Trees

, Volume 25, Issue 5, pp 785–799

QualiTree, a virtual fruit tree to study the management of fruit quality. II. Parameterisation for peach, analysis of growth-related processes and agronomic scenarios

Authors

  • José M. Mirás-Avalos
    • INRA, UR1115 Plantes et Systèmes de culture Horticoles (PSH)
    • Facultad de CienciasUniversidade da Coruña
  • Gregorio Egea
    • Universidad Politécnica de Cartagena, Plaza del Cronista Isidoro Valverde
    • Department of Soil Science, School of Human and Environmental SciencesThe University of Reading
  • Emilio Nicolás
    • Departamento de Riego, Centro de Edafología y Biología Aplicada del SeguraCSIC
    • Unidad Asociada al CSIC de Horticultura Sostenible en Zonas Áridas (UPCT-CEBAS)
  • Michel Génard
    • INRA, UR1115 Plantes et Systèmes de culture Horticoles (PSH)
  • Gilles Vercambre
    • INRA, UR1115 Plantes et Systèmes de culture Horticoles (PSH)
  • Nicolas Moitrier
    • INRA, UR1115 Plantes et Systèmes de culture Horticoles (PSH)
  • Pierre Valsesia
    • INRA, UR1115 Plantes et Systèmes de culture Horticoles (PSH)
  • María M. González-Real
    • Universidad Politécnica de Cartagena, Plaza del Cronista Isidoro Valverde
  • Claude Bussi
    • INRA, UE695 Recherches Intégrées (UERI)
    • INRA, UR1115 Plantes et Systèmes de culture Horticoles (PSH)
Original Paper

DOI: 10.1007/s00468-011-0555-9

Cite this article as:
Mirás-Avalos, J.M., Egea, G., Nicolás, E. et al. Trees (2011) 25: 785. doi:10.1007/s00468-011-0555-9

Abstract

In this paper, QualiTree, a fruit tree model designed to study the management of fruit quality, and developed and described in a companion paper (Lescourret et al. in Trees Struct Funct, 2010), was combined with a simple light-interception sub-model, and then parameterised and tested on peach in different situations. Simulation outputs displayed fairly good agreement with the observed data concerning mean fruit and vegetative growth. The variability over time of fruit and vegetative growth was well predicted. QualiTree was able to reproduce the observed response of trees to heterogeneous thinning treatments in terms of fruit growth. A sensitivity analysis showed that the average seasonal growth rates of the different organs were sensitive to changes to the values of their respective initial relative growth rates and that stem wood was the tree organ the most affected by a change in the initial relative growth rates of other organs. QualiTree was able to react to simulated scenarios that combined thinning and pest attacks. As expected, thinning intensity and the percentage damage caused by pests significantly affected fruit yield and quality traits at harvest. These simulations showed that QualiTree could be a useful tool to design innovative horticultural practices.

Keywords

Carbon allocationGrowthFruitSensitivity analysis

Introduction

Carbon partitioning in fruit trees is controlled by several interrelated factors that include photosynthesis, the number and location of competing sinks, storage capacity and transport. Accordingly, cultivation practices such as pruning and thinning seek to manage carbon partitioning in order to obtain the best results in terms of fruit size, quality and production (Corelli-Grappadelli and Coston 1991).

In this respect, models offer a potential to understand and manage fruit quality. Modelling approaches that combine the advantages of crop models, which explicitly take cultivation practices or crop genotype into account (e.g., Hoogenboom et al. 2004; Rinaldi et al. 2007), and ecophysiological models which represent the functioning of plants (e.g., in the case of fruit trees: Buwalda 1991; Grossman and DeJong 1994b; Allen et al. 2005; Costes et al. 2008; Lopez et al. 2008) provide valuable foundations. In a companion paper (Lescourret et al. 2010), a virtual tree model (QualiTree) combining agronomic and physiology viewpoints and describing carbon transfer within the plant, reproductive and vegetative growth, and the development of fruit quality was presented. This model describes the variability of fruit and leafy shoot growth within the tree since it accounts for the effects of tree architecture on carbon allocation and considers each fruiting unit (FU) as a subunit. Moreover, it can simulate cultivation practices such as pruning and thinning. These practices influence light interception through the canopy, a key factor governing photosynthesis that explains part of the within-tree variability of fruit growth (Seeley et al. 1980; Génard and Baret 1994). An interesting feature of QualiTree is that it can be combined with a sub-model to calculate the amount and distribution of daily light in the canopy.

Several models have been developed to predict temporal and spatial variations of light interception in plant canopies. Some of them are based on simple premises, such as considering only one dimension and a uniform turbid medium (Monsi and Saeki 1953). These simple premises can be assumed for annual crops, but they are inadequate for trees. By contrast, complex 3D models of light interception by canopies have been developed (see a recent review by Chelle and Andrieu 2007). These models individualise canopy elements in order to accurately compute light interception and photosynthesis, and thus require long calculation times. Other approaches consider geometric shapes filled with homogeneous turbid medium (Charles-Edwards and Thornley 1973; Norman and Welles 1983), which renders them more suitable to be linked to QualiTree because they use a relatively simple approach to calculate light interception and simultaneously consider tree canopy shape. A simple light interception model based on previous works by Charles-Edwards and Thornley (1973) and de Pury and Farquhar (1997) was incorporated into QualiTree. It embodies the advantages of turbid medium models while also taking account of temporal changes in leaf density within the canopy and the special canopy shapes caused by tree training and between-tree competition for light, depending on planting distances.

This paper mainly focuses on the carbon economy in QualiTree. First of all, we briefly describe QualiTree and the light interception model. We then identify the carbon economy parameters of QualiTree that are not already available in the literature, for two different peach tree cultivars. Thirdly, we report on how the model was tested by comparing its predictions with experimental data from different situations (cultivar, growing conditions) used or not for parameterisation. The variables considered were the fruit and leafy shoot dry masses. Finally, the behaviour of QualiTree was studied in terms of three questions: (1) Is the model capable of reproducing different tree behaviours in terms of carbon exchanges? (2) Is it sensitive to parameters involved in representing carbon demand and exchange? (3) Is it able to react to diverse agronomic scenarios in terms of fruit production and quality?

The first question allowed to assess the ability of the model to describe within-tree carbon exchanges in different cultivars as they had been observed experimentally (Nicolás et al. 2006), whereas the second opened the way to considering the trade-offs regarding biomass allocation in the tree. The third question focused on whether the model could be used in the future for management purposes. To answer this, agronomic scenarios were simulated, based on field observations involving fruit thinning practices and aphid attacks. Thinning is one of the major practices that affects fruit size and quality (Lescourret and Génard 2005) and aphids are known to depress plant growth and cause extensive crop losses (Singh et al. 2004).

Materials and methods

QualiTree

QualiTree is a generic fruit tree model that describes the tree as a set of objects: FUs composed of fruits, leafy shoots and stem wood situated in a tree architecture, old wood (trunk and branches), coarse roots, and fine roots. QualiTree runs on a daily time step, from bloom or after bloom until the end of the fruit growing season, starting from an initial state of the tree (dry masses of tree organs and carbon reserve values; see “Input data”). It represents the growth in dry mass of all tree objects using a carbon-supply approach, simple allocation rules (priority sequence between processes—e.g., maintenance, then growth—or organs, e.g., leafy shoot growth, then fruit growth; use of reserve areas as buffers; passive carbon storage) and simple equations of carbon assimilation (based on leaf area for photosynthesis) and growth requirements (demands) taken mostly from the FU carbon model developed by Lescourret et al. (1998).

Regarding the use of reserve areas as buffers, reserve mobilisation from carbon reserves may occur in each tree organ except for fruit. It is assumed that a fixed fraction of reserves, constant during the season (organ-specific model parameter, Rmx), can be mobilised everyday.

Two main principles are applied to restore carbon balances within the tree. First, the coordination theory (Reynolds and Chen 1996; Chen and Reynolds 1997) is used to propose that the imbalance (Im) between leafy shoots and fine roots defined as the ratio of dry structural masses of young shoots and fine roots to the shoot:root ratio at equilibrium (model parameter, SReq) changes the demands of leafy shoots and fine roots. Second, carbon exchanges occur between the tree objects, with proportionality to the supply of the donor, the demands of the recipient and a decreasing effect of geometric distance between donor and recipient objects according to a negative power law. Three main equations lie at the core of these carbon balance principles. First, the demands of the stem wood, old wood and coarse root compartments are based on the following equation of potential growth in dry mass (DM, g) according to degree-days (dd):
$$ {\frac{{\Updelta {\text{DM}}_{\text{x}} }}{{\Updelta {\text{dd}}}}} = {\text{RGR}}_{\text{x}}^{\text{ini}} {\text{DM}}{}_{\text{x}}\,{\text{e}}^{{ - \theta_{x} {\text{dd}}}} $$
(1)
where subscript x is sw for stem wood, ow for old wood and cr for coarse roots, \( {\text{RGR}}_{\text{x}}^{\text{ini}} , \) the initial relative growth rate, and θx are parameters (dd−1).
Second, the demands of fruit or leafy shoots of the FU and of fine roots are based on the following equation of potential growth:
$$ {\frac{{\Updelta {\text{DM}}_{\text{x}} }}{{\Updelta {\text{dd}}}}} = {\text{RGR}}_{\text{x}}^{\text{ini}} {\text{Im}}^{a} g({\text{dd}}){\text{DM}}_{\text{x}} \left( {1 - {\frac{{{\text{DM}}_{\text{x}} }}{{{\text{Im}}^{a} {\text{DM}}_{\text{x}}^{ \max } }}}} \right) $$
(2)
where subscript x is f for fruit, ls for leafy shoots and fr for fine roots, \( {\text{RGR}}_{\text{x}}^{\text{ini}} \) (dd−1) is the initial relative growth rate (model parameter), Im (dimensionless) is the imbalance between leafy shoots and fine root masses defined previously, exponent a is 0 for fruit, −1 for leafy shoots and 1 for roots, and g(dd) is defined as:
$$ \begin{gathered} g({\text{dd}}) = 1\quad {\text{if}}\;{\text{dd}} < {\text{dd}}_{\min } \hfill \\ g({\text{dd}}) = {\frac{{{\text{dd}}_{ \max } - {\text{dd}}}}{{{\text{dd}}_{ \min } - {\text{dd}}}}}\quad {\text{if}}\;{\text{dd}}\;{\text{is}}\;{\text{between}}\;{\text{dd}}_{ \min } \;{\text{and}}\;{\text{dd}}_{ \max } \hfill \\ g({\text{dd}}) = 0\quad {\text{if}}\;{\text{dd}} < {\text{dd}}_{\max } \hfill \\ \end{gathered} $$
(3)
with ddmin and ddmax as organ-specific parameters (dd).
\( {\text{DM}}_{\text{ls}}^{ \max } \) (g) is the product of the leafy shoot number of the FU and the maximum mass of an average individual leafy shoot \( {\text{DM}}_{{i{\text{ls}}}}^{ \max } \) (g). With respect to the set of fine roots, \( {\text{DM}}_{\text{fr}}^{ \max } \) (g) is calculated assuming that its ratio to the maximum mass of leafy shoots on the tree is equal to the shoot:root ratio at equilibrium SReq:
$$ {\text{DM}}_{\text{fr}}^{ \max } = {\frac{{N_{\text{ls}} {\text{DM}}_{{i{\text{ls}}}}^{\max } }}{{{\text{SR}}_{\text{eq}} }}} $$
(4)
where Nls is the number of leafy shoots on the tree.
Third, the equation depicting the carbon flow from each tree object i to each object j, Fij, is:
$$ F_{ij} = {\frac{{{\text{ACP}}_{i} {\text{Demand}}_{j} }}{{\sum\nolimits_{j = 1}^{n} {{\text{Demand}}_{j} } }}}{\text{dist}}_{ij}^{ - k} $$
(5)
where ACPi is the available carbon pool of i (gC), i.e., the carbon pool remaining after satisfaction of maintenance respiration (and of leaf growth if i is an FU) from an initial pool made of photosynthates (if i is an FU; see “Light interception model”) and of mobilised reserves, Demandj (gC) is the carbon demand of j, distij (mm) the geometric distance between i and j, n is the total number of objects exchanging carbon and k is a positive parameter (dimensionless). Parameter k expresses the effect of distance on carbon exchange: when k is close to zero, the distance has no effect and carbon is distributed proportionally to carbon demands, whereas high values for k lead to severe effects of distance.

QualiTree represents the development of several quality traits for fruit: fruit size, the proportion of the total mass made up of fruit flesh, the dry matter content of the flesh, flesh concentrations of various sugars, and a sweetness index. The development of fruit quality traits was based on an integrated fruit model (Lescourret and Génard 2005) that combines sub-models of fresh mass (Fishman and Génard 1998; Lescourret et al. 2001) and sugars (Génard and Souty 1996; Génard et al. 2003).

QualiTree variables are subject to change as a result of climate and cultivation practices, such as pruning, thinning or pest attacks. For example, shoot removal by pruning, or shoot reduction by pest attacks, induces reactions by leafy shoots and fine roots in the model, following the coordination principle evoked above and represented in Eq. 2. Thinning is considered on the basis of the number of fruits on each FU, which acts on the source–sink carbon relationships within the tree. Further details on QualiTree can be found in a companion paper (Lescourret et al. 2010).

Light interception model

The light interception model is a simple model that predicts radiation interception by a tree within an orchard. It is mainly based on previous works by Charles-Edwards and Thornley (1973) and de Pury and Farquhar (1997). It calculates the incident light-flux density, encompassing its direct and diffuse components, on a horizontal surface at various positions within the tree. The basic assumptions are (a) the beam travelling through the canopy is attenuated according to Beer’s law; (b) foliage is uniformly distributed in the space volume occupied by the canopy; and (c) the leaf angle distribution is spherical (see Electronic Supplementary Material for details).

The canopy is described as a complex shape using two ellipsoids: an external ellipsoid encompassing the tree crown and an internal ellipsoid without leaves at the top centre of the canopy. This corresponds to the current shapes applied in peach tree training, taken as an example. Peach trees are usually goblet-trained, i.e., shoots growing in the centre of the crown are pruned to enable deeper light penetration into the canopy. Two planes cutting the top and bottom of the ellipsoids were added so that the final tree shape would be realistic with regard to usual peach-training practices (Fig. 1). As shading by neighbouring tree is considered (Fig. 1), the orchard was characterised by specifying row and within-row spacings as well as the row orientation relative to the northerly direction. In this way, only a few parameters are necessary to describe both the tree and the orchard.
https://static-content.springer.com/image/art%3A10.1007%2Fs00468-011-0555-9/MediaObjects/468_2011_555_Fig1_HTML.gif
Fig. 1

Schematic diagram of the tree within the orchard and calculation of the path length through the vegetation. h is the row spacing, x, y and z the Cartesian axes. θ is the elevation angle, Q or Q′ the position where the ray enters the canopy and P or P′ the position of the FU. Two cases are represented: (1) the path goes through the area with no vegetation, so two path lengths are calculated within the same canopy; (2) the path goes through the vegetation area from a neighbouring tree

In QualiTree, following the principles of the FU carbon model developed by Lescourret et al. (1998), the photosynthesis during a day is calculated at the scale of each FU, as a sum of hourly photosynthesis of leaves over hours where the radiation received, in terms of photosynthetically active photon flux density (PPFD), is positive. The photosynthesis per unit leaf area and per unit time uses the empirical formulation of Higgins et al. (1992) with PPFD and light-saturated leaf photosynthesis as drivers. Thus, coupling the light interception model to QualiTree required computing of the received radiation for each FU. Received radiation is dependent on the length of the path within the canopy along which radiation must travel to reach target points in the canopy (Fig. 1), and on leaf area density. Because of vegetative growth during the season, light interception is altered by variations in the leaf area density.

Experimental data

Data were used to estimate some of the model parameters, namely k (Eq. 5) and the initial growth rates of fine roots (Eq. 2) and of old wood (Eq. 1), and also to test the model. They were taken from several experiments on vegetative and reproductive growth performed at two locations and concerning two cultivars of Prunus persica, one early-maturing (Alexandra) and one late-maturing (Suncrest). These cultivars have displayed different behaviours, especially with respect to fruit growth (Génard et al. 1998).

Data on the Alexandra cultivar were taken from studies conducted in 1997 on an orchard planted in 1985 at the INRA Avignon Research Centre (SE France). The trees were grafted on GF 677 rootstock and planted at 5 m × 5 m spacings on a silt–clay soil. Routine horticultural care for commercial fruit production was ensured. Full bloom occurred on March 12. One tree was chosen as being representative of the orchard. This tree, referred to as Alexandra hereinafter, was hand-thinned 30 days after full bloom (DAFB) in order to obtain high- and low-crop load treatments, respectively. One scaffold was lightly thinned to generate a high-crop load, while a second was heavily thinned to produce a low-crop load, and different FUs were alternately lightly or heavily thinned in the remaining two scaffolds. The corresponding ratios of leafy shoots per fruit were 2.6, 5.2 and 4.1. Leafy shoots are long leafy shoots in the case of peach crops, where FUs are 1-year-old fruit-bearing shoots. The total numbers of fruits per tree were normal (commercial level). The diameters and lengths of tree axes, and insertion and phyllotaxic angles were measured in order to obtain a description of the tree architecture, which constituted a model input (see “QualiTree”).

Suncrest data were generated in 1998 from an orchard planted in 1982 at the INRA Experimental Station in Gotheron (Valence, Rhone Valley). The orchard conditions and tree treatments (including different thinning procedures) were the same as those described for Alexandra, except that trees were grafted on GF 305 rootstock. Full bloom occurred on March 20. The architecture of a representative tree, referred to as Suncrest hereinafter, was described in the same way as for Alexandra. In this tree, the ratios of leafy shoots per fruit for the high, low and alternate crop loads were 4.2, 12.7 and 10.

For both cultivars, the diameters of all fruits were measured using digital callipers perpendicular to the fruit suture on each FU. Data were collected every 3–5 days from 61 or 75 DAFB until 103 or 133 DAFB (harvest time) for Alexandra and Suncrest, respectively, when the fruit growth curves displayed a saturation pattern. Fruit diameter (mm) was converted to dry mass (g) using allometric relationships for both cultivars (Ben Mimoun et al. 1996). Leafy shoot length (m) was also measured for each FU four times during fruit growth in Alexandra, and twice in Suncrest, at the beginning of fruit growth and near fruit harvest. Lengths were converted to dry mass (g) using the allometric relationship developed by Walcroft et al. (2004).

Furthermore, the model was tested with two Alexandra trees grown in containers, using all the parameters previously estimated for the Alexandra orchard-grown tree except for the initial relative growth rate of fine roots, which was newly estimated to account for the effect of the container on root growth. Experiments were performed in 2003 on trees grafted on GF 677 rootstock planted in 1999 and cultivated outdoors in 110-L containers. The trees were goblet-trained and received routine horticultural care (Gibert et al. 2005). Full bloom occurred on March 24. Measurements were taken from 35 to 85 DAFB (harvest time). Data on tree architecture and fruit and leafy shoot growth were recorded as described above.

Input data

Climatic data sets (global radiation and temperature) collected at INRA weather stations located close to the experimental fields were used as model inputs.

Data on the diameter and length of different tree parts at full bloom (i.e., trunk, scaffolds, branches and FU) were used to calculate distances between the virtual tree objects and their initial dry biomass. For this purpose, the trunk, branches and FU were considered as conic-section structures; their volumes were calculated and then transformed into biomass using a wood-density value of 0.77 g cm−3 (dry mass: fresh volume; unpublished experiments). The calculation of distances was as follows (Lescourret et al. 2010). The barycentre of old wood was located halfway between the trunk base and the mean point of insertion of the FU. The fine root barycentre was located so that the ratio of the distances between old wood and fine roots and the trunk base was equal to the shoot:root ratio at equilibrium, and the coarse root barycentre was located halfway between the trunk base and the fine root barycentre. Distances between FUs were calculated according to the pathways between FU on the real tree architecture. For example, the whole set of distances ranged from 2 to 413 cm in Alexandra (mean = 190 cm) and from 0.5 to 656.5 cm in Suncrest (mean = 372.7 cm).

According to several authors (Grossman and DeJong 1994a, b; Miller and Walsh 1988; Rufat and DeJong 2001), the root system mass of peach ranges from approximately 27 to 38% of the old wood (trunk and branches) compartment mass. For this reason, 30% was considered when calculating the initial root mass. However, QualiTree requires separate values for the coarse and fine root masses. The initial values for fine root dry mass were assumed to be proportional to the current-year aboveground parts of the tree (Kozlowski et al. 1991). The proportionality coefficient was the shoot:root ratio at equilibrium (SReq, see “QualiTree”).

Carbon reserve values for old wood (8%) and coarse roots (8%) were obtained from the work of Jordan and Habib (1996) and Mediene et al. (2002). Reserve values for stems (5.5%) and leafy shoots (16%) at the initial stage of fruit development were obtained from Lescourret and Génard (2005).

Parameter identification

Newly identified parameter values concerning the carbon economy in QualiTree are presented in Table 1. They were either identified from the literature, estimated from published data or estimated globally during this project by running QualiTree. All other parameters, including those specific to Alexandra or Suncrest, were presented in Génard et al. (1998), Lescourret et al. (1998) and Lescourret and Génard (2005). They are not mentioned in Table 1, except for the initial relative growth rates that were varied for a sensitivity analysis (“Sensitivity analysis”), but in Suppl. Table 1 of Electronic Supplementary Material.
Table 1

Newly identified (from literature, estimated from published data or estimated globally in this work) parameter values concerning carbon economy in QualiTree

Parameter

Definition (corresponding equation)

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 (Eq. 5)

A, AC

Dimensionless

0.006

This work

S

0.003

 

Specific parameters for leafy shoots

 ddmin

Minimum degree-day value (Eq. 3)

Degree-days

0

Data from Bussi et al. (2005)

 ddmax

Maximum degree-day value (Eq. 3)

Degree-days

1,100

Data from Bussi et al. (2005)

 \( {\text{RGR}}_{\text{ls}}^{\text{ini}} \)

Leafy shoot initial relative growth rate (Eq. 2)

A, AC

Degree-days−1

1.09 × 10−2

Data from Bussi et al. (2005)

S

1 × 10−3

Lescourret et al. (1998)

 \( {\text{DM}}_{\text{ls}}^{ \max } \)

Leafy shoot maximal dry mass (Eq. 2)

g

6.75

Data from Bussi et al. (2005)

Specific parameters for fruits

 ddmin

Minimum degree-day value (Eq. 3)

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 (Eq. 3)

A, AC

Degree-days

986.93

Data from Lescourret et al. (1998) and Gibert et al. (2005, 2010)

S

1,800

Lescourret and Génard (2005)

 \( {\text{RGR}}_{\text{f}}^{\text{ini}} \)

Fruit initial relative growth rate (Eq. 2)

A, AC

Degree-days−1

0.0107

Data from Lescourret et al. (1998) and Gibert et al. (2005, 2010)

S

4.04 × 10−3

Lescourret and Génard (2005)

 \( {\text{DM}}_{\text{f}}^{ \max } \)

Potential dry mass of fruits at maturity (Eq. 2)

A, AC

g

36.86

Data from Lescourret et al. (1998) and Gibert et al. (2005, 2010)

S

59.22

Lescourret and Génard (2005)

Reserve mobilisation

 Rmls

Leafy shoot and fine roots mobile fraction of reserves

Dimensionless

0.026

Lescourret and Génard (2005)

 Rmow

Old wood, coarse root and 1-year-old stem wood mobile fraction of reserves

Dimensionless

0.02

Moing and Gaudillère (1992), Ashworth et al. (1993), Spann et al. (2008)

Growth for different structural parts

 \( {\text{RGR}}_{\text{sw}}^{\text{ini}} \)

Stem wood initial relative growth rate (Eq. 1)

Degree-days−1

7 × 10−4

Berman and DeJong (2003)

 \( {\text{RGR}}_{\text{ow}}^{\text{ini}} \)

Old wood and coarse root initial relative growth rate (Eq. 1)

A, AC

Degree-days−1

9.5 × 10−4

This work

S

4 × 10−4

This work

 \( {\text{RGR}}_{\text{fr}}^{\text{ini}} \)

Fine root initial relative growth rate (Eq. 2)

A

Degree-days−1

0.01

This work

AC

0.0001

This work

S

0.05

This work

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

Potential leafy shoot growth parameters (Eq. 2), namely the initial relative growth rate (\( {\text{RGR}}_{\text{ls}}^{\text{ini}} \)) and maximum dry mass (\( {\text{DM}}_{\text{ls}}^{ \max } \)), were estimated from data collected on unpruned and defruited stems in Alexandra (Bussi et al. 2005).

Carbohydrate remobilisation values are known to be very similar in different plants such as peach, pistachio and dogwood: between 0.01 and 0.02 day−1 in all cases (Ashworth et al. 1993; Moing and Gaudillère 1992; Spann et al. 2008). Therefore, for the trunk, coarse root and stem wood compartments, 0.02 day−1 was the reserve mobilisation value considered in the simulations. For leafy shoots and fine roots, the value obtained by Lescourret and Génard (2005) for young tissues was used (Table 1).

The shoot:root ratio at equilibrium (SReq), defined as the ratio between current-year aboveground and belowground parts of the tree at the end of the reproductive period, was estimated from peach trees under different growing conditions (Grossman and DeJong 1994a; Hipps et al. 1995; Mediene et al. 2002; Rieger and Marra 1994). For unpruned and unthinned peach trees under no water stress, the shoot:root ratios observed ranged from 3.5 to 6.3, with an average of 4.6, which was taken as a parameter value (Table 1).

Three parameters were estimated globally by running QualiTree, for each of the Alexandra and Suncrest cultivars: the parameter expressing the effect of distance between tree objects on carbon exchange within the tree (k, Eq. 5); the initial relative growth rate of fine roots (\( {\text{RGR}}_{\text{fr}}^{\text{ini}} \), Eq. 2) and that of old wood (\( {\text{RGR}}_{\text{ow}}^{\text{ini}} \), Eq. 1; Table 1). The value of the initial relative growth rate of coarse roots (\( {\text{RGR}}_{\text{cr}}^{\text{ini}} \)) was considered to be equal to that of old wood. The criterion (A) to be minimised for this estimation was a weighted sum of differences averaged over the FU, for two observable variables fairly close to the processes to be parameterised, i.e., the leafy shoot and fruit dry masses:
$$ A = {\frac{1}{{\sigma_{y}^{2} }}}\frac{1}{n_{i}}\sum\limits_{i} {\left[ {\frac{1}{n}\sum\limits_{j = 1}^{{n_{i} }} {(y_{ij} - y_{ij}^{\text{s}} )^{2} } } \right]} + {\frac{1}{{\sigma_{z}^{2} }}}\frac{1}{n}\sum\limits_{i} {\left[ {{\frac{1}{{n_{i} }}}\sum\limits_{j = 1}^{{n_{i} }} {(z_{ij} - z_{ij}^{\text{s}} )^{2} } } \right]} $$
(6)
where yij and zij are the observed averages for leafy shoot and fruit dry mass per FU (i) and per date (j), respectively; \( y_{ij}^{\text{s}} \) and \( z_{ij}^{\text{s}} \) the corresponding simulated average values of leafy shoot and fruit dry mass per FU (i) and per date (j), respectively; ni, the number of dates for FU (i); n, the total number of FU; \( \sigma_{y}^{2} \), the variance of yij; and \( \sigma_{z}^{2} \), the variance of zij.

Comparison of observed and simulated values

Relative Root Mean Square Error (RRMSE) was used to compare the mean observed and simulated values of fruit or leafy shoot dry masses per individual FU at the same dates. RRMSE is a commonly used criterion in the case of non-linear models (Kobayashi and Salam 2000). It is defined as:
$$ {\text{RRMSE}} = {\frac{1}{{\bar{y}}}}\sqrt {\frac{1}{N}\sum\limits_{i = 1}^{N} {(y_{i} - y_{i}^{\text{s}} )^{2} } } $$
(7)
where i refers to a given FU at a given date, yi is the observed value, \( {y_{i}^{\text{s}} } \) the corresponding simulated value, N the total number of observed data, and \( \bar{y} \) the mean of observed values. The lower the RRMSE, the more accurate is the simulation.

As explained above, the trees implemented in the model underwent different loading treatments between the FU or main scaffolds (see “Experimental data”). The ability of the model to account for the effects of these treatments was assessed. For this purpose, the statistical unit of analysis was the single FU. The effect of each treatment on mean leafy shoot and fruit individual dry mass per FU was evaluated for both cultivars using analysis of variance.

Sensitivity analysis

A sensitivity analysis was performed to identify the parameters with the greatest influence on the average growth rates of the different tree organs (coarse roots, old wood, fine roots, stem wood, leafy shoots and fruits) over the growing season (from 61 to 103 DAFB in Alexandra and from 75 to 133 DAFB in Suncrest). The model was considered to be sensitive to a parameter for a given output when a 20% change in this parameter led to a variation of at least 5% in the output. The parameters considered were those expressing the effect of distance between tree objects on carbon exchange within the tree (k), the shoot:root ratio at equilibrium (SReq), and the initial relative growth rates of the different organs (old wood: \( {\text{RGR}}_{\text{ow}}^{\text{ini}} \); fine roots: \( {\text{RGR}}_{\text{fr}}^{\text{ini}} \); stem wood: \( {\text{RGR}}_{\text{sw}}^{\text{ini}} \); leafy shoots: \( {\text{RGR}}_{\text{ls}}^{\text{ini}} \); fruits: \( {\text{RGR}}_{\text{f}}^{\text{ini}} \)).

Agronomic scenarios

The scenarios were built by combining three basic factors: cultivar (Alexandra or Suncrest), thinning intensity (no thinning, 15 cm, and 25 cm between fruits, 25 cm corresponding to commercial thinning) and a “pest attack” factor describing the occurrence of pests (yes–no) and their effect in the event of occurrence. Thinnings were performed at stage II of fruit growth (61 and 75 DAFB in Alexandra and Suncrest, respectively). The pest effect was defined as a combination of a pattern of damage (three patterns), and percentage damage (loss of 2 or 5% of leafy shoot dry mass per day during the period of damage, which is realistic according to the data obtained by Grechi et al. (2008) on peach tree attack by green aphids). The three patterns of damage were defined as follows, knowing that temperatures higher than 30°C kill aphids:
  1. 1.

    A treated attack. The period of damage was between 80 and 85 DAFB for Alexandra, and between 85 and 90 DAFB for Suncrest, corresponding approximately to the time of maximum infestation observed by Grechi et al. (2008). In this case, a 10-day halt in vegetative growth was assumed to occur from the onset of the attack until the beginning of vegetative regrowth (i.e. from 80 to 90 DAFB in Alexandra and from 85 to 95 DAFB in Suncrest), because of (a) the effects of an insecticide application, which kills aphid populations in 5 days, and (b) five further days for the tree to recover.

     
  2. 2.

    A non-treated attack. Damage started at 80 DAFB for Alexandra and at 85 DAFB for Suncrest, with no subsequent vegetative growth because the orchard was not treated. In the case of Alexandra, the loss of vegetative dry mass remained until the end of the simulation because temperatures higher than 30°C (i.e. that kill aphids) were not expected. However, for Suncrest, the loss of vegetative dry mass was stopped at 115 DAFB when high temperatures were assumed to have killed the aphid population. Vegetative regrowth was assumed to start 5 days later (120 DAFB).

     
  3. 3.

    A non-treated attack late in the season. The damage started on 103 DAFB for Alexandra and 95 DAFB for Suncrest. At this stage, it was impossible to apply an insecticide, because its half-life would impede fruit commercialisation. For Suncrest, the damage lasted for 7 days, after which the aphid population was assumed to die as a result of temperatures higher than 30°C. A 12-day halt in vegetative growth was assumed to occur from the onset of damage, followed by vegetative regrowth. For Alexandra, high temperatures were not expected during the simulation period, and the damage lasted for 7 days, after which the fruits were harvested.

     

A simulation experiment was designed by crossing cultivar, thinning intensity and pest attack (yes–no), where the modality “yes” encompassed the six types of attack explained above (three patterns with two percentage damage rates). This yielded 42 scenarios that could be analysed by variance analysis using complete models. The pest attack data (36 of the 42 scenarios) were then further analysed. In every analysis, the output variables were fruit yield, fruit average dry mass, total dry mass of leafy shoots and average dry mass of leafy shoots. Moreover, four fruit quality traits (average fruit fresh mass, dry matter content of the flesh, proportion of total mass consisting of fruit flesh and sweetness index) were analysed for the Suncrest cultivar only. To achieve this, the simulations used the Suncrest-specific parameters found in Fishman and Génard (1998), Génard et al. (2003) and Lescourret and Génard (2005); see Suppl. Table 1 of Electronic Supplementary Material for further details.

Data analyses were performed using R software version 2.7.1 (R Development Core Team 2008).

Results

Model parameterisation and test

The newly identified parameter values are presented in Table 1. They generally differed between cultivars. The values of the parameter expressing the effect of distance between tree objects on carbon exchange within the tree (k) were very low. With such values, although the distribution and mean of distances were different between Alexandra and Suncrest (see “Input data”), the component of Eq. 5 expressing the effect of distance (distancek) was very similar between Alexandra and Suncrest and indicative of non-limitation of within-tree distances, since it ranged from 0.95 to 0.98 in Alexandra (mean = 0.96) and from 0.97 to 0.99 in Suncrest (mean = 0.98) according to the within-tree distance. Leafy shoot dry mass simulated values fitted correctly with those observed (RRMSE = 0.22, 0.25, 0.28 and 0.36 for Alexandra, Suncrest and each Alexandra tree grown in containers, respectively). The low variability observed for trees grown in containers and the high variability observed for trees grown in orchards were well simulated (Fig. 2), although the variability in Alexandra was underestimated in the last two dates.
https://static-content.springer.com/image/art%3A10.1007%2Fs00468-011-0555-9/MediaObjects/468_2011_555_Fig2_HTML.gif
Fig. 2

Testing of the model against experimental data for the Alexandra and Suncrest trees and the two Alexandra trees grown in containers. Variations in leafy shoot growth among monitored shoots (mean ± SD) as a function of DAFB, either observed (black squares and black lines) or simulated (white circles and dotted lines). The total number of FU (n) is indicated on each plot. Times of fruit harvest are 103 (Alexandra), 133 (Suncrest) and 85 DAFB (Alexandra trees grown in containers)

Simulated values for fruit dry mass satisfactorily reproduced the observed data for the orchard-grown Alexandra tree and for one of the container-grown trees (RRMSE = 0.15 and 0.10). For the other trees, the simulated results were acceptable (RRMSE = 0.20 and 0.23) with an underestimation in the last days before harvest (Fig. 3).
https://static-content.springer.com/image/art%3A10.1007%2Fs00468-011-0555-9/MediaObjects/468_2011_555_Fig3_HTML.gif
Fig. 3

Testing of the model against experimental data for the Alexandra and Suncrest trees and the two Alexandra trees grown in containers. Variations in fruit growth among monitored shoots (mean ± SD) as a function of DAFB, either observed (black squares and black lines) or simulated (white circles and dotted lines). The total number of FU (n) is indicated on each plot. Times of fruit harvest are 103 (Alexandra), 133 (Suncrest) and 85 DAFB (Alexandra trees grown in containers)

The ability of the model to reproduce the observed response of trees to heterogeneous thinning treatments was evaluated in both the cultivars, using RRMSE calculations and a variance analysis with cultivar and crop load treatment as factors. Near to fruit harvest (99 and 122 DAFB in Alexandra and Suncrest, respectively), there was a large difference between cultivars but no difference between crop load treatments, for simulated or observed leafy shoot data (Table 2). Significant effects of cultivar and crop load treatment on fruit dry mass at harvest were found for simulated or observed data (Table 2). For leafy shoot or fruit, a good agreement was found between average simulated and observed values for differently loaded scaffolds in both cultivars (with a constant but very slight—about 1 g—underestimation for Alexandra fruit; Table 3). The Suncrest data observed displayed significant differences in the fruit dry mass obtained in differently loaded scaffolds, the average fruit dry mass being higher in low-loaded scaffolds. The same differences were observed relative to the simulated corresponding fruit masses. Such differences were not observed for Alexandra, which was correctly simulated.
Table 2

Observed and simulated mean values of fruit and leafy shoot mass according to cultivar and crop load

Factor

Modality

Observed fruit average mass (g)

Simulated fruit average mass (g)

Observed leafy shoot average mass (g)

Simulated leafy shoot average mass (g)

Mean

Mean square

Mean

Mean square

Mean

Mean square

Mean

Mean square

Cultivar

Alexandra

18.36

424.6***

17.02

559.2***

5.23

473.3***

5.31

431.12***

Suncrest

22.67

21.96

1.16

1.43

Crop load

High crop

18.69

207.5***

19.05

56.6***

2.67

1.3

2.90

0.69

Low crop

24.47

22.23

2.77

2.91

Alternative crop

20.50

19.82

2.66

2.88

Alternative crop load

Alternative high

20.01

68.2**

20.02

42.6*

3.26

3.1

3.21

0.014

Alternative low

21.63

20.81

2.33

2.78

Mean square values correspond to a variance analysis (see main text for details). Significant differences are also indicated

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

Table 3

Observed and simulated effects of crop load on average fruit and leafy shoot individual dry mass per FU (g) at harvest for Alexandra and Suncrest and corresponding RRMSE

Crop load

Observed values

Simulated values

RRMSE

Alexandra fruit dry mass (g)

 High crop (H)

17.2 ± 2.5 (n = 10)

16.1 ± 2.3 (n = 10)

0.18

 Low crop (L)

19.6 ± 1.7 (n = 13)

17.9 ± 1.5 (n = 13)

0.15

 Alternative crop (A)

18.3 ± 1.9 (n = 23)

17.1 ± 1.5 (n = 23)

0.15

 Alternative high (AH)

17.9 ± 1.7 (n = 12)

16.5 ± 1.1 (n = 12)

0.15

 Alternative low (AL)

18.8 ± 2.1 (n = 11)

17.6 ± 1.7 (n = 11)

0.14

Suncrest fruit dry mass (g)

 High crop (H)

19.5 ± 2.8 (n = 14)

20.7 ± 2.3 (n = 14)

0.18

 Low crop (L)

26.2 ± 4.4 (n = 22)

23.8 ± 2.2 (n = 22)

0.23

 Alternative crop (A)

21.7 ± 3.2 (n = 30)

21.3 ± 2.8 (n = 30)

0.19

 Alternative high (AH)

20.0 ± 2.8 (n = 15)

20.0 ± 1.5 (n = 15)

0.18

 Alternative low (AL)

23.0 ± 3.1 (n = 15)

22.3 ± 3.1 (n = 15)

0.20

Alexandra leafy shoot dry mass (g)

 High crop (H)

5.07 ± 2.14 (n = 10)

5.23 ± 0.77 (n = 10)

0.28

 Low crop (L)

5.56 ± 1.28 (n = 13)

5.39 ± 0.72 (n = 13)

0.16

 Alternative crop (A)

5.11 ± 1.73 (n = 23)

5.30 ± 0.88 (n = 23)

0.28

 Alternative high (AH)

5.58 ± 1.12 (n = 12)

5.43 ± 0.64 (n = 12)

0.29

 Alternative low (AL)

4.61 ± 2.08 (n = 11)

5.18 ± 1.08 (n = 11)

0.25

Suncrest leafy shoot dry mass (g)

 High crop (H)

1.18 ± 0.79 (n = 14)

1.45 ± 0.93 (n = 14)

0.18

 Low crop (L)

1.32 ± 0.60 (n = 22)

1.62 ± 0.70 (n = 22)

0.18

 Alternative crop (A)

1.05 ± 0.67 (n = 30)

1.29 ± 0.80 (n = 30)

0.20

 Alternative high (AH)

1.12 ± 0.73 (n = 15)

1.38 ± 0.87 (n = 15)

0.15

 Alternative low (AL)

1.01 ± 0.69 (n = 15)

1.25 ± 0.82 (n = 15)

0.15

The number of FU is indicated

Sensitivity analysis

The only parameters that did not influence any of the accounted outputs in either cultivar, at least within the range of variation examined, were those expressing the effect of distance between tree objects on carbon exchange within the tree (k) and \( {\text{RGR}}_{\text{fr}}^{\text{ini}} \). All other parameters exerted an influence on at least one of the model outputs in one of the trees (Tables 4, 5).
Table 4

Model sensitivity to parameters for Alexandra

Parameter

Parameter variation (%)

AGRfr

AGRcr

AGRow

AGRsw

AGRls

AGRf

k

+20

−0.14

−1.04

−0.96

3.82

−0.18

0.49

−20

0.13

1.01

0.95

−3.91

0.18

−0.53

\( {\text{RGR}}_{\text{fr}}^{\text{ini}} \)

+20

1.85

0.39

0.38

4.28

2.38

−0.27

−20

−3.16

−0.43

−0.42

−5.02

−3.40

0.33

\( {\text{RGR}}_{\text{ow}}^{\text{ini}} \)

+20

−1.22

9.19

9.20

17.67

−1.58

−4.55

−20

1.03

12.65

12.67

26.21

1.48

4.25

\( {\text{RGR}}_{\text{sw}}^{\text{ini}} \)

+20

−0.08

−0.61

−0.60

24.64

−0.10

−0.40

−20

0.07

0.60

0.60

23.16

0.10

0.40

\( {\text{RGR}}_{\text{ls}}^{\text{ini}} \)

+20

2.78

1.45

1.44

6.36

5.64

0.33

−20

−3.92

−1.98

−1.96

7.71

7.96

−0.56

\( {\text{RGR}}_{\text{f}}^{\text{ini}} \)

+20

−0.68

−4.94

−4.93

17.35

−1.03

6.99

−20

0.59

4.76

4.75

34.41

0.93

10.12

SReq

+20

13.46

3.27

3.25

6.41

2.94

1.59

−20

16.22

−4.42

−4.40

7.09

−3.89

−2.38

Variations are expressed as a percentage of the reference value on the basis of a ±20% variation of each model parameter. Variations greater than 5% are indicated in bold

AGRfr average growth rate of fine roots, AGRcr average growth rate of coarse roots, AGRow average growth rate of old wood, AGRsw average growth rate of stem wood, AGRls average growth rate of leafy shoots, AGRf average growth rate of fruits

Table 5

Model sensitivity to parameters for Suncrest

Parameter

Parameter variation (%)

AGRfr

AGRcr

AGRow

AGRsw

AGRls

AGRf

k

+20

−0.01

−0.78

−0.75

1.82

−0.07

0.52

−20

0.01

0.79

0.75

−2.20

0.06

−0.55

\( {\text{RGR}}_{\text{fr}}^{\text{ini}} \)

+20

0.08

−0.21

−0.21

0.42

1.47

−0.21

−20

−0.12

0.20

0.20

−0.50

−2.17

0.21

\( {\text{RGR}}_{\text{ow}}^{\text{ini}} \)

+20

−0.10

7.92

7.92

7.91

−1.31

5.30

−20

0.09

10.79

10.80

10.19

1.34

5.61

\( {\text{RGR}}_{\text{sw}}^{\text{ini}} \)

+20

−0.01

−1.49

−1.49

28.53

−0.05

−1.10

−20

0.02

1.57

1.57

26.45

0.05

1.14

\( {\text{RGR}}_{\text{ls}}^{\text{ini}} \)

+20

0.34

0.31

0.31

0.21

19.70

0.19

−20

−0.34

−0.31

−0.31

−0.21

19.80

−0.19

\( {\text{RGR}}_{\text{f}}^{\text{ini}} \)

+20

−0.04

−4.19

−4.19

16.55

−0.31

9.06

−20

0.04

4.35

4.35

26.70

0.31

11.00

SReq

+20

18.72

0.85

0.84

0.78

2.96

0.43

−20

22.92

−1.14

−1.13

−1.46

−3.62

−0.52

Variations are expressed as a percentage of the reference value on the basis of a ±20% variation of each model parameter. Variations greater than 5% are indicated in bold

AGRfr average growth rate of fine roots, AGRcr average growth rate of coarse roots, AGRow average growth rate of old wood, AGRsw average growth rate of stem wood, AGRls average growth rate of leafy shoots, AGRf average growth rate of fruits

The average growth rate of fine roots varied only with the shoot:root ratio at equilibrium (SReq) in both cultivars. This variable was reduced by 13.5% in Alexandra and by 18.7% in Suncrest when SReq was increased by 20%. The average growth rate of leafy shoots, fruits and old wood varied only with their corresponding initial relative growth rate, or also with \( {\text{RGR}}_{\text{ow}}^{\text{ini}} \) for the average growth rate of fruits in Suncrest. The average growth rate of stem wood varied with a large range of input parameters in addition to \( {\text{RGR}}_{\text{sw}}^{\text{ini}} \). It decreased when \( {\text{RGR}}_{\text{ow}}^{\text{ini}} \) or \( {\text{RGR}}_{\text{f}}^{\text{ini}} \) increased in both cultivars. Moreover, it increased when SReq or \( {\text{RGR}}_{\text{ls}}^{\text{ini}} \) increased in Alexandra but not in Suncrest.

Agronomic scenarios

In terms of the global analysis, the three factors of cultivar, thinning and the presence–absence of pest attack exerted a significant influence on fruit yield (Table 6). The only significant interaction in the analysis was between cultivar and thinning relative to yield. Fruit average mass was significantly affected by thinning and pest attacks. Fruits under thinning treatments were approximately 11% (15 cm spacing between fruits) and 21% (25 cm spacing between fruits) larger than those resulting from the unthinned treatment, and the average fruit mass was reduced by 8% in the case of pest attacks. Leafy shoot total mass was logically reduced by pest attacks, and considerably affected by cultivar as shown previously (Table 2). Alexandra’s leafy shoot total masses were almost sixfold those of Suncrest, because of a strong cultivar effect on leafy shoot average mass.
Table 6

Mean values for yield, fruit and shoot mass according to the agronomic scenarios with and without pest effects (main effects only)

Factor

Modality

Yield (g)

Fruit average mass (g)

Leafy shoot total mass (g)

Leafy shoot average mass (g)

Mean

Mean square

Mean

Mean square

Mean

Mean square

Mean

Mean square

Cultivar

Alexandra

1,723.22

74,891*

19.07

1.4

1,982.48

15,780,928***

4.02

115.1***

Suncrest

1,807.67

18.71

756.53

0.71

Thinning

Unthinned

2,531.47

15,175,849***

17.11

85.8***

1,356.78

4,387

2.34

0

Thinned 15 cm

1,703.12

18.92

1,369.81

2.37

Thinned 25 cm

1,061.74

20.63

1,381.92

2.39

Attack

Non-attacked

1,892.62

113,223*

20.22

12.4**

1,893.53

1,922,220*

3.24

5.4

Attacked

1,744.25

18.66

1,282.17

2.22

Cultivar × Thinning

 

144,239**

 

0.5

 

4,294

 

0

Cultivar × Attack

 

52,791

 

6.2

 

234,542

 

2.2

Thinning × Attack

 

13,978

 

0.1

 

83

 

0

Cultivar × Thinning × Attack

 

3,321

 

0.2

 

81

 

0

Mean square values correspond to a variance analysis (see main text for details)

Significant differences are also indicated. *** p < 0.001; ** p < 0.01; * p < 0.05

Thinning positively affected the four quality traits considered, whereas pest attacks negatively influenced all of them. The effects were significant, but the only significant interaction concerned the dry matter content of the flesh (Table 7).
Table 7

Mean values of fruit quality traits for Suncrest trees according to the agronomic scenarios with and without pest effects (main effects only)

Factor

Modality

Fruit average fresh mass (g)

Proportion of total mass consisting of fruit flesh (%)

Dry matter content of the flesh (%)

Sweetness Index

Mean

Mean square

Mean

Mean square

Mean

Mean square

Mean

Mean square

Thinning

Unthinned

108.39

122,862***

72.93

3,006.2***

13.29

101.3***

7.01

76.9***

Thinned 15 cm

119.39

74.68

13.59

7.28

Thinned 25 cm

128.04

75.99

13.86

7.50

Attack

Non-attacked

130.55

82,783***

76.70

25,411.6***

14.23

193.9***

7.85

156.9***

Attacked

112.58

73.55

13.36

7.06

Thinning × Attack

 

511

 

1.8

 

1.5*

 

0.6

Mean square values correspond to a variance analysis (see main text for details)

Significant differences are also indicated. *** p < 0.001; ** p < 0.01; * p < 0.05

For the analysis restricted to attacked trees (see Suppl. Tables 2 and 3 of Electronic Supplementary Material), cultivar exerted a significant influence on all mass variables except for fruit average dry mass. Suncrest produced higher yields than Alexandra, but the latter had higher average and total leafy shoot dry masses. As for the patterns of attack, the greatest reductions in fruit yield in both Alexandra and Suncrest were observed when trees suffered from non-treated attacks (pattern 2), whereas the smallest reductions were observed when trees experienced pest attacks late in the season (pattern 3). However, these differences were not significant. The percentage damage negatively influenced mass variables, the greater damage producing a more marked effect. When the percentage damage was 5% per day of pest attack, fruit average dry mass or yield was reduced by 4 and 20% in Alexandra and Suncrest, respectively, and the leafy shoot total dry mass was reduced by 35% (Alexandra) and 51% (Suncrest). Interactions between the factors considered were not significant, except that between cultivar and thinning on fruit yield and that between cultivar and percentage damage on fruit average dry mass. In the case of Suncrest, thinning significantly improved all quality traits while percentage damage significantly decreased them. Regarding the pattern of attack, non-treated attacks (pattern 2) caused the greatest reductions in all fruit quality traits: fruit average fresh mass was reduced by 23%, the sweetness index by 18%, the dry matter content of the flesh by 11% and the proportion of dry mass consisting of fruit flesh by 7%. Treated attacks (pattern 1) and attacks late in the season (pattern 3) caused similar but lower (twofold or more) reductions in fruit quality.

Discussion and conclusion

QualiTree satisfactorily reproduced observed within-tree variations in fruit and leafy shoot dry masses. One major factor affecting this variability was the light intercepted, which has been suggested to be very important (Gary et al. 1998) and worth simulating (Génard et al. 2008). QualiTree accounts for this by means of the light-interception sub-model that can calculate the amount of light intercepted by each FU and considers several factors that influence this light interception, such as canopy shape and shade from neighbouring trees. QualiTree was also capable of reproducing the differences in tree response to heterogeneous thinning treatments between an early-maturing (Alexandra) and a late-maturing (Suncrest) cultivar, as suggested by experiments under orchard conditions (Nicolás et al. 2006). In those experiments, fruit grew better on low-loaded scaffolds than on high-loaded scaffolds, but the differences were only significant for Suncrest. This had been interpreted in terms of a lower carbon transport rate in the whole tree in the late-maturing cultivar (Nicolás et al. 2006) as also suggested by other authors (Inglese et al. 2002; Walcroft et al. 2004). However, relative to the parameter expressing the effect of distance between tree objects on carbon exchange within the tree (k), the very low estimated values for Alexandra or Suncrest found during the present study suggested that within-tree distances were not limiting in any case. The leaf:fruit ratio was more contrasted between thinning treatments for Suncrest than for Alexandra during the experiment, and apparently this was sufficient to explain the responses of the observed and virtual trees.

The average seasonal growth rates of the different organs were sensitive to changes in the values of their respective initial relative growth rates in both cultivars, except in the case of fine roots. In QualiTree, stem wood was the organ most markedly affected by a change in the initial relative growth rates of other organs, and thus by their carbon requirements. An increase of the initial relative growth rate of fruits exerted a major negative influence on the average growth rate of stem wood in both cultivars. This result is in line with the model assumptions, since in the model fruit and stem are competing sinks (Lescourret et al. 2010). It is also in agreement with the data reported by Grossman and DeJong (1995), who studied early- and late-maturing peach cultivars and found that stem dry masses in fruited trees were lower than in defruited trees, implying a greater capacity of fruits as a sink. \( {\text{RGR}}_{\text{ow}}^{\text{ini}} \) also had a major negative influence on the average growth rate of stem wood, showing that biomass accumulated in old wood at the expense of stem wood. The average growth rate of stem wood also decreased when the initial relative growth rate of leafy shoots decreased.

One interesting result was the lack of an effect of the initial relative growth rate of fruits on fine roots, although several authors had noted a possible competition between fruits and roots (Miller and Walsh 1988; Berman and DeJong 2003; Abrisqueta et al. 2008). Only the parameter SReq (shoot:root ratio at equilibrium) exerted a strong influence on fine roots. This is in line with a principle of QualiTree that is to restore the imbalance between leafy shoots and fine roots defined in reference to SReq. Concerning parameter k (referring to carbon transfers within the plant), a 20% variation around the estimated value (which was low) exerted no major influence on the outputs considered.

The results of agronomic scenarios indicate that, as reported under field conditions by many authors (Berman and DeJong 2003; Marsal et al. 2003; Nicolás et al. 2006), fruit load exerted a strong influence on the final fruit average dry mass and yield simulated by our model. Other logical results were also obtained, such as the positive effects of thinning on fruit quality and the negative effects of pest attacks on fruit yield and quality, especially when attacks were severe or not treated. In addition, Suncrest was more sensitive to pest attacks than Alexandra in our simulations. This is probably because vegetative growth was very low in Suncrest when compared to Alexandra (Fig. 2), so that leafy shoots remaining after the attack were not capable of supplying sufficient assimilates to the fruits. The results of these simulations are of interest in terms of integrated fruit production because they may enable a clearer understanding of crop–pest systems and the effects of one or several practices on their functioning (Grechi et al. 2008; Mercier et al. 2008).

In conclusion, QualiTree offered satisfactory results in terms of describing fruit and leaf masses within peach trees. Although further tests are required relative to the whole range of the fruit quality criteria it considers, QualiTree proved to be a useful tool to simulate the effects of diverse agronomic scenarios on yield, fruit size and quality. Practices such as thinning and pruning can now be simulated, as can vegetative losses due to pest attacks. Further developments are planned in order to improve this model, such as linking it with a water uptake model to enable the simulation of irrigation practices, broadening the predictive capacities of the model and simulating combinations of practices under different conditions. Ultimately, this may allow us to apply the principles of crop management design to horticulture by means of simulations (Bergez et al. 2010).

Acknowledgments

We are grateful to the IRRIQUAL project (EU-FP6-FOOD-CT-2006-023120) for financial support. J.M. Mirás Avalos thanks the Universidade da Coruña for partially funding his research stay in Avignon. G. Egea is grateful to the FPU programme of the Spanish Ministry of Education and the Fundación Ramón Areces (Madrid, Spain) for financially supporting his research. E. Nicolás is also grateful to the SÉNECA (05665/PI/07) and CONSOLIDER INGENIO 2010 (MEC CSD2006-0067) projects for providing funds to finance his research stay in Avignon. We thank Vicky Hawken for correcting the English.

Supplementary material

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Supplementary material (DOC 204 kb)

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© Springer-Verlag 2011