Plant material
The breeding population was derived from clone P1908 of Prunus davidiana and two cultivars of nectarine as follows (Pascal et al., 1998
). Firstly, P1908 was crossed with Prunus persica ‘Summergrand’ (S) and an F1 progeny was obtained. Then, one F1 hybrid resistant to powdery mildew was back-crossed to S to produce a BC1 progeny. Finally, BC1 individuals were used to pollinate P. persica ‘Zéphir’ (Z) to derive the breeding population (BC2). S and Z are, respectively, yellow and white nectarine cultivars with large fruit.
The study was conducted in three orchards, in the St Paul and Garrigues experimental sites of the INRA Research Centre of Avignon (France) and in the orchard of Gotheron near Valence (120 km north from Avignon). BC2 genotypes and the three parents were planted in the orchards of St Paul and Gotheron in a completely randomized design with one tree per genotype. One tree of these genotypes were also available in the collection orchard at the Garrigues site. In the three sites all genotypes were grafted on GF305 seedling rootstocks and grown under optimal conditions of irrigation, fertilization, and pest control. Trees were 3-years-old in 2001. Data were also used from an experiment carried out in 2000 in Avignon (Quilot et al., 2002) on trees of P1908 and S, grown in 50 l pots.
Experiments
Experiments were carried out to measure the parameter values for each of the BC2 genotypes and the three parents. Moreover, specific experiments were performed in order to evaluate the predictive quality of the newly parameterized model. Table 2 presents a summary of the characteristics of each experiment.
Parameterization and analysis of goodness-of-fit
Experiments were performed in St Paul in 2002 on 139 genotypes of the BC2 population, S, Z, and P1908 (StPBC202). It was necessary to ensure that all fruits were under non-limiting source conditions (i.e. under maximum growth conditions). For this purpose fruits were harvested at an early stage, leaving only a very light fruit load. These experiments were used to estimate some parameters from non-destructive measurements. Experiments carried out at the Garrigues site in 2001 and 2002 (GarBC2) only consisted of the destructive sampling of fruits and leafy-shoots throughout growth and at maturity in order to estimate other parameters. The StPBC202 dataset was then used to check the goodness-of-fit of the model.
Test of the predictive quality of the model
Three other experiments were carried out in order to test the predictive quality of the different parts of the model parameterized with the StPBC202 and GarBC2 datasets.
Experiments were performed in 2001 in St Paul on 87 out of the 139 BC2 genotypes of the StPBC202 dataset, as well as on S and Z (StPBC201). Again a light fruit load was applied to each tree. Dry mass of fruit and stone was measured and values of the other outputs of the model, i.e. fresh mass of fruit and stone, flesh dry matter content, and sugar variables, were predicted.
Experiments on P1908 and S in St Paul in 2000 (StP00) were performed using two leaf-to-fruit ratio treatments referred to as ‘heavy’ and ‘medium’ (5 and 30 leaves per fruit, respectively). There were applied to chosen shoot-bearing-fruits (i.e. 1-year-old woody stems (‘shoots’), bearing fruits and leafy shoots) isolated from tree by girdling. The leafy shoot vegetative growth was stopped during fruit growth by removing the new terminal and lateral apices. The sugar accumulation part of the model was not tested here since no sugar concentration data were available.
In the experiments performed on six BC2 genotypes in Gotheron in 2002 (GotBC202), a heavy fruit load (one growing leafy shoot per fruit) was left on the shoot-bearing-fruits again isolated from the tree by girdling.
Field measurements
Non-destructive measurements:
Fruit cheek diameter was measured once a week from the end of May (about 85 d or 590 degree-days after full bloom) to fruit maturity (from mid June to September depending on the genotype). For StPBC201 and StPBC202 experiments, three to five fruits per tree and per genotype were recorded. For GotBC202 experiments, three fruits per shoot and two to five shoots were monitored per genotype. Associated changes in the length of the leafy shoots were also monitored weekly during the same period, to evaluate shoot growth demand. For StP00 experiments, 23 shoots per genotype bearing from one to eight fruits were monitored.
The photosynthetic response to radiation intensity and leaf conductance were studied in trees of StPBC201 and StPBC202 experiments. Measurements were taken with the ADC–LCA 4 portable photosynthesis system. They were made on several dates for each genotype on well-expanded sunlit leaves, between 07.00 h and 10.00 h standard time, in order to avoid stomatal closure because of high temperatures and water stress. Light saturation occurs around 1000 µmol m–2 s–1 under spring conditions in the South of France, so measurements made below 1000 µmol m–2 s–1 were not considered further. From these data, p1, corresponding to maximum light-saturated photosynthesis, was estimated.
Destructive measurements:
Monitored fruits were considered ripe when they stopped growing, softened, and were easily picked. The flesh fresh mass (Wfresh) was determined immediately after harvest. Fruit flesh was cut into small pieces. The flesh dry mass (Wdry) was determined after drying for 72 h at 70 °C to constant weight. For three monitored fruits from StPBC201 and StPBC202, some flesh was immediately frozen (–80 °C) until sugar analysis. For fruits from GotBC202, flesh pieces from the same shoot were bulk frozen as an average sample. For fruits from StP00, no sugar analysis was performed.
To compute dry (Wdry) and fresh (Wfresh) fruit, flesh and stone masses for each monitored fruit, several allometric relationships between fruit diameter and dry and fresh fruit masses, stone dry mass and fruit dry mass, stone fresh mass and stone dry mass, were determined for each genotype. To establish these relationships, fruit diameter and dry and fresh masses of fruit and stone were recorded. These measurements were carried out in 2001 and 2002 (i), at maturity, on five fruits per tree, (ii) at thinning, on the fruits removed, and (iii) throughout fruit growth on fruits sampled from trees at the Garrigues site.
The permeation coefficient of water vapour through the fruit surface, 
, was estimated by monitoring fruit mass loss, which is assumed to be proportional to the fruit surface area and to be driven by the difference in relative humidity between the air-filled space within the fruit (100% RH) and the ambient atmosphere. Freshly harvested fruits were placed in a controlled environment room (temperature, RH, and air speed) and periodically weighed. The fruit surface of each fruit was approximated as an ellipsoidal surface computed from the three diameters of the fruit. Measurements were performed (i) throughout growth on fruits at the Garrigues site and (ii) at maturity on monitored fruits not frozen for sugar analysis, from StPBC201 and StPBC202 experiments.
Shoots were characterized by two parameters: leaf area relative to the structural part of the leaf (SLA, m2 g–1), estimated from the measurements of surface and mass of 20 leaves for each genotype, and the leaf mass to leafy shoot mass ratio (r1), estimated from the measurement of 3–10 leafy shoots for each genotype. All measurements were made in the morning in May, so that reserves in the leaves were limited.
Environmental inputs and initial status
Hourly total radiation and daily temperature values were recorded at Avignon in 2001 and 2002 and at Gotheron in 2002. Degree-days were calculated from daily minimum and maximum temperatures with upper and lower temperature thresholds at 35 °C and 7 °C, respectively. Degree-days were summed from full-bloom to maturity for each genotype.
To take into account assimilation reduction due to shade, the model requires two series of hourly coefficients (Lescourret et al., 1998). The first one characterizes the mutual shading of leaves occurring within a shoot and the second one the mean light environment of a shoot. Both coefficients were calculated for GotBC202 and StP00 experiments only, using gap fractions derived from digitized hemispherical photographs (Génard and Baret, 1994).
Initial dry masses of the monitored 1-year-old stems, at the beginning of the simulations, were estimated from their volumes, calculated from the length and diameter of each stem considered to be cone-shaped and converted into dry mass on the basis of a mean peach wood specific dry weight (0.575 g cm–3). A sensitivity study conducted by Lescourret et al. (1998) showed that errors in assessing the initial reserves of leafy shoots and 1-year-old stems were not critical to the model response, so these initial reserves were set to the value taken by Lescourret et al. (1998), i.e. 10% of the initial dry masses of leafy shoots and 1-year-old stems. Initial total sugar concentration was approximated from early measurements performed by Quilot et al. (2004b).
Biochemical analysis
Frozen fruit flesh samples were immersed in liquid nitrogen and ground for 2 min to powder (Dangoumeau 300 ball-crusher, Prolabo). Five grams of the powder were mixed with 20 ml of ultra pure water. The mixture was centrifuged at 15 000 g for 15 min at 4 °C. The supernatant was immediately filtered through a Waters C18 cartridge (Waters) to eliminate any interfering apolar residues and through a 0.45 µm Sep-Pak filter (Jasco France) to eliminate large particles. The extract was stored at –80 °C (sealed tube), prior to sugar measurement by HPLC (see Gomez et al., 2002, for details).
Statistical analysis
Sensitivity analysis:
To select the parameters in the integrated model to be measured, the sensitivity of the model to parameter variation was tested. The model outputs (fresh fruit and stone masses, flesh dry matter content, and total sugar concentration) at maturity were compared for high and low values of each parameter and for two contrasting fruit loads corresponding to source and sink limiting conditions. The high and low parameter values were set to plus or minus 50% of the reference parameter values estimated for the ‘Summergrand’ cultivar. A default value taken from the literature (Lescourret et al., 1998) was used when no value was available for ‘Summergrand’. For each parameter and fruit load level, the sensitivity criterion was the difference between the output value for high (OH) and low (OL) values of the parameter, expressed as a percentage of the output value at maturity for the default parameter value (Oo): 100x(OH–OL)/(Oo). Parameters were selected for further study when the absolute value of the sensitivity criterion exceeded 5% for at least one of the four outputs and one of the two fruit loads considered.
Parameter estimation and comparison of parameter values between genotypes:
Parameter values were estimated for each genotype studied. It was then tested whether there was significant variation between genotypes.
Some parameters could be directly computed for each genotype as the mean of the observed values. For these parameters, between- and within-genotype variances were compared using a test of ‘comparison of means of various independent samples’. The result was compared to the critical value derived from the distribution of Fisher–Snedecor. Other parameters could be estimated by fitting a non-linear simple function to the observed data. Lastly, one parameter could only be estimated by calibrating the model for each of the genotypes, by comparing fresh fruit growth predictions and observations. In these two cases, the ‘nls’ procedure of Splus (Splus software, MathSoft Inc., Cambridge, MA) was used. This procedure is described by Chambers and Hastie (1992). To test whether the values of these parameters were significantly different between genotypes, different models were compared. A simple model corresponds to a unique adjustment curve whatever the genotype, i.e. the parameter values are equal for all genotypes (Quilot et al., 2002). In a complex model, adjustment curves are different between genotypes so that the values of all the parameters are specific to each genotype. Lastly, in intermediate models some parameters are constants and others are specific to each genotype. The null hypothesis of no difference in the parameter values between the genotypes was tested by performing a 
2 test. In all cases, a threshold level of probability (
) of 0.05 was used.
Determination of the relative importance of the genotypic key parameters:
The relative importance of the genotypic key parameters with regard to the between-genotype variation was compared according to three criteria: the sensitivity of the model to the parameter, the variation in the parameter value observed in the population, and the mean error of estimation of the parameter. It is worth taking into account parameter variation from one genotype to another only for those which show high sensitivity. Moreover, the larger the variation in a parameter value within a population, the more likely the parameter is to explain large output variation observed between genotypes.
Comparison between observed and predicted data:
Two criteria were used to evaluate the model for each quality trait and for each genotype. First, the goodness-of-fit of the model was evaluated on the basis of data used for the parameterization, i.e. the StPBC202 dataset. Second, the predictive quality of the model was evaluated with independent data sets (StPBC201, GotBC201, and StP00 datasets). The adopted criterion was the root mean squared error (RMSE), a common criterion to quantify the mean difference between simulation and measurement in the case of non-linear models (Kobayashia and Us Salam, 2000). The global goodness-of-fit of the model was computed by averaging the relative RMSE (RRMSE) values of all genotypes (see Quilot et al., 2004a, for details). Usually, RRMSE values greater than 0.5 are considered not to be relevant and values lower than 0.25 as suitable.
Spearman's rank correlation coefficients were also calculated with the ‘cor.test’ procedure of Splus. These coefficients compare the ranking of genotypes on the basis of observed and predicted values at maturity. Indeed, for use in breeding programmes, the ability of the model to rank the genotypes correctly is particularly important.
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