## 2 Materials and Methods  
### Plant Material and Experimental Design  
Experiment was carried out in spring 2020 (January 30 to June 24) in a greenhouse at Escuela Tecnica Superior Agronomic Engineering (E.T.S.I.A.) located at the University of Sevilla (Seville, Spain, 37\({}^{\circ}\) 21'09.71\" Lat. N, 5\({}^{\circ}\) 56'19.13\" Long. W, 33m a.s.l.). The greenhouse was a multi-tunnel with side and overhead ventilation. Covered with a multilayer sheet of EVA/EBA copolymers (INSASOL PLUS, from Solplast. Lorca, Murcia, Spain). The tomato plants, cultivar Summerbrix (Fito(r)), were grown in clay loam soil characterized by 28% sand; 33% silt and 38% clay; pH 7.36; total nitrogen 0.32%; organic matter 2.08%; electric conductivity 356 \(\upmu\)S/cm (1:5 pV); phosphorus 221 mg/Kg. Climatic conditions were monitored inside the greenhouse. Two sensors recorded mean, maximum and minimum values of temperature (T, \({}^{\circ}\)C) and relative humidity of the air (RH%). These sensors were linked to a data logger (CD-1000 from Campbell Scientific, Logan, UT, USA). The experiment comprised a randomized complete-block design, with two irrigation treatments and four repetitions per treatment. The trial had eight plots, with 30 plants per plot and a density of 2 plants per square meter. Irrigation was done by dripping (4 L-h\({}^{-1}\)), with 2 drippers per square meter, with two daily irrigations. Amount of water was controlled by solenoid valves in each plot. For the irrigation cuts that had the Regulated Deficit Irrigation (RDI) treatment, they were made using the stopcocks placed in each irrigation line. Irrigation treatments applied were:  
* Control: 125% of the crop evapotranspiration (ETc). Reference evapotranspiration (ETo) was estimated according to radiation model for greenhouses [13]. This simple model is well adapted to greenhouse structures in southern Spain [13]. The cultivation coefficients (Kc) of the FAO Manual 56, [PERSON] et al. [14] were used. * Regulated Deficit Irrigation (RDI): This treatment was based on crop water status, with leaf water potential. Treatment started from Day of the Year (DOY) 50, when the first inflorescence appeared. Then, RDI treatments were irrigated according to plant water status. For each phenological state of the crop, different irrigation thresholds:
* PHASE I: From transplantation to the appearance of the second inflorescence. For this phase, a threshold of \(-1\) MPa was established according to [PERSON] et al. [15]. * PHASE II: From the appearance of the second inflorescence until pink tomatoes are observed in the middle of the inflorescences. In this phase, an irrigation threshold of \(-0.85\) MPa was established according to [PERSON] et al. [13]. * PHASE III: From the end of phase III until harvest. For this third and last phase, an irrigation threshold of \(-1\) MPa was established according to [PERSON] et al. [15]. Leaf water potential was measured using a pressure chamber (PMS Instrument Company, Albany, OR, USA). Fully developed and sunny leaves were measured, on one central plant per plot, at solar midday, weekly. Irrigation amount was applied depending on the distance of the water potential of the leaf of each plot to the said threshold, with a maximum limit of \(5\) mm day\({}^{-1}\). ETc maximum estimated for the entire crop. If the reduction was less than 10%, an irrigation dose of 25% of control irrigation was applied. If the reduction was between 10 and 30%, a 50% dose of control treatment was provided. Total amount of water applied in control irrigation treatment was 614 mm and 290 mm for RDI. In order to describe the accumulative effect of the water deficit, the water stress integral (SI) was calculated from the \(\Psi\) data [16] during the period of water stress (Equation (1)). Equation (1) used a reference of \(-\)0.2 MPa. The expression used was:  
\[\mathrm{SI}=\left|\Sigma(\Psi-(-0.2))\right|\,*n \tag{1}\]  
(\(\Psi\): average midday stem water potential for any interval, \(n\): days number in the interval).