DOI: 10.1093/jxb/erf001

Ecophysiological analysis of genotypic variation in peachfruit growth

B. Quilot1,3, M. GeÂnard1, J. Kervella2 and F. Lescourret1

1Unite de Recherche Plantes et SysteÁmes de culture Horticoles, INRA, Domaine St Paul, Site Agroparc, 84914Avignon Cedex 9, France2Unite de GeÂneÂtique et Ame lioration des Fruits et LeÂgumes, INRA, Domaine St Paul, Site Agroparc, 84914Avignon Cedex 9, France

Received 29 September 2002; Accepted 8 March 2003

Abstract

Cultivated varieties generally differ greatly from wild

genotypes of the same closely related species.

However, the processes responsible for these differ-

ences have not been elucidated. To analyse vari-

ations in fruit mass, fruit growth was characterized in

a peach cultivar, a wild related species non-culti-

vated, 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 measure-

ments showed considerable variation between geno-

types for fruit mass at maturity, fruit growth and

source activity. The parameters of the ecophysiologi-

cal model for each genotype were estimated from

experimental data,. The model made it possible to

account for genotypic variations in fruit growth and

for genotype3fruit load interactions. Using the

model, it was shown that the main processes explain-

ing fruit growth variations among the genotypes

studied were differences in potential fruit growth.

Key words: ecophysiology, fruit growth, genotypes, model,

peach.

Introduction

Pest and disease sources of resistance are often found inwild related species. In peach (Prunus persica (L.)Batsch), resistance has been found, for example, in

Prunus kansuensis and Prunus davidiana (MassonieÂet al., 1982). A critical element of using such sources isthat they have very low values for agronomic traits.Several breeding cycles are necessary to achieve therequired agronomic improvement (Kervella et al., 1998).One of the major selection criteria is fruit mass, which is acomplex trait known to be greatly in¯uenced by theenvironment. Complex traits such as fruit mass are oftencontrolled by several QTL (Quantitative Trait Loci), whichmakes selection for this trait dif®cult. Moreover, observedvalues of complex traits are often affected by theenvironment and very often by interactions betweengenotype and environment. So experiments must berepeated over several years or in different locations totake the environmental effect into account. Aimed atincreasing the knowledge of fruit mass variations related toenvironmental conditions, the ecophysiological modellingapproach has been used successfully.

The aim of this study was to use models developed byplant ecophysiologists to identify the main physiologicalprocesses responsible for fruit mass differences betweengenotypes. A clone of the wild species P. davidiana, acommercial cultivar of P. persica and their hybrids wereused in this study. These genotypes were used in abreeding programme for disease resistance (Pascal et al.,1998). Besides the bene®ts of P. davidiana in terms ofresistance, it enhances the differences between thegenotypes studied, which should facilitate this newapproach. For this purpose, models were needed thatreproduced plant functioning through general processes,characterized by parameters depending mainly on geno-types. A few such models, simulating fruit growth in drymass through carbon (C) assimilation and allocation withinthe plant, were available (Buwalda, 1991; Grossman and

3 To whom correspondence should be addressed. Fax: +33 432 72 24 32. E-mail: quilot@avignon.inra.fr

ã Society for Experimental Biology 2002

Journal of Experimental Botany, Vol. 53, No. 374, pp. 1613±1625, July 2002

DeJong, 1994a; Bruchou and GeÂnard, 1999; Lescourretet al., 1998). The model of Lescourret et al. (1998) waschosen, which is a peach fruit growth model designedparticularly to analyse the variation in mean fruit growthbetween shoots under different environmental conditions.This model also offered the advantage of working at therelatively simple level of the shoot instead of working atthe whole tree level. Lastly, this model emphasizes sourceactivity and fruit demand. It can be hypothesized that thesetwo main complex processes, involved in fruit growth,may be responsible for growth variations betweengenotypes.

In the ®rst step of this study, an experimental approachwas developed that made it possible to characterize thesource and sink activity of the genotypes and to estimatethe model parameter values for each genotype. In a secondstep, the capacity of the model was tested to account (1) fordifferences in growth from one genotype to another, (2) fortheir response to load levels (two leaf-to-fruit ratios) and(3) for the observed variability in growth within a genotypeat a ®xed load level. In the last step, the model outputswere used to discuss whether source activity or fruitdemand was mainly responsible for variations in fruitgrowth between genotypes.

Materials and methods

C assimilation and allocation simulation model

A model of carbon partitioning at the shoot-bearing fruit level wasused (Lescourret et al., 1998; GeÂnard et al., 1998; Ben Mimoun et al.,1999). A detailed description of this model is given by Lescourretet al. (1998). A schematic representation of the model is provided inFig. 1, the equations of the model are presented in the Appendix andthe parameters in Table 1.

The shoot-bearing-fruit, isolated from the rest of the tree bygirdling, is composed of three main compartments: fruits, 1-year-oldstem and leafy shoots, with the last two compartments having astructural part and a storage part. For initialization, each compart-ment must be described. Precisely, the model requires as initialconditions the dry mass of the three compartments (fruit initial mass,1-year-old stem initial mass and leafy shoots initial mass) and thecarbon content of storage parts of 1-year-old stems and leafy shoots.The model runs on a daily basis. The pool of carbon assimilatesavailable daily for distribution is the carbon assimilated daily plusthe carbon mobilized from reserves if the demand of the sink organsexceeds the photosynthetic product. For a fruit-bearing shoot, themain outputs are mean dry mass per fruit and hly photosynthesis perunit leaf area.

Daily assimilation (Appendix, Equation 7) by the leaves resultsfrom hly photosynthesis calculated from photosynthetically activephoton ¯ux density (PPFD in mmol 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 anda shaded component using, as input data, fractions of leaves out ofthe shade occurring between shoots and within the shoot, recordedhly. Assimilation also depends on light-saturated leaf photosyn-thesis, 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 ®rst allocated to maintenance respiration (Appendix,Equation 10). Vegetative and fruit growth are given second and thirdpriority, respectively. Daily carbon demand for growth in each organis based on growth potential (Appendix, Equation 11), whichincludes the effect of already-accumulated biomass (Appendix,Equation 12).

Reserves play a buffer role between carbon assimilation andutilization. A constant proportion of reserves from the leafy shootcompartment and then from the 1-year-old stem can be mobilized inthe case of sink demand (Appendix, Equation 9 and 93). Ifassimilation is greater than sink demand, carbon is ®rst allocated tothe reserves of the leafy shoot compartment and then, if thiscompartment gets saturated, to the reserves of the 1-year-old stem.

This model has been tested by GeÂnard et al. (1998) for two peachcultivars: `Suncrest' and `Alexandra'. A few modi®cations havebeen made to adapt the modelling of fruit growth demand to thegenotypes studied.

Sensitivity of the model to variations in some parameters

To choose the model parameters to be measured in theseexperiments, the sensitivity of the model to parameter variationswas tested. Fruit dry mass at harvest was compared for high and lowvalues for each parameter, for two contrasting loading levelscorresponding to source and sink limiting conditions. Parameterswere tested independently.

For each loading level, the sensitivity criterion for one parameterwas the difference between fruit dry mass for high (DMH) and low(DML) values of the parameter, expressed as a percentage of fruit drymass at harvest for the default parameter value (DMo): 1003(DMH±DML)/(DMo). The model was considered very sensitive to aparameter when this difference exceeded 5% in absolute terms forat 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 modi®ed for r1and r2 for it led to illogical parameter values. In the special case ofPf

max, the impact of fruit assimilation on fruit dry mass at harvest wasto be tested so the default value and zero were taken as the high andlow values of Pf

max.

Plant material and experimental treatments

Experiments were carried out in Avignon (southern France) on apeach cultivar (Prunus persica L., Batch), Summergrand, and a wildrelated species, Prunus davidiana clone 1908, which is notcultivated, as well as on four hybrids (SD17, SD31, SD40, andSD69) derived by crossing them. Trees were grown in 50 l pots andirrigated with a complete nutrient solution. They received routinehorticultural care suitable for commercial orchards.

On 20 April 2000, two treatments with leaf-to-fruit ratios set toheavy and light loading levels were applied to shoot-bearing fruitsisolated from the tree by girdling. Heavy-loading level treatment, i.e.®ve leaves per fruit, corresponded to limiting source conditions andlight-loading level, i.e. 30 leaves per fruit, to limiting sinkconditions, for commercial peach varieties. These leaf-to-fruit ratioswere applied to Summergrand. However, to take into account thevariation in mean leaf area between genotypes, leaf-to-fruit ratioswere adapted for P. davidiana and the hybrids so that leaf area perfruit was similar from one genotype to another. In order to maintainthe leaf area constant throughout growth, leafy shoot vegetativegrowth was arrested by cutting the terminal apex and new lateralshoots were removed. Twenty shoots per genotype, bearing one toeight fruits, were monitored for each genotype. Fruit diameter weremeasured 2 d after treatment application and then once a week from9 May (400 degree-days) to harvest. Fruit dry mass could not be

1614 Quilot et al.

Fig. 1. Schematic representation of the model. PPFD is the photosynthetically active photon ¯ux density (mmol photon m±2 s±1). Modelparameters are indicated in italics at the steps where they intervene. Parameters to which the model is sensitive are in bold type. Since leafy shootgrowth was arrested in this experiment, leafy shoot growth demand was set to zero. Fruit photosynthesis was set to zero, given that it was shownthat it scarcely affected the model response. (Adapted from Lescourret et al., 1998.)

Genotypic variations in fruit growth 1615

inferred safely from fruit diameter before 9 May (400 degree-daysafter ¯owering), i.e. before stone hardening was complete.

Measurements

As stated above, some environmental variables were needed as inputdata for the model. Hourly total radiation and daily mean tempera-ture values were recorded at Avignon. Degree-days were calculatedfrom daily minimum and maximum temperatures with upper andlower temperature thresholds at 35 °C and 7 °C, respectively.Degree-day data were accumulated from full-bloom to harvest foreach genotype.

Besides the environmental variables, the input data consisted oflight interception coef®cients, the number of fruits per shoot and theinitial dry weights of the three compartments, and the initial reservesof 1-year-old stems and leafy shoots are also needed at the beginningof the simulations (400 degree-days after ¯owering). Initial drymasses of fruits and leafy shoots were estimated from therelationships between dimensions and dry masses, established foreach genotype in organs harvested from non-monitored shoots. One-year-old stem volumes, calculated from the length and diameter ofeach stem considered to be cone-shaped, were converted into drymass on the basis of a mean peach wood speci®c dry weight (0.575 g

Table 1. Symbols, de®nitions and units of the model parameters

Results of the sensitivity analysis performed on the parameter values estimated for the `Suncrest' cultivar by Lescourret et al. (1998) arepresented. The origin of the parameter values used in these simulations is mentioned.

ParameterDe®nition Unit Results of the sensitivity analysisa Origin

Light-load Heavy-load d

Leaf assimilationr1 Leaf structural mass/leafy shoot

structural massDimensionless 3.36b 7.6b x Experiments

SLA Speci®c´leaf area m2 g±1 29.22 30.73 x Experimentsp1 Light-saturated maximal leaf

photosynthesismmol CO2 m±2 s±1 34.55 51.22 x Experiments

p2 Concerns leaf photosynthesisregulation by reserves

mmol CO2 m±2 s±1 ±4.03 ±2.71 Ben Mimoun, 1997

r2 Leaf reserve mass/leafy shootreserve mass

Dimensionless ±1.56b ±1.12b Experiments

p3

p4

Concerns the calculation of leafphotosynthesis from radiationand light-saturated photosynthesis

mmol CO2 m±2 s±1

mmol CO2 mmol photon±1

±5.87

±21.78

±14.55

±37.04

x

x

Higgins et al., 1992

Higgins et al., 1992Fruit assimilationPf

max Light-saturated fruit photosynthesis mmol CO2 g±1 s±1 ±0.62c ±4.05c Lescourret et al., 1998Radiation in the shadep7 Concerns the calculation of

radiation received by shaded leavesmmol photon m±2 s±1 4.8 13.58 x Lescourret et al., 1998

p8 mmol photon m±2 s ±1 0.94 2.2 Lescourret et al., 1998r3 Dimensionless 3.38 10.5 x Lescourret et al., 1998

Reserves of assimilatesr4 Leafy shoot mobile fraction of reserves Dimensionless 3.23 0.36 Ben Mimoun, 1997r5 1-year-old stem mobile fraction of reservesDimensionless 3.28 3.13 Ben Mimoun, 1997r6 Threshold ratio of reserves in the leaves Dimensionless 0 0 Ben Mimoun, 1997

Maintenance respiration demandMRRb

st

MRRbOst

MRRleaf

MRRfruit

Maintenance respiration rate of1-year-old-stem (st), current-yearstem (Ost), leaf and fruit compartmentsat the reference temperature

g CHO g±1 s±1

g CHO g±1 s±1

g CHO g±1 s±1

g CHO g±1 s±1

±0.99±0.52±0.41±0.35

±1.51±1.14±1.47±3.3

Grossman and DeJong, 1994aGrossman and DeJong, 1994aGrossman and DeJong, 1994aDeJong and Goudriaan, 1989

Qst b10

QOst b10

Q10leaf

Q10fruit

Q10 value for 1-year-old-stem (st),current-year stem (Ost), leaf andfruit compartments

DimensionlessDimensionlessDimensionlessDimensionless

±0.17±0.07±0.06±0.05

±0.32±0.27±0.36±0.75

Grossman and DeJong, 1994bGrossman and DeJong, 1994bGrossman and DeJong, 1994bDeJong et al., 1987

Fruit growth demandddmax Threshold values concerning fruit growth Degree-days 99.17b 89.7b x ExperimentsGRCfruit Growth respiration coef®cient of fruit g g±1 ±1.83 ±7.43 x DeJong and Goudriaan, 1989RGRf

ini Initial relative fruit growth rate Degree-days±1 77.89 32.94 x Experiments

a Results were expressed by the relative variation in fruit dry mass at harvest in response to 100% of variation in the parameter value: 1003(DMH±DML)/(DMo), where DMo corresponds to fruit dry mass at harvest with the parameter value corresponding to the `Suncrest' cultivar. DMH and DML correspond tofruit dry mass at harvest with high and low parameter values. These values were set to 650% of the default value.

b The range of values was adapted to ®t the parameter de®nition and the range of values measured. For r1 and r2, the values of 0.7 and 1 were testedinstead of 0.35 and 1.05 since the lowest value measured was 0.72 and the highest one was 1. For ddmax, 1200 and 2000 were tested instead of 800 and2400.

c In the case of Pfmax, the default value and zero were taken as high and low values of Pf

max.d The model was considered very sensitive to a parameter (x) when the sensitivity criterion exceeded 5% in absolute value for one of the two crop loads.

1616 Quilot et al.

cm±3). Since the sensitivity study conducted by Lescourret et al.(1998) showed that errors in assessing the initial reserves of leafyshoots 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-oldstems. As regards light interception, the model requires two series ofhourly coef®cients in order to take into account assimilationreduction due to the shade effect (Lescourret et al., 1998). The®rst one characterizes the mutual shading of leaves occurring withina shoot and the second one the mean light environment of a shoot.Since leafy shoot growth was arrested, the former was taken to beconstant throughout the period. Each coef®cient of the latter isassumed to decrease linearly from a value of 1, at the bloomingperiod (shade is nil), towards a threshold reached when there is nomore vegetative growth in the tree, and then to level off (Lescourretet al., 1998). Both series of coef®cients were calculated using gapfractions derived from digitized hemispherical photographs (GeÂnardand Baret, 1994).

In the model, shoots had to be characterized by two parameters:speci®c leaf area (SLA, m2 g±1), which was estimated from themeasurements 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 foreach genotype (Appendix, Equation 3). All these measurementswere made in the morning.

Photosynthetic response to light levels and stomatal conductancewere measured with two types of portable photosynthesis system.One, ADC±LCA 4, measured photosynthesis at natural radiation.With the second, CIRAS, arti®cial radiation was applied.

Measurements were made on well-expanded sunlit leaves early inthe morning on several dates for each genotype. The maximum leafphotosynthesis value, the parameter p1, was estimated from thesedata (Appendix, Equation 2).

To compute fruit dry matter growth on monitored shoots,relationships between fruit diameter and fruit dry mass were neededfor each genotype. To establish these relationships, ten fruits pergenotype were sampled for non-monitored shoots every 2 weeksthroughout the fruit growth period. After recording fruit cheekdiameter, fruits were subjected to temperatures of 70 °C for 72 h, andthen dry mass was measured.

From the dry mass of fruits grown on the lightly-loaded shoots, theparameters of fruit growth demand were estimated (Appendix,Equations 8 and 9).

Dry mass data of fruits grown on the heavily-loaded shoots werenot used for parametrizing the fruit growth equation. It was used totest model behaviour in the case of limiting source conditions.

Comparison between genotypes

For traits directly derived from measurements, such as r1, SLA, meanmeasured and predicted light-saturated photosynthesis rates, andmean fruit diameter and dry mass, genotypes were compared usingnon-parametric tests for independent samples, since not all the traitswere distributed normally. First, the Kruskal±Wallis test was used.Then, if the null hypothesis was rejected, i.e. none of the genotypeswere equal, Noether's multiple range test was performed todetermine which genotypes were signi®cantly different at the 0.05level.

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=p13[1±exp(±h3x)], was adjusted to light-saturated photosynthesis data as a function of stomatal conductanceusing a non-linear least-squares procedure. The complex model withthe two parameters p1 and h speci®c to each genotype was comparedto the simple model with only two parameters, irrespective of thegenotype. In this statistical comparison, the null hypothesis was thatthe parameter values for p1 and h were the same for all thegenotypes. To test this hypothesis, a c2 test was performed (P <0.05)(Huet et al., 1992).

To ®t the potential fruit growth equation to data of lightly-loadedshoots, a non-linear mixed-effects method for repeated measuresdata was used (Lindstrom and Bates, 1990) which is particularlydesigned to analyse growth curve data. The null hypothesis of nodifference in RGR

between genotypes was tested by comparing the simple model,where the curve varies with the fruits, with a complex model, where

Fig. 2. Light-saturated photosynthesis plotted against photosynthetically active photon ¯ux density (PPFD) for the six genotypes studied.Measurements were taken on well-expanded sunlit leaves early in the morning, on several dates from treatment application to harvest. Data wereacquired with the ADC-LCA 4 portable photosynthesis system (closed circles) under natural radiation and with the CIRAS portable photosynthesissystem (dashes) under arti®cial radiation.

Table 2. Comparison of the genotypes for mean fruit diameterat maturity

Data from fruits of the light-loading treatments only.

Genotype Mean diameter at maturity (mm)

P. davidiana 29.96 aa

SD69 35.48 a bSD40 39.15 b cSD31 41.21 b c dSD17 42.45 c dSummergrand 55.03 d

a In each column, values with the same letter are not signi®cantlydifferent according to Noether's test (P=0.05).

Genotypic variations in fruit growth 1617

the curve varies with the genotypes and fruits. Comparison wasmade using a likelihood ratio test (ANOVA method).

Comparison between observed and predicted data

To compare observations and model predictions, fruit dry massvalues were compared using a mean error of prediction (MEP) foreach fruit load treatment of each genotype. It was de®ned as thesquare root of the `Mean Squared Error of Prediction' criterion(Wallach and Gof®net, 1987):

MEP �

��������������������������������������������������������������Pshoot

Pdate

�predicted ÿ observed�2

Number of observations

vuut

All data analyses were performed with the Splus language (Splussoftware, MathSoft Inc., Cambridge, MA).

Results

The experimental measurements revealed variationsbetween genotypes for both source activity and fruitgrowth. As regards source activity, photosynthesis ratesunder light-saturated conditions were sometimes verylow for P. davidiana and the hybrids (Fig. 2). Fruitdiameter growth, monitored experimentally, showedconsiderable variations among genotypes.Summergrand exhibited very good fruit growth from9 May to harvest (measurement period), whereas P.davidiana fruits had enlarged earlier. Hybrid fruits hadalso enlarged early but, during the measurement periodthey grew more than P. davidiana fruits. SD17, SD31and SD40 fruits reached signi®cantly greater diametersat maturity than P. davidiana fruits (Table 2).

Model adaptation and sensitivity analysis

The model was adapted with respect to three points forthe purpose of this study. Since leafy shoot growth wasarrested in this experiment, leafy shoot growth demand

was set to zero. Fruit photosynthesis, which was shownscarcely to affect the model response, was set to zero.Lastly, the modelling of fruit growth demand wasadapted.

In the model, fruit growth demand depends onpotential dry mass. Accordingly, only data for lightly-loaded shoots were used to estimate growth curveparameters. In the initial Lescourret et al. model,potential fruit mass reaches a plateau at maturity andthe potential fruit growth equation is a mixture oflogistic and temporal factors. In this experiment, fruitgrowth appeared to be exponential after the beginningof the measurements, and most of them stoppedgrowing suddenly at maturity, when the sum ofdegree-days (dd) after bloom reached ddmax. Thus,the equation we used for the potential growth of fruitin terms of degree-days was:

DWpotf

Ddd� RGRini

f �Wf

and

DWpotf

Ddd� 0 if dd � ddmax

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 leafassimilation (Fig. 1). Two others, p7 and r3, were involvedin the expression of radiation received by shaded leaves.The last three, ddmax, GRCfruit, and RGRf

ini, concerned

Table 3. Mean and, when available, standard deviation (between parentheses) of the ®ve parameter values estimated for eachgenotype

Genotype SLA (m2 g±1) p1 (mmol CO2 m±1 s±1) r1 RGRfini

(degree-days±1)ddmax

(degree-days)Estimatedvalues

Mean Values foreach genotypeb

Singlevaluec

P. davidiana 0.010 aa 19.7 0.908 (0.06) b c 5.8e-4 (2.85e-5) a 1350SD17 0.012 a 25.6 0.834 (0.04) a 8.8e-4 (1.5e-4) b c 1550SD31 0.013 a 0.0124 15.3 18.35 0.872 (0.04) a b 8.0e-4 (2.12e-5) a b 1550SD40 0.012 a 18.3 0.927 (0.02) c 9.4e-4 (6.7e-5) b c 1400SD69 0.012 a 21.1 0.878 (0.04) a b c 7.6e-4 (1.0e-4) a b 1600Summergrand 0.015 a 20.9 0.887 (0.03) b 1.55e-3 (2.5e-4) c 1500

a In each column, values with the same letter are not signi®cantly different according to Noether's test (P=0.05).b Values of the parameter p1 derived from the complex model with two parameters speci®c to each genotype.c Values of the parameter p1 derived from the simplest model with two parameters independent of each genotype.

1618 Quilot et al.

fruit growth demand. Of these ten parameters, ®ve couldnot be measured (GRCfruit, p3, p4, p7, and r3). Their rangeof variation and effect will be discussed later.

Comparison between genotypes andparametrization

With regard to the ®ve remaining parameters (SLA, p1, r1,ddmax, RGRf

ini), it was tested whether their values weresigni®cantly different between the genotypes. Values ofthe other 20 parameters, for which the model was sensitiveto only ®ve (Table 1), were taken from the literature. The

origin of the parameter values used in the simulations isgiven in Table 1.

The values of SLA did not differ signi®cantly from onegenotype to another (Table 3). In the model, the valueaveraged for all genotypes (SLA=0.0124 m2 g±1) wastherefore used.

The parameter p1 is the maximum value of light-saturated leaf photosynthesis in the absence of leafreserves. The plateau reached when radiation increases isgenerally used to estimate the p1 value. This method couldnot be used because photosynthesis rates were low inexpected saturating radiation (Fig. 2). However, photo-synthesis appeared to be closely linked to stomatalconductance. To test whether the plateau (p1) was thesame whatever the genotype, a monomolecular equationrelating photosynthesis to stomatal conductance wastherefore used, with one of the two parameters corres-ponding to the plateau value. In the statistical comparisonbetween the complex model (with parameters speci®c toeach genotype; Table 3) and the simplest model (with onlytwo parameters, independent of the genotype), the nullhypothesis of `no difference between genotypes for p1values' was not rejected. Therefore p1 was set to the valueestimated (18.35 mmol m±2 s±1) by the simplest model, forall the genotypes. Figure 3 presents the experimental dataand the adjusted curve calculated from the simplest model.

Some genotypes differed signi®cantly for r1 values(Table 3). In the model, r1 values speci®c to each genotypewere used. However, the range of these values was lowerthan the range considered in the sensitivity analysis.

The values of ddmax were calculated from the fruitmaturity date for each genotype. RGRf

ini was estimated by®tting dry mass data as an exponential function of degree-days, for each genotype, using non-linear mixed-effectsmodels. A simple model, where the curve varies withfruits, was compared with a complex model, where thecurve varies with genotypes and fruits. In the latter, RGRf

ini

parameters had a ®xed component, depending on thegenotype, and a random component. The null hypothesis ofno genotype differences for RGRf

ini was rejected by alikelihood test ratio (P value=2.66e±15). Thus, the com-

Fig. 4. Genotypic variability in relative potential fruit growth.Potential fruit growth per unit of initial fruit dry mass (g g±1) isplotted against thermal time. The equation used for the potential fruitgrowth (g) in terms of degree-days was: DWf

pot/Ddd=RGRfini3Wf and

DWfpot/Ddd=0 if dd > ddmax, where RGRf

ini is the initial relativegrowth rate (dd±1) and Wf fruit weight (g). ddmax corresponds to themean fruit maturity date for each genotype. Parameter values of theequation for potential growth were estimated for each genotype fromdata for the light-loading treatment only (limiting sink conditions).

Fig. 3. Relationships between light-saturated photosynthesis and stomatal conductance for the six genotypes studied. Measurements were taken onwell-expanded sunlit leaves early in the morning, on several dates from treatment application to harvest.

Genotypic variations in fruit growth 1619

Fig. 5. Mean dry mass per fruit of each shoot monitored. (Open circles) Observed values for lightly-loaded shoots (A) and (closed circles)observed values for heavily-loaded shoots (B). The dotted line shows the values predicted by the model for each shoot monitored. (C) Predictedvalues at each date of measurement plotted against corresponding observed values, for lightly-loaded shoots (closed circles) and heavily-loadedshoots (open circles). Mean error of prediction (MEP) for each treatment and each genotype are indicated in the low right-hand corner of thecorresponding plot.

1620 Quilot et al.

plex model was kept and the values of RGRfini were

reconstituted from random and ®xed effects data for eachfruit, and the mean and standard deviation was calculatedfor each genotype. Noether's multiple range test showedthat the RGRf

ini values of P. davidiana and ofSummergrand were signi®cantly different (Table 3).SD69 and SD31 differed signi®cantly fromSummergrand, and SD17 and SD40 appeared to bedifferent from P. davidiana. However, no signi®cantdifference was found between the four SD hybrids. Forthe RGRf

ini values six different values were taken, corres-ponding to the mean for each genotype. To emphasizedifferences in fruit demand resulting from RGRf

ini differ-ences between genotypes, the potential growth curves ofthe different genotypes per unit of initial fruit dry masswere plotted (Fig. 4). Potential growth was very low for P.davidiana and intermediate between the parent levels forthe hybrids.

Values used in the model for SLA, p1, r1, ddmax, andRGRf

ini are reported in Table 3.

Comparison between observed and predicted data

Mean dry mass growth per fruit was predicted by themodel for each lightly-loaded shoot monitored and com-pared to that observed experimentally (Fig. 5A). Theequation of fruit demand for growth used in the modelappeared to be very robust since it made it possible tosimulate the overall shape of fruit growth curves forgenotypes with very different growth patterns. The MEPvalue was always less than 2.28 g for fruit dry mass valuesranging from 22.81 to 27.13 g.

The model was able to reproduce fruit growth forheavily-loaded shoots (Fig. 5B). This can be considered asuccessful test of the model since this treatment had notbeen used for parametrization. Lastly, the model accur-ately predicted the magnitude of growth variations within atreatment, which depended on the genotype. These vari-ations explained most of the variations in fruit mass atmaturity probably because they partly determined fruitdemand.

Figure 5C, plotting predicted data against observed data,further illustrates the consistency between observationsand simulations for both loading treatments.

Variations in genotype response to load levels

A fruit load treatment effect appeared only in the case ofSummergrand, for which fruits of heavily-loaded shootsgrew more slowly than fruits of lightly-loaded shoots. ForP. davidiana and the hybrids, the heavy-loading leveltreatment applied to the shoots was not severe enough toplace them under limiting source conditions. Differencesin initial fruit mass, already observed between fruit loadingtreatments by the time simulations were started (400degree-days after ¯owering), did not vary with time. Thesedifferences seemed to determine differences in fruit massat harvest. The major effect of treatment was hypothesizedto occur at the beginning of growth, between treatmentapplication and the beginning of the simulations (Table 4).

Table 4. Comparison of measured fruit dry mass between loading treatment for two different dates: 22 April 2000, 2 d afterapplying the loading treatments and 9 May 2000, the date at which fruit dry mass may be inferred from fruit diameter andsimulations begin

Mean and standard deviation of mean fruit dry mass (between parentheses) are presented. For most genotypes, differences are signi®cant on 9May, i.e. 2.5 weeks after applying the treatment.

Genotypes 22 April 2000 9 May 2000

Lightly-loaded shoots Heavily-loaded shoots Lightly-loaded shoots Heavily -loaded shoots

P. davidiana 1.11 (0.26) 1.09 (0.20) 3.07 (0.53) 2.67 (0.58)Summergrand 2.70 (0.54) 2.45 (0.58) 5.34 (0.98) 3.18 (0.54)a

SD17 0.82 (0.13) 0.74 (0.13) 3.41 (0.69) 2.49 (0.15)a

SD31 0.63 (0.10) 0.56 (0.12)a 3.67 (0.32) 2.75 (0.58)a

SD40 0.53 (0.06) 0.51 (0.06) 2.19 (0.36) 1.74 (0.38)a

SD69 0.48 (0.07) 0.47 (0.06) 2.60 (0.33) 1.90 (0.19)a

a Indicates signi®cantly different values between the two treatments for each date (Noether's test, P=0.05).

Table 5. Mean and standard deviation (between parentheses)of measured light-saturated photosynthesis rates after 400degree-days and of predicted P1

max values (mmol CO2 m±2 s±1)

Genotype Measured P1max a Predicted P1

max

P. davidiana 5.22 (4.59)b ac 4.84 (1.36) aSD40 7.34 (3.82) b 7.03 (3.85) a bSD31 7.66 (4.43) b 8.28 (2.47) bSD17 7.82 (3.70) b 7.45 (3.22) bSD69 11.11 (4.83) c 6.46 (1.44) a bSummergrand 15.10 (4.88) d 14.45 (4.03) c

a Mean from data recorded over about 10 different days.b Standard deviation of the mean presented in parentheses.c In each column, values with the same letter are not signi®cantly

different according to Noether's test (P=0.05).

Genotypic variations in fruit growth 1621

To test this hypothesis, the model was run with the sameinitial fruit mass for all genotypes. Leaf area per fruit wasthe 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 notsigni®cant and fruit growth followed the same growthpattern whatever the treatment. For these genotypes, fruitdemand seemed to be limiting, both for heavily andlightly-loaded shoots.

Major physiological processes responsible for thevariation in growth between genotypes

The ®ve parameters studied (SLA, p1, r1, ddmax, andRGRf

ini) made it possible to predict variability between thegenotypes studied accurately. To show the processesresponsible for the main variations between genotypes,the range of parameter values for the various genotypeswere considered further.

Of the ®ve parameters studied, the three involved insource activity (SLA, p1, r1) either did not signi®cantlydiffer from one genotype to another (SLA and p1) orexhibited small variations between genotypes (r1). Indeed,when the actual value of r1 estimated for each genotypewas replaced by the bounding values for r1 in theexperiment, the fruit dry mass at harvest was barelymodi®ed. The relative variation in fruit dry mass at harvest(1003(DM±DMo)/DMo) did not exceed 0.21% for any ofthe genotype shoot loads. Therefore, it could be concludedthat fruit growth demand was the main physiologicalprocess responsible for the variability in fruit growthbetween the genotypes.

Model contribution explaining the low rates of light-saturated photosynthesis observed for P. davidianaand the hybrids

To assess whether fruit demand limitation was more likelyto be involved than source activity limitation, despite lowphotosynthesis levels, a study was made of the output ofthe model for P1

max (mmol CO2 m±2 s±1), the predicted light-

saturated leaf photosynthetic rate altered by leaf accumu-lation of reserves. The predicted values of P1

max werequalitatively consistent with the measured light-saturatedphotosynthesis rates (Table 5). Whatever the P. davidianashoot considered, photosynthesis never reached p1 (Fig.6). Even in the case of heavily-loaded shoots, fruit demandand photosynthesis were low and leaves stored carbohy-drates. For SD69 and SD31 and to a lesser extent for SD17and SD40, a similar scenario happened (Fig. 6). For thelatter three, fruit demand of some shoots was suf®cient forreserves to decrease towards zero and for photosynthesis tobecome closest to p1 at the end of growth. This was thegeneral case for Summergrand shoots whatever their load.In Summergrand shoots, fruit demand at the end of growthwas high enough to mobilize C assimilates from reservesand to increase maximal photosynthesis to p1.

Discussion and conclusion

Theser results strongly suggest that differences in fruitgrowth between genotypes were due to limitation in fruitdemand. Low photosynthetic activity observed for P.davidiana and the hybrids was a consequence of low sinkdemand and not the cause of limited fruit growth. Asregards the limitation of stomatal conductance for P.davidiana and the hybrids, it can be hypothesized that itwas also a consequence of low sink demand. A possibleeffect of girdling may be invoked. Thus, preventingphloem transport could favour reserve accumulation inthe shoot, which would otherwise be exported to otherparts of the tree. However, a few measurements ofphotosynthesis, on shoots without girdling, show situationswhere stomatal conductance remains low (data not shown).

Other hypotheses, anaerobiosis and root restriction,which could have occurred under these container-growingconditions, seemed to be less consistent in explaining lowexperimental values for photosynthesis rates. Indeed,stomatal conductance and photosynthesis rate values forSummergrand were not so low, though all genotypes were

Fig. 6. Predicted values for the actual light-saturated leaf photosynthetic rate as altered by leaf accumulation of reserves (P1max) for the different

genotypes. P1max for leaves of the heavily-loaded shoots (dashed line) and lightly-loaded shoots (solid line). The upper line represents the

maximum value of estimated light-saturated leaf photosynthesis (p1=18.35).

1622 Quilot et al.

grafted on to the same rootstock and managed in the sameway. Reduction in leaf photosynthesis as a result of leafstarch accumulation is also supported by numerous studies.Ben Mimoun (1997) observed very low leaf photosyn-thesis values and leaf starch accumulation in peach shootswithout fruit. Physiological and biochemical studies onvarious species have suggested that photosynthesis isfeedback-regulated by the accumulation of carbohydratesin source leaves (Azcon-Bieto, 1983; Foyer, 1988; Sawadaet al., 1986; Goldschmidt and Huber, 1992). This feedbackinhibition mechanism may explain the low photosynthesisrates of P. davidiana and the hybrids in which fruit growthwas limited and photosynthesis activity slowed down earlyin the morning even, though water stress was negligible.

Parameters that were not measured, i.e. GRCfruit, p3, p4,p7, and r3, were unlikely to in¯uence the model outputs,since variations in these parameters are expected to be lowwithin closely related species. The fruit growth respirationcoef®cient, GRCfruit, was taken from DeJong andGoudriaan (1989). The inter-speci®c variations in thisparameter are not considerable. For tomato, the valueestimated by Penning de Vries et al. (1989) was 0.112 g Cg±1 DW and, for cucumber, the estimated value was 0.043g C g±1 DW (Marcelis and Baan Hofman-Eijer, 1995). Asregards intra-speci®c variations, for seven apple cultivars,values ranged between 0.053 and 0.060 g C g±1 DW anddid not differ signi®cantly (Walton et al., 1999). Withrespect to peach cultivars, GRCfruit was found to be similarfor an early (`June Lady') and a late-maturing (`O'Henry')cultivar (DeJong et al., 1987).

p3 and p4 are parameters of the equation used tocalculate photosynthesis per unit leaf area and per unit time(P, mmol CO2 m±2 s±1) from the photosynthetically activephoton ¯ux density, PPFD (input data, mmol photon m±2

s±1). They are taken from the formulation of Higgins et al.(1992) who described the net photosynthetic response toPPFD for different plants, including peach (Prunuspersica L. Batsch. cultivar `Red Haven'). Of the plantstested by Higgins et al. (1992), the three stone fruit species,almond, olive and peach, showed quite similar p3 and p4values (respectively, 3.0337, 2.8284 and 2.2048 for p3 and0.0576, 0.0580 and 0.0580 for p4). The variability shouldnot be higher between the commercial peach P. davidianaand the hybrids than between almond, olive and peach.Thus, it can be assumed that p3 and p4 values forSummergrand, P. davidiana and the hybrids are close toeach other and to those for Red Haven (2.2048 and 0.0580,respectively).

The parameters p7 and r3 are used to calculate theradiation received by shaded organs (PPFDshaded) and ofsunlit organs (PPFDsunlit) and assessed by Lescourret et al.(1998) in the cultivar Suncrest. The variability in theseparameters within a species or between two related specieswas not studied.

Low potential fruit growth, as suspected for P.davidiana and the hybrids, is consistent with the produc-tion of a large number of fruits each enclosing a singleseed. This behaviour can represent a selective advantageand is quite typical among wild and slightly domesticatedspecies, such as P. davidiana, the dispersion of whichdepends on fruit transport by animal consumers (Janzen,1983). In the case of a single big seed, the protective role ofthe fruit seems to be more important than its attractionfunction and the number of fruits more important than theirsize. Low fruit growth after stone formation could alsoallow reduced competition between vegetative and fruitgrowth during late spring and summer. Thus, survival ofthe tree and dispersion of the species could both besatis®ed. hypotheses can be formulated on the physio-logical processes that are responsible for the low fruitdemand. It may result from the preferential partitioning ofcarbohydrates towards the stone during the ®rst stages offruit growth. The observation of early stone formation in P.davidiana supports this view. Variations in cell number orcell size could also explain low fruit demand. Fruit size hasbeen regarded as a function of cell number in the earlystages of development and cell size in the ®nal stages offruit growth, after pit-hardening (Batjer and Westwood,1958; Westwood et al., 1967). Differences in fruit sizebetween peach cultivars have been shown to be due todifferences in mesocarp cell count that are determinedearly in the growth of the ovary (Scorza et al., 1991). Themajor effect of the experimental treatments at the begin-ning of growth emphasized the bene®ts of studying theearly stages of fruit growth.

The evaluation of the genotypes appeared more relevantunder conditions of lightly-loaded shoots. In fact, differ-ences in fruit growth between genotypes were morepronounced under these conditions. Moreover, theseconditions can be reproduced easily, whatever thegenotype, year or site. From potential growth data, themodel made it possible to predict growth for heavily-loaded shoots, taking environmental conditions intoaccount.

Simulations and experimentations allowed the iden-ti®cation of two parameters linked to fruit demandwhich appeared to predict fruit growth variationsbetween genotypes accurately. These parameters couldnow be used to characterize genotypes and theirgenetic control could be studied. For this purpose,ecophysiological parameters would be scored among alarge progeny and a QTL search would be performed.Such works have already been performed at themolecular level in order to study metabolic control.For example, metabolic ¯uxes in the cell wereconsidered as model traits for quantitative genetics(Bost et al., 1999). This QTL analysis approach toecophysiological traits stemming from models shouldmake it possible to explain the variations in a complex

Genotypic variations in fruit growth 1623

trait by a series of parameters derived from the modeland likely to be linked to few QTL and moreindependent of the environment. Finally, this approachmakes it easier to understand the genetic determinismand to select this trait.

Acknowledgements

We gratefully acknowledge J Hostalery, V Serra, R Laurent, and MAuge for their assistance in the ®eld experiments used in this paper,and T Pascal and F Pfeiffer, who allowed us to bene®t from theirfamiliarity with the trees studied. We are indebted to B Ney forhelpful discussions and to two anonymous reviewers for help inimproving this paper. We thank AM Wall for improving the English.

Appendix

The main equations used in the model to predict fruit growth from Cassimilation and allocation are described. The model parameters, inbold italics, are de®ned in Table 1.

Leaf assimilation

The total leaf area LA (m2) of a stem is computed from the dry massof the structural part of the leafy shoots, WSls (g), and the speci®cleaf area, SLA (m2 g±1), as follows:

LA = WSls 3 r1 3 SLA (1)

Light-saturated leaf photosynthesis P1max (mmol CO2 m±2 s±1) is

modulated by the level of reserves in the leaves:

Pmax1 � p1ÿ p2

WR1

WR1 �WS1

� ��2�

where WRl and WSl denote the dry masses of reserves and ofstructural parts in the leaves, respectively. The model assumes thatWRl is a constant proportion of the dry mass of reserves in the leafyshoots, WRls (g):

WRl = r2 3 WRls and according to (1): WSl = r1 3 WSls (3)

Photosynthesis per unit leaf area and per unit time is calculatedfrom the photosynthetically active photon ¯ux density (PPFD, mmolphoton m±2 s±1):

P1 � �Pmax1 � p3� � 1ÿ e

ÿp4� PPFD

Pmax1 � p3

� �� �ÿ p3 �4�

Fruit assimilation

Photosynthesis per unit fruit mass and per unit time is a function ofdegree-days after full bloom (dd), fruit dry mass, Wf (g), and PPFD:

Pf= Pfmax 3f(dd, Wf, PPFD) (5)

Radiation in the shade

PPFD is modulated in the case of shaded leaves:

PPFDshaded = p7 3 (1 ± e±p8 3 PPFDsunlit) + r3 3 PPFDsunlit (6)

and total leaf area, LA, is separated into a sunlit and a shadedcomponent.

C assimilation

Lastly, the amount of C produced by leaf photosynthesis during theday, Clp (g d±1), is computed as the sum of hourly photosynthesis bysunlit and shaded leaves. k is the conversion coef®cient (0.0432)from mmol CO2 s±1 to g h±1.

Clp �Xh�

Psunlit1 � LAsunlit

!�

Xh�

Pshaded1 � LAshaded

!" #� k

�7�

In the same way, the photosynthetic contribution of fruits isseparated 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:

Cfp �Xh�

Psunlitf �W sunlit

f

!�

Xh�

Pshadedf �W shaded

f

!" #� k

�8�

Reserve mobilization

If the amount of carbohydrates available from current photosyn-thesis is less than the amount required by the system, a mobileamount of reserves can be mobilized from the leafy shootcompartment.

r43CCls (g d±1) (9)

If it is insuf®cient, additional reserves from the 1-year-old stemmay be used

r53CCst (9¢)

CCls and CCst are the carbon content of the storage part of the leafyshoots and the 1-year-old stem, respectively.

Maintenance respiration demand

Maintenance respiration demand MR (g d±1) is calculated from theQ10 concept, in the same way as for the different organ groups (i), 1-year-old stem, current-year stem, leaves and fruits:

MRi �MRRi � �Qi10�

�ÿ �ref

10�Wi � �3600�H� �10�

where MRRi is the maintenance respiration rate (g g±1 s±1) of organ iat reference temperature qref (°C), Q i

10 is the Q10 value for organgroup i, q is the mean temperature of the day (°C), Wi (g) is the drymass of the organ group (i), and 36003H is the conversioncoef®cient from seconds to days. H=24 for any group except theleaves, for which only dark hours are considered.

Fruit growth demand

Daily carbon demand D (g d±1) for fruit growth can be written as:

1624 Quilot et al.

D � DWpotf

Ddd� Ddd

Df� �CCfruit � GRCfruit� �11�

where DWfpot/Ddd (g dd±1) is the potential growth rate in terms of

degree-days after full bloom dd, CCfruit and GRCfruit the carbonconcentration and growth respiration coef®cient of fruit, respect-ively (dimensionless). Ddd /Dt (dd d±1) is entered as a series of valuesin order to convert data from days to degree-days.

Potential fruit growth in terms of degree-days was calculatedincluding an effect of fruit mass, Wf (g), representing sink size andddmax (dd), the sum of degree-days corresponding to fruit maturity:

DWpotf

Ddd� RGRini

f �Wf andDW

potf

Ddd� 0 if dd � ddmax �12�

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