Agricultural Water Management 250 (2021) 106851

Available online 11 March 20210378-3774/© 2021 Elsevier B.V. All rights reserved.

Modeling kernel weight of hybrid maize seed production with different water regimes

Rongchao Shi a, Ling Tong a, Risheng Ding a, Taisheng Du a,*, Manoj Kumar Shukla b

a Center for Agricultural Water Research in China, China Agricultural University, Beijing 100083, China b Department of Plant and Environmental Sciences, New Mexico State University, Las Cruces, NM 88003, USA

A R T I C L E I N F O

Handling Editor: Dr. R. Thompson

Keywords: Grain filling characteristic Water deficit Plant growth rate Kernel weight model Source-sink relationship

A B S T R A C T

Kernel weight (KW) is the key to ensuring seed vigor in hybrid maize (Zea mays L.) production, and irrigation is important for ensuring KW in arid regions. Irrigation experiments were conducted in an arid region of Northwest China to investigate the effects of water deficit on KW, plant growth rate per kernel after silking (PGRKAS), lag phase duration (LPD), kernel growth rate during effective grain filling (KGREGF), and effective grain filling duration (EGFD), which included a 50% water deficit at the vegetative stage, and a 50% and 100% water deficit at the flowering and grain-filling stages in 2018 and 2019. A restricted pollination treatment and two defoliation treatments (three and six leaves were removed from the top 14 days after silking) were conducted under each irrigation treatment in 2019 to obtain a wide range of data on grain filling characteristics and aboveground biomass. The results showed that a 50% water deficit at the vegetative stage shortened EGFD and LPD in both years. The 50% and 100% water deficit at the grain-filling stage decreased KW, PGRKAS, EGFD, and KGREGF in 2019, but had no significant differences in each indices in 2018 due to heavy rainfall. We found a bilinear plateau relationship between relative KGREGF (RKGREGF) and relative PGRKAS (RPGRKAS) as well as a logistic relation-ship between relative EGFD and RPGRKAS/RKGREGF. Combined with the Jensen model to simulate biomass characteristic parameters (the maximum aboveground biomass, the day of year of the maximum absolute growth rate, and the initial growth rate), the KW–water model performed well in predicting the KW of hybrid maize seed production under different irrigation treatments. This research provides a quantitative method for modeling the KW of hybrid maize seed production, which considers the source-sink relationship under different water regimes in arid areas.

1. Introduction

Seed vigor is an important index of seed quality and determines the potential for rapid and uniform emergence of plants (Wen et al., 2018). Kernel weight (KW) is one of the components of seed quality that affects crop performance; high seed quality can increase yield by 15–20% (Ambika et al., 2014). Studies have shown that KW is positively corre-lated with seed vigor (Roy et al., 1996; Gholami et al., 2009; Ghazi and Al-Karaki, 2010). In addition, the difference in yield can be observed for similar kernel number per unit land, indicating that the difference in KW can significantly affect yield determination. The irrigation schedule is key to increasing KW, while deficit irrigation is an important strategy to improve water use efficiency in arid regions. Therefore, modeling the KW under a water deficit is useful for ensuring yield and seed vigor. However, few studies have been conducted on modeling KW under

different water regimes. Maize is the third most widely grown cereal after rice and wheat in

the world (Eskandari et al., 2018). Hybrid maize lines shows numerous agronomic benefits including higher yield and disease resistance compared with conventional maize. The production of hybrid maize seeds is the key to ensuring the wide planting of maize. Unlike con-ventional maize, hybrid maize seed production is divided into male and female inbreds. In order to prevent self-pollination, female inbreds are detached from the top. The grain-filling process of maize is often divided into three phases: the lag phase, effective grain-filling phase, and physiological maturity phase (Bewley and Black, 1985). The lag phase begins after ovary fertilization and is characterized by a rapid increase in kernel water content and relatively little dry matter accumulation (Prado et al., 2013). The effective grain-filling phase is the key period of kernel formation and is characterized by a rapid, nearly linear increase

* Corresponding author. E-mail address: dutaisheng@cau.edu.cn (T. Du).

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https://doi.org/10.1016/j.agwat.2021.106851 Received 6 October 2020; Received in revised form 7 February 2021; Accepted 3 March 2021

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in dry matter accumulation. In the third phase, the kernel growth rate decreases and the kernels reach the final KW (Melchiori and Caviglia, 2008). A bilinear plateau model of KW is often used to describe this process, which includes a linear growth period before reaching the final weight, but neglects KW gained during the lag phase (Borras et al., 2003; Gambín et al., 2007; Severini et al., 2011; Edreira et al., 2014).

A water deficit at different growth stages affects KW by changing the source-sink ratio after flowering (Borras and Westgate, 2006; Wang et al., 2019). Ouattar et al. (1987) found that no irrigation from the lag phase to maturity reduced KW by 50%, but no irrigation from linear filling to maturity did not significantly change KW. However, NeSmith and Ritchie (1992a) found that a water deficit duration for 12 days at the flowering stage produced larger kernels. However, a water deficit at the vegetative and flowering stages significantly decreased kernel numbers (Wang et al., 2017). In addition, assimilation supply may be insufficient because of a water deficit at different growth stages. Therefore, an efficient irrigation schedule is of great significance for realizing high yield and quality of hybrid maize seeds.

The effective grain-filling duration and kernel growth rate are two important grain-filling characteristics and primary KW drivers (Borras and Gambín, 2010; Wei et al., 2019). The lag phase is critical for establishing the potential KW and kernel growth rate (Gambín et al., 2008). The grain-filling characteristics are affected by water deficits during the grain-filling stage. Studies have shown that no irrigation at the grain-filling stage significantly shortened the effective grain filling duration, but did not significantly reduce the kernel growth rate (Ouattar et al., 1987; NeSmith and Ritchie, 1992b; Westgate, 1994). However, the grain-filling characteristics of maize under a water deficit at the vegetative and flowering stages have not been studied.

KW is usually simulated by kernel growth rate and grain-filling duration, and many researchers have related the two grain-filling characteristics to other factors. At the kernel level, the kernel growth rate is positively correlated with kernel maximum water content, and the potential kernel growth rate can be estimated from kernel water content at the end of the lag phase (Borras et al., 2003; Borras and Gambín, 2010). The grain-filling duration is correlated to the kernel desiccation rate, and it can be studied as a linear function of thermal time from maximum water content to physiological maturity (Gambín et al., 2007). At the single-plant level, plant growth rate per kernel is often used to estimate the kernel growth rate (Borras and Westgate, 2006; Echarte et al., 2006; Gambín et al., 2006, 2008; Borras and Gambín, 2010). In the CERES-Maize model, kernel growth rate is calculated from the potential kernel growth rate, environmental factors, and assimilate availability (Jones et al., 2003; Ma et al., 2018). In this study, we quantified the relationships between grain filling character-istics (kernel growth rate during effective grain filling and effective grain filling duration) and plant growth rate to simulate the KW of hybrid maize seed production under different water deficits at different growth stages.

Water shortages are a major factor restricting the development of the seed industry in arid regions, and it is important to ensure the seed vigor of hybrid maize under a water deficit to realize sustainable develop-ment. Therefore, the objectives of this study were to: (1) investigate the response of grain filling characteristics of hybrid maize seed production to a water deficit at different growth stages; (2) establish the relation-ships between grain filling characteristics and plant growth rate; and (3) predict the KW under different water regimes in arid areas.

2. Materials and methods

2.1. Field experiment

Field experiments were conducted in 2018 and 2019 at Shiyanghe Experimental Station of China Agricultural University, located in Wuwei City, Gansu Province (37◦52N, 102◦50E; altitude 1581 m). The experi-mental site has a typical continental temperate climate, with an annual

average temperature of 8.8 ◦C, mean sunshine duration of 3000 h, and a frost-free period of 150 d. The annual mean precipitation is 164.4 mm, and the annual mean evaporation is 2000 mm. The groundwater table is below 25 m. The soil in the experimental station is classified as sandy loam, with a mean dry bulk density of 1.38 g cm− 3, wilting point water content of 0.12 cm3 cm− 3, and field water capacity water content of 0.29 cm3 cm− 3 in the 0–1 m soil layer.

Before sowing, all plots were fertilized with 100 kg N ha− 1, 225 kg P2O5 ha− 1, and 60 kg K2O ha− 1 as basal fertilizers. After fertilization, the soil surface in each plot was partially covered with transparent plastic film (polyethylene blown film, 0.015 mm thick and 1.2 m wide, Shan-dong Jining Zhongqu Double Star Plastic Products Factory, Jining, China). The width of the bare soil between the two strips of plastic film mulch was 0.4 m. The drip-irrigated plots with four rows of hybrid maize were top dressed with 100 kg N ha− 1 during the vegetative and flow-ering stages. The spacing of drip irrigation belts was 0.8 m, the distance between emitters was 0.3 m, and the flow rate was 2.5 L h− 1. The total planting density of male and female inbreds was 9.75 plants m− 2. The row spacing was 40 cm, and the planting spacing was 25 cm for male and female inbreds. To ensure the emergence of seedlings, the female par-ents were irrigated with 30 mm immediately after sowing for all treat-ments during both years. The cultivars, planting dates of female parents, first and second batch of male parents, and planting proportions are given in Table 1. Maize was sown in one row of male parents with six rows of female parents in 2018 and one row of male parents with five rows of female parents in 2019. The two batches of male inbreds were planted in the same rows, with six plants each from the first and second batches placed in an alternating pattern. The female inbreds were detasseled on 3 July 2018 and 15 July 2019, and the harvesting dates were 17 Sept. in each year. Weeding and pest control measures followed local practices.

The study consisted of two experiments, of which Exp. I was an irrigation experiment, and Exp. II added defoliation and restricted pollination treatments based on Exp. I. In Exp. I, 16 irrigation treatments during vegetative (V), flowering (F), and grain filling (G) stages were carried out each year. The sufficient irrigation depth per event (I) was the difference between evapotranspiration and effective precipitation (≥ 5 mm) (Wang et al., 2021). The evapotranspiration was the product of the crop coefficient (Kc) and reference crop evapotranspiration (ET0), where Kc values were 0.33, 0.90, 1.10, 1.02, and 0.80 at the seedling, vegetative, flowering, grain-filling, and maturity stages, respectively (Jiang, 2016). And ET0 was calculated by the meteorological data during the last irrigation period (Allen et al., 1998). There were no irrigation treatments at the seedling and maturity stages. The two irrigation levels applied at the vegetative stage were 100% I and 50% I, and the three irrigation levels applied at the flowering and grain-filling stages were 100% I, 50% I, and 0 I. The irrigation depth and times during each growth stage in 2018 and 2019 are presented in Table 2. Under the control treatment (V2F2G2), the maize inbred lines were irrigated every 10 days starting from June 5, 2018 and June 4, 2019. And all the irri-gation events in the different treatments were made in the same day. A randomized block design with three replicates per irrigation treatment was used. The experimental plot size was 4.8 m wide and 46 m long, and

Table 1 Cultivars, planting date of female parents (FP), first (MP1) and second batch of male parents (MP2), and planting proportions of hybrid maize seed production in each year.

Year Cultivar Planting date Planting proportion

FP MP1 MP2 MP:FPa MP1:MP2b

2018 TRF2018 Apr 18 Apr 26 May 2 1:6 6:6 2019 JDD1903 Apr 17 May 1 May 8 1:5 6:6

a Planting proportions of MP and FP in rows. b MP1 and MP2 were planted in the same rows, with six plants each from MP1

and MP2 placed in an alternating pattern.

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a buffer area (6 m wide and 46 m long) separated the different treat-ments. Female inbreds were planted in the buffer zones.

In order to obtain the grain-filling characteristics and aboveground plant biomass with different source-sink relationships, another experi-ment was added in 2019. In Exp. II, a split-plot design was used to decrease the kernel number and assimilation during the effective grain- filling phase. The 16 irrigation treatments for Exp. I in 2019 were the main effects, and a restricted pollination treatment and two defoliation treatments were secondary effects. Pollination was prevented in approximately 50 apical ears with paper bags two days after silking as a restricted pollination treatment. About 10 leaves remained after detas-seling of female inbreds, and three and six leaves were removed from the top as the 30% and 60% defoliation treatments, respectively. Under each treatment, 50 female inbreds plants were defoliated 14 days after silk-ing. The Exp. II was only used to establish the relationships between grain-filling characteristics and plant growth rate.

Under different irrigation treatments, 30 female inbreds plants were tagged to record the dates of silking (at least one silk exposed 1 cm from the husk). Silking date was the day when 50% of female inbreds reached silking. Every 4–7 days in each year, four plants and 1500 kernels (300 kernels, ×5 replicates) per treatment were dried in an oven at 85 ◦C to a constant weight to obtain aboveground biomass and KW, respectively. The growth of KW was obtained using a bilinear plateau model:

KW =

{a + b × TTAS, TTAS < ca + b × c, TTAS ≥ c (1)

where TTAS is the thermal time after silking (◦C d), and is calculated by the difference between mean daily air temperature and the base tem-perature of 0 ◦C (Borras and Otegui, 2001); b is the kernel growth rate during effective grain filling (KGREGF, mg ◦C− 1 d− 1); c is the total grain filling duration (◦C d); − a/b is the lag phase duration (LPD, ◦C d); and the effective grain-filling duration (EGFD, ◦C d) was calculated by the difference between c and LPD.

The soil water content was measured every 3–5 days using a Diviner 2000 (Sentek Pty Ltd., Adelaide, Australia) at a depth of 1 m. In each plot, two PVC tubes were installed below the bare soil and mulch, and the measurements were calibrated by the gravimetric method. Fig. 1 shows the trends of mean soil volumetric water content in the 0–1 m soil layer under different irrigation treatments in 2018 and 2019. The crop evapotranspiration was calculated as:

ET = Pe + I+W − R − D − ∆W (2)

where ET is evapotranspiration (mm), Pe is the effective precipitation (mm), I is the irrigation depth (mm), W is the supplement from groundwater (mm), R is the surface runoff (mm), D is the deep drainage (mm), and ΔW is the variation in soil water storage (mm). W is negli-gible because the groundwater table is below 25 m. R is zero because the experimental site is flat. D was ignored because the soil water content at the 0.9–1.0 m layer did not change before and after irrigation.

Meteorological data were logged by an automatic weather station (Hobo, Onset Computer Corp., Bourne, MA, USA). The meteorological data for both growth stages are shown in Fig. 2.

2.2. KW-water model

The KW was estimated using the following equation (Echarte et al., 2006):

KW = KGREGF × EGFD (3)

Because the cultivars were different during the two years, the values of KGREGF, EGFD, and plant growth rate per kernel after silking (PGRKAS, mg ◦C− 1 d–1) were expressed relative to the control treatment (V2F2G2) each year. Studies have shown that there is a linear rela-tionship between kernel growth rate and plant growth rate (Gambín et al., 2006, 2008; Borras and Gambín, 2010). However, when the assimilate availability approaches saturation, the kernel growth rate reaches its maximum (Borras et al., 2004). Therefore, we developed a bilinear plateau model to establish the relationship between relative KGREGF (RKGREGF) and relative PGRKAS (RPGRKAS):

RKGREGF =

{d + e × RPGRKAS, RPGRKAS < f

d + e × f , RPGRKAS ≥ f (4)

PGRKAS =ΔBAS

TTAS × KN× 103 (5)

In Eq. (4), d, e, and f are fitting parameters, and the model was fitted using an iterative optimization technique in 1stOpt software (7D-Soft High Technology Inc. CN). In Eq. (5), ΔBAS is the aboveground biomass gain after silking (g), and KN is the kernel number per plant.

We found a logistic relationship between relative EGFD (REGFD) and RPGRKAS/RKGREGF:

Table 2 Irrigation depth (mm) and times under different irrigation treatments at vegetative, flowering, and grain-filling stages of hybrid maize seed production in 2018 and 2019.

Treatment 2018 2019

Vegetative Flowering Grain-filling Vegetative Flowering Grain-filling 48–77b 78–103 104–136 47–86 87–106 107–137

V2F2G2a 125.0 (3)c 84.7 (3) 29.2 (3) 82.2 (3) 60.4 (2) 133.8 (4) V2F2G1 125.0 (3) 84.7 (3) 14.6 (3) 82.2 (3) 60.4 (2) 66.9 (4) V2F2G0 125.0 (3) 84.7 (3) 0 82.2 (3) 60.4 (2) 0 V2F1G2 125.0 (3) 42.4 (3) 29.2 (3) 82.2 (3) 30.2 (2) 133.8 (4) V2F1G1 125.0 (3) 42.4 (3) 14.6 (3) 82.2 (3) 30.2 (2) 66.9 (4) V2F1G0 125.0 (3) 42.4 (3) 0 82.2 (3) 30.2 (2) 0 V2F0G2 125.0 (3) 0 29.2 (3) 82.2 (3) 0 133.8 (4) V2F0G1 125.0 (3) 0 14.6 (3) 82.2 (3) 0 66.9 (4) V1F2G2 62.5 (3) 84.7 (3) 29.2 (3) 41.1 (3) 60.4 (2) 133.8 (4) V1F2G1 62.5 (3) 84.7 (3) 14.6 (3) 41.1 (3) 60.4 (2) 66.9 (4) V1F2G0 62.5 (3) 84.7 (3) 0 41.1 (3) 60.4 (2) 0 V1F1G2 62.5 (3) 42.4 (3) 29.2 (3) 41.1 (3) 30.2 (2) 133.8 (4) V1F1G1 62.5 (3) 42.4 (3) 14.6 (3) 41.1 (3) 30.2 (2) 66.9 (4) V1F1G0 62.5 (3) 42.4 (3) 0 41.1 (3) 30.2 (2) 0 V1F0G2 62.5 (3) 0 29.2 (3) 41.1 (3) 0 133.8 (4) V1F0G1 62.5 (3) 0 14.6 (3) 41.1 (3) 0 66.9 (4)

a V, vegetative; F, flowering; G, grain-filling; 2, 100% irrigation; 1, 50% irrigation; 0, no irrigation. b Days after sowing of start each growth stage – days after sowing of end each growth stage. c Numbers between parentheses indicate irrigation times at each growth stage.

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Fig. 1. Trends of volumetric soil water content during hybrid maize seed production under different treatments in (a–d) 2018 and (e–h) 2019. S, seedling; V, vegetative; F, flowering; G, grain-filling; M, maturity; 2, 100% irrigation; 1, 50% irrigation; 0, no irrigation; DAS, days after sowing; Irrigation of V2F2G2;

rainfall.

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REGFD =g

1 + e− h×

(RPGRKASRKGREGF

− i

) + j (6)

where g, h, i, and j are fitting parameters. A water deficit at the vegetative and flowering stages delayed silking;

therefore, we used a logistic curve to fit biomass dynamics and calculate aboveground biomass gain after silking (Huang et al., 2018; Ding et al., 2019):

B(t) =BM

1 + e− k×(t− T) (7)

where B(t) (g) is the aboveground biomass at a given time t, t is the day of year (DOY), BM is the maximum aboveground biomass (g), T is the DOY of the maximum absolute growth rate, and k is the initial growth rate.

∆BAS = B(TH) − B(TS) (8)

In this equation, TH is the DOY of the harvest, and TS is the DOY of silking.

Linear relationships were found between the relative values of biomass characteristic parameters (BM i/BM CK, ki/kCK, and Ti/TCK) and relative seasonal evapotranspiration (ETi/ETCK), which was similar to the relationship between relative yield and ETi/ETCK (Fig. 3). Therefore, biomass characteristic parameters were fitted using Jensen, Minhas, and Rao models under different water regimes (Jensen, 1968; Minhas et al., 1974; Rao et al., 1988):

Jensen model

BP

BPCK=

∏3

i=1

(ETi

ETCK

)λi

(9)

Minhas model

BP

BPCK=

∏3

i=1

[

1 −

(

1 −ETi

ETCK

)2]δi

(10)

Rao model

BP

BPCK=

∏3

i=1

[

1 − Ci

(

1 −ETi

ETCK

)]

(11)

where BP is biomass characteristic parameters (BM, k, and T), BPCK is the biomass parameter with sufficient irrigation treatment (V2F2G2); i = 1, 2, 3 is vegetative, flowering, and grain-filling stages, respectively; ETi and ETCK are evapotranspiration in the ith growth stage and sufficient irrigation treatment (mm); and λi, δi, and Ci are the water sensitivity indexes of BP at the ith growth stage.

2.3. Data analysis

The models were calibrated using the 12 irrigation treatments (V2F2G2, V2F1G0, V2F0G2, V1F2G0, V1F1G1, and V1F0G2 in each year), and validated using the other 20 irrigation treatments in both years.

SAS 9.3 software (SAS Institute, USA) was used for multiple linear fitting and the means comparison with Duncan multiple-range test at the 5% probability level. 1stOpt 1.5 was used for bilinear fitting. And the figures were made using Microsoft Excel 2010 (Microsoft Corporation, WA, USA) and Origin 2018 (Originlab Corporation, MA, USA). The

Fig. 2. Daily reference evapotranspiration (ET0), average relative humidity (RH), air temperature (Ta), and solar radiation (Rs) in 2018 (a and b) and 2019 (c and d). DAS, days after sowing; S, seedling; V, vegetative; F, flowering; G, grain-filling; M, maturity.

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modeling performance was evaluated with the regression coefficient (r), coefficient of determination (R2), relative root mean square error (RRMSE), average relative error (ARE), modeling efficiency (EF; Nash and Sutclffe, 1970), and agreement index (dIA; Willmott, 1981):

r =

∑n

i=1MiPi

∑n

i=1M2

i

(12)

R2 =

⎡

⎢⎢⎣

∑n

i=1

(Pi − P

)(Mi − M

)

∑n

i=1

(Pi − P

)2 ∑n

i=1

(Mi − M

)2√

⎤

⎥⎥⎦

2

(13)

RRMSE =1M

1n∑n

i=1(Pi − Mi)

2

√

(14)

ARE =

∑n

i=1|Pi − Mi|

nM(15)

EF = 1 −

∑n

i=1(Pi − Mi)

2

∑n

i=1

(Mi − M

)2 (16)

dIA = 1 −

∑n

i=1(Pi − Mi)

2

∑n

i=1

(Pi − M

+

Mi − P

)2 (17)

where n is the number of data samples, Pi is the predicted value, Mi is the measured value, P is the mean of the predicted values, and M is the mean of the measured value.

3. Results and discussion

3.1. Evapotranspiration, plant growth rate per kernel after silking, and grain filling characteristics

The ET, KW, LPD, KGREGF, PGRKAS, and EGFD are shown in Table 3. Because of the high rainfall during the grain-filling stage in 2018 (Fig. 1), there were no significant differences in ET, KW, PGRKAS, KGREGF, and EGFD under irrigation treatments at this stage. The whole stage ET ranged from 257.6 to 436.5 mm in 2018 and from 300.5 to 530.9 mm in 2019, and the KW ranged from 308.5 to 341.0 mg in 2018

Fig. 3. Linear relationships between (a) relative yield (Yi/YCK) and relative seasonal evapotranspiration (ETi/ETCK) as well as relative biomass characteristic pa-rameters [(b) BM i/BM CK, (c) ki/kCK and (d) Ti/TCK] and ETi/ETCK. BM, the maximum aboveground biomass; T, the DOY of maximum absolute growth rate; k, initial growth rate.

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and from 171.7 to 312.3 mg in 2019. A water deficit at vegetative and grain-filling stages significantly reduced KW. The treatment of V2F0G2 had the highest KW and increased by 1.7% in 2018 and 3.8% in 2019 compared to the control treatment (V2F2G2). This result was similar to that of NeSmith and Ritchie (1992a). Borras et al. (2004) suggested that increasing the assimilate availability per kernel post flowering could only increase the KW marginally. However, when maize crops were exposed to the source strength reduction, KW showed a large decrease. Compared to V2F2G2, ET decreased by 16.6% and 19.3% in V2F0G2 treatment, but PGRKAS increased by 6.0% and 6.1% in 2018 and 2019, respectively. The increasing assimilate availability per kernel after silking may be the reason for the increased KW under a water deficit at the flowering stage.

The plant growth rate per kernel is usually reduced with stress (Gambín et al., 2008; Severini et al., 2011). PGRKAS ranged from 0.463 to 0.569 mg ◦C− 1 d–1 in 2018 and 0.212–0.693 mg ◦C− 1 d–1 in 2019. A 50% water deficit at the vegetative stage shortened LPD significantly in both years, but a 50% and 100% water deficit at flowering and grain-filling stages had no effects on LPD, except for V1F0G2 and V1F0G1 in 2018. A water deficit of 50% at the vegetative stage short-ened EGFD significantly in both years, but decreased KGREGF only in 2019. The kernel water content at the end of the lag phase is often used to estimate the kernel sink capacity (Borras and Gambín, 2010). Therefore, the shorter LPD under a water deficit at the vegetative stage is one reason for the reduction of KW, KGREGF, and EGFD (Maddonni et al., 1998). A water deficit of 50% and 100% at the grain-filling stage decreased PGRKAS, KGREGF, and EGFD in 2019. Some studies showed that a water deficit at the grain-filling stage significantly shortened the EGPD by accelerating kernel desiccation but did not reduce kernel growth rate significantly (Ouattar et al., 1987; NeSmith and Ritchie, 1992b; Westgate, 1994; Sala et al., 2007). In this study, the shortage of

assimilates caused by a water deficit at the grain-filling stage may be the reason for the reduction in KGREGF. A water deficit at the flowering stage increased KGREGF significantly but had no significant effects on EGFD. The increase in KW caused by a water deficit at the flowering stage was due to the increase in KGREGF rather than increasing EGFD. Gambín et al. (2007) also suggested that increasing the assimilate availability per kernel did not increase EGFD in maize.

3.2. The relationships between grain filling characteristics and plant growth rate

The bilinear plateau relationship between RKGREGF and RPGRKAS for Exps. I and II is shown in Fig. 4a. RKGREGF increased with increasing RPGRKAS. When RPGRKAS≥ 1.06, RKGREGF = 1.03, which is the po-tential RKGREGF. When RPGRKAS = 0, RKGREGF = 0.67, which is RKGREGF of ΔBAS = 0. The logistic relationship between REGFD and RPGRKAS/RKGREGF fitted by the data of Exps. I and II is shown in Fig. 4b. The REGFD increased as RPGRKAS/RKGREGF increased. When RPGRKAS/RKGREGF approached infinity, REGFD = 1.03, which was a potential REGFD. When RPGRKAS/RKGREGF = 0, REGFD = 0.73, which is the REGFD of ΔBAS = 0.

The amount of assimilates available per kernel during lag phase determines the endosperm cell number and potential KW (Jones et al., 1996; Borras and Westgate, 2006; Borras and Gambín, 2010). Studies have shown that the plant growth rate around flowering is positively correlated with kernel growth rate, but plant growth rate during the effective grain filling stage had little effect on kernel growth rate (Andrade and Ferreiro, 1996; Echarte et al., 2006; Gambín et al., 2006, 2008; Borras and Gambín, 2010). Although the potential kernel size has been established at the end of the lag phase, reducing the amount of assimilates during the effective filling phase such as defoliation and

Table 3 Effects of different treatments on evapotranspiration (ET), kernel weight (KW), plant growth rate per kernel after silking (PGRKAS), lag phase duration (LPD), kernel growth rate during effective grain filling (KGREGF), and effective grain filling duration (EGFD) of hybrid maize seed production in 2018 and 2019.

Year Treatment ET KW PGRKAS LPD KGREGF EGFD (mm) (mg) (mg ◦C− 1 d− 1) (◦C d) (mg ◦C− 1 d− 1) (◦C d)

2018 V2F2G2a 436.5ab 335.2b 0.536b 367.7a 0.462bc 714.5a V2F2G1 431.5a 335.6b 0.544b 362.1a 0.463bc 726.9a V2F2G0 432.7a 335.1b 0.531b 368.0a 0.466b 715.8a V2F1G2 395.8b 336.7b 0.529b 364.6a 0.462bc 724.7a V2F1G1 394.1b 336.7b 0.525b 363.7a 0.460bcd 717.6a V2F1G0 392.2b 336.1b 0.519b 364.3a 0.463bc 722.6a V2F0G2 363.9c 341.0a 0.568a 367.1a 0.475a 718.2a V2F0G1 363.6c 340.2a 0.569a 366.8a 0.477a 714.3a V1F2G2 349.8d 313.0d 0.473c 326.1b 0.454cd 690.5b V1F2G1 350.6d 313.2d 0.468c 326.1b 0.455cd 683.2b V1F2G0 345.0d 313.9d 0.470c 330.0b 0.454cd 687.8b V1F1G2 316.4e 317.4c 0.463c 326.3b 0.456d 692.7b V1F1G1 316.9e 317.3c 0.477c 329.1b 0.457cd 693.2b V1F1G0 313.0e 316.5c 0.480c 329.4b 0.457cd 691.0b V1F0G2 263.0f 308.5e 0.469c 292.9c 0.450e 681.2b V1F0G1 257.6f 308.9e 0.466c 299.9c 0.446e 692.4b

2019 V2F2G2 530.9a 300.7b 0.653bc 311.8a 0.429b 700.7a V2F2G1 468.5bc 261.2f 0.517e 305.4a 0.388ef 675.5c V2F2G0 424.0de 227.6i 0.365h 307.3a 0.370g 614.8e V2F1G2 475.7b 304.8b 0.689ab 319.3a 0.429b 709.3a V2F1G1 415.5ef 269.2de 0.535e 308.3a 0.399d 676.7c V2F1G0 376.7h 236.4h 0.406g 324.2a 0.382f 617.9e V2F0G2 428.7d 312.3a 0.693a 321.2a 0.439a 710.7a V2F0G1 390.0g 273.2d 0.542e 314.6a 0.402d 680.6c V1F2G2 458.7c 282.6c 0.617cd 278.1b 0.411c 684.3bc V1F2G1 413.2f 245.3g 0.452f 262.3b 0.375g 649.5d V1F2G0 348.6j 208.7j 0.307i 272.0b 0.362h 576.4f V1F1G2 409.2f 287.6c 0.592d 271.8b 0.412c 696.5ab V1F1G1 362.3i 224.9i 0.413g 273.0b 0.363h 619.3e V1F1G0 300.5l 171.7k 0.258j 279.6b 0.324i 530.6g V1F0G2 338.5j 266.4ef 0.507e 284.6b 0.389e 677.2c V1F0G1 316.8k 173.6k 0.212k 279.6b 0.324i 536.3g

a V, vegetative; F, flowering; G, grain-filling; 2, 100% irrigation; 1, 50% irrigation; 0, no irrigation. b Different letters in columns indicate significant differences among treatments within a year at a 5% probability level using Duncan’s multiple range test.

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shading will disrupt the source-sink balance (Borras and Gambín, 2010). In this study, the plant growth rate after silking was used to establish a relationship with KGREGF (Fig. 4a), which considered the source-sink changes throughout the total grain-filling phase. The EGFD is affected by the source-sink ratio during the grain-filling period (Cirilo and Andrade, 1996; Borras and Otegui, 2001; Echarte et al., 2006). Gambín et al. (2006) suggested that EGFD tended to be longer for genotypes with higher ratios between plant growth rate per kernel and kernel growth rate during the effective grain filling period, which is consistent with our results.

When ΔBAS= 0, the kernel growth is mainly restricted by the source, and the assimilates stored in vegetative organs of the plant are trans-ferred to kernels (Uhart and Andrade, 1995). Wang et al. (2019) sug-gested that the upper limit of KW was 178.4 mg and the lower limit of KW was 155.6 mg when the post-flowering biomass gain of hybrid maize seed production was zero. In this study, when ΔBAS= 0, KW= 164.0, and 147.2 mg in 2018 and 2019, respectively. Borras et al. (2004) showed that the KW increased by 16% at the assimilate avail-ability per kernel saturation during the grain-filling stage. We found that the potential kernel weights were 355.6 and 319.3 mg in each year and increased by 6.1% compared with the control treatment.

3.3. Modeling biomass characteristic parameters and kernel weight under different irrigation treatments

The models of Rao, Jensen, and Minhas were used to simulate the biomass characteristic parameters (BM, k, and T). The water sensitivity indices of biomass characteristic parameters at vegetative, flowering, and grain-filling stages calibrated for 12 irrigation treatments during both years are shown in Table 4. For BM, the highest R2 of 0.93 and the lowest RRMSE of 0.042 were obtained for the Jensen model. The BM was found to be more sensitive to a water deficit at the grain-filling stage than the vegetative and flowering stages. For k, the Jensen model pro-duced the highest R2 of 0.97 and the lowest RRMSE of 0.035. The negative values of water sensitivity indices indicated that a water deficit at each growth stage increased k. For T, the Minhas model gave the highest R2 of 0.92 and the lowest RRMSE of 0.008. The lower values of water sensitivity indices at each growth stage indicated that a water deficit had little effect on T.

The measured biomass characteristic parameters and the predicted values by different models validated by 20 irrigation treatments during both years are shown in Fig. 5. Although the Rao model had the best validation results for BM, the Jensen model had the highest R2, EF, and

dIA, and the lowest ARE for k and T among the three models. Therefore, the Jensen model was the most suitable for simulating aboveground biomass gain after silking.

Water production functions are often used to describe the relation-ship between crop yield and evapotranspiration at different growth stages. Chen et al. (2014) developed water production functions to predict the fruit quality of tomatoes under a water deficit at different growth stages. Wang et al. (2018) used water production functions to estimate the flowering characteristics of hybrid maize seed production under a water deficit at different growth stages. In this study, the forms of water production functions were used to quantify the relationships between biomass characteristic parameters (BM, k, and T) and crop evapotranspiration at the vegetative, flowering, and grain-filling stages.

Using the Jensen model to simulate aboveground biomass gain after silking, the fitted results of the KW–water model are shown in Fig. 6; KW was underestimated by 1% under different irrigation treatments. The KW–water model performed well in predicting the KW of hybrid maize seed production over a wide range (171.7–340.2 mg), and it can be used to simulate KW under different water regimes in arid regions.

Our previous results indicated that a water deficit at the flowering stage improved seed vigor by increasing KW, and water deficit at the vegetative and flowering stages reduced seed vigor by decreasing KW (Shi et al., 2020). Therefore, combined with the Water-Flowering model (Wang et al., 2018) to predict kernel number, the optimal irrigation

Fig. 4. (a) The relationship between relative kernel growth rate during effective grain filling (RKGREGF) and relative plant growth rate per kernel after silking (RPGRKAS), and (b) the relationship between relative effective grain filling duration (REGFD) and RPGRKAS/RKGREGF. ○ The 6 irrigation treatments in 2018. • 6 irrigation treatments in 2019. △ Defoliation treatments under different irrigation treatments in Exp. II. □ The restricted pollination treatments under different irrigation treatments in Exp. II.

Table 4 The calibration results of water sensitivity indices of biomass characteristic parameters (BM, k and T) at the vegetative, flowering and grain-filling stages for different models, calibrated using 12 irrigation treatments in 2018 and 2019. R2, determination coefficients; RRMSE, relative root mean square error.

Parametera Model Water Sensitivity Index R2 RRMSE

Vegetative Flowering Grain- filling

BM Jensen 0.158 0.219 0.423 0.93 0.042 Minhas 0.156 0.180 0.301 0.90 0.049 Rao 0.598 0.471 0.584 0.82 0.072

k Jensen -0.552 -0.463 -0.536 0.97 0.035 Minhas -0.410 -0.325 -0.293 0.95 0.044 Rao -1.195 -0.824 -0.631 0.88 0.078

T Jensen 0.054 0.061 0.075 0.91 0.008 Minhas 0.047 0.050 0.047 0.92 0.008 Rao 0.143 0.128 0.098 0.88 0.011

a BM, maximum aboveground biomass (g); T, DOY of maximum absolute growth rate; k, initial growth rate.

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depth at the different growth stages to ensure yield and seed vigor of hybrid maize under a water deficit must be investigated in next research plan.

4. Conclusions

This study was conducted to investigate the effects of water deficit at different growth stages on grain filling characteristics of hybrid maize seed production, and to simulate kernel weight (KW) under a water deficit by kernel growth rate during effective grain filling (KGREGF) and effective grain filling duration (EGFD). Research has shown that a 50% water deficit at the vegetative stage shortened EGFD and the lag phase duration, while a 100% water deficit at the flowering stage increased

KW because of the increase in plant growth rate per kernel after silking (PGRKAS). We established a bilinear plateau relationship between rela-tive KGREGF (RKGREGF) and relative PGRKAS (RPGRKAS), and a logistic relationship between relative EGFD and RPGRKAS/RKGREGF. The Jensen model was the best for predicting biomass characteristic parameters to obtain aboveground biomass gains after silking. The KW–water model performed well in predicting the KW of hybrid maize seed production and underestimated by 1% under different water regimes. Our research is useful for ensuring seed vigor of hybrid maize production under limited water availability in arid areas.

Fig. 5. The validation results of water sensitivity indices of biomass characteristic parameters (BM, k and T) for (a–c) Jensen, (d–f) Minhas, and (g–i) Rao models, validated using 20 irrigation treatments in 2018 and 2019. BM, the maximum aboveground biomass; T, the DOY of maximum absolute growth rate; k, initial growth rate; R2, determination coefficients; RRMSE, relative root mean square error; ARE, average relative error; EF, modeling efficiency; dIA, agreement index.

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Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was partially supported by the National Natural Science Foundation of China, China; (51725904), the Research Projects of Agricultural Public Welfare Industry in China, China; (201503125), and the Discipline Innovative Engineering Plan, China (111 Program, B14002).

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Fig. 6. The validation results of the KW–water model, validated using 20 irrigation treatments in 2018 and 2019. KWMea, measured kernel weight; KWPre, predicted kernel weight; R2, determination coefficients; RRMSE, relative root mean square error; ARE, average relative error; EF, modeling efficiency; dIA, agreement index.

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