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:

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 ofIowere calculated from the estimation of the optical air mass and the ratio between measured Ioand 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)

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 calculated as , where θ is the solar zenith angle, P is the atmospheric pressure and P0 is the 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:

(2)

where Isis 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 calculated according to Goudriaan (1982) as kb = 0.5*(1-)0.5/cos  ( = scattering coefficient;  = solar zenith angle), whereas the diffuse component (kd) was computed as kd = 0.8*(1-)0.5 (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 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:

(3)

where B0 is the luminosity of the sky at the zenith. In the absence of a plant or any obstruction, the light-flux density through a horizontal plane, I0, is given by for a SOC.

The diffuse light-flux density through a horizontal plane at a point P coming from all the sectors is given by:

(4)

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

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

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 organs on carbon exchange within the tree / A, AC
S / Dimensionless / 0.006
0.003 / This work
Specific parameters for leafy shoots
R1 / Proportion of leaves in the structural dry weight of leafy shoots / - / Dimensionless / 0.70 / Ben Mimoun (1997)
SLA / Specific Leaf Area / - / m2g-1 / 14.84 x 10-3 / Ben Mimoun (1997)
p1 / Light-saturated maximal leaf photosynthesis / - / µmol CO2 m-2 s-1 / 20.14 / Ben Mimoun (1997)
p2 / Specific parameter for photosynthesis calculation / - / µmol CO2 m-2 s-1 / 66.95 / Ben Mimoun (1997)
r1r / Proportion of leaf reserve carbon in the total reserve carbon of leafy shoots / - / Dimensionless / 0.70 / Ben Mimoun (1997)
p4 / Specific parameter for photosynthesis calculation / - / µmol CO2 µmol photons-1 / 0.058 / Higgins et al. (1992)
GRCls / Leafy shoot growth respiration coefficient / - / g g-1 / 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)
RGRlsini / Leafy shoot initial relative growth rate / A, AC
S / degree-days-1 / 1.09 x 10-2
1 × 10-3 / Data from Bussi et al. (2005)
Lescourret et al. (1998)
DMlsmax / 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
S / degree-days / 462.68
839 / Data from Lescourret et al. (1998) and Gibert et al. (2005, 2010)
Lescourret and Génard (2005)
ddmax / Maximum degree-day value / A, AC
S / degree-days / 986.93
1800 / Data from Lescourret et al. (1998) and Gibert et al. (2005, 2010)
Lescourret and Génard (2005)
RGRfini / Fruit initial relative growth rate / A, AC
S / degree-days-1 / 0.0107
4.04 × 10-3 / Data from Lescourret et al. (1998) and Gibert et al. (2005, 2010)
Lescourret and Génard (2005)
DMfmax / Potential dry mass of fruits at maturity / A, AC
S / g / 36.86
59.22 / Data from Lescourret et al. (1998) and Gibert et al. (2005, 2010)
Lescourret and Génard (2005)
Pf / Fruit photosynthetic rate / - / mol CO2 g-1 s-1 / 7.22 x 10-3 / Lescourret et al. (1998)
p5 / Parameter for calculation of photosynthesis / A, AC
S / g-1 / 0.0311
0.0376 / Lescourret et al. (1998)
Lescourret et al. (1998)
p6 / Parameter for calculation of photosynthesis / - / (m2 s)/mol photon / 0.005 / Pavel and DeJong (1993)
p7 / Parameter for calculation of photosynthesis / - / mol photon/(m2 s) / 60 / Lescourret et al. (1998)
p8 / Parameter for calculation of photosynthesis / - / (m2 s)/mol photon / 0.01 / Lescourret et al. (1998)
r3 / - / Dimensionless / 0.04 / Lescourret et al. (1998)
Parameters common to all organs
MRRstb / 1-year-old stem and fine roots maintenance respiration rate at the reference temperature / - / gC gbiomass-1 s-1 / 9.93 x 10-9 / Grossman and DeJong (1994b)
MRRowb / Trunk and coarse root maintenance respiration rate at the reference temperature / - / gC gbiomass-1 s-1 / 1 x 10-9 / Grossman and DeJong (1994b)
MRRls / Leafy shoots maintenance respiration rate at the reference temperature / - / gC gbiomass-1 s-1 / 43.45 x 10-9 / Grossman and DeJong (1994b)
MRRf / Fruits maintenance respiration rate at the reference temperature / - / gC gbiomass-1 s-1 / 7.81 x 10-9 / DeJong and Goudriaan (1989)
Q10st / Q10 value for 1-year-old stem, old wood and fruits / - / Dimensionless / 1.96 / Grossman and DeJong (1994a)
Q10ls / Q10 value for leafy shoots / - / Dimensionless / 2.11 / Grossman and DeJong (1994a)
Q10cr / Q10 value for coarse and fine roots / - / Dimensionless / 2 / Grossman and DeJong (1994a)
TetaRef / Reference temperature / - / ºC / 20 / Grossman and DeJong (1994a)
CCls / Carbon content for leafy shoots / - / g C g-1 / 0.4262 / Ben Mimoun (1997)
CCf / Carbon content for fruits / - / g C g-1 / 0.4242 / Ben Mimoun (1997)
CCow / Carbon content for stem wood, old wood, coarse roots and fine roots / - / g C g-1 / 0.461 / Ben Mimoun (1997)
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 roots and stem wood / - / g C g-1 / 0.086 / Penning de Vries et al. (1989)
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 mobile fraction of reserves / - / Dimensionless / 0.02 / Moing and Gaudillère (1992)
Ashworth et al. (1993)
Spann et al. (2008)
CCRls / Carbon content in leafy shoot reserves / - / g g-1 / 42.62 x 10-2 / Ben Mimoun (1997)
CCRst / Carbon content in stem wood, trunk, coarse root and fine root reserves / - / g g-1 / 46.10 x 10-2 / Ben Mimoun (1997)
Growth for different structural parts
RGRswini / Stem wood initial relative growth rate / degree-days-1 / 7 × 10-4 / Berman and DeJong (2003)
RGRowini / Old wood and coarse root initial relative growth rate / A, AC
S / degree-days-1 / 9.5 × 10-4
4 × 10-4 / This work
This work
Fruit quality parameters
Share1 / Parameter for the calculation of the proportion of stone growth per total fruit growth / A, AC
S / g / 3.9
5.8 / Data from Lescourret et al. (1998) and Gibert et al. (2005, 2010)
Lescourret and Génard (2005)
Share2 / Parameter for the calculation of the proportion of stone growth per total fruit growth / A, AC
S / g-1 / 0.0863
0.1 / Data from Lescourret et al. (1998) and Gibert et al. (2005, 2010)
Lescourret and Génard (2005)
stone1 / Parameter for calculation of the part of total mass consisting of fruit flesh / A, AC
S / g g-1 / 0.7
1.17 / Data from Lescourret et al. (1998) and Gibert et al. (2005, 2010)
Lescourret and Génard (2005)
stone2 / Parameter for calculation of the part of total mass consisting of fruit flesh / A, AC
S / g / 4.76
3.82 / Data from Lescourret et al. (1998) and Gibert et al. (2005, 2010)
Lescourret and Génard (2005)
ph / Proportion of carbon as sucrose in the phloem sap / S / Dimensionless / 0.34728 / Génard et al. (2003)
k1,1 / Relative rate of decrease of k1 (t), the relative rate of sucrose transformation to glucose and fructose / S / day-1 / 0.11856 / Génard et al. (2003)
k1,2 / Time at which k1 (t) = 1 day-1 / S / day / 62.99 / Génard et al. (2003)
k2 / Relative rate of sorbitol transformation to glucose / S / day-1 / 0.43573 / Génard et al. (2003)
K3 / Relative rate of sorbitol transformation to fructose / S / day-1 / 0.5141 / Génard et al. (2003)
K4 / Ratio of the relative rate of glucose and fructose transformation to the relative growth rate / S / Dimensionless / 2.5573 / Génard et al. (2003)
csu / Carbon content of sucrose / - / gC g-1 sucrose / 0.421 / Génard and Souty (1996)
cso / Carbon content of sorbitol / - / gC g-1 sorbitol / 0.395 / Génard and Souty (1996)
cg / Carbon content of glucose / - / gC g-1 glucose / 0.4 / Génard and Souty (1996)
cf / Carbon content of fructose / - / gC g-1 fructose / 0.4 / Génard and Souty (1996)
ax / Ratio of area of the composite membrane of the fruit area / A, AC
S / Dimensionless / 0.0273
0.0266 / Data from Gibert et al. (2005, 2010)
Lescourret and Génard (2005)
Dw / Water density / - / g cm-3 / 1 / Fishman and Génard (1998)
Hf / Relative humidity of air space in fruit / - / Dimensionless / 0.996 / Fishman and Génard (1998)
Lx / Conductivity of the composite membrane for water transport / - / g cm-2 bar-1 day-1 / 0.23328 / Fishman and Génard (1998)
 / Cell wall extensibility coefficient / - / bar-1 day-1 / 0.24 / Fishman and Génard (1998)
Y / Threshold value of hydrostatic pressure needed for growth / - / bar / 5 / Fishman and Génard (1998)
 / Empirical parameter relating fruit area (cm2) to fruit mass (g) / A, AC
S / Dimensionless / 3.457
6.049 / Data from Gibert et al. (2005, 2010)
Fishman and Génard (1998)
 / Empirical parameter relating fruit area (cm2) to fruit mass (g) / A, AC
S / Dimensionless / 0.725
0.601 / Data from Gibert et al. (2005, 2010)
Fishman and Génard (1998)
psat1 / Parameter for the calculation of the saturated vapour pressure / - / bar / 0.008048 / Fishman and Génard (1998)
psat2 / Parameter for the calculation of the saturated vapour pressure / - / ºC-1 / 0.0547 / Fishman and Génard (1998)
posmotre / Parameter for the calculation of the osmotic pressure of the individual fruit / - / bar / 7.6 / Fishman and Génard (1998)

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.

Factor \ Variable / Yield / Fruit average mass / Leafy shoot total mass / Leafy shoot average 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 * Percentage / 28926 / 0.1 / 82 / 0
Pattern * Percentage / 5843 / 0.6 / 556989 / 2.2
Cultivar * Thinning * Pattern / 1719 / 0 / 23 / 0
Cultivar * Thinning * Percentage / 3734 / 0.4 / 80 / 0
Cultivar * Pattern * Percentage / 23 / 0 / 503887 / 2.1
Thinning * Pattern * Percentage / 1332 / 0 / 49 / 0
Cultivar * Thinning * Pattern * Percentage / 117 / 0 / 50 / 0

*** 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 fresh mass / Proportion of total mass consisting of fruit flesh / Dry matter content of the flesh / Sweetness Index
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 * Percentage / 425 / 4.1 / 1 / 0.5
Pattern * Percentage / 1 / 1 / 1.3 * / 0.6
Thinning * Pattern * Percentage / 0 / 0 / 0 / 0

*** p < 0.001; ** p < 0.01; * p < 0.05

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