The fruit is a hierarchically organized organ composed of cells from different tissues. Its quality, defined by traits such as fruit size and composition, is the result of a complex chain of biological processes. These processes involve exchanges (transpiration, respiration, photosynthesis, phloem and xylem fluxes, and ethylene emission) between the fruit and its environment (atmosphere or plant), tissue differentiation, and cell functioning (division, endoreduplication, expansion, metabolic transformations, and vacuolar storage). In order to progress in our understanding of quality development, it is necessary to analyse the fruit as a system, in which processes interact. In this case, a process-based modelling approach is particularly powerful. Such a modelling approach is proposed to develop a future 'virtual fruit' model. The value of a virtual fruit for agronomists and geneticists is also discussed.

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Approximately 3 weeks after pollination, the water import rate per unit tomato fruit area generally decreases linearly with fruit radius. In order to explain why, in the first 3 weeks, the water import rate of the fruit is lower than predicted by this regression, a model of water flow through the pedicel and a model of water import based on the potential of water entering the fruit and calyx transpiration were formulated. Using data sets available in the literature, these models predict a water potential drop along the pedicel that decreases sharply during the first 3 weeks, while the calculated hydraulic conductivity of the pedicel phloem, which is presumed to be the main pathway of the water imported in the tomato fruit, increases sharply in the lower range of values known for plant phloem conductivity. These models also predict an increase in water import into young fruit when calyx transpiration is decreased, which is consistent with data from the literature. In order to explain the increasing pedicel phloem conductivity, a model of water flow in the pedicel sieve tubes was formulated based on the literature data for the fruit stalk of Lupinus albus. It was suggested that the conductivity might increase because of the development of pores in the sieve plates. Using this hypothesis, the increase in pore radius values within an acceptable range was calculated. This study shows that, under a wide range of conditions, water import in young tomato fruit is limited by the low potential of the water entering the fruit due to pedicel resistance and calyx transpiration. It provides a model to predict young tomato fruit expansion and a testable hypothesis, which can be checked by measuring the size of the phloem component in the fruit pedicel.

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Because it is difficult to obtain transverse views of the plant phloem sieve plate pores, which are short tubes, to estimate their number and diameters, a method based on longitudinal views is proposed. This method uses recent methods to estimate the number and the sizes of approximately circular objects from their images, given by slices perpendicular to the objects. Moreover, because such longitudinal views are obtained from slices that are rather close to the plate centres whereas the pore size may vary with the pore distance from the plate edge, a sieve plate reconstruction model was developed and incorporated in the method to consider this bias. The method was successfully tested with published longitudinal views of phloem of Soybean and an exceptional entire transverse view from the same tissue. The method was also validated with simulated slices in two sieve plates from Cucurbita and Phaseolus. This method will likely be useful to estimate and to model the hydraulic conductivity and the architecture of the plant phloem, and it could have applications for other materials with approximately cylindrical structures.