Production Practices and Quality Assessment of Food Crops. Vol. 1

which depends on climate and irrigation, was assumed to be inversely proportional
to the maximum daily shrinkage (MDS) of trunks measured using the
micromorphometric method (Huguet, 1985; Garnier and Berger, 1986).
The model assumes that trees are optimally fertilized and that carbon acquisition
by photosynthesis is sufficient for well-irrigated trees to reach full potential fruit
growth. The fruit receives a daily solution flow from the plant (F) and loses water
by transpiration (T) and carbon by respiration (R). Thus growth is
dW fresh = F – R – T
dt
Modelling Fruit Quality 65
Respiration is calculated as in the SWAF model. Transpiration is a function of
fruit mass (W fresh), hourly global solar radiation (GR) and skin area of the fruit
(Génard and Huguet, 1996).
The model assumes that a maximal flow (F max) is determined by the restricted
vascular cross-sectional area of the fruit peduncle. Moreover, the solution flow is
considered to increase and decrease with plant and fruit water potential, respectively,
which has been stated for xylem flow and is thought to be effective for phloem
flow towards the fruit (Lang et al., 1986), though the process involved is more
complex. The water potential of a fruit depends on the osmotic potential of its
cells, which is usually related to sugar content in the fruit, and on the pressure
potential due to the resistance of tissues to deformation. Sugar concentration
increases with fruit transpiration per unit mass and with peach mass as indicated
by Chapman et al. (1991) and Génard et al. (1991). Pressure potential seems to
increase with fruit size (Bussières, 1994). The plant water potential is assumed to
be inversely proportional to MDS.
Consequently, the model assumes that the flow:
– has a maximal value F max;
– increases with fruit mass (W fresh) and with transpiration per unit mass (T w), since
W fresh and T w will cause a decrease in the osmotic potential of the fruit;
– levels off at high fruit size, when the fruit pressure potential compensates for
the decrease in osmotic potential;
– decreases with MDS.
According to the previous assumptions, the flow is computed using the following
empirical equation
F = A 1(1 – e –A2(WfreshTw)A3) with A i = a i
and otherwise F = F max
MDS ( )
MDSo
where A i are empirical functions of the effect of water stress on the daily solution
flow F, and a i, b i and F max parameters. MDSo is a calibration parameter related to
the trunk characteristics of the tree. The product W fresh T w is equal to fruit transpiration
(T), which is an important stimulator of fruit growth in the model.
bi
, if F < F max