Modeling the influence of temperature and water potential on seed germination of Allium tenuissimum L.

Seed germination

Seeds of A. teniussimum were collected from a temperate desert steppe area in Dongsu County (43°51′36″N, 113°40′02″E, 1,060 m a.s.l. (meters above sea level)), Inner Mongolia during October 2015 (approved by Yuping Rong, China Agricultural University). After that, the seeds were naturally dried, surface cleaned and put into a sealed glass container, and then stored at 4 °C in a refrigerator until needed for experimentation (April 2016).

Germination assays were conducted in a growth chamber (SPX-250-GB, Hengyu, China) located at the Grassland Science Department, China Agricultural University, Beijing, China with an 8 h light/16 h dark day/night lighting pattern. The light intensity and relative humidity were set as 6000 lx and 50%. Mature Seeds were sterilized for 5 min with 10% NaClO and then washed with distilled water (Rong, Li & Johnson, 2015). For the germination tests, 100 seeds were placed in glass Petri dishes (90 mm inner diameter) containing two layers of filter paper (1001-090, Whatman, UK) saturated with distilled water (Ψ = 0 MPa) or solutions of different water potential levels (Ψ = −0.2, −0.4 and −0.6 MPa). Petri dishes were then transferred to the chamber and germination was characterized at four constant temperature settings (11, 15, 20, 24 and 28 °C), each replicated four times for each water potential level. Different water potential levels were produced by mixing aqueous solutions of polyethylene glycol (PEG) 6000 with distilled water according to Michel & Kaufmann (1973). A vapour pressure osmometer (Model 5100C, Wescor, Inc., Logan, UT, USA) was used to measure Ψ of solutions and create desired levels for all temperature settings. To maintain constant Ψ and avoid fungal attack, seeds incubated on PEG 6000 solutions were transferred to fresh solutions every 2 d. Germination was scored daily by observing radicle protrusion. Seed germination was defined depend on the length of radicle. Normally seeds were regarded as germinated when the length of radicle was more than 2 mm (Saleem et al., 2019). To avoid errors in recording germination, germinated seeds were removed after being counted. Furthermore, germination tests were terminated when no new germinated seeds were counted for three consecutive days.

Germination analysis

Germination rates (GR_g) were calculated using the equation: GR_g = 1/t_g, where t_g is the duration to radicle emergence. Estimations of germination rate for the 50th percentile (GR₅₀) in each replicate were calculated by interpolation using curves fit to the time course data. To determine the optimal germination temperature, germination rates at 20 and 24 °C were compared. If final germination percentage at 20 °C was significantly greater than germination at 24 °C, the optimal temperature was assumed to be 20 °C.

HT model

The relationship between GR_g and Ψ was described by using the following equation: (1)${\displaystyle {\theta }_{\mathrm{H}}=\left[\Psi -{\Psi }_{\mathrm{b}}\left(\mathrm{g}\right)\right]{\mathrm{t}}_{\mathrm{g}}}$ where θ_H is the hydrotime (MPa d) constant of the seeds required for germination, Ψ_b(g) is the theoretical threshold or base Ψ that will prevent the germination of fraction g. The parameters in the HT model were estimated according to the equation: (2)${\displaystyle \text{Probit}\left(\mathrm{g}\right)=\left[\left(\Psi -{\theta }_{\mathrm{H}}∕{\mathrm{t}}_{\mathrm{g}}\right)-{\Psi }_{\mathrm{b}}\left(50\right)\right]∕{\sigma }_{\Psi \mathrm{b}}}$ where Ψ_b(50) is the base water potential for attain the 50th percentile of germination, and σ_Ψb is the standard deviation of Ψ_b(g) in seed lots. To examine whether parameters of this model can be accurately used to quantify the sensitivity of seed populations to the variation of Ψ, the [1-(Ψ/Ψ(g))] t_g factor derived from Bradford (1990) was applied to normalize germination time courses at reduced Ψ in this study. Germination time course can be normalized by this factor at any Ψ to the corresponding time course that would occur in water for the seed population using the parameters from the HT model. All normalized data from different temperature conditions were plotted on a common thermal time scale, using the estimated T_b at 0 MPa.

HTT model

The HTT model describes seed germination patterns when T and Ψ both vary; Alvarado & Bradford, 2002. The relationship between GR_g and variable conditions of T and Ψ are described by Eq. (3) for sub-optimal T, and modified Eq. (4) for supra-optimal T:

(3)${\displaystyle {\theta }_{\mathrm{HT}}=\left(\mathrm{T}-{\mathrm{T}}_{\mathrm{b}}\right)\left[\Psi -{\Psi }_{\mathrm{b}}\left(\mathrm{g}\right)\right]{\mathrm{t}}_{\mathrm{g}}}$ (4)${\displaystyle {\theta }_{\mathrm{HT}}=\left\{\Psi -{\Psi }_{\mathrm{b}}\left(\mathrm{g}\right)-\left[{\mathrm{K}}_{\mathrm{T}}\left(\mathrm{T}-{\mathrm{T}}_{\mathrm{o}}\right)\right]\right\}\left(\mathrm{T}-{\mathrm{T}}_{\mathrm{b}}\right){\mathrm{t}}_{\mathrm{g}}}$ where θ_HT is the hydrothermal constant and T_b is the base temperature. In Eq. (4), [K_T(T −T_o)] applies only in the supra-optimal range of T and K_T is the slope of the relationship between Ψ_b(50) and temperatures when T > T_o; T_o is the optimum temperature. The value of Ψ_b(g) is set equal to the distribution of Ψ_b(g) at T_o, and (T −T_b) is equal to (T_o − T_b). Parameter values in above models can be obtained by probit analysis according to Eqs. (5) and (6) for sub- and supra-optimal T, respectively.

(5)${\displaystyle \text{Probit}\left(\mathrm{g}\right)=\left[\left(\Psi -{\theta }_{\mathrm{HT}}∕\left(\mathrm{T}-{\mathrm{T}}_{\mathrm{b}}\right){\mathrm{t}}_{\mathrm{g}}\right)-{\Psi }_{\mathrm{b}}\left(50\right)\right]∕{\sigma }_{\Psi \mathrm{b}}}$ (6)${\displaystyle \text{Probit}\left(\mathrm{g}\right)=\left[\left(\Psi -{\theta }_{\mathrm{HT}}∕\left(\mathrm{T}-{\mathrm{T}}_{\mathrm{b}}\right){\mathrm{t}}_{\mathrm{g}}\right)-{\mathrm{K}}_{\mathrm{T}}\left(\mathrm{T}-{\mathrm{T}}_{\mathrm{o}}\right)-{\Psi }_{\mathrm{b}}\left(50\right)\right]∕{\sigma }_{\Psi \mathrm{b}}}$

As described in Alvarado & Bradford (2002), the values of K_T and T_o were varied for germination time courses at T >T_o until a fit was obtained that resulted in values of θ_HT, Ψ_b(50) and σ_Ψb matching those obtained at or below T_o.

Statistical analyses

A two-way analysis of variance (ANOVA) was carried out using SPSS 19.0 for Windows (SPSS Inc., Chicago, IL, USA) to evaluate the influence of T, Ψ, and their interactions on seed germination variables of A. teniussimum. The results showed with mean and SE value of four replicates. All probit analyses of HT and HTT models were fitted in SAS 8.2 statistical package (SAS Institute, Cary, NC, USA) using the PROC PROBIT routine, which employs a maximum-likelihood weighted regression method (Bradford, 1990; Dahal & Bradford, 1994).

Seed germination in response to temperature and water potential

Results of analysis of variance indicated that the final germination percentage (FGP) of A. tenuissimum seeds was significantly influenced by T (F = 587.9, P <0.0001), Ψ (F = 643.0, P < 0.0001), and their interactions (F = 24.2, P < 0.0001) (Fig. 1, Table S1). When values of Ψ remained constant, FGP increased as T increased within sub-optimal ranges (11 to 20 °C), while it declined within supra-optimal ranges (24 to 28 °C). In distilled water (i.e., Ψ = 0 MPa), FGP changed from 72.0 ± 1.4 to 94.8 ± 1.4% over various T conditions. Maximum FGP was observed at 20 °C under all levels of Ψ and ranged from 55.0 ± 5.3 to 94.8 ± 1.4%. For all T settings, FGP decreased with decreasing Ψ levels. Few seeds germinated under the combination of −0.6 MPa and 11 °C. In contrast, FGP reached 94.8 ± 1.4% when seeds were incubated in water at 20 °C, indicating that the seeds in this analysis were non-dormant.

Hydrotime analysis

Parameters generated by the HT model are presented in Table 1. Values of θ_H decreased from 6.4 MPa d at 11 °C to 4.4, 4.2, 3.0 and 3.0 MPa d at 15, 20, 24 and 28 °C, respectively. This suggests that the time required for germination declined as T increased within sub-optimal ranges, while it remained constant at supra-optimal ranges. Values of Ψ_b(50) increased as T increased from 11 to 28 °C. Notably, estimated values of Ψ_b(50) increased more positively at supra-optimal temperatures, rising from −0.40 MPa at 24 °C to −0.16 MPa at 28 °C. Values of σ_Ψb varied from 0.20 to 0.37 MPa across all regimes of T. Specifically, values of σ_Ψb were nearly constant within the range of 15 to 24 °C, indicating that the variation in Ψ_b among all seeds in this A. tenuissimum population was small.

The curves in Figs. 2A–2E are germination time courses predicted by HT model based on the Ψ_b(g) threshold distributions (Figs. 2F–2G) and the estimated parameters (Table 1). At each T setting, the predicted curves closely matched actual seed germination data under the various Ψ levels (Figs. 2A–2E). Normalization of germination time courses across various Ψ levels at sub- and supra-optimal T levels incorporated into a common curve are shown in Fig. 3. At sub-optimal T, the difference between groupings of normalized observations and common curve is indistinct (Fig. 3A). However, the grouping of normalized observations at 28 °C did not resemble the profile from the common curve and fell into a distinct group (Fig. 3B). This indicates that the estimates of HT model interacted with T. Furthermore, these HT estimates consistently showed the largest shift in Ψ_b with increasing T (Figs. 2F–2G) and the grouping of normalized observations accurately predicted seed germination in this population.

Hydrothermal time analysis

Parameters for the HTT model, estimated in the sub- and supra-optimal T ranges, are shown in Table 2. The hydrothermal time requirement (θ_HT) for seed germination was 43.9 MPa °C d. Values T_b and Ψ_b(50) were estimated to be 7.0 °C and −0.67 MPa, respectively. FGP increased until 20.5 °C (T_o), then it declined towards ceiling temperatures (T_c(g)), at which germination theoretically ceased when T exceeded T_o. In addition, T_c(50), the ceiling temperature for germination of 50%, was 27.2 °C. The estimates for K_T was 0.1 MPa °C⁻¹, indicating that Ψ declined by 0.1 MPa for every degree that T exceeds T_o. Applying the HTT models using the A. tenuissimum germination data resulted in high R² values at both sub-optimal (R² = 0.89) and supra-optimal (R² = 0.81) T ranges, indicating a high degree of congruency between predicted and observed germination responses.

Seed germination of A. tenuissimum in response to various temperature and water availability conditions

Successful establishment of cultivated plants depends on rapid and uniform seed germination (Fakhfakh, Anjum & Chaieb, 2018; Bidgolya et al., 2018); however, suitable water availability and temperature conditions for seed germination are only available during a short period in most arid and semi-arid regions (Fakhfakh, Anjum & Chaieb, 2018; Belo et al., 2014; Watt & Bloomberg, 2012). Here, we presented a comprehensive study of seed germination responses to different temperatures and water potential levels in A. tenuissimum, an important wild onion species from temperate-desert steppes of north central Asia (He, 2008; Li & Zhang, 2011). Our results showed that final germination percentage of A. tenuissimum strongly depended on the interaction of these two factors. Furthermore, applying HTT models to our dataset provided insights into suitable conditions to enhance consistent germination responses of this valuable native species. Later, we discuss in detail the nuances of our results that underpin this methodological approach and expedite industrialization of wild species under stressful environmental conditions.

Numerous studies have illustrated how temperature-dependent seed germination is related to the geographical and ecological distribution of a particular species such as common vetch (Vicia sativa) (Liu, 2010), Stipa species (Ronnenberg, Wesche & Hensen, 2008) and temperate sedges (Carex) (Schütz & Rave, 1999). For A. tenuissimum, the final germination percentage was quite high (i.e., 92.5 to 94.8%) in the temperature range of 15 to 20 °C (Fig. 1). In some mediterranean grassland species, 15 °C and 20 °C also were found to be the best temperature for seed germination (Herranz, Ferrandis & Martínez-Sánchez, 1998; Marques & Draper, 2012). In contrast, the lower temperatures for preferable germination of A. tenuissimum seeds was consistent with a prior study of wild species of Allium distributed in temperate desert steppe (Zhao, Li & Badema, 2011). In any constant temperatures, final germination percentage declined when seeds were incubated at reduced water potential levels (Fig. 1). This response is likely associated with enzyme activity and oxygen availability of seeds, which are known to decrease when germinated at unfavorable temperatures and limiting moisture conditions (Bewley & Black, 1994). Furthermore, higher incubation temperatures and more negative values of water potential during germination likely induced secondary dormancy of seeds, leading to prolonged seed germination over non-optimal temperatures and more negative water potential levels (Fig. 2).

Predicting seed germination with mathematical models

Mathematical models to predict and quantify the influence of environmental factors on seed germination are essential when little information is known about the ideal conditions for potential agronomic species such as zucchini (Cucurbita pepo) (Atashi et al., 2015), red brome (Bromus rubens) and cheatgrass (Bromus tectorum) (Horn, Nettles & Clair, 2015), and safflowers (Carthamus tinctorius) (Bidgolya et al., 2018). While accounting for the influence of only temperature, TT models can successfully predict germination time courses in sub-optimal temperature ranges, but they become less effective at predicting germination in supra-optimal temperature ranges (Bradford, 2002; Bewley et al., 2013), which spurred the development of hydrothermal models combine the influences of temperature and water availability on seed germination (Windauer et al., 2012). Such HT and HTT models have been widely applied and accurately describe seed germination across variable temperatures and water potential levels (Alvarado & Bradford, 2002; Bakhshandeh et al., 2015; Bakhshandeh et al., 2017). In addition, normalizing thermal time scales, as we did for the germination time courses of A. tenuissimum (Bradford, 1990; Bradford, 2002), accurately described the influences of temperature and water availability (Fig. 3A). However, the grouping of normalized observations at 28 °C fell into a distinct group instead of resembling the profile from the common curve (Fig. 3B). Similarly, previous studies documented that HT analysis was unable to predict the germination time courses at supra-optimal temperatures (Bakhshandeh et al., 2017; Rowse & Finch-Savage, 2010), suggesting that HT estimates were not consistent across variable temperatures. In other words, grouping of normalized observations resulted in large shifts in the theoretical threshold or base water potential (Ψ_b(g)) that can prevent the fraction of germination as temperature increases (Rong, Li & Johnson, 2015). Furthermore, when the distribution of Ψ_b(g) overlaps with 0 MPa at a given temperature, germination of some seeds may be inhibited (Alvarado & Bradford, 2002; Larsen et al., 2004; Watt, Bloomberg & Finch-Savage, 2011). For this reason, Alvarado & Bradford (2002) developed the HTT model to account for the linear increase of Ψ_b(g) value as temperature increased above T_o in order to eliminate the positive shift in Ψ_b(g) values at supra-optimal temperatures. This modified model can quantify and predict both final germination percentage and germination rate across different temperatures and water potential levels at which seed germination occurs (Bakhshandeh et al., 2015; Rowse & Finch-Savage, 2010) as we observed for germination time course of A. tenuissimum seeds at supra-optimal temperatures, which were well described by HTT model (i.e., R² = 0.81).

Model parameters and their biological roles

Because changes in dormancy state are related to Ψ_b (Meyer, Debaenegill & Allen, 2000) and high temperatures often induce secondary dormancy, soil water availability is critical for seed germination at supra-optimal temperatures (Hills, Staden & Thomas, 2003). Likewise, values of Ψ_b(50) (−0.74 to −0.16 MPa) determined in our analysis revealed that seeds of A. tenuissimum are relatively sensitive to water restrictions at temperatures above T_o. Thus, seeds of A. tenuissimum should be germinated at sub-optimal temperatures to enhance crop establishment in arid and semi-arid regions. Results from HT analysis also indicated that the minimum value of Ψ_b(50) was observed at 11 °C and then increased, particularly in supra-optimal temperature ranges. Similar to our results, the linear increase of Ψ_b(50) has been observed in zucchini (Atashi et al., 2015), watermelon (Bakhshandeh et al., 2015), and sesame (Bakhshandeh et al., 2017). In general, the Ψ_b(50) value of a seed lot gives an indication of its tolerance to water stress. If water potential levels are more negative than Ψ_b(50), germination times will be extended and germination rates will be reduced (Bradford, 2002). This could be caused by a decrease in both enzyme activity and oxygen availability during the seed germination period, particularly when germinated at supra-optimal temperatures (Bewley et al., 2013). When soil temperature approaches T_o, less negative water potential levels will cause an increase in the activity of enzymes and water uptake rate (Kebreab & Murdoch, 1999).

Base water potential coefficient (σ_Ψb) is related to life history strategy of various species (Bradford, 1990) and indicates the uniformity of seed germination among individual seeds within a seed lot. A smaller value of σ_Ψb represents an increasingly uniform germination among seed population (Bradford & Still, 2004; Bidgolya et al., 2018). The values of σ_Ψb we estimated for A. tenuissimum seeds varied from 0.20 to 0.37 MPa, indicating that there was less variation in Ψ_b among individual seeds and that uniform germination was observed. This pattern is likely a reflection of survival adaptations to harsh environments. Under initial favorable soil temperature and water availability, faster and uniform germination will allow plants to possibly dominate a plant community in space and time (Wang et al., 2009). In contrast, most plant populations must adopt a different germination strategy to mitigate the harsh environment-induced damage on germination by allowing a few seeds to rapidly germinate, and then delaying germination until consistent suitable environment conditions are reached before the remaining seeds germinate (Bradford, 1990; Batlla et al., 2009; Watt, Bloomberg & Finch-Savage, 2011; Rong, Li & Johnson, 2015). Consistent with our results, the variation of Ψ_b was small and σ_Ψb varied from 0.16 to 0.31 MPa among Vicia sativa seeds (Liu, 2010), indicating that the long-term cultivation and domestication can result in uniform germination.

The hydrotime (MPa d) constant of the seeds required for germination (θ_H) represents the inherent speed of seed germination in a seed lot (Bradford & Still, 2004). Our results showed that θ_H declined from 6.4 to 3.0 MPa d as temperature increased from 11 °C to 24 °C, indicating that germination rate was faster at higher temperatures (Fig. 2, Table 1). Similarly, other studies reported that θ_H was constant in supra-optimal temperature ranges, but it increased as temperature declined in the range of sub-optimal temperatures (Bakhshandeh et al., 2015; Dahal & Bradford, 1994). Thus, seed germination was greatly altered with decreasing temperature.

Seed germination responses to temperature are commonly characterized with three cardinal temperatures ( T_b, T_o and T_c) estimated according to the HTT model (Bewley et al., 2013). These cardinal temperatures of A. tenuissimum seeds were T_b = 7.0 °C, T_o = 20.5 °C, and T_c(50) = 27.2 °C, respectively. In practical terms, these values suggest A. tenuissimum seeds should not be sown in soils where temperature do not exceed 7.0 °C. Maximum final germination percentage would be observed as soil temperature approaches 20.5 °C, a value when some seeds within the population will probably germinate quickly if they are not exposed to water stress or dormancy induction within optimal ranges (Rong, Li & Johnson, 2015; Windauer et al., 2012). In addition, because seeds of A. tenuissimum germinated in a relatively narrow range of temperature according to estimations of T_c(50), seeds of A. tenuissimum are likely unable to tolerate high soil temperature. From a crop production standpoint, our results document that seed germination of A. tenuissimum occurs over a soil temperature range of 7.0 to 27.2 °C, but 20.5 °C is the optimal temperature. These estimated cardinal temperatures are consistent with wild Allium species (Zhao, Li & Badema, 2011).