Elsevier Science Publishers B.V., Amsterdam

A mathematical model of carbon acquisition and utilisation by kiwifruit vines J.G. B u w a l d a MAF Technology, Ruakura Agricultural Centre, Hamilton, New Zealand (Accepted 16 January 1991)

ABSTRACT Buwalda, J.G., 1991. A mathematical model of carbon acquisition and utilisation by kiwifruit vines. Ecol. Modelling, 57: 43-64. A mathematical model of carbon acquisition and utilisation by a kiwifruit (Actinidia deliciosa) vine during the growing season is described. The model includes specific features of deciduous fruit crops, such as maintenance of perennial biomass, growth of deciduous tissues, and hydrolysis and restoration of carbon reserves. Canopy net photosynthesis is computed hourly according to incident radiation, solar angle, radiation attenuation through the canopy, radiation response of photosynthesis and leaf area, and summed to generate daily totals. Daily maintenance respiration is estimated using mean daily ambient temperature and biomass carbon and nitrogen contents. Daily carbon demands for biomass synthesis, including the costs of growth respiration, are estimated using potential growth rates for individual organs. The daily availability of carbon for partitioning is that from 7-day running means of daily photosynthesis and reserve hydrolysis. Carbon is partitioned first for maintenance of existing biomass, and then remaining carbon is partitioned for growth of individual organs according to their respective sink strengths which, in turn, depend on their potential relative growth rates. A simulation of the seasonal carbon balance for a kiwifruit vine growing at Hamilton (New Zealand) indicated that maximum depletion of carbon reserves during spring was 103 g C m - z . Biomass synthesis for an entire growing season totalled 225 g C m - 2 for the shoot (including the leaves), 319 g C m -2 for the fruit, and 58 g C m -2 for the fibrous roots. Biomass synthesis for the fibrous roots was very similar to simulated senescence. Biomass synthesis of all vine components was limited by carbon supply, and the seasonal patterns of carbon allocation for growth of vine organs closely resembled field measurements reported elsewhere. Simulated carbon acquisition (photosynthesis) totalled 1773 g C m -2 for the growing season. For the whole vine, the carbon cost of maintenance exceeded that for growth. Synthesis and maintenance of shoots accounted for 40% of total carbon utilisation, while that for fruit accounted for 33%. Varying the fruit number led to proportionally similar changes in simulated total fruit biomass, so that average fruit size was relatively insensitive to fruit number. However, allocation of carbon for fibrous root growth and regeneration of reserves decreased with increasing fruit number. While simulated photosynthesis increased with shoot number and hence leaf area, the marginal gains at high shoot densities were less than the marginal costs 0304-3800/91/$03.50

© 1991 - Elsevier Science Publishers B.V. All rights reserved

44

J.G. BUWALDA

of tissue synthesis and maintenance.Hence the optimum leaf area (m2 m -2 ground area), associated with maximumallocation of carbon to fruit growth and regeneration of reserves, was about 3.5. The main advantages of this model include the value for identifyingcritical components of the whole plant C economy,the capacity to integrate plant-environment interactions at the whole plant level, and the potential for application to other deciduous fruit crops. A major limitation of the model at present is the lack of adequate published data for testing and validation.

1. INTRODUCTION The carbon (C) economy of a plant includes acquisition by photosynthesis and utilisation for synthesis and maintenance of biomass. In spite of expanding knowledge of the physiology of individual components of the C economy, integration at the whole-plant level is still difficult. Mathematical modelling is being used increasingly to describe plant-environment interactions (e.g. Thornley, 1976; Goudriaan, 1977; De Wit, 1978; Sheehy et al., 1979; Norman and Campbell, 1983; Johnson and Thornley, 1984; Van Keulen, 1986), and can be valuable for considering the relative importance of components of the C economy. Most published C balance models have been for arable crops and pasture plants, and usually with species that complete their life cycle in one year. There have been relatively few studies with deciduous fruit crops (Heim et a1.,1979; Guitierrez et al., 1985; Seem et al., 1986; Abdel-Razik, 1989) or other perennial species (e.g. Makela and Hari, 1986; Janecek et al., 1989). Features such as maintenance of perennial biomass, mobilisation and regeneration of reserves, turnover of roots, synthesis of deciduous tissues, and ontogenetic changes in growth rates of different organs should be described specifically for deciduous fruit crops. While previously published C balance models (Helm et al., 1979; Guitierrez et al., 1985; Seem et al., 1986; Abdel-Razik, 1989) for deciduous fruit crops treat some aspects very similarly (e.g. the dependence of canopy photosynthesis on leaf area and incident radiation), there has been no commonality in the description of components such as the demands of C for growth and the partitioning of C for growth of each organ. Kiwifruit (Actinidia deliciosa (A. Chev) C.F. Liang and A.R. Ferguson vat. Deliciosa 'Hayward') is a useful species for studying the C economy of a deciduous fruit crop. Carbon acquisition for this species is strongly limited by incident radiation (Buwalda and Smith, 1990a). Root growth is strongly affected by even subtle manipulations of C acquisition (Buwalda and Smith, 1990b; Buwalda, 1991). As roots of kiwifruit vines are extremely sensitive to anoxia (Smith et al., 1989), such effects on root growth and

C A R B O N A C Q U I S I T I O N AND U T I L I S A T I O N BY K I W I F R U I T

45

hence tolerance to below-ground stresses are likely to be particularly important. Presented here is a mathematical model of C acquisition and utilisation during the growing season for a kiwifruit vine. The major objectives of this model are: (1) to present a conceptual framework for mathematical modelling of the C economy of deciduous fruit crops, and to test hypotheses regarding the control of C acquisition and utilisation; (2) to summarise current knowledge and describe the relative significance of individual components of the C economy of a kiwifruit vine, with particular reference to unusual features of a deciduous fruit crop; and (3) to integrate knowledge of plant-environment interactions, so that consequences at the whole-plant level may be predicted. In this paper the capacity of the model to meet these objectives is considered. Application of this model for identifying principle factors limiting C acquisition, the relative importance of different C sinks, and the potential to influence C allocation to the harvested portion (fruit) through management of fruit load and leaf area is also presented. 2. THE MODEL The model, shown schematically in Fig. 1, simulates canopy photosynthesis, potential growth and maintenance costs, balance of C supply and demand, and partitioning for maintenance and growth. The effects of external environmental influences on C acquisition and partitioning are not shown in Fig. 1, but are included in the model. The vine is divided into five organs: shoot, including the leaves, SH; fruit, FT; s t e m , including the cordon and laterals, ST; structural root, RS; fibrous root, RF. For ST, RS and RF, the biomass C values at the start of the growing season are defined as input parameters. The proportional biomass distribution among organs can be very similar for vines varying greatly in total biomass (Buwalda and Smith, 1987). Accordingly, the initial quantities of C within the ST, RS and RF at the start of the growing season are linearly related to the bud density after winter pruning, viz. 1.5 g C per bud for ST, 7.0 g C per bud for RS, and 1.5 g C per bud for RF. The model considers growth for SH, FT, and RF only, since in mature vines, growth of ST and RS accounts for only a very small proportion of total growth (Buwalda and Smith, 1987). While Fig. 1 shows only a total C cost for respiration for each organ of the vine, the model examines the costs of respiration for maintenance and growth separately. Net inputs of C are those from photosynthesis, while net outputs during the growing season are losses through respiration and senescence of fibrous roots. The C available for partitioning for growth and maintenance is that available from photosynthesis and .reserves.

J.G.BUWALDA

46

I

~ ~1~

-'~v

I

SHOOT SH

BIOMASS

D,

I ~

~

~

BIOMASSFT

STEM BIOMASS

ST

C POOL

STRUCTURAL ROOT BIOMASS

RS

FIBROUS ROOT BIOMASS

RF

Fig. 1. Schematic representation of a carbon balance model for the kiwifruit vine. Rectangles represent C states, valves represent processes affecting C states, and lines represent C flows. The model simulates the C economy from bud burst in spring until the time of fruit harvest only. Losses of C in harvested fruit, senescent leaves, and pruned shoots are therefore not included. Kiwifruit is grown principally on one of two trellis types, known as horizontal and 'T-bar' pergolas, respectively (Sale, 1985). A horizontal

CARBON ACQUISITION AND UTILISATION BY KIWIFRUIT

47

pergola is assumed here, as canopies grown on this trellis type show greater horizontal and vertical homogeneity than canopies on T-bar pergolas (Sale, 1985). Hence canopy architecture and radiation attenuation through the canopy can be more easily described for this trellis type. Vertical and horizontal heterogeneity are also dependent on the density of shoots, temporal spread of bud burst, and shoot growth rates. In practice, high producing vines are generally characterised by vigorous and uniform shoot growth (Sale, 1985). Accordingly, the assumption of vertical and horizontal homogeneity of canopy elements is considered an acceptable simplification. The mineral nutrient status and the water balance of the vine are assumed to be non-limiting and are not explicitly addressed here.

2.1

Carbon acquisition

Carbon acquisition is computed as the integral of photosynthesis for all leaf layers in the canopy, with the rate at each layer dependent on the level of photosynthetically active radiation (Pan) transmitted to that layer. Radiation attenuation through successive leaf layers depends on the spatial arrangement of the leaves. Morgan (1988) showed that inclination angles for leaves in a kiwifruit canopy trained on a horizontal pergola followed an ellipsoidal distribution, and had a mean value of 33 °. No significant azimuthal preference was detected. Radiation extinction with canopy depth (m 2 leaf area m -z allocated ground area, otherwise known as leaf area index) may be described by an equation identical to Beer's law (Monsi and Saeki, 1963): I=I°

e-kL

(la)

where I is the radiation flux at the considered canopy depth, I o is the incident radiation at the top of the canopy, L is the leaf area between the top of the canopy and the considered level, and k is an extinction co-efficient d e p e n d e n t on projected area of shadow cast on to a horizontal surface by leaf area L. Only PAR is considered here, so I and I o have units of ixmol PAR m -2 s -1. Radiation transmission through kiwifruit leaves is normally very low ( < 3%; Buwalda, unpublished results), so has not been included in equation (la). The attenuation of radiation through a plant canopy depends on the angles of leaf inclination (o-) and solar elevation (~b), and may be represented by the extinction co-efficient, k. The decreasing ratio of sunlit to shaded leaves with increasing canopy depth is reflected in this extinction coefficient. Campbell (1986) presented a relationship between k and ~b for a canopy with an ellipsoidal distribution of leaf inclination angles, and regression co-efficients for this relationship may be estimated using the

48

J.G. B U W A L D A

equation of Wang and Jarvis (1988). Assuming o-= 33° (Morgan, 1988), the extinction co-efficient at any time of the season may be described as: k = (5.89 + 1/tan2~b)l/2/3.11

(lb)

This equation illustrates the dependence of k on 4~, having values of 1.36 where ~b = 15 o and 0.80 when 4) = 45 o. While equations la and lb provide spatial averages of radiation intensity at any given canopy depth, they ignore the impact of sunflecks, which may be significant to the C economy of leaves at understory positions (Pearcy, 1988). However, the average radiation intensities for leaves at such positions are usually very low, so that errors resulting from the use of average radiation intensities are likely to have very little impact on the simulated C economy for the whole vine. Gross photosynthesis for individual kiwifruit leaves (Ago), ixmol CO 2 m -2 s -~) can be described using a rectangular hyperbolic response to incident radiation, I (Buwalda and Smith, 1990a): AmaxeI Ago) - A max + e l

(2a)

where e describes the response of AgO) to increasing I at low levels of I (the quantum yield, mol CO 2 mo1-1 PAR; Field et al., 1989), and Ama x is the radiation saturated rate of AGO). While the rectangular hyperbola may not necessarily be the best representation of the radiation response of photosynthesis (Johnson et al., 1989), it can be analytically integrated over the depth of the crop canopy. Parameter estimates for equation (2a) have been obtained from measurements of net assimilation of CO z for individual leaves at varying irradiance, so this equation actually represents the radiation response of net photosynthesis for single l e a v e s (An(l)). Buwalda and Smith (1990a) estimated parameter parameter values of e = 0.0356 mol CO 2 mo1-1 PAR and Ama x = 26.27 ixmol CO 2 m -2 s -1 for kiwifruit leaves in mid summer. Ontogenetic changes in Ama x (Dick, 1987) are taken into account by altering the value five times during the season. While A max may vary with leaf position within the canopy, the estimate of Ama x appropriate to well exposed leaves is usually adequate for the simulation of A . at all leaf positions (Hirose and Werger, 1987). For a leaf at any position within the canopy, photosynthesis may be described using equation (2a), once the attenuation of radiation to that position within the canopy has been estimated (using equation 1). Photosynthesis for all leaf positions within the canopy (A.(c)) can be integrated: A.(c)

f Lt Area x + e k I J0 Amax+ e k I o

o e-kL

dL

(2b)

CARBON ACQUISITION AND UTILISATION BY KIWIFRUIT

49

where L t is the total leaf area (m 2 m-2). An analytical solution for equation (2b) (Thornley, 1976) can then be solved for L t (or any other position, L, within the canopy):

Arnax A,~c)-

~

[ Amax + EkI ° In Amax + EkI o e - k L

(2C)

The instantaneous rate of A,~c) is computed at hourly intervals, using integrated hourly data for incident radiation at the top of the canopy and daily values of leaf area. The daily integral of A,~c) represents daily C acquisition by the leaves, net of respiration during daylight. This integral is converted to mass units (g C m -2 d - l ) , for consistency with the remainder of the model. 2.2

Carbon demands for maintenance respiration

The C requirements for respiration are separated into maintenance and growth components, to allow subsequent partitioning of a limited C supply to reflect relative priorities of maintenance of existing biomass and synthesis of new biomass. The CO 2 evolved in the turnover of labile compounds, maintenance of gradients of ions and metabolites across membranes, and non-growth processes such as those involved in acclimation to a changing or harsh environment, represents maintenance respiration (Penning de Vries, 1975). The C demand for maintenance is computed here daily for each vine organ. The maintenance cost for any organ depends on biomass, chemical composition (particularly the N concentration, which reflects protein turnover), and ambient temperature (Penning de Vries, 1975; Thornley, 1976; Amthor, 1989). The daily C requirement for maintenance respiration for each organ (Rmi) is therefore; R m i = m i C i e ri~r- 2°)

(3a)

where m i is a maintenance respiration co-efficient (g C g-i C d -1) for organ i, C i is the current biomass (g C) for organ i, r i is a temperature response co-efficient for organ i (a Q10 of 2 is assumed), and T is the mean daily temperature ( o C). A linear relationship between the N concentration for each organ (N~, g N g-1 C) and m (at 20°C) is assumed:

m i = 0.4 N/ d -a

(3b)

The values of N/ are varied on five occasions during the season, to reflect seasonal changes in tissue N concentrations (Smith et al., 1987; Clark and Smith, 1988). For example, the values of mi (g C g-1 C d -1) at 120 days after bud burst, at about the middle of the growing season, are 0.029 for

50

J.G. BUWALDA

msH, 0.014 for mVT, 0.007 for mST , 0.011 for mRS , and 0.014 for mRF. These rates are within the range of published estimates of m, which range from 0.026 to 0.078 g C g-1 C d-~ for leaves, 0.001-0.029 g C g-~ C d-1 for storage organs, and 0.009-0.139 g C g-~ C d - l for roots (see Amthor, 1989). For leaves, the hourly estimates on A n~c) already account for respiration during daylight. Daily maintenance estimates of SH are therefore adjusted according to the daylength and the proportion of SH biomass C included in the leaf blades. 2.3

Carbon demands for growth

The daily C demands for growth are computed according to 'potential' growth rates of each organ, and include the d e m a n d for C skeletons for the synthesis of new biomass and the associated growth respiration that provides energy and reductant (Penning de Vries et al., 1974). Potential growth rates on any day may differ from actual growth rates, when the total C available for partitioning is less than that required to support the potential growth rates. The model considers growth for SH, FR and R F only, as annual changes in the biomass of the perennial organs (ST and RS) are negligible (Buwalda and Smith, 1987). Measured growth rates may not represent potential growth rates, especially if measured growth was limited by C supply. Examples of maximum growth are therefore used to represent potential growth. For each organ i, the specific C content (g C g-1 DW) and the potential growth rate (g Dw d - ~) accordingly determine the demand for C skeletons for growth (Cskeli). The potential SH growth rate is considered here as the product of the number of shoots still growing and the growth rate of each shoot. The total number of shoots (m -2 ground area) depends on the number of buds on laterals after dormant pruning (bud number) and the proportion of these buds from which shoots emerge in spring (bud burst); these are input parameters for the model. The model considers the shoot number to increase linearly from zero to the maximum value during the 14 days after earliest bud burst, according to the typical pattern for kiwifruit vines (McPherson et al., 1988). As individual shoots stop growing at different times during the season, the canopy at any time can comprise non-terminated and terminated shoots (Buwalda and Smith, 1990a), with growth at any time limited to nonterminated shoots. The extension of individual non-terminated shoots may be described as a function of temperature (Fig. 2), and the shoot biomass is linearly related to shoot length (Fig. 3a). If the growth rate of nonterminated shoots is considered as the potential growth rate, the relation-

CARBON ACQUISITION AND UTILISATION BY KIWIFRUIT

51

2.5

o

y = 6.835e-O6x 2 + 1.24e-O3x

- O.

E ¢-- 1,5

o 3 O t-o3

1.0

~'~'

r , " ~ ,

, , ,

0.5

0

0

100 Growing

200 degree

300 days

400

after

bud

500 burst

Fig. 2. Relationship of extension of non-terminated shoots of kiwifruit vines to thermal time (growing degree days above a base temperature of 8 ° C). Data were obtained from destructive measurements of growth of individual shoots of kiwifruit vines in the field after the date of bud burst had been recorded. Air temperatures in the canopy were constantly monitored. The fitted line has the equation shown.

24

(=) y = 9.95x - 0.24

16

r z = 0.98

J

tx

-

,...A- ,

E

.0 .0

J •

8

_c 03

Z 0 0.4

A

•

I

,

(b)

E

0.3

.

y = 0.160x

-

0.002

.~'~'

r z : 0.98 L

I

j"

~A~"

tt

0.2

m

_~

,

~a•..-

tx

v

I

&

0.1

0

II~

•

I

0,5

l

I

I

I

I

1.0

1.5

2.0

2.5

5hoof

length

(m)

Fig. 3. Relationship of (a) biomass and (b) leaf area of non-terminated shoots of kiwifruit vines to shoot length. Data obtained as described for Fig. 2. The fitted lines have the equations shown.

52

J.G. B U W A L D A

ships described in Figs. 2 and 3 can be used to describe potential daily demand for C skeletons for SH growth (g C m-2), as the product of the potential biomass C increment of individual non-terminated shoots and the number of non-terminated shoots. Fruit growth commences about 400 growing degree days, above a base temperature of 8 ° C, after bud burst (Morley-Bunker and Salinger, 1987). An initial biomass of 0.25 g C per fruit at flowering is assumed. Subsequent daily d e m a n d for C skeletons for FT growth (g C m -2) is equal to the product of the fruit number (an input parameter for the model) and the potential incremental C content of individual fruit. The mean final fresh weight of fruit on vines with very low crop loads rarely exceeds 140 g (Cooper et al., 1988), which corresponds to about 10.3 g C per fruit. The seasonal pattern of C accumulation by such fruit is considered here to represent the potential growth. The biomass of individual fruit increases rapidly during the first 50-60 days after flowering and then more slowly during the remaining 100-110 days until harvest (Walton and De Jong, 1990). For a fruit attaining a final size of 10.3 g C, daily growth can be described with a pair of linear regressions, with a slope of 0.073 g C d - l during the first 60 days after flowering and a slope 0.049 g C d 1 for the remainder of the season. These slopes are used to define the daily d e m a n d for C skeletons for individual fruit. The C demands for root growth are difficult to assess from any published data, as the likelihood of C availability limiting root growth of kiwifruit vines is high (Buwalda and Smith, 1990a). The relative rate of growth of root length (m m - 1 d - 1) in late summer (the peak period of root growth; Buwalda and Hutton, 1988) is assumed here to represent the potential R F growth rate. As fibrous root makes up more than 98% of the root length of kiwifruit vines (Wilson, 1988), the relative growth rate for root length can be converted to g g - 1 d - 1, using the weight : length ratio for fibrous roots (Wilson, 1988) and then to daily demand for C skeletons for R F growth (g C m-2), using the biomass C content of RF at the start of the season (an input parameter). A potential relative growth rate of R F of 0.0030 g C g - l C d -1 at 2 0 ° C (Buwalda and Hutton, 1988) and an exponential response of root growth rate to temperature, doubling with each 10 °C increase, are assumed. The C cost of growth respiration for each organ i (Rgi, g C), computed using elemental analysis data (McDermitt and Loomis, 1981), must be added to the demand for C skeletons for biomass synthesis. Walton et al. (1990) accordingly estimated the total cost of biosynthesis (which includes growth respiration) of a kiwifruit berry to be 1.21 g glucose g-1 DW, after calculating a growth respiratory cost (Rgrx) equivalent to 0.128 g C g-1 assimilated C. Growth respiration costs calculated similarly for other or-

C A R B O N A C Q U I S I T I O N AND U T I L I S A T I O N BY K1WIFRU1T

53

gans of the vine are 0.200 g C g C -1 for SH (RgSH) and 0.126 g C g-1 C for R F (RgRF). For any day, the C d e m a n d for growth of each organ i (CDemi) is: CDemi = (CSke,i "{-Rgi)

(4a)

and the total C demand for growth for the whole vine (CD~m) CDem = E(Cskel i "-~Rgi) 2.4

(4b)

Carbonpartitioning for growth and ma&tenance

The C available for partitioning is that from photosynthesis and hydrolysis of reserves. The capacity for C release from reserves is considered to decline during the season, in accordance with a diminishing reserve pool. This may be described simply; Cnyd = CDef(1 -- ( x / ( 2 -- x)))

(5)

where CHyd (g C m - 1) is the quantity of C hydrolysed from reserves on any day, CDef (g C m -z) is the deficit between daily C demand and net photosynthesis, and x is the number of days since bud burst, expressed as a proportion of the total length of the growing season. Carbon reserves may be hydrolysed from ST, RS and RF, and distribution of such hydrolysis among~these organs in direct proportion to their respective biomass C contents on any day is assumed. Carbon demands for maintenance are met first and any remaining C, including hydrolysed reserves, may be used for growth. While the control of C partitioning in deciduous fruit crops is poorly understood, models fitted empirically to experimental data have been used. However, the importance of 'sink strength' for determining C partitioning is generally agreed. Seem et al. (1986) simulated C partitioning in apple according to empirically defined competitive strengths of individual sinks, that were constant throughout the season. Abdel-Razik (1989) simulated partitioning in olive according to "scaled competitive-advantage measurements", but provided no details of the values for various parts of the plant. Sink strength has been related to the number of growing cells in a particular organ (Sunderland, 1960), relative growth rate (Gifford and Evans, 1981), and proximity of sink to the C sources (Farrar, 1980). Accordingly, sink strength is likely to vary during the growing season, and a dynamic scheme for modelling this is required. Sink strength for each organ (ss i) is defined here as a function of the potential relative growth rate for that organ, in units of g C and including associated costs of growth

54

J.G. BUWALDA

respiration (~CDemiC/-1 St) and an empirical value reflecting sink proximity to source (Pi): ssi =

1 ~CDemipi Ci 8t

(6a)

Where the potential relative growth rates of the various sinks differ strongly, the relative values of ss are affected only slightly by large variations in the value of Pi. P values of 10 for SH (the immediate source of photosynthetic C), 2 for RF (a source of C reserves) and 1 for FT have been assumed. The relative sink strengths for each organ (RSSi) can then be defined: SSi RSSi ~" ~SSi

(6b)

The RSSi values are then used to estimate the relative allocations of C to each organ (RAi): RAi = C D e m i - (CDemi(1 -- RSSi)(1 --(CAvaillCDem)))

(6c)

and actual partitioning of C to each organ for growth (Cpari) is then: Cpari ~-- RAi(CAvail/~RAi)

(6d)

When C demand exceeds supply, this partitioning scheme suggests that the fraction of the C for growth actually allocated is greater for organs with high potential relative growth rates than for organs with low potential relative growth rates. Carbon partitioned in this way is used for growth of SH, FT and RF. The growth respiration costs for each organ are assumed to represent a constant proportion of the total C partitioned, so growth will be limited in direct proportion to the fraction of required C actually allocated. For SH, growth of individual non-terminated shoots is assumed to proceed always at the potential (temperature dependent) rate. Hence the fractional allocation of the C required for growth determines the proportion of currently non-terminated shoots that remain in that state. Leaf area of non-terminated shoots is then incremented using the relationship in Fig. 3b. Concomitant cessation of extension and leaf area expansion for individual shoots has been assumed. The C partitioned for FF and RF growth is assumed to be distributed uniformly amongst all parts of the respective organs. Senescence of fibrous roots will affect the maintenance costs for this organ. The results of Buwalda and Hutton (1988) suggest that root growth and senescence proceed simultaneously, and annual turnover may be

CARBON ACQUISITION AND UTILISATION BY KIWlFRUIT

55

50-100% of the total fibrous root biomass. Their data suggest that turnover rate ('rc RF) may be related to temperature: TC R F = 0 . 0 0 2 8

e s i ( T - 20)

(6)

where s i is the temperature response of root turnover (a Q10 or 2 is assumed), and T is the mean daily temperature. 3. M O D E L S I M U L A T I O N S

3.1

Seasonal carbon balance

Meteorological data for the 1988-89 growing season at Hamilton, New Zealand (latitude 38.2 o S) were used to simulate the seasonal C economy for kiwifruit vine. The simulations assumed the vine had been dormant pruned to 40 buds m -2, bud burst in spring was 42% and the vines had 40 fruit m -z. These initial values are typical for well managed vines in New Zealand (Sale, 1985). The initial biomass C values of ST, RS and R F were as indicated in Section 2. The reserve C status was initialised at 0, so that deviation from this initial value represented the status at any time. All other parameters were as indicated in the above description of the model. A 7-day running mean of daily photosynthesis was used to compute deficits between supply and demand and hence the depletion or regeneration of reserves, to smooth effects of daily C deficits on the growth of vine organs. The simulated seasonal C balance of the kiwifruit vine is shown in Fig. 4a. Cumulative depletion of reserves reached 72 g C m -e during the first 28 days after bud burst, when canopy photosynthesis was limited by small leaf area and C demands for SH growth and maintenance of the perennial biomass exceeded daily supply. Maximum reserve depletion was 103 g C m -2, at 103 days after bud burst (about 40 days after flowering), when FT growth was rapid. Regeneration of C reserves occurred principally from 125 to 165 days after bud burst. The SH biomass C increased most rapidly in the 80 days after bud burst, and then more slowly until SH growth ceased about 120 days after bud burst (Fig. 4b). The termination of growth of individual shoots and hence the canopy was simulated entirely in terms of C balance and allocation for shoot growth. The final SH biomass was 225 g C m-2. FT growth averaged 0.064 g C d-1 per fruit during the first 60 days after flowering, and then 0.039 g C d-1 per fruit during the subsequent 100 days until fruit harvest. The difference between these actual rates and the potential rates of growth described in Section 2.3 was also entirely the consequence of simulated C balance and C allocation for fruit growth. The final biomass for FT was 319 g C m -2. R F biomass decreased during spring, as reserve depletion and

56

J.G. B U W A L D A

20 0

(a)

E -20 U

),

-40 -60 -so

rY

-100 -120 350 300

i

i

l

I

i

,

I

(b) "Fruif

E 250

s

200 .-

I

I

s" s / / . • • ' ~

Shoof

15o

.off 100 m

5O

/

"

Fibrous roof I

0

i

I

60

120 180 240 Days affer bud bursf Fig. 4. Simulated cumulative (a) C balance (acquisition less use) and (b) biomass C contents for the shoot, fruit and fibrous root of a kiwifruit vine.

root senescence exceeded growth. Accumulation of biomass C for R F was most rapid between 120 and 150 days after bud burst, and the R F biomass at the end of the season was very similar to that at bud burst. 3.2

Carbon sinks

Simulated photosynthesis for the entire growing season totalled 1773 g C m -2. The largest single C sink appeared to be maintenance of SH biomass (Fig. 5a), accounting for more than 25% of the total C use. Within 45 days of bud burst, daily maintenance of SH biomass became a larger sink than daily maintenance of the perennial biomass. Maintenance of FT and RS accounted for 13% and 17%, respectively, of the total C use and, on a daily basis, were nearly as expensive as SH to maintain towards the end of the season. Synthesis of FT and SH were also large sinks (Fig. 5b), accounting for 20% and 15%, respectively, of the total C use. The C cost of daily SH growth exceeded that for FT during the first 60 days of the growing season only. Thereafter, daily FT growth was the largest growth sink in the vine.

CARBON

4

"~

ACOUISITION

AND UTILISATION

57

BY KIWIFRUIT

- Ca)

Shoot Fruit

2

c

", . . . .

-

Structural

-

"

Fibrousroof

~E 0

Sternl

4 '-Q

root

(b)

3

cJ 2

__~

(3

Fibrous 0

,i 0

I 60

,

I

•

120 Days a f t e r

180

= 240

bud b u r s t

Fig. 5. Seasonal trend of simulated C use (g C m -2 d - 1 ) for (a) maintenance and (b) growth of vine organs.

The C cost of RF growth exceeded that for SH after about 150 days but never represented more than 20% of the cost of FT growth. Maintenance and synthesis of RF and maintenance of ST were relatively small C sinks. The cumulative C cost of growth for all organs of the vine was similar to that for biomass maintenance during the first 90 days after bud burst, but subsequently maintenance costs exceeded those of growth (Fig. 6a). Simulated C use exceeded supply regularly during the first 30 days after bud burst, and then again between 60 and 110 days after burst (Fig. 6b). Carbon supply regularly exceeded demand for the following 60 days, but was generally less than demand during the last 30 days of the growing season. According to the assumptions of the model, biomass synthesis is limited when C demands exceed availability. The co-incidence of C availability and the potential growth rates of vine organs determines the net effects of C deficits on vine growth. In the simulations presented here, C availability limited growth of SH during the first 30 days after bud burst but more severely between 60 and 110 days after bud burst. FT growth and RF growth were limited by C availability throughout their respective growing

58

J.G. BUWALDA (a)

? E ¢J

1 U

0 4.5

-

(b)

3.0 E o

=

1.5

o

c

t

~, g

-1.5

-3.0

a

-4.5

i

I

60

=

I

i

120

I

,

180

I

240

Days after bud burst

Fig. 6. Seasonal trend of simulated (a) C use (g C m -2 d -l) for maintenance and growth within an entire vine, and (b) daily balance of C acquisition and use (g C m -2 d-l). periods, but mainly during the first 50 days after flowering (about 60-110 days after bud burst). 3.3

Influence of fruit load and shoot density

The sensitivity of the simulated C balance to changes in fruit load and shoot density are shown in Table 1. Decreasing the fruit load by 20% decreased FT biomass by 19% and therefore increased the average fruit weight by only 1%. Increasing the fruit load by 20% increased FT biomass by 18%, but decreased the average fruit weight by only 2%. However, changing the fruit load from 32 to 48 fruit m -2 changed the C reserve status at the end of the growing season from a surplus to a deficit (Table 1). The differences in C reserves at the end of the season were slightly less than the differences in C biomass of FT. Changing the shoot number led to greater than proportional changes in the simulated final SH biomass and leaf area (Table 1). While photosynthesis continued to increase with increasing shoot number (and hence leaf area), marginal gains at high shoot numbers were less than the marginal

59

CARBON ACQUISITION AND UTILISATION BY K I W l F R U I T

TABLE 1 Simulated leaf area, biomass C contents of shoot, fruit and fibrous root, cumulative photosynthesis, and C reserve status at harvest for vines with varying fruit load and shoot density Leaf area

Biomass (g C m -2)

(m2 m - 2 )

Shoot

Fruit

Fibrous

C Reserves

Photosynthesis

(g C m -2)

(g C m -2)

root Fruit number (m -2) 32 4.18 40 3.50 48 3.62

243 203 208

258 319 376

69 60 50

49 2 - 54

Shoot number (m -2) 11.8 2.50 15.1 3.50 18.5 4.23

144 203 245

320 319 317

57 60 58

- 16 2 - 11

1556 1773 1890

cost of synthesis and maintenance of the extra SH biomass. FT biomass C appeared to reach a maximum at 15.1 shoots m -2, when the final leaf area was 3.50 m 2 m -2, although varying the shoot density from 11.8 to 18.5 m -2 (leaf area = 2.50-4.23 m 2 m -2) led to very little difference in the simulated FT biomass at the end of the season. However, simulated RF biomass and C reserves at the end of the season peaked at a shoot number of 15.1 m -2 (leaf area = 3.5 m 2 m-2). This shoot density appeared to be the optimum, under the conditions of the simulations presented here, for FT growth, RF growth and regeneration of reserves. 4. DISCUSSION

The value of mathematical modelling for analysis of spatial and temporal trends in the C economy of a plant and effects of plant-environment interactions will depend on the accuracy with which the processes of C acquisition and use are described and the accuracy of parameter estimates in those descriptions. While this model includes many parameters with estimated rather than measures values, it nevertheless appears to stimulate annual growth reasonably. The seasonal trends of leaf area, FT biomass and RF growth and senescence simulated here (Fig. 4, Table 1) are very similar to those measured in independent experiments in the field (Buwalda and Smith, 1990b; Buwalda, 1991). The reduction in the relative growth rate of SH, seen in field measurements as leaf area approaching a plateau value about 120 days after bud burst (Buwalda and Smith, 1990b), is

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J,G. B U W A L D A

stimulated by the model entirely in terms of C balance and allocation for growth of SH. The seasonal progression of growth sinks from SH to FT to RF is clearly evident in the simulations. Data of the seasonal trends of biomass growth for kiwifruit vines in the field, while not yet available, will allow better testing of the goodness-of-fit of this model. The simulated consequences of changing fruit and shoot numbers (Table 1) are generally consistent with measured consequences in the field (Burge et al., 1987; Cooper et al., 1988; Buwalda and Smith, 1990b). FT growth was relatively insensitive to changes in the leaf to fruit ratio, compared to R F growth and the regeneration of C reserves. This was due to the high sink strength (i.e. high relative growth rate) of fruit, particularly during the first 60 days after flowering. While FT biomass can be increased by increasing fruit load, the effects on R F growth and C reserves can lead to reduced flowering and hence fruit production in the following season (Burge et al., 1987; Cooper et al., 1988). The annual balance of C supply and utilisation is seen here in terms of the C reserve status. The maximum depletion of C reserves (103 g C m -2) represented about 26% of the initial C content of the whole vine, and about 6% of the total C acquired by photosynthesis during the growing season. Different forms of equation (5) may be used to indicate greater or lesser capacities for reserve depletion. Functional descriptions of reserve mobilisation and regeneration (considered here in empirical terms only) should assist our understanding of effects of C balance on growth. The strong sensitivity of simulated final reserve status to shoot and fruit densities, and hence C demands for growth and maintenance, is consistent with field results discussed above. Canopy photosynthesis, on a seasonal basis, appeared to respond to increasing leaf area over a relatively wide range (Table 1). However, the increasing costs of tissue maintenance relative to marginal gains in canopy photosynthesis resulted in the total C available for growth of FT and RF maximising when the leaf area was about 3.50 m 2 m - 2 . The optimum leaf area will depend on the level of incident radiation. The 1988-89 growing season included a period of low incident radiation between 90 and 130 days after bud burst, and the optimum leaf area may be higher than that suggested here in seasons with higher average incident radiation and hence total canopy photosynthesis. The ability of our model to simulate realistically the consequences of vine management decisions, such as shoot number (affected by dormant pruning) and fruit number (affected by flower a n d / o r fruit thinning) indicates its capacity to accommodate features of the C economy specific to deciduous fruit crops. A significant feature of the model presented here is the dynamic scheme suggested for estimating C partitioning for growth of vine organs. This

C A R B O N A C Q U I S I T I O N AND U T I L I S A T I O N BY K I W I F R U I T

61

scheme suggested that the growth of SH, FT and RF were most affected by C supply at different times of the growing season. The close resemblance between the C partitioning suggested by this scheme and that observed in field measurements (Buwalda and Smith, 1990b) suggests that the control of partitioning within the vine has been represented adequately. In particular, the model suggested that peak C allocation for root growth occurred at 120-150 days after bud burst (Fig. 5b), which is exactly the period of independently observed maximum root growth in the field (Buwalda, 1991). However, published data for the seasonal trends of growth and C utilisation for kiwifruit vines are still insufficient for detailed testing of the validity of the C partitioning scheme and the overall C balance model. The relative importance of components of the C economy indicated in our initial simulations provides a focus for future studies of C acquisition and utilisation. While our simulations suggest but C costs of maintenance, particularly of deciduous organs, exceed those for growth, the accuracy of these simulations is unknown in the absence of published measurements of specific maintenance respiration rates for all kiwifruit tissues. As simulated R m is greater for the shoots than for other plant tissues (Fig. 5a), errors in the estimation of R m s H a r e likely to be very significant. The simulated C cost of shoot growth and maintenance (equivalent to about 40% of total C acquisition; Fig. 5) appears to exceed that for growth and maintenance of fruit (equivalent to about 33% of total C acquisition; Fig. 5). Such simulations suggest that utilisation of acquired C for fruit production is relatively inefficient. Our assumption that specific maintenance respiration rates for all organs of the vine are linearly related to the tissue N concentrations assumes constant protein contents (per unit N) and protein turnover rates, but this is by no means certain (Amthor, 1989). The simulated maintenance costs will vary with differences between plant organs in the specific maintenance rate per unit N (m i) a n d / o r the Q~0 of Rmi. Fruit photosynthesis (Blanke and Lenz, 1989) probably re-fixes some of the C respired within fruit, thereby reducing the net C costs of FT. As biomass synthesis in our simulations was limited by C supply for much of the growing season (Fig. 6), any factor improving respiratory efficiency is likely to increase plant yield (Sheehy et al., 1979; Morgan and Austin, 1983; Gifford et al., 1985). The conceptual framework of the model presented here may be appropriate for describing the C economy of other deciduous fruit crops. The model accounts for features that are especially significant for deciduous fruit crops, such as depletion and regeneration of reserves, growth of deciduous tissues, and turnover of a portion of the root system. Relationships describing potential growth rates of plant tissues, and parameter estimates for equations estimating radiation attenuation through the

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canopy, response of photosynthesis to incident radiation, and dependence of respiration on tissue N, specific to any other crop, could simply by substituted for those here. ACKNOWLEDGEMENTS

This research was partially funded by the New Zealand Kiwifruit Marketing Board. I am grateful to E.F. Walton for useful discussions during this work. J.S. Davys and J.P. Curtis provided assistance with programming. The author was in receipt of an Alexander von Humboldt Fellowship at the Universit~it Bonn, Germany during part of this research. REFERENCES Abdel-Razik, M., 1989. A model of the productivity of olive trees under optimal water and nutrient supply in desert conditions. Ecol. Modelling, 45: 179-204. Amthor, J.S., 1989. Respiration and Crop Productivity. Springer, New York, 215 pp. Blanke, M.M. and Lenz, F., 1989. Fruit photosynthesis. Plant Cell Environ., 12: 31-46. Burge, G.K., Spence, C.B. and Marshall, R.R., 1987. Kiwifruit: effects of thinning on fruit size, vegetative growth, and return bloom. N.Z.J. Exp. Agric. 15: 317-324. Buwalda, J.G., 1991. Root growth of kiwifruit vines and the impact of canopy manipulations. In: H. Persson (Editor), Proc. ISRR Symp. Plant Root Systems and their Environment (in press). Buwalda, J.G. and Hutton, R.C., 1988. Seasonal changes in root growth of kiwifruit, Sci. Hortic., 36: 251-260. Buwalda, J.G. and Smith, G.S., 1987. Accumulation and partitioning of dry matter and mineral nutrients in developing kiwifruit vines. Tree Physiol., 3: 295-307. Buwalda, J.G. and Smith, G.S., 1990a. Acquisition and utilisation of carbon, mineral nutrients and water by the kiwifruit vine. Hortic. Rev., 12: 307-347. Buwalda, J.G. and Smith, G.S., 1990b. Effects of partial defoliation at various stages of the growing season on fruit yields, root growth and return bloom of kiwifruit vines. Sci. Hortic., 42: 29-44. Campbell, G.S., 1986. Extinction co-efficients for radiation in plant canopies calculated using an etlipsoidal inclination angle distribution. Agric. For. Meteorol., 36: 249-254. Clark, C.J. and Smith, G.S., 1988. Seasonal accumulation of mineral nutrients by kiwifruit. 2. Fruit. New Phytol., 108: 399-409. Cooper, K.M., Marshall, R. and Atkins, T.A., 1988. Controlling fruit size for profit. N.Z. Kiwifruit Spec. Publ., 2: 7-8. De Wit, C.T., 1978. Simulation of assimilation, respiration and transpiration of crops. Simulation monograph, Pudoc, Wageningen, Netherlands, 141 pp. Dick, J.K., 1987. Gas exchange in orchard grown kiwifruit vines. MSc thesis, University of Waikato, Hamilton, New Zealand. Farrar, J.F., 1980. Allocation of carbon to growth, storage and respiration in the vegetative barley plant. Plant Cell Environ., 3: 97-105. Field, C.B., Ball, J.T. and Berry, J.A., 1989. Photosynthesis - principles and field techniques. In: R.W. Pearcy, J.R. Ehleringer, H.A. Mooney and P.W. Rundel (Editors), Plant Physiological Ecology, Field Methods and Instrumentation, Routledge, Chapman & Hall, London, pp. 209-253.

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Gifford, R.M. and Evans, L.T., 1981. Photosynthesis, carbon partitioning and yield. Annu. Rev. Plant Physiol., 32: 485-509. Gifford, R.M., Lambers, H. and Morison, J.I.L., 1985. Respiration of crop species under CO 2 enrichment. Physiol. Plant., 63: 351-356. Goudriaan, J., 1977. Crop micrometeorology: a simulation study. Simulation monograph, Pudoc, Wageningen, Netherlands. Gutierrez, A.P., Williams, D.W. and Kido, H., 1985. A model of grape growth and development: the mathematical structure and biological considerations. Crop Sci., 25: 721-728. Heim, C., Landsberg, J.J., Watson, R.L. and Brain, P., 1979. Eco-physiology of apple trees: Dry matter partitioning by young golden delicious apple trees in France and England. J. Appl. Ecol., 16: 179-194. Hirose, T. and Werger, M.J.A., 1987. Nitrogen use efficiency in instantaneous and daily photosynthesis of leaves in the canopy of a Solidago altissima stand. Physiol. Plant., 70: 215-222. Janecek, A., Benderoth, G., Liideke, M.K.B., Kinderman, J. and Kohlmaier, G.H., 1989. Model of the seasonal and perennial carbon dynamics in deciduous-type forests controlled by climatic variables. Ecol. Modelling, 49: 101-124. Johnson, I.R. and Thornley, J.H.M., 1984. A model of instantaneous and daily crop photosynthesis. J. Theor. Biol., 107: 531-545. Johnson, I.R., Parsons, A.J. and Ludlow, M.M., 1989. Modelling photosynthesis in monocultures and mixtures. Aust. J. Plant Physiol., 16: 501-516. Makela, A. and Hari, P., 1986. Stand growth models based on carbon uptake and allocation in individual trees. Ecol. Modelling, 33: 205-229. McDermitt, D.K. and Loomis, R.S., 1981. Elemental composition of biomass and its relation to energy content, growth efficiency, and growth yield. Ann. Bot., 48: 275-290. McPherson, H., Stanley, J., Warrington, I. and Jansson, D., 1988. Dynamics of bud break and flowering. In: N.Z. Kiwifruit Spec. Publ. 2, New Zealand Kiwifruit Authority, Auckland, New Zealand, pp. 9-11. Monsi, M. and Saeki, T., 1953. Uber den Lichtfactor in de Pflanzengesellschaften und seine Bedeutung fiir die Stoffproduktion. Jpn. J. Bot. 14: 22-52. Morgan, C.L. and Austin, R.B., 1983. Respiratory loss of recently assimilated carbon in wheat. Ann. Bot., 51: 85-95. Morgan, E.R., 1988. The architecture and radiation regime of a kiwifruit stand. MSc. thesis, Massey University, Palmerston North, New Zealand. Morley-Bunker, M.J. and Salinger, M.J., 1987. Kiwifruit development - the effect of temperature on bud burst and flowering. Weather Clim., 7: 26-30. Norman, J.M. and Campbell, G.S., 1983. Application of a plant-environment model to problems in irrigation. In: D. Hillel (Editor), Advances in Irrigation, Academic Press, New York, pp. 158-188. Pearcy, R.W., 1988. Photosynthetic utilization of lightflecks by understory plants. Aust. J. Plant Physiol., 15: 223-238. Penning de Vries, F.W.T., 1975. The cost of maintenance processes in plant cells. Ann. Bot., 39: 77-92. Penning de Vries, F.W.T., Brunsting, A.H.M. and Van Laar, H.H., 1974. Products, requirements and efficiency of biosynthesis: a quantitative approach. J. Theor. Biol., 45: 339-377. Sale, P.R., 1985. Kiwifruit culture (2nd Revised Edition). Government Printer, Wellington. Seem, R.C., Elfving, D.C., Oren, T.R. and Eisensmith, S.P., 1986. A carbon balance model for apple tree growth and function. Acta Hortic., 184: 129-137.

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Sheehy, J.E., Corby, J.M. and Ryle, G.J.A., 1979. The use of a model to investigate the influence of some environmental factors on the growth of perennial ryegrass. Ann. Bot., 46: 343-365. Smith, G.S., Clark, C.J. and Henderson, H.V., 1987. Seasonal accumulation of mineral nutrients by kiwifruit. 1. Leaves. New Phytol., 106: 81-100. Smith, G.S., Buwalda, J.G., Green, T.G.A. and Clark, C.J., 1989. Effect of oxygen supply and temperature at the root on the physiology of kiwifruit vines. New Phytol., 113: 431-437. Sunderland, N., 1960. Cell division and cell expansion in the growth of the leaf. J. Exp. Bot., 11: 68-80. Thornley, J.H.M., 1976. Mathematical Models in Plant Physiology. Academic Press, London. Van Keulen, H., 1986. Crop yield and nutrient requirements. In: H. van Keulen and J. Wolf (Editors), Modelling of Agricultural Production: Weather, Soils and Crops. Simulation Monograph, Pudoc, Wageningen, Netherlands, pp. 155-181. Walton, E.F. and De Jong, T.M., 1990. Growth and compositional changes in kiwifruit berries from three California locations. Ann. Bot., 66: 285-296. Walton, E.F., De Jong, T.M. and Loomis, R.S., 1990. Comparison of four methods calculating the seasonal pattern and plant growth efficiency of a kiwifruit berry. Ann. Bot., 66: 297-307. Wang, Y.P. and Jarvis, P.G., 1988. Mean leaf angles for the ellipsoidal inclination angle distribution. Agric. For. Meteorol., 43: 319-321. Wilson, K.S., 1988. Water and energy relationships of kiwifruit. MSc thesis, University of Waikato, Hamilton, New Zealand.