2.5.3 Modeling of Fruit Quality
A wide range of mathematical models has found their application in the wider food
area (Tijskens et al. 2001). Important quality traits are manifested at the fruit scale.
This is especially true for fruit size, dry matter content, and percentage of edible
tissues. Fruit size and dry matter content result from the exchange of resources
with the plant and the atmosphere. The carbohydrate supply has often been
modeled according to the source/sink concepts (Léchaudel et al. 2005). An
important variable of these models is the fruit demand for carbohydrates which is
positively correlated to the seed number (Lescourret et al. 1998). In some models,
a more mechanistic approach has considered that processes involved in sugar
unloading from the phloem to the fruit tissues. For example, Fishman and Génard
(1998) and Bruchou and Génard (1999) modeled sugar phloem unloading through
mass flow, diffusion, and active transport.
In a postharvest context, the gas (O 2 , CO 2 , ethylene, and water vapor) fluxes
through the skin have been related to the concentrations gradients, according to
physical laws of gas diffusion. A model of fruit surface conductance to water vapor
has been proposed recently (Gibert et al. 2005), which could improve the prediction
of fruit transpiration as a function of fruit growth. More generally, fruit surface
conductance to gas needs to be modeled in the future because it has a strong
implication for fruit quality through its effect on fruit physiology, ripening, and
quality (Paul and Srivastava 2006). Biomass allocation to the fruit tissues (which
determines the percentage of edible tissues) also needs to be considered at the fruit
scale. However, to our knowledge, there is no mechanistic model of biomass allocation into fruit tissues. Establishing empirical laws relating the size of any given
tissue to that of another one or to that of the whole fruit may be a solution. Such laws
are common in biology, mainly in the framework of allometric growth (West et al.
1997). For example, the dry masses of each fruit tissue and the dry mass of the fruit
have been linked by allometric relationships (Lescourret and Génard 2005).
In order to assess the key processes underlying sugar concentration, an approach
combining ecophysiological modeling and quality trait loci (QTL) analysis was
proposed by Prudent et al. (2010). For this purpose, a first model predicting tomato
fruit sugar concentration was adapted from a previous model built on peach fruit
(Quilot et al. 2004), allowing the dissection of three interrelated elementary processes: the assimilate supply provided to the fruit, the metabolic transformation of
sugars into other compounds, and the dilution of sugars by water uptake. In this
work, two sources of variation were used to modulate the sugar concentration: a
genetic method and a physiological method. This approach allowed observation of
the inter-genotypic relationships first among elementary processes and then
between elementary processes and sugar concentration; estimation of whether two
different sources of variation for sugar concentration lead to similar changes in the
underlying processes; and identification at each QTL for sugar concentration those
processes which were supposedly involved.
2 Mathematical Modeling of Biosystems
69
A wide range of mathematical models has found their application in the wider food
area (Tijskens et al. 2001). Important quality traits are manifested at the fruit scale.
This is especially true for fruit size, dry matter content, and percentage of edible
tissues. Fruit size and dry matter content result from the exchange of resources
with the plant and the atmosphere. The carbohydrate supply has often been
modeled according to the source/sink concepts (Léchaudel et al. 2005). An
important variable of these models is the fruit demand for carbohydrates which is
positively correlated to the seed number (Lescourret et al. 1998). In some models,
a more mechanistic approach has considered that processes involved in sugar
unloading from the phloem to the fruit tissues. For example, Fishman and Génard
(1998) and Bruchou and Génard (1999) modeled sugar phloem unloading through
mass flow, diffusion, and active transport.
In a postharvest context, the gas (O 2 , CO 2 , ethylene, and water vapor) fluxes
through the skin have been related to the concentrations gradients, according to
physical laws of gas diffusion. A model of fruit surface conductance to water vapor
has been proposed recently (Gibert et al. 2005), which could improve the prediction
of fruit transpiration as a function of fruit growth. More generally, fruit surface
conductance to gas needs to be modeled in the future because it has a strong
implication for fruit quality through its effect on fruit physiology, ripening, and
quality (Paul and Srivastava 2006). Biomass allocation to the fruit tissues (which
determines the percentage of edible tissues) also needs to be considered at the fruit
scale. However, to our knowledge, there is no mechanistic model of biomass allocation into fruit tissues. Establishing empirical laws relating the size of any given
tissue to that of another one or to that of the whole fruit may be a solution. Such laws
are common in biology, mainly in the framework of allometric growth (West et al.
1997). For example, the dry masses of each fruit tissue and the dry mass of the fruit
have been linked by allometric relationships (Lescourret and Génard 2005).
In order to assess the key processes underlying sugar concentration, an approach
combining ecophysiological modeling and quality trait loci (QTL) analysis was
proposed by Prudent et al. (2010). For this purpose, a first model predicting tomato
fruit sugar concentration was adapted from a previous model built on peach fruit
(Quilot et al. 2004), allowing the dissection of three interrelated elementary processes: the assimilate supply provided to the fruit, the metabolic transformation of
sugars into other compounds, and the dilution of sugars by water uptake. In this
work, two sources of variation were used to modulate the sugar concentration: a
genetic method and a physiological method. This approach allowed observation of
the inter-genotypic relationships first among elementary processes and then
between elementary processes and sugar concentration; estimation of whether two
different sources of variation for sugar concentration lead to similar changes in the
underlying processes; and identification at each QTL for sugar concentration those
processes which were supposedly involved.
2 Mathematical Modeling of Biosystems
69