Journal of Experimental Botany, Vol. 53, No. 374, pp. 1613-1625,
July 1, 2002
© 2002 Oxford University Press
Ecophysiological analysis of genotypic variation in peach fruit growth
Received 29 September 2002; Accepted 8 March 2003
1 Unité de Recherche Plantes et Systèmes de culture Horticoles, INRA, Domaine St Paul, Site Agroparc, 84914 Avignon Cedex 9, France
2 Unité de Génétique et Amélioration des Fruits et Légumes, INRA, Domaine St Paul, Site Agroparc, 84914 Avignon Cedex 9, France
3 To whom correspondence should be addressed. Fax: +33 432 72 24 32. E-mail: quilot{at}avignon.inra.fr
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Abstract |
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 Top Abstract IntroductionMaterials and methodsResultsComparison between genotypes and...Discussion and conclusionAppendixReferences |
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Cultivated varieties generally differ greatly from wild genotypes of the same closely related species. However, the processes responsible for these differences have not been elucidated. To analyse variations in fruit mass, fruit growth was characterized in a peach cultivar, a wild related species non-cultivated, and four hybrids derived by crossing them. These genotypes offer a wide range of agronomic values. An ecophysiological model of peach fruit growth in dry mass was used. This model simulates carbon partitioning at the ‘shoot-bearing fruit’ level by considering three compartments: fruits, 1-year-old stems and leafy shoots. The experimental measurements showed considerable variation between genotypes for fruit mass at maturity, fruit growth and source activity. The parameters of the ecophysiological model for each genotype were estimated from experimental data,. The model made it possible to account for genotypic variations in fruit growth and for genotypexfruit load interactions. Using the model, it was shown that the main processes explaining fruit growth variations among the genotypes studied were differences in potential fruit growth.
Key words: Key words: ecophysiology, fruit growth, genotypes, model, peach.
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Introduction |
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TopAbstractIntroductionMaterials and methodsResultsComparison between genotypes and...Discussion and conclusionAppendixReferences |
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Pest and disease sources of resistance are often found in wild related species. In peach (Prunus persica (L.) Batsch), resistance has been found, for example, in Prunus kansuensis and Prunus davidiana (Massonié et al., 1982). A critical element of using such sources is that they have very low values for agronomic traits. Several breeding cycles are necessary to achieve the required agronomic improvement (Kervella et al., 1998). One of the major selection criteria is fruit mass, which is a complex trait known to be greatly influenced by the environment. Complex traits such as fruit mass are often controlled by several QTL (Quantitative Trait Loci), which makes selection for this trait difficult. Moreover, observed values of complex traits are often affected by the environment and very often by interactions between genotype and environment. So experiments must be repeated over several years or in different locations to take the environmental effect into account. Aimed at increasing the knowledge of fruit mass variations related to environmental conditions, the ecophysiological modelling approach has been used successfully.
The aim of this study was to use models developed by plant ecophysiologists to identify the main physiological processes responsible for fruit mass differences between genotypes. A clone of the wild species P. davidiana, a commercial cultivar of P. persica and their hybrids were used in this study. These genotypes were used in a breeding programme for disease resistance (Pascal et al., 1998). Besides the benefits of P. davidiana in terms of resistance, it enhances the differences between the genotypes studied, which should facilitate this new approach. For this purpose, models were needed that reproduced plant functioning through general processes, characterized by parameters depending mainly on genotypes. A few such models, simulating fruit growth in dry mass through carbon (C) assimilation and allocation within the plant, were available (Buwalda, 1991; Grossman and DeJong, 1994a; Bruchou and Génard, 1999; Lescourret et al., 1998). The model of Lescourret et al. (1998) was chosen, which is a peach fruit growth model designed particularly to analyse the variation in mean fruit growth between shoots under different environmental conditions. This model also offered the advantage of working at the relatively simple level of the shoot instead of working at the whole tree level. Lastly, this model emphasizes source activity and fruit demand. It can be hypothesized that these two main complex processes, involved in fruit growth, may be responsible for growth variations between genotypes.
In the first step of this study, an experimental approach was developed that made it possible to characterize the source and sink activity of the genotypes and to estimate the model parameter values for each genotype. In a second step, the capacity of the model was tested to account (1) for differences in growth from one genotype to another, (2) for their response to load levels (two leaf-to-fruit ratios) and (3) for the observed variability in growth within a genotype at a fixed load level. In the last step, the model outputs were used to discuss whether source activity or fruit demand was mainly responsible for variations in fruit growth between genotypes.
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Materials and methods |
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C assimilation and allocation simulation model
A model of carbon partitioning at the shoot-bearing fruit level was used (Lescourret et al., 1998; Génard et al., 1998; Ben Mimoun et al., 1999). A detailed description of this model is given by Lescourret et al. (1998). A schematic representation of the model is provided in Fig. 1, the equations of the model are presented in the Appendix and the parameters in Table 1.
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The shoot-bearing-fruit, isolated from the rest of the tree by girdling, is composed of three main compartments: fruits, 1-year-old stem and leafy shoots, with the last two compartments having a structural part and a storage part. For initialization, each compartment must be described. Precisely, the model requires as initial conditions the dry mass of the three compartments (fruit initial mass, 1-year-old stem initial mass and leafy shoots initial mass) and the carbon content of storage parts of 1-year-old stems and leafy shoots. The model runs on a daily basis. The pool of carbon assimilates available daily for distribution is the carbon assimilated daily plus the carbon mobilized from reserves if the demand of the sink organs exceeds the photosynthetic product. For a fruit-bearing shoot, the main outputs are mean dry mass per fruit and hly photosynthesis per unit leaf area.
Daily assimilation (Appendix, Equation 7) by the leaves results from hly photosynthesis calculated from photosynthetically active photon flux density (PPFD in µmol photon m–2 s–1) (Appendix, Equation 4), total leaf area and the light environment of each shoot (Appendix, Equation 6). Total leaf area is separated into a sunlit and a shaded component using, as input data, fractions of leaves out of the shade occurring between shoots and within the shoot, recorded hly. Assimilation also depends on light-saturated leaf photosynthesis, which is regulated by the level of leaf reserves (Appendix, Equation 2). Carbon assimilation by fruits is calculated similarly (Appendix, Equations 5 and 8).
Carbon partitioning is based on organ demand and priority rules. Assimilates are first allocated to maintenance respiration (Appendix, Equation 10). Vegetative and fruit growth are given second and third priority, respectively. Daily carbon demand for growth in each organ is based on growth potential (Appendix, Equation 11), which includes the effect of already-accumulated biomass (Appendix, Equation 12).
Reserves play a buffer role between carbon assimilation and utilization. A constant proportion of reserves from the leafy shoot compartment and then from the 1-year-old stem can be mobilized in the case of sink demand (Appendix, Equation 9 and 9x). If assimilation is greater than sink demand, carbon is first allocated to the reserves of the leafy shoot compartment and then, if this compartment gets saturated, to the reserves of the 1-year-old stem.
This model has been tested by Génard et al. (1998) for two peach cultivars: ‘Suncrest’ and ‘Alexandra’. A few modifications have been made to adapt the modelling of fruit growth demand to the genotypes studied.
Sensitivity of the model to variations in some parameters
To choose the model parameters to be measured in these experiments, the sensitivity of the model to parameter variations was tested. Fruit dry mass at harvest was compared for high and low values for each parameter, for two contrasting loading levels corresponding to source and sink limiting conditions. Parameters were tested independently.
For each loading level, the sensitivity criterion for one parameter was the difference between fruit dry mass for high (DMH) and low (DML) values of the parameter, expressed as a percentage of fruit dry mass at harvest for the default parameter value (DMo): 100x(DMH–DML)/(DMo). The model was considered very sensitive to a parameter when this difference exceeded 5% in absolute terms for at least one of the two loading levels considered.
The high and low parameter values were set to plus or minus 50% of the model default parameter values estimated for the ‘Suncrest’ cultivar by Lescourret et al. (1998). This range was modified for r1 and r2 for it led to illogical parameter values. In the special case of Pfmax, the impact of fruit assimilation on fruit dry mass at harvest was to be tested so the default value and zero were taken as the high and low values of Pfmax.
Plant material and experimental treatments
Experiments were carried out in Avignon (southern France) on a peach cultivar (Prunus persica L., Batch), Summergrand, and a wild related species, Prunus davidiana clone 1908, which is not cultivated, as well as on four hybrids (SD17, SD31, SD40, and SD69) derived by crossing them. Trees were grown in 50 l pots and irrigated with a complete nutrient solution. They received routine horticultural care suitable for commercial orchards.
On 20 April 2000, two treatments with leaf-to-fruit ratios set to heavy and light loading levels were applied to shoot-bearing fruits isolated from the tree by girdling. Heavy-loading level treatment, i.e. five leaves per fruit, corresponded to limiting source conditions and light-loading level, i.e. 30 leaves per fruit, to limiting sink conditions, for commercial peach varieties. These leaf-to-fruit ratios were applied to Summergrand. However, to take into account the variation in mean leaf area between genotypes, leaf-to-fruit ratios were adapted for P. davidiana and the hybrids so that leaf area per fruit was similar from one genotype to another. In order to maintain the leaf area constant throughout growth, leafy shoot vegetative growth was arrested by cutting the terminal apex and new lateral shoots were removed. Twenty shoots per genotype, bearing one to eight fruits, were monitored for each genotype. Fruit diameter were measured 2 d after treatment application and then once a week from 9 May (400 degree-days) to harvest. Fruit dry mass could not be inferred safely from fruit diameter before 9 May (400 degree-days after flowering), i.e. before stone hardening was complete.
Measurements
As stated above, some environmental variables were needed as input data for the model. Hourly total radiation and daily mean temperature values were recorded at Avignon. Degree-days were calculated from daily minimum and maximum temperatures with upper and lower temperature thresholds at 35 °C and 7 °C, respectively. Degree-day data were accumulated from full-bloom to harvest for each genotype.
Besides the environmental variables, the input data consisted of light interception coefficients, the number of fruits per shoot and the initial dry weights of the three compartments, and the initial reserves of 1-year-old stems and leafy shoots are also needed at the beginning of the simulations (400 degree-days after flowering). Initial dry masses of fruits and leafy shoots were estimated from the relationships between dimensions and dry masses, established for each genotype in organs harvested from non-monitored shoots. One-year-old stem volumes, calculated from the length and diameter of each stem considered to be cone-shaped, were converted into dry mass on the basis of a mean peach wood specific dry weight (0.575 g cm–3). Since the 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, these initial reserves were set to the value taken by Lescourret et al., i.e. 10% of the initial dry masses of the leafy shoots and 1-year-old stems. As regards light interception, the model requires two series of hourly coefficients in order to take into account assimilation reduction due to the shade effect (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. Since leafy shoot growth was arrested, the former was taken to be constant throughout the period. Each coefficient of the latter is assumed to decrease linearly from a value of 1, at the blooming period (shade is nil), towards a threshold reached when there is no more vegetative growth in the tree, and then to level off (Lescourret et al., 1998). Both series of coefficients were calculated using gap fractions derived from digitized hemispherical photographs (Génard and Baret, 1994).
In the model, shoots had to be characterized by two parameters: specific leaf area (SLA, m2 g–1), which was estimated from the measurements of surface and mass of 20 leaves for each genotype (Appendix, Equation 1), and the leaf mass to leafy shoot mass ratio (r1), which was estimated from the measurements of the shoots for each genotype (Appendix, Equation 3). All these measurements were made in the morning.
Photosynthetic response to light levels and stomatal conductance were measured with two types of portable photosynthesis system. One, ADC–LCA 4, measured photosynthesis at natural radiation. With the second, CIRAS, artificial radiation was applied. Measurements were made on well-expanded sunlit leaves early in the morning on several dates for each genotype. The maximum leaf photosynthesis value, the parameter p1, was estimated from these data (Appendix, Equation 2).
To compute fruit dry matter growth on monitored shoots, relationships between fruit diameter and fruit dry mass were needed for each genotype. To establish these relationships, ten fruits per genotype were sampled for non-monitored shoots every 2 weeks throughout the fruit growth period. After recording fruit cheek diameter, fruits were subjected to temperatures of 70 °C for 72 h, and then dry mass was measured.
From the dry mass of fruits grown on the lightly-loaded shoots, the parameters of fruit growth demand were estimated (Appendix, Equations 8 and 9).
Dry mass data of fruits grown on the heavily-loaded shoots were not used for parametrizing the fruit growth equation. It was used to test model behaviour in the case of limiting source conditions.
Comparison between genotypes
For traits directly derived from measurements, such as r1, SLA, mean measured and predicted light-saturated photosynthesis rates, and mean fruit diameter and dry mass, genotypes were compared using non-parametric tests for independent samples, since not all the traits were distributed normally. First, the Kruskal–Wallis test was used. Then, if the null hypothesis was rejected, i.e. none of the genotypes were equal, Noether’s multiple range test was performed to determine which genotypes were significantly different at the 0.05 level.
In the case of adjusted parameters, p1 and RGRfini, another method had to be used consisting of comparing adjustment models.
To compare genotypes for photosynthetic properties, a two-parameter curve, y=p1x[1–exp(–hxx)], was adjusted to light-saturated photosynthesis data as a function of stomatal conductance using a non-linear least-squares procedure. The complex model with the two parameters p1 and h specific to each genotype was compared to the simple model with only two parameters, irrespective of the genotype. In this statistical comparison, the null hypothesis was that the parameter values for p1 and h were the same for all the genotypes. To test this hypothesis, a 
2 test was performed (P <0.05) (Huet et al., 1992).
To fit the potential fruit growth equation to data of lightly-loaded shoots, a non-linear mixed-effects method for repeated measures data was used (Lindstrom and Bates, 1990) which is particularly designed to analyse growth curve data. The null hypothesis of no difference in RGR
between genotypes was tested by comparing the simple model, where the curve varies with the fruits, with a complex model, where the curve varies with the genotypes and fruits. Comparison was made using a likelihood ratio test (ANOVA method).
Comparison between observed and predicted data
To compare observations and model predictions, fruit dry mass values were compared using a mean error of prediction (MEP) for each fruit load treatment of each genotype. It was defined as the square root of the ‘Mean Squared Error of Prediction’ criterion (Wallach and Goffinet, 1987):
All data analyses were performed with the Splus language (Splus software, MathSoft Inc., Cambridge, MA).
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Results |
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The experimental measurements revealed variations between genotypes for both source activity and fruit growth. As regards source activity, photosynthesis rates under light-saturated conditions were sometimes very low for P. davidiana and the hybrids (Fig. 2). Fruit diameter growth, monitored experimentally, showed considerable variations among genotypes. Summergrand exhibited very good fruit growth from 9 May to harvest (measurement period), whereas P. davidiana fruits had enlarged earlier. Hybrid fruits had also enlarged early but, during the measurement period they grew more than P. davidiana fruits. SD17, SD31 and SD40 fruits reached significantly greater diameters at maturity than P. davidiana fruits (Table 2).
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Model adaptation and sensitivity analysis
The model was adapted with respect to three points for the purpose of this study. Since leafy shoot growth was arrested in this experiment, leafy shoot growth demand was set to zero. Fruit photosynthesis, which was shown scarcely to affect the model response, was set to zero. Lastly, the modelling of fruit growth demand was adapted.
In the model, fruit growth demand depends on potential dry mass. Accordingly, only data for lightly-loaded shoots were used to estimate growth curve parameters. In the initial Lescourret et al. model, potential fruit mass reaches a plateau at maturity and the potential fruit growth equation is a mixture of logistic and temporal factors. In this experiment, fruit growth appeared to be exponential after the beginning of the measurements, and most of them stopped growing suddenly at maturity, when the sum of degree-days (dd) after bloom reached ddmax. Thus, the equation we used for the potential growth of fruit in terms of degree-days was:
and
where RGRfini is the initial relative growth rate (dd–1) and Wf fruit weight (g).
According to the sensitivity analysis, the model was very sensitive to 10 out of the 25 parameters (Table 1). Five of them, SLA, p1, r1, p3, and p4, concerned leaf assimilation (Fig. 1). Two others, p7 and r3, were involved in the expression of radiation received by shaded leaves. The last three, ddmax, GRCfruit, and RGRfini, concerned fruit growth demand. Of these ten parameters, five could not be measured (GRCfruit, p3, p4, p7, and r3). Their range of variation and effect will be discussed later.
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Comparison between genotypes and parametrization |
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With regard to the five remaining parameters (SLA, p1, r1, ddmax, RGRfini), it was tested whether their values were significantly different between the genotypes. Values of the other 20 parameters, for which the model was sensitive to only five (Table 1), were taken from the literature. The origin of the parameter values used in the simulations is given in Table 1.
The values of SLA did not differ significantly from one genotype to another (Table 3). In the model, the value averaged for all genotypes (SLA=0.0124 m2 g–1) was therefore used.
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The parameter p1 is the maximum value of light-saturated leaf photosynthesis in the absence of leaf reserves. The plateau reached when radiation increases is generally used to estimate the p1 value. This method could not be used because photosynthesis rates were low in expected saturating radiation (Fig. 2). However, photosynthesis appeared to be closely linked to stomatal conductance. To test whether the plateau (p1) was the same whatever the genotype, a monomolecular equation relating photosynthesis to stomatal conductance was therefore used, with one of the two parameters corresponding to the plateau value. In the statistical comparison between the complex model (with parameters specific to each genotype; Table 3) and the simplest model (with only two parameters, independent of the genotype), the null hypothesis of ‘no difference between genotypes for p1 values’ was not rejected. Therefore p1 was set to the value estimated (18.35 µmol m–2 s–1) by the simplest model, for all the genotypes. Figure 3 presents the experimental data and the adjusted curve calculated from the simplest model.
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Some genotypes differed significantly for r1 values (Table 3). In the model, r1 values specific to each genotype were used. However, the range of these values was lower than the range considered in the sensitivity analysis.
The values of ddmax were calculated from the fruit maturity date for each genotype. RGRfini was estimated by fitting dry mass data as an exponential function of degree-days, for each genotype, using non-linear mixed-effects models. A simple model, where the curve varies with fruits, was compared with a complex model, where the curve varies with genotypes and fruits. In the latter, RGRfini parameters had a fixed component, depending on the genotype, and a random component. The null hypothesis of no genotype differences for RGRfini was rejected by a likelihood test ratio (P value=2.66e–15). Thus, the complex model was kept and the values of RGRfini were reconstituted from random and fixed effects data for each fruit, and the mean and standard deviation was calculated for each genotype. Noether’s multiple range test showed that the RGRfini values of P. davidiana and of Summergrand were significantly different (Table 3). SD69 and SD31 differed significantly from Summergrand, and SD17 and SD40 appeared to be different from P. davidiana. However, no significant difference was found between the four SD hybrids. For the RGRfini values six different values were taken, corresponding to the mean for each genotype. To emphasize differences in fruit demand resulting from RGRfini differences between genotypes, the potential growth curves of the different genotypes per unit of initial fruit dry mass were plotted (Fig. 4). Potential growth was very low for P. davidiana and intermediate between the parent levels for the hybrids.
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ddmax, where RGRfini is the initial relative growth rate (dd–1) and Wf fruit weight (g). ddmax corresponds to the mean fruit maturity date for each genotype. Parameter values of the equation for potential growth were estimated for each genotype from data for the light-loading treatment only (limiting sink conditions).Values used in the model for SLA, p1, r1, ddmax, and RGRfini are reported in Table 3.
Comparison between observed and predicted data
Mean dry mass growth per fruit was predicted by the model for each lightly-loaded shoot monitored and compared to that observed experimentally (Fig. 5A). The equation of fruit demand for growth used in the model appeared to be very robust since it made it possible to simulate the overall shape of fruit growth curves for genotypes with very different growth patterns. The MEP value was always less than 2.28 g for fruit dry mass values ranging from 22.81 to 27.13 g.
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The model was able to reproduce fruit growth for heavily-loaded shoots (Fig. 5B). This can be considered a successful test of the model since this treatment had not been used for parametrization. Lastly, the model accurately predicted the magnitude of growth variations within a treatment, which depended on the genotype. These variations explained most of the variations in fruit mass at maturity probably because they partly determined fruit demand.
Figure 5C, plotting predicted data against observed data, further illustrates the consistency between observations and simulations for both loading treatments.
Variations in genotype response to load levels
A fruit load treatment effect appeared only in the case of Summergrand, for which fruits of heavily-loaded shoots grew more slowly than fruits of lightly-loaded shoots. For P. davidiana and the hybrids, the heavy-loading level treatment applied to the shoots was not severe enough to place them under limiting source conditions. Differences in initial fruit mass, already observed between fruit loading treatments by the time simulations were started (400 degree-days after flowering), did not vary with time. These differences seemed to determine differences in fruit mass at harvest. The major effect of treatment was hypothesized to occur at the beginning of growth, between treatment application and the beginning of the simulations (Table 4). To test this hypothesis, the model was run with the same initial fruit mass for all genotypes. Leaf area per fruit was the sole factor varying between the heavy-load and light-load simulations for a given genotype. In the case of P. davidiana and the hybrids, the effect of treatment was not significant and fruit growth followed the same growth pattern whatever the treatment. For these genotypes, fruit demand seemed to be limiting, both for heavily and lightly-loaded shoots.
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Major physiological processes responsible for the variation in growth between genotypes
The five parameters studied (SLA, p1, r1, ddmax, and RGRfini) made it possible to predict variability between the genotypes studied accurately. To show the processes responsible for the main variations between genotypes, the range of parameter values for the various genotypes were considered further.
Of the five parameters studied, the three involved in source activity (SLA, p1, r1) either did not significantly differ from one genotype to another (SLA and p1) or exhibited small variations between genotypes (r1). Indeed, when the actual value of r1 estimated for each genotype was replaced by the bounding values for r1 in the experiment, the fruit dry mass at harvest was barely modified. The relative variation in fruit dry mass at harvest (100x(DM–DMo)/DMo) did not exceed 0.21% for any of the genotype shoot loads. Therefore, it could be concluded that fruit growth demand was the main physiological process responsible for the variability in fruit growth between the genotypes.
Model contribution explaining the low rates of light-saturated photosynthesis observed for P. davidiana and the hybrids
To assess whether fruit demand limitation was more likely to be involved than source activity limitation, despite low photosynthesis levels, a study was made of the output of the model for P1max (µmol CO2 m–2 s–1), the predicted light-saturated leaf photosynthetic rate altered by leaf accumulation of reserves. The predicted values of P1max were qualitatively consistent with the measured light-saturated photosynthesis rates (Table 5). Whatever the P. davidiana shoot considered, photosynthesis never reached p1 (Fig. 6). Even in the case of heavily-loaded shoots, fruit demand and photosynthesis were low and leaves stored carbohydrates. For SD69 and SD31 and to a lesser extent for SD17 and SD40, a similar scenario happened (Fig. 6). For the latter three, fruit demand of some shoots was sufficient for reserves to decrease towards zero and for photosynthesis to become closest to p1 at the end of growth. This was the general case for Summergrand shoots whatever their load. In Summergrand shoots, fruit demand at the end of growth was high enough to mobilize C assimilates from reserves and to increase maximal photosynthesis to p1.
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Discussion and conclusion |
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Theser results strongly suggest that differences in fruit growth between genotypes were due to limitation in fruit demand. Low photosynthetic activity observed for P. davidiana and the hybrids was a consequence of low sink demand and not the cause of limited fruit growth. As regards the limitation of stomatal conductance for P. davidiana and the hybrids, it can be hypothesized that it was also a consequence of low sink demand. A possible effect of girdling may be invoked. Thus, preventing phloem transport could favour reserve accumulation in the shoot, which would otherwise be exported to other parts of the tree. However, a few measurements of photosynthesis, on shoots without girdling, show situations where stomatal conductance remains low (data not shown).
Other hypotheses, anaerobiosis and root restriction, which could have occurred under these container-growing conditions, seemed to be less consistent in explaining low experimental values for photosynthesis rates. Indeed, stomatal conductance and photosynthesis rate values for Summergrand were not so low, though all genotypes were grafted on to the same rootstock and managed in the same way. Reduction in leaf photosynthesis as a result of leaf starch accumulation is also supported by numerous studies. Ben Mimoun (1997) observed very low leaf photosynthesis values and leaf starch accumulation in peach shoots without fruit. Physiological and biochemical studies on various species have suggested that photosynthesis is feedback-regulated by the accumulation of carbohydrates in source leaves (Azcon-Bieto, 1983; Foyer, 1988; Sawada et al., 1986; Goldschmidt and Huber, 1992). This feedback inhibition mechanism may explain the low photosynthesis rates of P. davidiana and the hybrids in which fruit growth was limited and photosynthesis activity slowed down early in the morning even, though water stress was negligible.
Parameters that were not measured, i.e. GRCfruit, p3, p4, p7, and r3, were unlikely to influence the model outputs, since variations in these parameters are expected to be low within closely related species. The fruit growth respiration coefficient, GRCfruit, was taken from DeJong and Goudriaan (1989). The inter-specific variations in this parameter are not considerable. For tomato, the value estimated by Penning de Vries et al. (1989) was 0.112 g C g–1 DW and, for cucumber, the estimated value was 0.043 g C g–1 DW (Marcelis and Baan Hofman-Eijer, 1995). As regards intra-specific variations, for seven apple cultivars, values ranged between 0.053 and 0.060 g C g–1 DW and did not differ significantly (Walton et al., 1999). With respect to peach cultivars, GRCfruit was found to be similar for an early (‘June Lady’) and a late-maturing (‘O’Henry’) cultivar (DeJong et al., 1987).
p3 and p4 are parameters of the equation used to calculate photosynthesis per unit leaf area and per unit time (P, µmol CO2 m–2 s–1) from the photosynthetically active photon flux density, PPFD (input data, µmol photon m–2 s–1). They are taken from the formulation of Higgins et al. (1992) who described the net photosynthetic response to PPFD for different plants, including peach (Prunus persica L. Batsch. cultivar ‘Red Haven’). Of the plants tested by Higgins et al. (1992), the three stone fruit species, almond, olive and peach, showed quite similar p3 and p4 values (respectively, 3.0337, 2.8284 and 2.2048 for p3 and 0.0576, 0.0580 and 0.0580 for p4). The variability should not be higher between the commercial peach P. davidiana and the hybrids than between almond, olive and peach. Thus, it can be assumed that p3 and p4 values for Summergrand, P. davidiana and the hybrids are close to each other and to those for Red Haven (2.2048 and 0.0580, respectively).
The parameters p7 and r3 are used to calculate the radiation received by shaded organs (PPFDshaded) and of sunlit organs (PPFDsunlit) and assessed by Lescourret et al. (1998) in the cultivar Suncrest. The variability in these parameters within a species or between two related species was not studied.
Low potential fruit growth, as suspected for P. davidiana and the hybrids, is consistent with the production of a large number of fruits each enclosing a single seed. This behaviour can represent a selective advantage and is quite typical among wild and slightly domesticated species, such as P. davidiana, the dispersion of which depends on fruit transport by animal consumers (Janzen, 1983). In the case of a single big seed, the protective role of the fruit seems to be more important than its attraction function and the number of fruits more important than their size. Low fruit growth after stone formation could also allow reduced competition between vegetative and fruit growth during late spring and summer. Thus, survival of the tree and dispersion of the species could both be satisfied. hypotheses can be formulated on the physiological processes that are responsible for the low fruit demand. It may result from the preferential partitioning of carbohydrates towards the stone during the first stages of fruit growth. The observation of early stone formation in P. davidiana supports this view. Variations in cell number or cell size could also explain low fruit demand. Fruit size has been regarded as a function of cell number in the early stages of development and cell size in the final stages of fruit growth, after pit-hardening (Batjer and Westwood, 1958; Westwood et al., 1967). Differences in fruit size between peach cultivars have been shown to be due to differences in mesocarp cell count that are determined early in the growth of the ovary (Scorza et al., 1991). The major effect of the experimental treatments at the beginning of growth emphasized the benefits of studying the early stages of fruit growth.
The evaluation of the genotypes appeared more relevant under conditions of lightly-loaded shoots. In fact, differences in fruit growth between genotypes were more pronounced under these conditions. Moreover, these conditions can be reproduced easily, whatever the genotype, year or site. From potential growth data, the model made it possible to predict growth for heavily-loaded shoots, taking environmental conditions into account.
Simulations and experimentations allowed the identification of two parameters linked to fruit demand which appeared to predict fruit growth variations between genotypes accurately. These parameters could now be used to characterize genotypes and their genetic control could be studied. For this purpose, ecophysiological parameters would be scored among a large progeny and a QTL search would be performed. Such works have already been performed at the molecular level in order to study metabolic control. For example, metabolic fluxes in the cell were considered as model traits for quantitative genetics (Bost et al., 1999). This QTL analysis approach to ecophysiological traits stemming from models should make it possible to explain the variations in a complex trait by a series of parameters derived from the model and likely to be linked to few QTL and more independent of the environment. Finally, this approach makes it easier to understand the genetic determinism and to select this trait.
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Acknowledgements |
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We gratefully acknowledge J Hostalery, V Serra, R Laurent, and M Auge for their assistance in the field experiments used in this paper, and T Pascal and F Pfeiffer, who allowed us to benefit from their familiarity with the trees studied. We are indebted to B Ney for helpful discussions and to two anonymous reviewers for help in improving this paper. We thank AM Wall for improving the English.
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Appendix |
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The main equations used in the model to predict fruit growth from C assimilation and allocation are described. The model parameters, in bold italics, are defined in Table 1.
Leaf assimilation
The total leaf area LA (m2) of a stem is computed from the dry mass of the structural part of the leafy shoots, WSls (g), and the specific leaf area, SLA (m2 g–1), as follows:
LA = WSls x r1 x SLA(1)
Light-saturated leaf photosynthesis P1max (µmol CO2 m–2 s–1) is modulated by the level of reserves in the leaves:
where WRl and WSl denote the dry masses of reserves and of structural parts in the leaves, respectively. The model assumes that WRl is a constant proportion of the dry mass of reserves in the leafy shoots, WRls (g):
WRl = r2 x WRls and according to (1): WSl = r1 x WSls(3)
Photosynthesis per unit leaf area and per unit time is calculated from the photosynthetically active photon flux density (PPFD, µmol photon m–2 s–1):
Fruit assimilation
Photosynthesis per unit fruit mass and per unit time is a function of degree-days after full bloom (dd), fruit dry mass, Wf (g), and PPFD:
Pf= Pfmax xf(dd, Wf, PPFD)(5)
Radiation in the shade
PPFD is modulated in the case of shaded leaves:
PPFDshaded = p7 x (1 – e–p8 x PPFDsunlit) + r3 x PPFDsunlit(6)
and total leaf area, LA, is separated into a sunlit and a shaded component.
C assimilation
Lastly, the amount of C produced by leaf photosynthesis during the day, Clp (g d–1), is computed as the sum of hourly photosynthesis by sunlit and shaded leaves. k is the conversion coefficient (0.0432) from µmol CO2 s–1 to g h–1.
In the same way, the photosynthetic contribution of fruits is separated into two components, concerning sunlit and shaded fruits. The amount of C produced by fruit photosynthesis during the day, Cfp (g d–1), is computed similarly to the leaf case:
Reserve mobilization
If the amount of carbohydrates available from current photosynthesis is less than the amount required by the system, a mobile amount of reserves can be mobilized from the leafy shoot compartment.
r4xCCls (g d–1)(9)
If it is insufficient, additional reserves from the 1-year-old stem may be used
r5xCCst(9')
CCls and CCst are the carbon content of the storage part of the leafy shoots and the 1-year-old stem, respectively.
Maintenance respiration demand
Maintenance respiration demand MR (g d–1) is calculated from the Q10 concept, in the same way as for the different organ groups (i), 1-year-old stem, current-year stem, leaves and fruits:
where MRRi is the maintenance respiration rate (g g–1 s–1) of organ i at reference temperature 
ref (°C), Qi10 is the Q10 value for organ group i, is the mean temperature of the day (°C), Wi (g) is the dry mass of the organ group (i), and 3600xH is the conversion coefficient from seconds to days. H=24 for any group except the leaves, for which only dark hours are considered.
Fruit growth demand
Daily carbon demand D (g d–1) for fruit growth can be written as:
where 
Wfpot/dd (g dd–1) is the potential growth rate in terms of degree-days after full bloom dd, CCfruit and GRCfruit the carbon concentration and growth respiration coefficient of fruit, respectively (dimensionless). dd /t (dd d–1) is entered as a series of values in order to convert data from days to degree-days.
Potential fruit growth in terms of degree-days was calculated including an effect of fruit mass, Wf (g), representing sink size and ddmax (dd), the sum of degree-days corresponding to fruit maturity:
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