The research site was at Gucheng Agrometeorological Experimental Station of China Meteorological Administration. It was located in Dingxing County, Baoding City, Hebei Province, China (39° 08′ N, 115° 40′ E), belonging to the maize planting zone across wide Northern China. The station was equipped with an auto-rain-shelter, which covered an area of 750 m² and was divided into 42 trial plots, each was 2 m-wide × 4 m-long and was isolated by 3 m-deep concrete walls to prevent soil water exchange horizontally. The site has a typical cinnamon soil, containing 13.67 g kg^-1 organic C, 0.87 g kg^-1 total N, 25.76 mg kg^-1 available P, and 118.55 mg kg^-1 available K. The soil bulk density is 1.37 g cm^-3, and pH is 8.1. The average field capacity and wilting point is 0.23 and 0.07 g g^-1, respectively (Fang et al., 2013).

A 2-years’ maize field experiment responding to six initial soil water statuses was conducted in 2013 and 2014. Zhengdan 958, the most popular maize genotype in China was used in both years’ experiments. In 2013, the maize was sown on 27 June with a 50 cm line spacing and a 30 cm row spacing, giving a plant density of 6.5 plants m^-2. In 2014, the maize was sown on 24 June with a 50 cm line spacing and a 25 cm row spacing, giving a plant density of 8.0 plants m^-2. Diammonium Phosphate fertilizer was applied at 300 kg ha^-1 before sowing each year, equal to the fertilization level of local field. All other agronomic managements were identical to the local field in both years.

A completely randomized block design with three replicate plots was applied in both years. Irrigation was performed every other day to ensure the relative soil moisture of 0–50 cm depth of each trial plot is above 65%, maintaining normal growth of maize plants before they expanded the 7th leaf (July 24th, 2013) and the 3rd leaf (July 2nd, 2014), respectively (Guo et al., 2001; Xiao et al., 2011). Then, six different irrigations were performed. In 2013, the irrigation amounts (named 1st–6th treatments) were 100, 80, 60, 40, 25, and 15 mm, respectively, equivalent to 125, 100, 75, 50, 30, and 20% of the local average precipitation in late July (80 mm), respectively. In 2014, the irrigation amounts (named 1st–6th treatments) were 150, 120, 90, 60, 30, and 10 mm, respectively, equivalent to 100, 80, 60, 40, 20, and 7% of the local average precipitation in July (150 mm), respectively. No extra irrigation was performed thereafter. Precipitation was blocked completely by the auto-rain-shelter during the entire growth period.

We made one observation in the seedling stage on July 9th, 2014, and two observations in the jointing stage on July 31st, 2013, and August 8th, 2013, respectively. Eleven indicators involving plant water status, leaf gas exchange, morphology and biomass of maize were measured as candidates to investigate their responses to soil water deficit. They are moisture content of the stem and the leaf (LMC and SMC), net photosynthetic rate (Pn), transpiration rate (Tr), stomatal conductance (Gs), leaf area (LA), root–shoot ratio (R/S), dry biomass of the leaf, the stem, and the root (LDB, SDB, and RDB), and total dry biomass of the plant (TB).

The tipping point of plant growth characteristic is the very point when values of the characteristic start to deviate significantly from those with sufficient water supply, resulting from a decline in soil water content below a critical level (Thompson et al., 2007; Czajkowski et al., 2009). Here, the method named as one-side upper and lower tolerance limits for normal population was newly adopted to identify the tipping point of each growth characteristic.

Tolerance limit refers to either of two quantities that specify the endpoints of a tolerance interval. A tolerance interval is an estimated interval within which at least a certain proportion P of the population falls at a given level of confidence γ (ISO 16269-6, 2005; Krishnamoorthy and Mathew, 2009; Young, 2014). Their rigorous statistical definitions could be found in Young (2014). ISO 16269-6 (2005) provides computational formulas of tolerance intervals and limits for different distribution populations. Given the sampling methods of the field experiment, formulas of one-side upper and lower tolerance limits for normal population with unknown variance and unknown mean were used here (Eqn. 3 and 4).

In the above, U(X) and L(X) are one-side upper and lower tolerance limits for normal population, respectively; is the sample mean and S is the sample variance; k is the tolerance factor, varying with the sample size n, the confidence level P, and the γ percentile of the population included, which could refer to ISO 16269-6 (2005) or be calculated directly (Krishnamoorthy and Mathew, 2009).

To be specific, according to the results of Duncan multiple test, the growth characteristics from experimental treatments which had received larger amounts of irrigation while had no significant differences were thought to be still free of soil water deficit. Its tipping point was obtained by calculating the tolerance limit of the observed samples from these treatments. In terms of a growth characteristic which decreases as soil moisture drops below a certain level, its tipping point could be found by calculating the lower tolerance limit of these observed samples. It means that the characteristic would be unlikely lower than this tolerance lower limit when soil water is sufficient, while values of this characteristic would be probably lower than this limit once it was confronted with soil water stress. Accordingly, the tipping points of growth characteristics whose values would increase once confronted with water stress could be found by calculating the upper tolerance limits of observed samples that free of soil water deficit.

Since the formulas above could be used only when the samples normally distributed, we should first check the normality of the samples.

The tipping points of different growth characteristics were further quantified by their values of critical RSM thresholds, which were calculated in terms of the tipping points and the quadratic polynomial regression models between each growth characteristic and RSM (Eqn. 5).

Where X is the observed values of a maize growth characteristic; RSM (%) is the relative soil moisture of 0–30 cm depth; a, b, and c are the fitting coefficients of the regression model.

One-way Multivariate Analysis of Variance (One-way MANOVA) was performed on RSM and each growth characteristic to assess their differences among treatments. Their means of each treatment were then compared by Duncan multiple test at 0.05 significance level. Factor analysis was used to extract a common factor from LMC and SMC to represent maize water status, and a common factor from net Pn, Gs, and Tr to represent leaf gas exchange, which would be subjected to exploratory path analysis to figure out how maize growth characteristics respond to soil water. Normality of the observed samples that would be subjected to the tolerant limits calculation was examined with Shapiro–Wilk method (Razali and Wah, 2011). All statistical analyses were performed by SPSS 17.0 software (SPSS Inc., Chicago, IL, United States), except that exploratory path analysis was performed by IBM SPSS AMOS 21.0 (SPSS Inc., Chicago, IL, United States). Figures were plotted by Origin 8.5 (OriginLab, United States). The critical RSM of each sensitive growth characteristic was calculated by Matlab software (Mathworks Matlab R2010b, United States). The data were shown as the mean ± standard deviation (mean ± SD).

The first common factors extracted from leaf and SMC based on the data of July 09, 2014, July 31, 2013, and August 08, 2013 account for 95.56, 85.64, and 82.57% of total variance, respectively. The first common factors extracted from net Pn, Gs, and Tr based on the data of July 09, 2014, July 31, 2013, and August 08, 2013 account for 97.94, 86.92, and 94.84% of total variance, respectively. These common factors were subjected to exploratory path analysis as representatives of plant water status and leaf gas exchange. An initial exploratory path diagram (Supplementary Figure S2a) was established to evaluate both the direct and indirect effects of soil water on plant water status, leaf gas exchange, leaf area, and plant total biomass. The maximum likelihood method was adopted to calculate the regression weight of each path and the squared multiple correlation (R²) of each dependent variate. Insignificant paths were deleted in order to attain the criteria of the goodness-of-fit indices. The final path models were shown in Supplementary Figures S2b–d, respectively. The model fit summary (Supplementary Table S4) showed that the path analysis model generally had a reasonable fit for all the observation data (Arbuckle, 2010). Although the effective paths were not identical among path models based on different data, the results generally showed that RSM had the most significant total effects on plant water status, less on leaf gas exchange and leaf area, and the least on plant total biomass; besides, its effects on plant water status were direct, while its effects on leaf area, leaf gas exchange, and plant total biomass were major indirect. Plant water status generally had higher total effects than RSM on leaf gas exchange, leaf area, and plant total biomass, and its effects on leaf gas exchange and leaf area were direct, while it affected plant total biomass major indirectly via leaf area (Supplementary Tables S5, S6).

Samples of all these sensitive growth characteristics distributed normally (P > 0.05) (Table 4), and they all decreased due to soil water stress (Figures 1, 2). Thus, their tipping points were identified by calculating the lower tolerance limits of the observed samples at 0.95 lower confidence level and including 95% percentile of the population (γ = 0.95, P = 95%) (Eqn. 4; Tables 5, 6). The values of critical RSM were further calculated. The critical RSM threshold was about 72% for SMC, about 65% for LMC, about 62, 60, 58, and 46% for Tr, net Pn, Gs, and leaf area, respectively, in seedling stage (Figure 1 and Table 5). In jointing stage, the critical RSM was about 64% for both stem and LMC, about 53, 51, 48, and 46% for net Pn, Tr, Gs, and leaf area, respectively (Figure 2 and Table 6).

The three performed observation days were identically clear days, and their daily dynamics of temperature, total radiation, wind speed were quite close, except that VPD of July 9th, 2014 was relatively higher than that of July 31st, 2013 and August 8th, 2013 (Supplementary Figure S1).

A threshold response of plant growth to soil or plant water status had been observed, that is, plant growth or physiological traits would remain almost constant until the water status was lower than a critical point (Blum, 1996; Sadras and Milroy, 1996; Ray et al., 2002; Novák, 2009; Gholipoor et al., 2012). In this study, maize growth characteristics appeared no significant difference among treatments with relatively higher soil moisture despite their soil water status were apparently different, however, they diverted significantly only in treatment(s) with lower soil moisture which was (were) below a certain level (Tables 1–3), implying their threshold responses to soil water status. Besides, the treatment differences were not identical among maize growth characteristics (Tables 2, 3), suggesting that they may have diverse critical soil moisture thresholds, namely, different sensitivities to soil water deficit. In both stages, growth characteristics related to plant water status (stem and LMC), leaf gas exchange (net Pn, Tr, and Gs), and leaf area varied at relatively higher soil moisture and thus were more sensitive to soil water deficit, while biomass-related characteristics appeared no significant difference under such wide soil water status (Tables 2, 3).

The results showed that the critical soil moisture thresholds were not identical either among growth characteristics or between stages (Tables 5, 6). In general, the critical soil moisture thresholds of maize growth characteristics in the seedling stage were higher than that in the jointing stage except that the critical soil moisture thresholds of leaf area were almost identical in both stages. The possible reason was that, in the seedling stage, compared to the jointing stage, the leaf water potential was higher (Sengupta and Majumder, 2014), the root was shallower, and leaves were smaller, which would result in weaker transpiration and poorer capability of soil water absorption (Kang and Liu, 1993). Thus, more abundant soil moisture was required to maintain high soil water potential to reduce the resistance of water absorption and to ensure water supply in the seedling stage (Ishida et al., 1992; Ying et al., 2015; Zhang et al., 2015).

Sadras and Milroy (1996) reviewed soil water thresholds (quantified by plant available water, PAW) of leaf expansion and leaf gas exchange among different species obtained under diverse experimental conditions. The average PAW threshold of leaf water potential was 0.61 ± 0.09, Gs was 0.37 ± 0.05, and leaf expansion was 0.56. Schmidt et al. (2001) found the tipping point of Gs of maize when PAW was 0.36. Ray et al. (2002) verified that the critical PAW of transpiration varied from 0.3 to 0.4 under different VPD. In our study, the PAW thresholds (converted from soil moisture) for SMC, LMC, Tr, net Pn, Gs, and leaf area were 0.58, 0.48, 0.43, 0.40, 0.37, and 0.19, respectively, in the seedling stage, while they were 0.46, 0.46, 0.27, 0.30, 0.22, and 0.19, respectively, in the jointing stage. The thresholds of Tr and Gs of this study were quite close to those from previous studies, in particular, those in the seedling stage almost coincided with the above results. However, these might merely coincidence, because these thresholds may vary dramatically among plant species, genotypes, phonology, soil property (i.e., soil texture and soil bulk density), root distribution, evaporative environment, growing conditions, and may also be influenced by regression models used and variations in determining the lower limit of PAW (Doorenbos and Kassam, 1980; Sadras and Milroy, 1996; Thompson et al., 2007; Casadebaig et al., 2008; Wu et al., 2011a; Schoppach and Sadok, 2012; Andrianasolo et al., 2016). For instance, PAW thresholds of maize could range from 0.27 to 0.85 for leaf expansion, and from 0.07 to 0.85 for leaf transpiration (Sadras and Milroy, 1996).

The specific critical soil moisture thresholds of plant growth characteristics were not comparable among different studies, however, they may well reflect the sequence of changes in maize responding to soil water deficit (Sadras and Milroy, 1996). The critical RSM thresholds of maize showed the sequence of changes in maize as SMC > LMC > Tr > Pn > Gs > LA in seedling stage and SMC ≥ LMC > Pn > Tr > Gs > LA in jointing stage. Our study verified that plant water status was one of the earliest response to soil water deficit (Hsiao, 1973; Hsiao et al., 1976), followed by maize growth characteristics related to leaf water status, such as leaf water potential, leaf relative water content, and LMC which have long been used to indicate water stress (Hsiao, 1973; Hsiao et al., 1976; Ackerson et al., 1977; Kumar et al., 1994). Our study also showed that stem was more sensitive to water stress than leaf (Westgate and Boyer, 1985; McCutchan and Shackel, 1992; Shackel et al., 1997; Naor, 2000; Intrigliolo and Castel, 2006; Abrisqueta et al., 2015).

It has been found that stomata closed prior to decreases in Tr and Pn when confronted with water stress (Hsiao, 1973; Hsiao et al., 1976). However, in our study, the critical soil moisture of Gs in both stages were slightly lower than those of Tr and Pn. This was possibly because that Gs was quite sensitive to various factors more than soil water. For instance, stomatal interactions with environmental factors such as light and CO₂ were complex and appeared to be mediated by several underlying processes (Hsiao, 1973). Increasing VPD between the leaf-air interface would also result in stomata closure regardless of soil water status (Farooq et al., 2009). Besides, hormones such as abscisic acid (ABA) would regulate stomata aperture during the early stage of drought, whereas factors such as leaf water potential, nutrition situation, pH of sap flow and farnesyltransferase activity could affect stomata’s sensitivity to ABA (Holbrook et al., 2002; Medrano et al., 2002). All these factors made Gs extremely variable, which resulted in greater variances within the samples that were subjected to tolerant limits calculation, yielding a broader tolerant limit and consequently lower critical RSM (Eqn. 4).

Expansion of mesophyll cells was thought to be even more sensitive to soil water deficit than the Gs and Pn (Hsiao, 1973; Hsiao et al., 1976; Fischer, 1980; Lambers et al., 2008). In contrast, our study found that leaf area responded at lower critical soil moisture than those of leaf gas exchange characteristics. In fact, they were not contradictory. Mesophyll cell expansion was a physiological process and thus responded instantly to water status, whereas leaf area was cumulative effects of soil water stress on mesophyll cell expansion as well as a result of adaptive growth of leaf under drought, which depended on not only expansion of all growing leaves, but also leaf number and the senescence of older leaves, consequently responding slower to drought (Reddy et al., 2003; Blum, 2011; Pinheiro and Chaves, 2011; Bodner et al., 2015).

Different sensitivities of maize growth characteristics to soil water deficit resulted from the way soil water affected them. The results of exploratory path analysis showed that soil water had the most significant total effects on plant water status, less on leaf gas exchange and leaf area. Besides, plant water status was directly affected by soil water, while leaf gas exchange and leaf area were more directly influenced by plant water status. Reductions in plant water status, especially leaf water status would give rise to a loss in turgor, which would on one hand reduce cell division and enlargement and consequently inhibit leaf expansion, on the other hand, lead to stomatal closure, consequently impeding CO₂ influx and H₂O outflux and thus leaf gas exchange (Hsiao, 1973; Blum, 2011; Pinheiro and Chaves, 2011; Sanders and Arndt, 2012). It implied that variations in leaf gas exchange and leaf area, to a greater extent, were secondary effects of soil water stress on plant water status, and thus they responded slower than plant water status to soil water deficit. The results of exploratory path analysis also showed that plant total biomass was directly influenced by leaf area, whereas soil moisture had no significantly direct effect on total biomass, nor had leaf water status, nor had leaf gas exchange. Plant total biomass was an accumulation of plant growth at various levels over a certain period, while soil moisture, plant water status, and leaf gas exchange were all instantaneous characteristics that only indicated water stress of the very time they were observed, so their effects could not be instantly detected from plant biomass. That’s why all these three characteristics appeared no significant direct effect on plant total biomass. However, long term effects of soil water deficit on leaf expansion and leaf gas exchange both appeared as a reduction in leaf area at the whole plant level, which led to decreased transpiration as well as lower intercepted radiation, and ultimately decreased biomass production (Reddy et al., 2003; Blum, 2011; Pinheiro and Chaves, 2011; Sanders and Arndt, 2012). It implies that changes in plant biomass were integrated results of all these secondary or even tertiary effects of soil water deficit in a longer term.