Article title: QualiTree, a virtual fruit tree to study the management of fruit quality. II. Parameterisation for peach, analysis of growth-related processes and agronomic scenarios
Journal name: Trees – Structure and Function
Author names: José M. Mirás-Avalos, Gregorio Egea, Emilio Nicolás, Michel Génard, Gilles Vercambre, Nicolas Moitrier, Pierre Valsesia, María M. González-Real, Claude Bussi, Françoise Lescourret
Corresponding author: Françoise Lescourret INRA, UR 1115 Plantes et Systèmes de culture Horticoles, Domaine Saint-Paul, Site Agroparc, 84914 AVIGNON Cedex 9, France E-mail: [email protected]
The supplementary material includes details on the light interception model and supplementary tables with the whole set of QualiTree parameters or from the analyses described in the main text.
Light interception model
Calculations
Unobstructed photosynthetic photon flux density (Io, waveband 400-700 nm) was obtained from global radiation data registered at climatic stations, considered to be 48% of global radiation (Dauzat et al.,
2001). The contribution of the direct (Ibo) and diffuse (Ido) components of Io were calculated from the estimation of the optical air mass and the ratio between measured Io and the extraterrestrial photosynthetic photon flux density (Iqbal 1983), which was estimated according to the method used by de Pury and
Farquhar (1997). Coordinates of the sun (i.e., zenith angle, hour angle, etc.) were determined from astronomical equations (Iqbal, 1983; de Pury and Farquhar, 1997; Lhomme et al., 2007).
Briefly, the proportion of diffuse radiation (fd) was calculated from a simple model of attenuation of radiation under a cloudless sky, adapted from Campbell (1977) and described by de Pury and Farquhar
(1997):
1 a m f d = m 1 (1) 1+ a 1 f a
1 where a is the atmospheric transmission coefficient of photosynthetically-active radiation, PAR, m is the optical air mass and fa is the proportion of attenuated radiation that reaches the surface as diffuse radiation, which has been observed to range from 40 to 45% under cloudless skies (Weiss and Norman, 1985). In our case, a value of 45% was used.
The optical air mass (m) is defined as the ratio of the mass of atmosphere penetrated per unit cross- sectional area of the solar beam to that penetrated for a site at sea level if the sun is directly overhead and is
P 1 calculated as m = , where θ is the solar zenith angle, P is the atmospheric pressure and P0 is the P0 cosθ atmospheric pressure at sea level.
Intercepted direct light-flux density
To determine the light-flux density through a horizontal plane at a point P, the model calculates the total path length of light within the canopy (S).
The direct light-flux density at a point P on a horizontal plane was calculated from the following equation:
1 I dP = I sexp kb S LADcosθs (2) 2
where Is is the incident direct light-flux density through a perpendicular plane to the beam direction, LAD is
the leaf area density, and s is the solar zenith angle. S is the path length that light goes through within the canopy to reach a given fruiting unit (FU).
The extinction coefficient for the direct radiation, which depends on the direction of the beam, was
0.5 calculated according to Goudriaan (1982) as kb = 0.5*(1-) /cos ( = scattering coefficient; = solar
0.5 zenith angle), whereas the diffuse component (kd) was computed as kd = 0.8*(1-) (Goudriaan, 1977,
1982). The scattering coefficient of leaves (i.e., sum of the reflected and transmitted light) was assumed to be equal to 0.15.
Intercepted diffuse light-flux density
The calculation of diffuse radiation coming from a given direction is based on the model presented
2 by Den Dulk (1989). The sky hemisphere is divided into 46 sectors. In order to define these 46 sectors in the sky hemisphere, two different angles are considered: zenith angle (θ) and azimuth angle (Φ), both in radians. The unitary solid angle (Ω, in steradians) is then obtained by 2π/46.
The sky luminosity distribution is described as the standard overcast sky (SOC) model, as explained by Anderson (1966) and Charles-Edwards and Thornley (1973). B(θ,Φ) is a function describing the luminosity of the sky (W m-2 steradian-1) along a specified direction (θ,Φ). For a SOC, B depends upon θ
(Anderson, 1966), according to the following equation:
1 B = B 1+ 2cosθ (3) 3 0 where B0 is the luminosity of the sky at the zenith. In the absence of a plant or any obstruction, the light-flux
7π I = B density through a horizontal plane, I0, is given by 0 9 0 for a SOC.
The diffuse light-flux density through a horizontal plane at a point P coming from all the sectors is given by:
12Π 2Π 1 I d = Bexp kd S θ,φLADcosθsinθ dθ dφ (4) P 2 θ=0 φ=0
where kd is the extinction coefficient for diffuse radiation.
Input and output data
Input data required for the light interception model concern the orchard, the tree and the climate.
Regarding the orchard, localisation (geographical coordinates and altitude) should be provided as well as row and inter-row distances and row orientation in the northerly direction. Concerning the tree, dimensions
(crown diameters and tree height), the distance between the crown centre of gravity and the ground, the heights of the horizontal planes representing the crown base and top, as well as crown leaf area are inputs.
Climatic inputs at the hourly scale include global irradiation, relative humidity and temperature. The day of the year is also required. The outputs are the hourly direct and diffuse light flux densities for each FU. An example is presented on Suppl. Fig. 1.
Supplementary figure
3 Suppl. Fig. 1. Total Photosynthetically Active Radiation (PAR) intercepted by FU in early June in a peach tree (cv. Alexandra) simulated by QualiTree. Black lines are old wood and coloured lines are FU. Circles indicate the perspective: the larger the circle is, the closer to the observer the corresponding FU is. The colour represents the total PAR received by each FU (mol m-2 d-1).
Supplementary tables
4 Suppl. Table 1. Parameter values concerning carbon economy (6 groups of parameters) and fruit quality in
QualiTree.
Parameter Definition Cultivara Unit Value Origin Global parameters SReq Shoot:root ratio at equilibrium - Dimensionless 4.6 Grossman and DeJong (1994a) Rieger and Marra (1994) Hipps et al. (1995) Mediene et al. (2002) k Parameter expressing the effect of distance between A, AC Dimensionless 0.006 This work organs on carbon exchange within the tree S 0.003 Specific parameters for leafy shoots
R1 Proportion of leaves in the structural dry weight of leafy - Dimensionless 0.70 Ben Mimoun (1997) shoots SLA Specific Leaf Area - m2g-1 14.84 x 10-3 Ben Mimoun (1997) -2 -1 p1 Light-saturated maximal leaf photosynthesis - µmol CO2 m s 20.14 Ben Mimoun (1997) -2 -1 p2 Specific parameter for photosynthesis calculation - µmol CO2 m s 66.95 Ben Mimoun (1997)
r1r Proportion of leaf reserve carbon in the total reserve - Dimensionless 0.70 Ben Mimoun (1997) carbon of leafy shoots
p4 Specific parameter for photosynthesis calculation - µmol CO2 µmol 0.058 Higgins et al. (1992) photons-1 -1 GRCls Leafy shoot growth respiration coefficient - g g 0.10 Penning de Vries et al. (1989)
ddmin Minimum degree-day value - degree-days 0 Data from Bussi et al. (2005)
ddmax Maximum degree-day value - degree-days 1100 Data from Bussi et al. (2005) ini -1 -2 RGRls Leafy shoot initial relative growth rate A, AC degree-days 1.09 x 10 Data from Bussi et al. (2005) S 1 × 10-3 Lescourret et al. (1998) max DMls Leafy shoot maximal dry mass - g 6.75 Data from Bussi et al. (2005) Specific parameters for fruits
ddmin Minimum degree-day value A, AC degree-days 462.68 Data from Lescourret et al. (1998) and Gibert et al. (2005, 2010) S 839 Lescourret and Génard (2005)
ddmax Maximum degree-day value A, AC degree-days 986.93 Data from Lescourret et al. (1998) and Gibert et al. (2005, 2010) S 1800 Lescourret and Génard (2005) ini -1 RGRf Fruit initial relative growth rate A, AC degree-days 0.0107 Data from Lescourret et al. (1998) and Gibert et al. (2005, 2010) S 4.04 × 10-3 Lescourret and Génard (2005) max DMf Potential dry mass of fruits at maturity A, AC g 36.86 Data from Lescourret et al. (1998) and Gibert et al. (2005, 2010) S 59.22 Lescourret and Génard (2005) -1 -1 -3 Pf Fruit photosynthetic rate - mol CO2 g s 7.22 x 10 Lescourret et al. (1998) p5 Parameter for calculation of photosynthesis A, AC g-1 0.0311 Lescourret et al. (1998) S 0.0376 Lescourret et al. (1998) p6 Parameter for calculation of photosynthesis - (m2 s)/mol 0.005 Pavel and DeJong (1993) photon p7 Parameter for calculation of photosynthesis - mol photon/(m2 60 Lescourret et al. (1998) s) p8 Parameter for calculation of photosynthesis - (m2 s)/mol 0.01 Lescourret et al. (1998) photon r3 - Dimensionless 0.04 Lescourret et al. (1998) Parameters common to all organs b -1 -1 -9 MRRst 1-year-old stem and fine roots maintenance respiration - gC gbiomass s 9.93 x 10 Grossman and DeJong (1994b) rate at the reference temperature b -1 -1 -9 MRRow Trunk and coarse root maintenance respiration rate at - gC gbiomass s 1 x 10 Grossman and DeJong (1994b) the reference temperature -1 -1 -9 MRRls Leafy shoots maintenance respiration rate at the - gC gbiomass s 43.45 x 10 Grossman and DeJong (1994b) reference temperature -1 -1 -9 MRRf Fruits maintenance respiration rate at the reference - gC gbiomass s 7.81 x 10 DeJong and Goudriaan (1989) temperature st Q10 Q10 value for 1-year-old stem, old wood and fruits - Dimensionless 1.96 Grossman and DeJong (1994a) ls Q10 Q10 value for leafy shoots - Dimensionless 2.11 Grossman and DeJong (1994a) cr Q10 Q10 value for coarse and fine roots - Dimensionless 2 Grossman and DeJong (1994a) TetaRef Reference temperature - ºC 20 Grossman and DeJong (1994a) -1 CCls Carbon content for leafy shoots - g C g 0.4262 Ben Mimoun (1997) -1 CCf Carbon content for fruits - g C g 0.4242 Ben Mimoun (1997) -1 CCow Carbon content for stem wood, old wood, coarse roots - g C g 0.461 Ben Mimoun (1997) and fine roots
r6ow Maximum ratio of reserves for old wood and roots - Dimensionless 1 This work (default estimation)
r6sw Maximum ratio of reserves for stem wood - Dimensionless 0.2 Ben Mimoun (1997)
r6ls Maximum ratio of reserves for leafy shoots - Dimensionless 0.3 Quilot et al. (2004) GRCow Growth respiration coefficient for old wood, coarse - g C g-1 0.086 Penning de Vries et al. (1989) roots and stem wood
5 Parameter Definition Cultivara Unit Value Origin GRCls Growth respiration coefficient for leafy shoots - g C g-1 0.1 Penning de Vries et al. (1989) GRCf Growth respiration coefficient for fruits - g C g-1 0.0843 DeJong and Goudriaan (1989) GRCnr Growth respiration coefficient for new roots - g C g-1 0.09 Penning de Vries et al. (1989) Reserve mobilization
Rmls Leafy shoot and fine roots mobile fraction of reserves - Dimensionless 0.026 Lescourret and Génard (2005)
Rmow Old wood, coarse root and one year old stem wood - Dimensionless 0.02 Moing and Gaudillère (1992) mobile fraction of reserves Ashworth et al. (1993) Spann et al. (2008) -1 -2 CCRls Carbon content in leafy shoot reserves - g g 42.62 x 10 Ben Mimoun (1997) -1 -2 CCRst Carbon content in stem wood, trunk, coarse root and - g g 46.10 x 10 Ben Mimoun (1997) fine root reserves Growth for different structural parts ini -1 -4 RGRsw Stem wood initial relative growth rate degree-days 7 × 10 Berman and DeJong (2003) ini -1 -4 RGRow Old wood and coarse root initial relative growth rate A, AC degree-days 9.5 × 10 This work S 4 × 10-4 This work Fruit quality parameters
Share1 Parameter for the calculation of the proportion of stone A, AC g 3.9 Data from Lescourret et al. (1998) growth per total fruit growth and Gibert et al. (2005, 2010) S 5.8 Lescourret and Génard (2005) -1 Share2 Parameter for the calculation of the proportion of stone A, AC g 0.0863 Data from Lescourret et al. (1998) growth per total fruit growth and Gibert et al. (2005, 2010) S 0.1 Lescourret and Génard (2005) -1 stone1 Parameter for calculation of the part of total mass A, AC g g 0.7 Data from Lescourret et al. (1998) consisting of fruit flesh and Gibert et al. (2005, 2010) S 1.17 Lescourret and Génard (2005)
stone2 Parameter for calculation of the part of total mass A, AC g 4.76 Data from Lescourret et al. (1998) consisting of fruit flesh and Gibert et al. (2005, 2010) S 3.82 Lescourret and Génard (2005)
ph Proportion of carbon as sucrose in the phloem sap S Dimensionless 0.34728 Génard et al. (2003) -1 k1,1 Relative rate of decrease of k1 (t), the relative rate of S day 0.11856 Génard et al. (2003) sucrose transformation to glucose and fructose -1 k1,2 Time at which k1 (t) = 1 day S day 62.99 Génard et al. (2003) -1 k2 Relative rate of sorbitol transformation to glucose S day 0.43573 Génard et al. (2003) -1 K3 Relative rate of sorbitol transformation to fructose S day 0.5141 Génard et al. (2003)
K4 Ratio of the relative rate of glucose and fructose S Dimensionless 2.5573 Génard et al. (2003) transformation to the relative growth rate -1 csu Carbon content of sucrose - gC g sucrose 0.421 Génard and Souty (1996) -1 cso Carbon content of sorbitol - gC g sorbitol 0.395 Génard and Souty (1996) -1 cg Carbon content of glucose - gC g glucose 0.4 Génard and Souty (1996) -1 cf Carbon content of fructose - gC g fructose 0.4 Génard and Souty (1996)
ax Ratio of area of the composite membrane of the fruit A, AC Dimensionless 0.0273 Data from Gibert et al. (2005, area 2010) S 0.0266 Lescourret and Génard (2005) -3 Dw Water density - g cm 1 Fishman and Génard (1998)
Hf Relative humidity of air space in fruit - Dimensionless 0.996 Fishman and Génard (1998) -2 -1 -1 Lx Conductivity of the composite membrane for water - g cm bar day 0.23328 Fishman and Génard (1998) transport Cell wall extensibility coefficient - bar-1 day-1 0.24 Fishman and Génard (1998) Y Threshold value of hydrostatic pressure needed for - bar 5 Fishman and Génard (1998) growth Empirical parameter relating fruit area (cm2) to fruit A, AC Dimensionless 3.457 Data from Gibert et al. (2005, mass (g) 2010) S 6.049 Fishman and Génard (1998) Empirical parameter relating fruit area (cm2) to fruit A, AC Dimensionless 0.725 Data from Gibert et al. (2005, mass (g) 2010) S 0.601 Fishman and Génard (1998) psat1 Parameter for the calculation of the saturated vapour - bar 0.008048 Fishman and Génard (1998) pressure psat2 Parameter for the calculation of the saturated vapour - ºC-1 0.0547 Fishman and Génard (1998) pressure posmotre Parameter for the calculation of the osmotic pressure of - bar 7.6 Fishman and Génard (1998) the individual fruit a(-) means that the parameter is assumed to be cultivar-independent. (A) Alexandra, (S) Suncrest and (AC) Alexandra in containers are early- and late-maturing cultivar and an early-maturing cultivar grown in containers, respectively.
Suppl. Table 2. Mean square values and significance levels of the different effects considered in the variance analysis of fruit and shoot masses according to the agronomical scenarios where a pest attack occurred.
6 Factor \ Variable Yield Fruit average Leafy shoot total Leafy shoot average mass mass mass Cultivar 74891 * 1.4 15780928 *** 115.1 *** Thinning 1517849 *** 85 *** 4387 0 Pattern 3374 0.3 82810 0.5 Percentage 234389 ** 25.9 *** 2233967 * 5.8 Cultivar * Thinning 144239 ** 0.5 4294 0 Cultivar * Pattern 8174 0.9 129507 0.9 Cultivar * Percentage 68909 8 * 272070 1.8 Thinning * Pattern 970 0 22 0 Thinning * 28926 0.1 82 0 Percentage Pattern * Percentage 5843 0.6 556989 2.2 Cultivar * Thinning * 1719 0 23 0 Pattern Cultivar * Thinning * 3734 0.4 80 0 Percentage Cultivar * Pattern * 23 0 503887 2.1 Percentage Thinning * Pattern * 1332 0 49 0 Percentage Cultivar * Thinning * 117 0 50 0 Pattern * Percentage *** p < 0.001; ** p < 0.01; * p < 0.05
Suppl. Table 3. Mean square values and significance levels of the different effects considered in the variance analysis of fruit quality traits of the Suncrest trees according to the agronomical scenarios where a pest attack occurred.
Factor \ Variable Fruit average Proportion of Dry matter content of Sweetness Index fresh mass total mass the flesh consisting of fruit flesh Thinning 99840 *** 2525 *** 78.5 *** 61.1 *** Pattern 4831 *** 53.4 ** 2.2 * 0 Percentage 39510 *** 1334.1 *** 79.8 *** 68.9 *** Thinning * Pattern 56 0.3 0 0 Thinning * 425 4.1 1 0.5 Percentage Pattern * Percentage 1 1 1.3 * 0.6 Thinning * Pattern * 0 0 0 0 Percentage
7 *** p < 0.001; ** p < 0.01; * p < 0.05
References
Anderson MC (1966) Stand structure and light penetration. II. A theoretical analysis. J. Appl Ecol 3:41-54
Ashworth EN, Stirm VE, Volenec JJ (1993) Seasonal variations in soluble sugars and starch within woody
stems of Cornus sericea L. Tree Physiol 13: 379-388.
Ben Mimoun M (1997) Vers la maîtrise de la variabilité des fruits au sein de l'arbre: étude et modélisation de
la croissance des pêches (Prunus persica) à l'échelle du rameau. Thèse de Doctorat, INA PG, 98 p.
Berman ME, DeJong TM (2003) Seasonal patterns of vegetative growth and competition with reproductive
sinks in peach (Prunus persica). J Horticult Sci Biotech 78 (3): 303-309.
Bussi C, Lescourret F, Génard M, Habib R (2005) Pruning intensity and fruit load influence vegetative and
fruit growth in an early-maturing peach tree (cv. Alexandra). Fruits 60 (2): 133-142.
Campbell GS (1977) An Introduction to Environmental Biophysics. Springer-Verlag, New York
Charles-Edwards DA, Thornley JHM (1973) Light interception by an isolated plant. A simple model. Ann
Bot-London 37:919-928
Dauzat J, Rapidel B, Berger A (2001) Simulation of leaf transpiration and sap flow in virtual plants: model
description and application to a coffee plantation in Costa Rica. Agric For Meteorol 109:143-160 de Pury DGG, Farquhar GD (1997) Simple scaling of photosynthesis from leaves to canopies without the
errors of big-leaf models. Plant Cell Environ 20:537-557
DeJong TM, Goudriaan J (1989) Modeling peach fruit growth and carbohydrate requirements: re-evaluation
of the double-sigmoid growth pattern. J Am Soc Hortic Sci 114: 800-804.
Den Dulk JA (1989) The interpretation of remote sensing, a feasibility study. PhD. Thesis, Wageningen. The
Netherlands
Fishman S, Génard M (1998) A biophysical model of fruit growth: Simulation of seasonal and diurnal
dynamics of mass. Plant, Cell and Environment 21 (8):739-752
Génard M, Lescourret F, Gomez L, Habib R (2003) Changes in fruit sugar concentrations in response to
assimilate supply, metabolism and dilution: a modeling approach applied to peach fruit (Prunus
persica). Tree Physiol 23: 373-385.
Génard M, Souty M (1996) Modeling the peach sugar contents in relation to fruit growth. Journal of the
American Society for Horticultural Science 121 (6):1122-1131
8 Gibert C, Génard M, Vercambre G, Lescourret F (2010) Quantification and modelling of the stomatal,
cuticular and crack components of peach fruti surface conductance. Functional Plant Biology 37:
264-274.
Gibert C, Lescourret F, Génard M, Vercambre G, Pérez Pastor A (2005) Modelling the effect of fruit growth
on surface conductance to water vapour diffusion. Ann Bot 95: 673-683.
Goudriaan J (1977) Crop micrometeorology: a simulation study. Simulation Monographs. Pudoc,
Wageningen, 249 pp
Goudriaan J (1982) Potential production processes. In: Penning de Vries FWT, Laar, HV (Eds.) Simulation
of plant growth and crop production.. Centre for agricultural publishing and documentation.
Wageningen, The Netherlands, 98-112
Grossman YL, DeJong TM (1994a) Carbohydrate requirements for dark respiration by peach vegetative
organs. Tree Physiol 14: 37-48.
Grossman YL, DeJong TM (1994b) PEACH: A simulation model of reproductive and vegetative grotwh in
peach trees. Tree Physiol 14: 329-345.
Higgins SS, Larsen FE, Bendel RB, Radamaker GK, Bassman JH, Bidlake WR, Al Wir A (1992)
Comparative gas exchange characteristics of potted, glass-house-grown almond, apple, fig, grape,
olive, peach and Asian pear. Sci Hortic 52: 313-329.
Hipps NA, Pagès L, Huguet JG, Serra V (1995) Influence of controlled water supply on shoot and root
development of young peach trees. Tree Physiol 15: 95-103.
Iqbal M (1983) An introduction to solar radiation. Academic Press, Toronto, Canada
Lescourret F, Ben Mimoun M, Génard M (1998) A simulation model of growth at the shoot-bearing fruit
level. I.Description and parameterization for peach. Eur J Agron 9: 173-178.
Lescourret F, Génard M (2005) A virtual peach fruit model simulating changes in fruit quality during the
final stage of fruit growth. Tree Physiol 25: 1303-1315.
Lhomme JP, Vacher JJ, Rocheteau A (2007) A simple approach to modeling radiation interception by fruit-
tree orchards. Agric For Meteorol 142:12-24
Mediene S, Jordan MO, Pagès L, Lebot J, Adamowicz S (2002) The influence of severe shoot pruning on
growth, carbon and nitrogen status in young peach trees (Prunus persica). Tree Physiol 22: 1289-
1296.
9 Moing A, Gaudillère JP (1992) Carbon and nitrogen partitioning in peach/blum grafts. Tree Physiol 10: 81-
92.
Pavel EW, DeJong TM (1993) Seasonal CO2 exchange patterns of developing peach (Prunus persica) fruits
in response to temperature, light and CO2 concentration. Physiol Plantarum 88: 322-330.
Penning de Vries FWT, Jansen DM, ten Berge HFM, Bakema A (1989) Simulation of ecophysiological
processes of growth in several annual crops. In: Simulation Monographs, vol. 29. Pudoc,
Wageningen.
Quilot B, Génard M, Kervella J (2004) Leaf light-saturated photosynthesis for wild and cultivated peach
genotypes and their hybrids: A simple mathematical modelling analysis. J Horticult Sci Biotech 79:
546-553.
Rieger M, Marra F (1994) Responses of young peach trees to root confinement. J Am Soc Hortic Sci 119:
223-228.
Spann TM, Beede RH, DeJong TM (2008) Seasonal carbohydrate storage and mobilization in bearing and
non-bearing pistachio (Pistacia vera) trees. Tree Physiol 28: 207-213.
Weiss A, Norman JM (1985) Partitioning solar radiation into direct and diffuse, visible and near-infrared
components. Agric For Meteorol 34:205-213
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