Simulating genotypic variation of fruit quality in an advanced peachxPrunus davidiana cross

Abstract

RESEARCH PAPER

Simulating genotypic variation of fruit quality in an advanced peachxPrunus davidiana cross

B. Quilot^1,*, M. Génard², F. Lescourret² and J. Kervella¹

¹Unité de Génétique et Amélioration des Fruits et Légumes, INRA, Domaine St Maurice, BP94, F-84143 Montfavet Cedex, France
²Unité de Recherche Plantes et Systèmes de Culture Horticoles, INRA, Domaine St Paul, Site Agroparc, F-84914 Avignon Cedex 9, France

^* To whom correspondence should be addressed. Fax: +33 4 32 72 27 02. E-mail: [email protected]

Received 7 December 2004; Accepted 2 September 2005

Ecophysiological models are increasingly expected to describe genotypic variation within breeding populations. Accordingly, the ability of an ecophysiological model of peach to explain variation in fruit quality among 100 genotypes of a second backcross progeny derived from a clone of wild peach (Prunus davidiana) crossed with two commercial nectarine (Prunus persica) varieties was explored. Experimental measurements were carried out to calibrate the model for each genotype. The predictive quality of the model was tested on several independent datasets. The genotypic variation in dry and fresh growth of the fruit and the stone were effectively described by the model. Prediction of the amount of total sugar in flesh at maturity was accurate, whereas prediction of flesh dry matter content and total sugar concentration was suitable but less accurate. This approach and the results have allowed physiological processes to be ranked according to their contribution to the variation in fruit quality between genotypes. Fruit growth demand and the hydraulic conductance in the fruit were the main processes that explained the fruit quality variation. Shortcomings and further potential uses of the model are discussed.

Key words: Fruit, genotypic variation, growth, modelling, Prunus persica, sugars

Journal of Experimental Botany 2005 56(422):3071-3081.

Introduction

 

Ecophysiological models have generally been developed and calibrated on a few varieties of a given species. Increasingly, it is required that they also describe the genetic variation between varieties or within a breeding population. The ecophysiological models, which are able to represent genotypic variation accurately, require genetic coefficients that are specific to each genotype and constant under a wide range of environmental conditions (Boote et al., 2001; Tardieu, 2003). It is not clear whether current ecophysiological models are efficient for such applications. Adequate models should be mechanistic enough to give a representative description of physiological processes. However, very complex models are not suitable when a large number of genotypes needs characterization, because they require too many inputs, expensive or time-consuming measurements, and large amounts of plant material. Studies are thus still needed to test the potential uses of current ecophysiological models for plant breeding, to identify their limitations, and to specify the necessary modifications for such applications.

The present study aims to test the efficiency of an ecophysiological model developed to simulate genotypic variation in fruit quality traits. Quality traits were chosen because they are under the control of many processes and environmental factors. Peach was selected for study because ecophysiological models (Lescourret et al., 1998; Fishman and Génard, 1998; Quilot, 2003) that reproduce important quality traits (fruit and stone sizes, flesh dry matter content, and total sugar amount in the flesh) are available for this species.

This study used a population of genotypes derived from a clone of wild peach (Prunus davidiana) with three generations of crosses with commercial varieties of nectarine (Prunus persica). The ecophysiological model used was a combination of three sub-models dealing with carbon balance, water balance, and sugar accumulation. Adaptations of the model were necessary to take into account the specific behaviours of the genotypes studied. Initially, the results are presented of a sensitivity analysis to reveal the parameters to which the model is most sensitive. These parameters are expected to explain most of the variations within outputs. Secondly, the values of most of the model parameters were estimated for each genotype. Their variations between genotypes were analysed to identify genotypic key parameters. A third step examined the genotypic ability of the model to describe fruit and stone growth and flesh sugar concentration. The predictive quality of the model was also evaluated. Finally, the relative contribution of the genotypic key parameters to variations in fruit quality was analysed.

The model

 

The model integrates three sub-models developed independently, all concerning the stage of fruit enlargement at the end of cell division. The modelled system is the ‘shoot bearing fruit’ which is represented by three interconnected compartments: fruits including flesh and stone, 1-year-old stems, and leafy shoots. The focus here is on the processes that particularly relate to the fruit quality issue, giving emphasis to equations that were added or modified to describe the behaviour of wild genotypes. The main variables predicted by the integrated model are dry and fresh masses of fruit and stone, flesh dry matter content, and total sugar amount and concentration in the flesh. The parameters are presented in Table 1. (Details about the processes described by the sub-models and the equations are given as supplementary data in the Appendix which is available at JXB online.)

The carbon assimilation and allocation sub-model (Lescourret et al., 1998; Génard et al., 1998; Quilot et al., 2002) simulates carbon partitioning based on organ demand and priority rules. Flesh growth potential demand was described in terms of degree-days by a logistic equation (see Equation 9 of the Appendix in the supplementary data at JXB online) which enabled both logistic and exponential growth to be described by modifying the value of the parameter which contributes to the slowing down of growth with the maturation process. Since the population studied showed high variation in stone versus flesh partitioning, an equation relating stone growth to fruit growth (see Equation 10 of the Appendix in the supplementary data at JXB online) was added to describe the potential stone growth. Sugar accumulation is simulated by a simple sub-model that predicts the increase of total sugar concentration in the flesh during fruit growth (Quilot et al., 2004b). A function depending on the thermal time describes the partitioning of total sugar between sucrose and other sugars for each genotype (see Equation 17 of the Appendix in the supplementary data at JXB online). The sub-model of water flux simulates fruit growth in fresh mass (Fishman and Génard, 1998). The rate of change of the amount of water in the flesh is computed daily from the water flux through xylem and phloem and the water loss due to fruit transpiration.

Materials and Methods

 

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 (W_fresh) was determined immediately after harvest. Fruit flesh was cut into small pieces. The flesh dry mass (W_dry) 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 (W_dry) and fresh (W_fresh) 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 (O_H) and low (O_L) values of the parameter, expressed as a percentage of the output value at maturity for the default parameter value (O_o): 100x(O_H–O_L)/(O_o). 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.

Results

 

Sensitivity analysis
The relative variation in the model outputs caused by the variation in the values of each parameter were analysed (see Table SP1 in the supplementary data at JXB online). Thirteen of the 39 parameters for fruit load and an additional 12 parameters in the case of heavy fruit load were considered as important for further study. The 13 parameters were related to fruit growth demand, stone build-up, flesh mass increase, and total sugar accumulation. Among them, two were not estimated: Y, the threshold value of hydrostatic pressure needed for growth and _oc, the fruit osmotic pressure due to compounds other than soluble sugars. The 12 additional parameters (associated with heavy fruit load) were related to light interception, C assimilation, and fruit growth demand. Nine of them, p and k involved in the regulation of leaf photosynthesis by reserves, the ratio of leaf reserve mass to leafy shoot reserve mass, the growth respiration coefficient of fruit, and the parameters associated with leaf assimilation, radiation intensity in shade, and reserve mobilization (r₂, GRC_fruit, p₄, p₇, r₃, r₄, r₆,) could not easily be measured for a large number of genotypes. Thus, 14 parameters of the 25 parameters selected based on the sensitivity analysis were measured for many or all genotypes studied. The values for the 11 remaining parameters that were not measured were fixed to values taken from the literature or from related experiments (Quilot et al., 2004a).

Variation in parameter values between genotypes and parameterization
A total of 23 parameters of the model were not measured and their values were taken from the literature or from related experiments (Quilot et al., 2004a). The origin of the parameter values used in the simulations is given in Table 1. As regards the 14 parameters selected based on the sensitivity analysis, the variation in their values between genotypes was analysed (Table 3).

For two of them, r₁ and p₁, the variation between genotypes was not significant. Accordingly, for the leaf structural mass to leafy shoot structural mass ratio (r₁), the general average (0.672) was used. The light-saturated leaf photosynthesis (p₁) was set to the single value (19.47 µmol m^–2 s^–1) estimated for all genotypes. For the four parameters involved in allometric relationships (see Equations 10 and 14 of the Appendix in the supplementary data at JXB online), statistical models were compared. and s₁ were found to be genotype-dependent and k_stone and s₂ were constants. The specific leaf area (SLA) was measured for 49 genotypes and significant differences were found among these genotypes. Since SLA appeared to have no effect on the model outputs in the case of light fruit load (see Table SP1 of the Appendix in the supplementary data at JXB online), the averaged value (0.0169 m² g^–1) was used. For heavy fruit load simulations, the specific genotypic values were used (StP00 and GotBC₂02).

For the other six parameters, k_sugar, r_su, , and aL, large differences were observed between genotypes and the range of the observed values was higher than the range considered in the sensitivity analysis. For the coefficient of the transfer function between sugars and other compounds, k_sugar, the values estimated by Quilot et al. (2004b) were used on the same StPBC₂02 dataset. The estimation of the values of , the permeation coefficient of fruit surface to water vapour, was very time-consuming and required many fruits. This parameter was estimated for 41 genotypes. A mean value was used for the others, although the 41 genotypes displayed high variation in values.

The model parameterized as described above was then used to estimate values of aL, the hydraulic conductance per unit of fruit surface, by calibration. Great variations in the values of aL, higher than those tested through the sensitivity analysis, were observed in the population. Since , as well as aL, are involved in the computation of water accumulation in the fruit, the aL estimation probably contains the genotypic variation that was not included in the values. Therefore, for the 41 genotypes with individual estimates of , the effect on aL values of setting a constant value of , instead of the specific value, was computed. This accounted for 10% of variation in aL. This is not negligible, but it is small in comparison with genotypic variation in aL.

Finally, four out of the 14 parameters measured or estimated were considered constant, whereas the other ten (s₁, k_sugar, r_su, , and aL for both fruit loads, and SLA for heavy fruit loads only) were considered as genotypic key parameters.

Goodness-of-fit of the model on the basis of data used for parameterization
The observed genotypic variation in dry and fresh fruit masses was well reproduced by the model (Fig. 1). The equation of fruit demand for growth appeared very robust as it reproduced the large range of growth patterns displayed by the population. The goodness-of-fit criteria (RRMSE) ranged from 0.030 to 0.376 for fruit dry matter growth and from 0.041 to 0.311 for fruit fresh growth depending on genotype (see Table SP2 of the Appendix in the supplementary data at JXB online). The observed data at maturity were also reproduced well for all the output variables (Fig. 2, line 1). For dry and fresh masses of fruit and stone, and flesh dry matter content, individual RRMSE ranged from 0 to 0.4 and mean RRMSE over the population from 0.06 to 0.1 (Table 4). The mean RRMSE of the two variables relating to total sugar were nearly equal to 0.1 and were satisfactory. However, individual RRMSE were highly variable between genotypes since they ranged from 0.002 to 0.6. Hence, for some genotypes total sugar amount and concentration were not well reproduced by the model.

The model performed very well in ranking genotypes for dry and fresh fruit masses, fresh stone mass, and total sugar amount in the flesh, with the Spearman correlation coefficient ranging from 0.91 to 0.98 (Fig. 2). For flesh dry matter content and total flesh sugar concentration, the Spearman correlation coefficient reached 0.8 and 0.73, respectively, still a good performance.

Predictive quality of the model for independent data
The model was used to predict fruit observations from independent data under various fruit load conditions. Observations from 87 BC₂ genotypes grown under light fruit load (StPBC₂01 dataset), from seven BC₂ genotypes grown under heavy fruit load (GotBC₂02 dataset) and from S and P1908 for two contrasted fruit loads (StP00 dataset) were used to test the ability of the model to predict fruit quality.

The model correctly predicted growth kinetics of dry and fresh (see Figures SP1 and SP2 of the Appendix in the supplementary data at JXB online) fruit masses for different environmental and growing conditions (year, site, light and heavy fruit loads). Mean RRMSE for growth of dry and fresh fruit varied between 0.17 and 0.3 depending on the experiment (see Table SP2 of the Appendix in the supplementary data at JXB online). The ability of the model to rank the genotypes at maturity appeared accurate for both dry and fresh fruit masses, with the Spearman correlation coefficients from 0.62 to 0.94 (Fig. 2, lines 2, 3, and 4). However, it was less accurate when leafy shoot growth was to be considered (Fig. 2, line 3). In addition to its ability to reproduce variation between genotypes, the model was able to reproduce variations between fruits of the same tree (see Fig. SP1 of the Appendix in the supplementary data at JXB online).

The model predictions appeared especially good for dry and fresh stone masses. Mean RRMSE at maturity ranged from 0.063 to 0.147 for these two variables, and individual RRMSE values never exceeded 0.19 (Table 4). Similarly, the Spearman correlation coefficient varied between 0.75 and 0.98 depending on the experiment (Fig. 2, lines 2, 3, and 4).

Predictions of flesh dry matter content were good as indicated by the RRMSE criteria, but according to the Spearman correlation coefficient were moderately accurate. Mean RRMSE did not exceed 0.17 (Table 4), whereas the Spearman correlation coefficient varied between 0.49 and 0.83 (Fig. 2, lines 2, 3, and 4).

Considering total sugar variables, predictions were globally less accurate, but the accuracy depended on the experiment and the genotype. These variables appeared to be predicted better in the case of light fruit load. Mean RRMSE varied between 0.23 and 0.51 (Table 4) and the Spearman correlation coefficient ranged from 0.22 to 0.78 (Fig. 2, lines 2 and 3).

Determination of the relative importance of the ten genotypic key parameters
The relative importance of the 10 genotypic key parameters was compared with respect to the 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 (Table 5).

Thus, rules were established taking into account these aspects in order to define the score of each parameter and to rank them. A qualitative score was defined for each criterion attributing different numbers of stars to different levels of the criteria (Table 5). A global score was then defined as the total number of stars. The parameters SLA and had only four stars, and were considered the least important among the ten. aL and were considered the most important genotypic parameters of the model.

Discussion

 

Simulation of genotypic variation in fruit quality
An ecophysiological model was used to reproduce variation between genotypes, between fruit loads, and among fruits of the same tree for different years (2001 and 2002), sites (St Paul and Gotheron), and growing conditions (orchards or pots). This study confirmed that the ecophysiological model used was efficient in simulating genotypic variation under various growing conditions. However, it was less accurate when fruit load was heavy.

Importance of the 11 parameters not measured
Eleven of the parameters that largely influenced the outputs were not measured for a large number of genotypes. Two parameters, involved in the regulation of leaf photosynthesis through leaf reserves (p, k), were investigated separately in a study of six highly contrasted genotypes (Quilot et al., 2004a). Their values appeared to be equal for all genotypes. Two others, p₄ and GRC_fruit, involved in leaf assimilation and fruit growth respiration, were unlikely to influence the model outputs. Indeed, Quilot et al. (2002) suggested, on the basis of data from the literature, that variation in these parameters within closely related species were small. As far as is known, no data are available on variation in r₂, p₇, r₃, r₄, and r₆ within a species or between two related species. However, it is assumed that these five parameters barely affect model outputs, since they influence sources that only influence growth in dry mass and for which predictions were accurate even under heavy fruit load conditions. Variation in Y and _oc was more likely to create output variation. Indeed, the wall yielding threshold pressure (Y), was shown to range from 0.3 MPa to 0.8 MPa for various fruit cells belonging to distant species (Green and Cummins, 1974). The sensitivity analysis tested this range and showed high variation in all outputs at both fruit loads. Although variation between closely related species and their hybrids may be lower than interspecific variations, further information is needed on the variation of this parameter. Similarly, variation in the osmotic pressure induced by compounds other than sugars (_oc), may induce high variation in the output values. As far as is known, no data are available on the variation in _oc. Nevertheless, _oc is likely to display large variation between genotypes because of qualitative and quantitative variation in soluble cellular compounds (organic acids, amino acids, potassium ...). Peach genotypes are known to vary widely in organic acid concentrations (Wu et al., 2003). However, it seems that organic acids account for less than half of the osmotic pressure induced by osmotically active compounds other than sugars. Little is known on the influence of amino acids and minerals on the osmotic pressure in peach fruit (Moing et al., 1998, 2003; Lobit et al., 2002). Finally, variation in Y and _oc between genotypes are probably not negligible. Ignoring this variation may have resulted in a poor estimation of aL.

The major physiological processes responsible for variation in fruit quality
The use of an ecophysiological model and the identification of genotypic key parameters highlighted the major physiological processes responsible for genotypic variation in different fruit quality criteria. The description of fruit quality under non-limiting fruit growth conditions revealed large variation between genotypes, suggesting that fruit growth demand was one of the main processes responsible for fruit mass variation in particular. Moreover, this process also influenced total sugar concentrations. Accordingly, and especially were identified as the major parameters according to different criteria. aL, associated with water flux in the fruit, also appeared to be a major parameter. It is not only involved in fruit fresh matter growth, but also in the dilution of dry matter and sugars. Therefore, it influences fruit fresh mass, dry matter content, and total sugar concentration. Another major parameter, k_sugar, was identified which is linked to sugar metabolism and appears to be of particular importance in describing the variation in dry matter content and total sugar concentration. The partitioning between sucrose and hexose sugars studied through r_su as well as the fruit transpiration (influenced by ) were shown to contribute to genotypic variation in fruit quality as well, although to a lower extent than the four previous processes. Lastly, the stone mass, described through was highly variable between genotypes and not negligible: an increase in resulted in a decrease in fruit fresh mass.

Potential uses of this approach
Different prospects can be envisaged for this approach. Indeed, the identification of both genotypic key parameters and main physiological processes involved in quality variation should be useful from a genetic point of view. These results point out the parameters that deserve further study. They could guide research towards these key processes and orientate breeding programmes, in the way suggested by Jackson et al. (1996). Further analysis of the genotypic parameters should be performed in order to determine their genetic control. Such a study has been performed by Quilot et al. (2005) on the genotypic key parameters identified in this paper. Model simulations may also be helpful in understanding fruit biology. The model may be used to study the links between the different processes, particularly when processes have opposite effects on a quality trait. The model can also be used to describe the genotypic variation in fruit quality under different climatic or fruit load conditions.

Supplementary data 

Supplementary material associated with this paper is available at Journal of Experimental Botany online. The Appendix shows a global presentation of the processes described by each of the three sub-models and presents the main equations of the model. Table SP1 presents the results of the sensitivity analysis of the model. Table SP2 and Figures SP1 and SP2 provide complementary illustrations of the adjustment quality of the model and its predictive quality.

Acknowledgements

We gratefully acknowledge J Hostalery for her assistance in the field experiments, J Besset for the experiments performed at the Gotheron site, and T Pascal for his advice on tree management. We thank E Rubio and L Gomez for sugar analyses. We are grateful to C Borel for critically revising the manuscript. We thank A Lacombe and Dr O Savolainen for improving the English. This research was funded in part by grants from the Ministère de la Recherche (PhD grant), from Région Provence-Alpes-Côte d'Azur (projects DEB 02-252 and DEB 03-543) and from the Institut National de la Recherche Agronomique, France (A.I.P. PFI P00232 [GenBank] and A.I.P. REA P00251 [GenBank] ).

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Figures

 

Fig. 1. Dry (A) and fresh (B) masses of fruits throughout fruit growth (days after bloom) for 9 BC₂ contrasted genotypes. Filled circles denote the observed values of various fruits of one genotype (StPBC₂02 dataset). The line shows the mean value predicted by the model for each genotype.

 

 

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Fig. 2. Predicted values at maturity plotted against corresponding observed values for dry and fresh fruit masses, stone fresh mass, flesh dry matter content, total sugar amount as carbon in flesh, and total sugar concentration. First line of graphs (1) correspond to data from StPBC₂02, the second (2) to the StPBC₂01 dataset, the third (3) to the GothBC₂02, and last (4) to StP00. Accordingly, the first line of graphs was used to check the goodness-of-fit of the model and the other three lines to test its predictive quality. Each point of the graphs from lines 1 to 3 represent an averaged value for one genotype. On the graphs of line 4, open diamonds stand for S replications and filled diamonds for P1908 replications, both fruit loads mixed. The Spearman correlation coefficient is indicated on the upper left-hand corner of the corresponding plot.

 

 

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Tables

 

Table 1. Symbols, definitions and units of the model parameters

Parameter Definition Unit Origin Leaf assimilation           r1 Leaf structural mass/leafy shoot structural mass Dimensionless Experiments     SLA Specific Leaf Area m2 g–1 Experiments     p1 Light-saturated maximal leaf photosynthesis µmol CO2 m–2 s–1 Experiments     p Concern leaf photosynthesis regulation by reserves Dimensionless Quilot et al. (2004a)     k   Dimensionless Quilot et al. (2004a)     r2 Leaf reserve mass/leafy shoot reserve mass Dimensionless Ben Mimoun (1997)     p3 Concern the calculation of leaf photosynthesis from radiation and light-saturated photosynthesis µmol CO2 m–2 s–1 Higgins et al. (1992)     p4   µmol CO2 µmol photon–1 Higgins et al. (1992) Radiation in the shade           p7 Concern the calculation of radiation received by shaded leaves µmol photon m–2 s–1 Lescourret et al. (1998)     p8   m2 s µmol photon–1 Lescourret et al. (1998)     r3   Dimensionless Lescourret et al. (1998) Reserve mobilization           r4 Leafy shoot mobile fraction of reserves Dimensionless Ben Mimoun (1997)     r5 1-year-old stem mobile fraction of reserves Dimensionless Ben Mimoun (1997)     r6 Threshold ratio of reserves in the leaves Dimensionless Ben Mimoun (1997) Maintenance respiration demand           MRROst Maintenance respiration rate of current-year stem (Ost), 1-year-old-stem (st), leaf and fruit compartments at the reference temperature s–1 Grossman and DeJong (1994a)     MRRst   s–1 Grossman and DeJong (1994a)     MRRleaf   s–1 Grossman and DeJong (1994a)     MRRfruit   s–1 DeJong and Goudriaan (1989)        Dimensionless Grossman and DeJong (1994b)      Q10 value for current-year stem (Ost), 1-year-old-stem (st), leaf and fruit compartments Dimensionless Grossman and DeJong (1994b)        Dimensionless Grossman and DeJong (1994b)        Dimensionless DeJong et al. (1987) Fruit growth demand           GRCflesh Growth respiration coefficient of fruit Dimensionless DeJong and Goudriaan (1989)      Initial relative flesh growth rate Degree-days–1 Experiments      Concerns the limitation of flesh growth g Experiments Stone elaboration            Potential stone dry mass at maturity g Experiments     kstone Empirical coefficient relating stone dry mass to fruit dry mass Empirical coefficients relating stone fresh mass to stone dry mass Dimensionless Experiments        Dimensionless Experiments        Degree-days–1 Experiments        Degree-days Experiments Fruit fresh mass elaboration           aL Hydraulic conductance per unit of fruit surface g cm–2 bar–1 h–1 Experiments     Y Threshold value of hydrostatic pressure needed for growth MPa Fishman and Génard (1998)      Cell wall extensibility coefficient in Lockhart's equation MPa–1 h–1 Fishman and Génard (1998)     oc Osmotic pressure in fruit due to other compounds than soluble sugars MPa Fishman and Génard (1998)     rsu Concerns the calculation throughout growth of the part of sucrose in the total amount of sugars in the flesh Dimensionless Experiments     s1 Empirical parameters relating fruit surface to fruit mass cm2 Experiments     s2   g Experiments      Permeation coefficient of fruit surface to water vapour cm h–1 Experiments Total sugar accumulation           ksugar Coefficient of the transfer function between sugars and other compounds d–1 Experiments

The origin of the values used in these simulations is mentioned.

 

Table 2. Characteristics of the five experiments and summary of the corresponding measurements

Parameterization and analysis of goodness-of-fit Parameterization Tests of predictive quality Dataset StPBC202 GarBC2 StPBC201 StP00 GothBC202 Year 2002 2001 and 2002 2001 2000 2002 Site St Paul Garrigues St Paul St Paul Gotheron Genotype P1908, S, Z, 139 BC2   P1908, S, Z, 87 BC2 P1908, S       50 BC2     6 BC2 Fruit load Very low Medium Low Medium and high High Shoot treatments       • Girdling • Girdling         • Leafy shoot growth stopped   Stem and shading characterization Stem length and diameter   Stem length and diameter • Stem length and diameter • Stem length and diameter         • Hemispherical photographs • Hemispherical photographs Weekly monitoring Fruit diameter   Fruit diameter Fruit diameter • Fruit diameter           • Leafy shoot length Destructive measurements during fruit growth   • Leaf and shoot mass           • Leaf area           • Fruit transpiration           • Fruit diameter and area           • Fruit and stone mass       Measurements on harvested fruits at maturity • Diameter • Diameter • Diameter • Diameter • Diameter   • Flesh and stone fresh and dry masses • Flesh and stone fresh and dry masses • Flesh and stone fresh and dry masses • Flesh and stone fresh and dry masses • Flesh and stone fresh and dry masses   • Fruit transpiration • Fruit transpiration       Biochemical analysis Sugar concentration of individual fruits Sugar concentration of individual fruits Mean sugar concentration of grouped fruits

 

Table 3. Parameter values observed in the population

Parameter Value Constanta Number of genotypes Experiments Min Max Mean r1         0.672 101 GarBC2, StPBC201 and StPBC202 SLAb 0.0143 0.0197 0.0169 (7.7)   49 GarBC2 p1         19.47 117 StPBC201 and StPBC202 0.0010 0.0050 0.0025 (36)   142 StPBC202 c 1.5 52.9 13.1 (87)   18 StPBC202 2.28 12.27 5.50 (32.5)   142 GarBC2, StPBC201 and StPBC202 kstone         0.583 142 GarBC2, StPBC201 and StPBC202 1.26 1.90 1.53 (7.8)   142 GarBC2, StPBC201 and StPBC202         0.0028 142 GarBC2, StPBC201 and StPBC202         354 142 GarBC2, StPBC201 and StPBC202 s1 4.77 5.51 5.09 (2.7)   142 GarBC2, StPBC201 and StPBC202 s2         0.6419 142 GarBC2, StPBC201 and StPBC202 aL 0.0021 0.0182 0.0071 (39.4)   142 StPBC202 197.16 752.4 349.6 (97.5)   41 GarBC2, StPBC202 rsu –0.26 0.51 0.29 (27.9)   142 StPBC202 ksugar 0.0032 0.1210 0.0335 (49.5) 142 StPBC202

A constant value is given when no difference was found between genotypes otherwise minimal, maximal, and mean values are given. The coefficient of variations of the parameter in the population is denoted between brackets. The number of genotypes used for the parameter estimation is indicated as well as the corresponding experimental designs.

^a When no significant difference was found between genotypes, a single value was estimated for all genotypes.

^bSLA was set to the mean value in case of light fruit load simulations (StPBC₂01 and StPBC₂02) and to the specific genotypic value in the case of heavy fruit load simulations (StP00, GothBC₂02).

^c Values of only for the 18 genotypes with logistic flesh growth. For genotypes with exponential flesh growth, it was set to the arbitrary high value of 3000 since they do not display a plateau at maturity.

 

Table 4. Estimated values of the relative mean squared error (RRMSE) for evaluating the adjustment quality of the model and its predictive quality at maturity

Traits at maturity Fruit Stone Flesh Dataset Dry mass (g) Fresh mass (g) Dry mass (g) Fresh mass (g) Dry matter content (g g–1) Total sugar amount as carbon (g) Total sugar concentration (g (100 g–1 FM)) Adjustment quality StPBC202 Min 0.001 0 0 0 0 0.002 0.002     Max 0.300 0.242 0.308 0.400 0.215 0.602 0.356     Mean 0.059 0.063 0.090 0.099 0.060 0.098 0.114 Predictive quality StPBC201 Min – 0.005 – 0 0 0.003 0.004     Max – 0.623 – 0.190 0.417 0.486 1.435     Mean – 0.168 – 0.063 0.135 0.269 0.231   GotBC202 Min 0.159 0.153 0.102 0.074 0.074 0.313 0.190     Max 0.265 0.270 0.172 0.157 0.161 0.654 0.484     Mean 0.199 0.203 0.147 0.108 0.110 0.512 0.385   StP00 P1908 0.088 0.146 – 0.061 0.132 – –     S 0.363 0.295 – 0.187 0.211 – – Mean 0.225 0.220 – 0.124 0.171 – –

Minimal, maximal and mean values of RRMSE are presented for each experiment and each output variable.

 

 

Table 5. Key genotypic parameters of the model are ordered from the least to the most noteworthy, according to three criteria: the sensitivity of the model to the parameter, the variation of the parameter value observed in the population, and the error of estimation of the parameter

Parameter Sensitivitya Averaged value of the parameter in the population Variation of the parameter value in the population Averaged value of the estimation error in the population Global scoree Standard deviation Coefficient of variationb SLA * 0.0169 0.0013 7.69 *c 0.0005 **d 4 * 1.53 0.12 7.84 * 0.058 ** 4 s1 **** 5.09 0.14 2.75 * 0.051 ** 7 *** 349.6 97.5 27.89 ** 40.3 ** 7 rsu ** 0.29 0.14 48.28 *** 0.053 ** 7 ** 5.50 1.79 32.55 *** 0.391 *** 8 ksugar *** 0.0335 0.0166 49.55 *** 0.00693 ** 8 f ** 13.1 11.45 87.4 **** 5.45 ** 8 aL **** 0.0071 0.0028 39.44 *** 0.00048 *** 10 **** 0.0025 0.0009 36 *** 0.000087 **** 11

^a Qualitative score (deduced from Table SP1of the Appendix in the supplementary data at JXB online) in the case of heavy fruit load. The more sensitive the model is to the parameter, the more this parameter gets stars.

^b Ratio between the standard deviation and the averaged value of the parameter in the population in percent.

^c Qualitative score deduced from the coefficient of variation. The smaller, the more stars.

^d Qualitative score deduced from the comparison between the averaged value of the estimation error of a parameter and the standard deviation of this parameter in the population. The smaller the former compared with the latter, the more stars.

^e Global score of the parameters considering the qualitative scores for the three criteria analysed. The score is the total number of stars.

^f Only the values of for the 18 genotypes with logistic flesh growth were considered.

 

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