Application of logistic model to estimate eggplant yield and dry matter under different levels of salinity and water deficit in greenhouse and outdoor conditions

COPYRIGHT © The Author(s) Published under a Creative Commons Attribution 4.0 International Licence (CC BY 4.0) Eggplant is an important product in greenhouse cultivation in the world. However, much of its production is done on the farm. Few studies have been conducted on modelling of its growth and yield. Considering the simplicity of the logistic models, only the temperature and dry matter data during the growing season are needed to calibrate them. Hence, we evaluated the performance of the logistic model in growth and yield prediction of eggplant in greenhouse and farm conditions. Eggplants were planted in 2012 and 2013 under different treatments of irrigation and salinity with a complete randomized block statistical design. Irrigation frequency treatments consisted of: daily (I1), weekly, (I2) and every 2 weeks of irrigation (I3). Each pot was irrigated to field capacity level. Four levels of salinity treatments are as follows: electrical conductivities (EC) of 0.8 (J1); 2.5 (J2); 5.0 (J3) and 7.0 (J4) dS∙m-1. The amount of plant dry matter was measured during the growing season (DM) and the amount of product (Y) at the end of the growing season. The logistic model was calibrated with the first-year data and validated with the second-year data. Logistic equation coefficients and harvest index were estimated as a function of the depth and electrical conductivity of irrigation water. The results showed that the accuracy of the logistic model for estimating DM during the growing season was good and predicted the product at the end of the growing season with acceptable accuracy. Also, the model’s agreement with the measured DM and Y was good. Application of logistic model to estimate eggplant yield and dry matter under different levels of salinity and water deficit in greenhouse and outdoor conditions


INTRODUCTION
Crop modelling has been gaining momentum over the past decade; partly due to the necessity of sustainable agriculture under environmental degradation along with population growth (Overman and Martin, 2001;Overman et al., 2003;Sepaskhah et al. 2011;Du et al., 2014;Camargo et al., 2015;Ramírez-Pérez et al., 2018). Such models help to assess the most appropriate planning in agro-environmental systems, through optimization of water and fertilizer application and finally maximizing returns to farmers. However, crops are highly dynamic systems emerging from an interface between cultivar factors, environmental conditions and management practices. The interaction of these determinants induces various stress patterns, resulting in different yield and growth patterns (Casadebaig et al., 2016). Deficiency in irrigation water quantity and quality leads to a reduction of water uptake and therewith significant evapotranspiration and yield limitation. Crop yield prediction according to water requirement or evapotranspiration is important in irrigation system design and evaluation (Ünlükara et al., 2010).
However, prearranged reduction of water application at certain stages of the growing season, called deficit irrigation, has been extensively studied and considered as a suitable irrigation strategy in dry regions (Rodrigues and Pereira, 2009;Geerts and Raes, 2009;Ghaemi and Rafiee, 2016). To obtain a precise description of crop growth features, a large number of variables have to be simultaneously taken into consideration, of which many are usually not available. Accordingly, crop models are divided into two general categories: dynamic and empirical (simple) models. Dynamic models simulate plant growth and development processes in relation to environmental factors and the movement of water in the soil. Consequently, these models require a large number of inputs, as model calibration is needed in various segments of such models. Measurement of some environmental factors and the calibration process are financially expensive and time-consuming (Kasampalis et al., 2018). A number of models, namely, WOFOST (Van Diepen et al., 1989), STICS (Brisson et al., 2003), APSIM (Keating et al., 2003), DSSAT (Jones et al., 2003), have been employed by researchers since they were first presented (Jin et al., 2018). In contrast, in empirical models, a detailed look at the mechanism of the environmental factors affecting plant growth is not considered. Instead, these models require fewer inputs. Further, they can be easily calibrated for a given location. Some examples of well-validated models in the country of the present study are presented by Ziaei and Sepaskhah (2003), Pirmoradan andSepaskhah (2006), andShabani et al. (2015). Simple models are still quite attractive to researchers (Basso and Ritchie. 2015), as they require fewer parameters and allow researchers to use literature or limited crop data to provide reasonable estimates of crop components (Dzotsi et al., 2015). Simple crop growth simulation models can be outlined as non-linear functions of a dependent variable (plant height, biomass accumulation or fruit growth dynamics) and an independent variable (time or growing degree days) (Lopez et al., 2000;Ruiz et al., 2012). One commonly used model is the logistic model, based on a sigmoid function of cumulative heat units (Shabani et al., 2015(Shabani et al., , 2018a(Shabani et al., , 2018b.  index (HI) was also related to the applied water and nitrogen as another empirical model. Wardhani and Kusumastuti (2013) showed the superiority of logistic models in describing maize growth height in comparison with the Gompertz model. They suggested two different models for the two distinct stages of plant growth, i.e., vegetative and generative stage. Mahbod et al. (2015) estimated yield and dry matter of winter wheat with the logistic model under different irrigation water regimes and nitrogen application rates. The total irrigation water, rainfall and nitrogen, plus residual soil mineral nitrogen, applied in the logistic model coefficients and the harvest index, predicted above-ground dry matter and grain yield with good accuracy.
Eggplant is an important vegetable crop, produced as 35.3 million tons from 1.9 million ha worldwide. Eggplant is ranked third within the greenhouse products, after tomato, pepper and cucumber. Around 94% of eggplant is produced in Asia (FAOSTAT, http://www.fao.org/faostat/). Despite extensive investigations on cereal crop growth modelling, few researchers have investigated vegetable crops such as eggplant (Keating et al., 2014;Zurayk et al., 1993). However, it is important that the use of low-quality water and its effect on crop growth dynamics should be taken into consideration, given ever-increasing water supply limitations throughout the world. For example, Assaha et al. (2013) assessed the salinity tolerance of eggplant under two levels of salinity stress. Abd El-Azeem et al. (2012) elucidated the effects of inoculation with plant growth-promoting rhizobacteria on eggplant growth, yield, and mineral content under salt stress. Therefore, this study aims to use the logistic model to simulate the effect of salinity and drought stresses on eggplant yield and above-ground dry matter in greenhouse and outdoor cultivation environments.

Experimental procedure
On 5 May 2012 and 18 May 2013, uniform seedlings of eggplant (Anamur RZ cultivar) were transplanted to both the field and plastic pots in the adjacent greenhouse located in Badjgah (29°36'N, 52°32'E), College of Agriculture, Shiraz University, Shiraz, Iran.
Each pot (with 35 cm diameter and 60 cm height), filled with the same field soil from the same depth, functioned as a microlysimeter. Some physical and chemical properties of the soil are presented in Table 1. Before transplanting, 1 g mono-ammonium phosphate was added to each soil pot, and 1 g, 0.5 g and 0.5 g potassium nitrate was applied to each pot, respectively, in the three different stages of the growth period (i.e. transplant, beginning of flowering and start of harvest). Weather parameters including net radiation (R n ), air temperature (T a ) and relative humidity (RH) were collected simultaneously from two automatic stations installed inside and outside the greenhouse. Changes of such parameters during the experimental periods are shown in Fig. 1.
Irrigation and salinity treatments were initiated after the establishment of plants (14 days after transplanting). The experiment was laid out according to a complete randomized design with 3 replicates per treatment. Irrigation frequency treatments consisted of: daily (I 1 ), weekly (I 2 ) and every 2 weeks of irrigation (I 3 ). Each pot was irrigated to the soil field capacity level. Four levels of salinity treatments were as follows: electrical conductivities (EC) of 0.8 (J 1 ); 2.5 (J 2 ); 5.0 (J 3 ) and 7.0 (J 4 ) dS•m -1 . Pots were weighed prior to each irrigation, and the weight of irrigation water amount (W I ) was computed as: where W and W FC are each pot weight (g) just before irrigation and at field capacity, respectively. W FC is calculated as the weight summation of plastic pots (W plastic pots ), dry soil (W dry soil ), water at field capacity (W θFC ) and plant (W plant  (2) W plastic pots , W dry soil and W θFC (ρ b × θ FC × soil volume) were defined at the beginning of the experiment and W plant was assessed using pot weight (W total ) and soil moisture (θ i−1 ) a day before irrigation as: where W θi1 is mass of soil water 1 day before irrigation, calculated as ρ b × θ i−1 × soil volume. Leaching fraction (LF) of 0.15 was considered for efficient irrigation as proposed by Ayers and Westcot (1985). Leachate was gathered and weighed after irrigation using empty pans placed underneath each pot. Table 2 shows the number of irrigations and total water applied in the outdoor and greenhouse treatments.
Crop dry matter (DM) was determined during 7 stages at 2-week intervals including harvest time. Seven extra pots were reserved for each treatment, the plants from which were used to measure dry matter at 6 stages during the growing season. Fruits per plant were gathered and weighed during August and September. Shoot and root dry weights were determined next. It should be noted that in eggplant cultivation there is the possibility of periodic and continuous harvests after the first crop. Therefore, harvest index values were calculated as the ratio of fruit weight at the first harvest to weight of above-ground dry matter.

Model theory
Logistic models using 'calendar days after planting' as the independent variable, may provide unsatisfactory estimates in regions with different climatic conditions (Mahbod et al., 2015). On the other hand, temperature is one of the most important factors governing plant growth (Sadek et al., 2013). Growing degree-days is considered as an important factor for all biological development due to its simple estimations of the accumulated heat energy available over the growing season or life cycle of an organism. The rate of growth and phenological development of individual plants has been found to increase almost linearly from a base to a limiting temperature threshold (Cesaraccio et al., 2001;Fealy, 2008). Therefore, to designate variable environmental conditions during growing season and planting dates, cumulative heat unit (GDD) was calculated as follows: where T min and T max are the daily minimum and maximum air temperature at Day i (°C), T b is the base temperature of 11°C according to Rouphael et al. (2010). No degree days were considered for days with average temperatures equal or below T b .
Distinct plant features such as crop height, canopy, population and biomass growth can be modelled by 'S-shaped' logistic functions of GDD as below (Shabani et al., 2018a): In this study, Y is considered as eggplant DM, and K, A, B and C are coefficients of the equation. In the calibration phase, K, A, B and C were determined using DM values measured in the first year of the experiment by Solver tool in MS Excel. These coefficients were then fitted to quadratic functions of seasonal applied water (I) and water salinity (EC) via stepwise multiple regression analysis. The calibrated experimental logistic model was then used to estimate eggplant DM for the second year. Finally, the predicted DM values were compared with the measured values in order to validate the model in the greenhouse and outdoor environments.

Statistical evaluation
Statistical parameters used to describe the model accuracy were coefficient of determination (R 2 ) (interpreted as the proportion of the variance in the dependent variable that is predictable from the independent variable, indicating the extent to which the dependent variable is predictable), normalized root mean square error (NRMSE), index of agreement (d) and F-test (Willmott et al., 1985): where P i and O i are the predicted and observed values, respectively, n is the data number, Ō and P are the observed and predicted mean values, respectively. The simulation is considered excellent with a NRMSE less than 0.1, good if the NRMSE is greater than 0.1 and less than 0.2, fair if the NRMSE is greater than 0.2 and less than 0.3, and poor if the NRMSE is greater than 0.3 (Jamieson et al., 1991;Mahbod et al., 2015). According to the d-index, the closer the index value is to 1, the better the agreement between the two variables that are being compared and vice versa. Table 3 indicates some eggplant growth traits, including final fruit yield per plant (Y), fruit size and shoot dry matter weights (shoot DM). As designated in Table 3, both irrigation and salinity significantly affected eggplant fruit yield. Nevertheless, the yield values were not significantly different in I 1 and I 2 treatments in either environment, except for outdoor cultivation in the second year (Table 4). Moreover, the deleterious effects of salt stress were reinforced by the prolongation of irrigation intervals, as has been reported by Rameshwaran (2015). Table 3 also shows EC e values for each irrigation and water salinity treatment. Such values ranged from 2.7 (I 1 J 1 ) to 18.8 (I 3 J 4 ) and 1.6 to 16.4 dSm -1 for outdoor and greenhouse pots, respectively. As the salinity of irrigation water (EC w ) increased, EC e tended to increase significantly for all watering frequency treatments in both outdoor and greenhouse environments. The higher EC e value observed in the outdoor treatments in comparison to the greenhouse pots was due to the higher evaporation occurring from the surface, as reported by Aragüés et al. (2005).    As shown in Table 3, longer irrigation intervals from I 1 to I 3 , escalate EC e values in both outdoor and greenhouse environments. Both water deficit and salinity significantly affected EC e values according to ANOVA analysis.

RESULTS AND DISCUSSION
Considering the environment as a cause of variations, a compound analysis of variance was exercised to compare the results of I and J treatments on greenhouse yields with the outdoor ones.
As shown in Table 5, no significant effect of environment was met on Y and EC e values, while it significantly affected ET C at 5%.
Given that the obtained results showed no significant difference in salinity of the saturated extract in the greenhouse and the outdoor conditions, EC e could not be considered as the effective factor for obtaining quadratic equations for estimation of B, C, and K, whereas irrigation water salinity was considered as an effective https://doi.org.10.17159/wsa/2020.v46.i3.8652 factor for its simplicity. On the other hand, due to the difference in the mean DM in the greenhouse and outdoor conditions, independent and separate logistic functions were fitted for the mentioned conditions.

Model calibration
First-year values of total plant dry matter accumulation (DM) and GDD were used to obtain the coefficients of Eq. 4 that are presented in Table 6 for greenhouse and outdoor conditions. As reported by Sepaskhah et al. (2011), the calibration coefficients are affected by agronomic management parameters. A similar trend was observed for this study, so that, K and B values increased with increasing levels of water and salinity. Furthermore, B values increased with higher water application levels and decreased at higher salinity levels. Thus, the calibrated K, B and C coefficients were fitted to quadratic functions based on seasonal applied water (I) and water salinity (EC) using stepwise multiple regression analysis. Such functions are given as follows: (10) Values are significant at 5% where n is the number of observations and p is the probability level. Values of A were not noticeably different at different levels of salinity and applied water, which agreed with the results of Mahbod et al. (2015), in which the values of A were assumed constant at different irrigation levels and nitrogen rates. Therefore, A was considered as a constant value of 100 000 according to the average of calculated A in each treatment.

Harvest index and yield
Using multiple regression analysis, harvest index (HI) as a function of seasonal irrigation water and water salinity, is determined as follows: Eggplant dry fruit yield (Y P ) was estimated from HI equation (Eq. 15) multiplied by predicted DM values at harvest time in 2012. The relationship between predicted (Y P ) and measured (Y M ) dry fruit yields in the first year are shown in Fig. 4. Low scatter of data, shown by high values of R 2 along with statistical factors d and NRSME close to 1 and 0, respectively, indicates high accuracy of the calibrated model in prediction of fruit yield.

Total dry matter
Measured values of irrigation water in the second year of experiment (2013), along with water salinity, were applied to estimate K, B and C coefficients using Eqs 9-14 for 2013. The obtained values are presented in Table 7. Total dry matter (DM P ) values for the second year were then obtained using the developed logistic model and GDD data. Such values were compared with the measured DM during the second growing season (DM m ) in order to validate the model.   Figure 5 indicates the comparison between DM P and DM m during the growing season for I 2 treatments in outdoor and greenhouse conditions. Satisfying agreement between the measured and predicted values of DM was also obtained for other treatments with good accuracy. The linear relationship between measured and estimated values of DM was compared with the 1:1 line to evaluate the model in Fig. 6

Fruit yield (Y)
Fruit yield was predicted using the estimated DM values (Eqs 5 and 9−14) and HI values obtained from Eq. 15 in the second year of experiment. The relationship between predicted and measured values of final DM, HI and DY are shown in Fig. 7, for outdoor (a), greenhouse (b) and total (c) treatments. NRMSE values in Fig. 7 show proper estimations of dry matter at the end of cropping season, inside and outside of the greenhouse. The outdoor value of the d index was close to 1 (0.9) indicating model accordance with measured values; however, the value obtained in the greenhouse was smaller (0.69). Despite the high value of R 2 in outdoor conditions, a considerably lower value was obtained for greenhouse conditions, implying that the fitted function in greenhouse conditions could not predict the variation of changes in total DM. On the other hand, accuracy in HI estimations was uppermost, obtaining NRMSE values of 0.04 in both conditions. Shabani et al. (2015) also found 0.02 for NRMSE in HI estimations and, according to Mahbod et al. (2015), HI values were predicted with proper precision. Errors of Y estimation in outdoor and greenhouse estimations increased up to 0.22 and 0.27, respectively, due to integration of total HI and DM estimation errors. Similar results were found by Mahbod et al. (2015) in which NRMSE values of crop estimation were 0.11 higher than those of DM. Generally, the logistic model precision was acceptable for eggplant crop yield estimation in both greenhouse and outdoor conditions.

CONCLUSIONS
The effect of irrigation regimes and water salinity on eggplant evapotranspiration, dry matter, and yield was studied in greenhouse and outdoor conditions, during two 110-day experiments conducted in two successive years (2012 and 2013). Final dry matter and fruit yield of eggplant were simulated with an empirical logistic growth model based on GDD under different levels of water deficit and salinity. Such models can only be applied for the same weather conditions under which models were developed. Therefore, the model was first calibrated using the measured DM values during the first year of experiment. Logistic function coefficients and the harvest index were related to total irrigation water application and water salinity. Finding acceptable accuracy in the calibrated model, the model was validated according to the DM and fruit yield data collected during the second year. Statistical analysis indicated that the accuracy of the model in DM, HI and Y estimations was fair, excellent and fair, respectively. d index values showed good accordance of the model with measured data. Hence, the logistic model can be used to predict eggplant DM and fruit yield.