Using mathematical models to evaluate germination rate and seedlings length of chickpea seed (Cicer arietinum L.) to osmotic stress at cardinal temperatures.

Cicer arietinum is the 3rd most important cool season legume crop growing in vast arid and semi-arid regions of the world. A lab experiment was designed using hydrothermal time model (HTT) to investigate the chickpea seed germination (SG) behavior, cardinal temperatures and germination responses across fluctuating temperatures (Ts) and water potentials (Ψs). Seeds of chickpea var. NIFA 1995 were germinated at six constant Ts (7, 14, 21, 28, 35 and 42°C) each having the following five water potentials: 0, -0.2, -0.4-0.6 and -0.8 MPa. Germination percentage (G%) decreased significantly at (*P ≤ 0.05) from 86.7% at 28°C in -0.2 MPa to 10% in -0.2 MPa at 7°C. The germination rate (GR = 1/t50) against different T percentiles exhibited that linear increase was observed in the GR pattern above and below the To. Based on the confidence intervals of the model coefficients and (R2: 0.96), the average cardinal temperatures were 4.7, 23 and 44.2°C for the base (Tb), optimal (To) and ceiling (Tc) temperatures respectively. θT1 value was observed maximum at 28°C in -0.2 MPa and decreases with decreasing Ψ (-0.8 MPa). In comparison with control, the θT2 value was also highest in -0.2 MPa at 28°C. The thermal time (TT) concept is well fitted to germination fraction data in distilled water with an R2 value increasing 0.972. The hydro time constant (θH) increased with an increase in T to To and then decreased when T>To. The ѱb(50) irregularly varied with increasing T, σΨb was also recorded lowest (0.166 MPa) at 28°C and highest (0.457 MPa) at 7°C. Based on the statistical analysis, cardinal temperatures, hydrothermal time constant (θHTT) and germination findings the HTT gives an insight into the interactive effect of T and Ψ on seed germination time courses under varying environmental conditions.

1. Introduction

Chickpea (Cicer arietinum L.) is the 3rd most authoritative cool season grain legume crop after the Phaseolus vulgaris and Pisum sativum, which are grown in vast arid and semi-arid regions of the world [1]. It is documented as one of the famous and oldest pulses cultivated from ancient times both in Europe and in Asia. Chickpea seeds are a decisive and inexpensive source of highly digestible nutrients such as vitamins, proteins, carbohydrates, minerals and potentially health beneficial phytochemicals especially for people in underprivileged countries [2]. After Turkey and India, Pakistan is the third largest commercial producer of chickpeas with a 7% segment in global production [3, 4]. In Pakistan, chickpea covers 73% of the land and shares 76% of the gross production [5, 6]. SG is the first and most complex morphological and physiological phase in the succession of plant development where many factors such as temperature, water potential, drought and flood affect it [7]. Temperature (T) and water potential (Ψ) are the two most important external features that affect seed germination rate and germination characteristics [8]. Depending on the water potential of the permeation medium, if it is reduced germination may be also stopped or decelerated [9]. GR is correlated with the differential magnitude between environment water potential and physiological threshold water potential for the emergence of seed radicle [10]. Similarly, when water is not limited, the soil temperature is the most important environmental factor affecting seed germination and consequently plant establishment in the field [11].

The earth’s climate is changing drastically in recent decades and these climate changes affect all the physiological phases of plant growth and development [12]. This changing climate increases the intensity and frequency of the abiotic factors that contrarily reduced agricultural production [13]. In these abiotic factors, temperature is the key factor affecting seed germination parameters in all plants [14]. However, it is significant that each taxon requires a certain range of Ts for seed germination called cardinal temperatures [15]. These are the minimum or base temperature (Tb), maximum or ceiling temperature (Tc) at which germination rate is minimum and optimum temperature (To) at which maximum germination occurs in a short period [16].

Gummerson developed mathematical thermal time (TT), hydro time (HT) and hydrothermal time model (HTT) to study the eco-physiological responses of seed germination to T, Ψ and their interaction (T × Ψ) [17]. Models can be quite useful in forecasting seed emergence time, dormancy and its use in crop management. Seed germination in the TT model is summarized in three cardinal temperatures (base, ceiling and optimum temperature). Similarly, the HT model is also described in three parameters (a) base water potential (Ψb) (b) hydro time constant (θH) and (c) Standard deviation of the base water potential (σΨb) [10]. The base water potential is the theoretical threshold describing the prevention of seed germination fraction. TT, HT and HTT are the best models for describing seed germination patterns with T, Ψ and their interactions (T × Ψ). In recent times, the hydrothermal time model has been extensively used by many researchers to individually and simultaneously inspect the results of both T and Ψ on seed germination outlines in several plants such as safflower (Carthamus tinctorius L.) [18], carrot (Daucus carota) [19], watermelon (Citrullus vulgaris) [20] as well as in weedy species.

Therefore, the objective of the current research work was: (i) to inspect the SG of C. arietinum at several Ts, Ψs and their interactions (T × Ψ) (ii) to explain chickpea seed SG behavior using models of the thermal time, hydro time and hydrothermal time (iii) to determine SG cardinal Ts and drought tolerance threshold (base water potential). To the best of our knowledge, this is the first research study from Pakistan related to the application of the HTT model to predict the germination patterns of C. arietinum under various Ts and Ψs.

2. Materials and methods

2.1. Seeds description and experiment protocol

Chickpea (Cicer arietinum L.) var. NIFA 1995 seeds were brought from Nuclear Institute for Food and Agriculture (NIFA), Peshawar, Khyber Pakhtunkhwa, Pakistan with a 95% viability rate. The variety is described as light brown, angular shaped with an average weight (0.22±2gm) and length (0.4±1cm). Before the experiment, the seeds were stored in sealed plastic bags at 4°C in dark.

The seeds were surface sterilized with 95% ethanol solution for 3 minutes and then washed with distilled water and shade dried at room temperature. The experiment was conducted according to randomized complete block design (RCBD), at various Ψs and Ts in an incubator (Memmert Beschickung-Loading-Model 100–800, Germany) from October to December 2020 at Plant Physiology Lab. Department of Botany, University of Peshawar [5, 21]. The experiment comprised of a wide range of constant temperatures (7, 14, 21, 28, 35 and 42°C) each having the following four Ψs (distilled water), -0.2, -0.4–0.6 and -0.8 MPa. The polyethylene glycol (PEG6000; Merck, Germany) was used for the preparation of Ψs solutions as suggested by [22]. Five accelerated aging periods (APP) of 24, 48, 72, 96 and 120 hours were used.

The standard germination test was performed by placing 35 seeds on Wathman No. 1 filter paper in Petri dishes moistened with 5 ml distilled water and PEG6000 solutions. The Petri dishes were randomly placed in an incubator in dark except for reading times. Each treatment has three replicates. Seeds were considered to have germinated when the radicle was 1 mm in length and was observed each day. The experiment was completed after 120 hours and germinated seeds were removed and counted for their germination parameters.

2.2. Data analysis

The germination data was analyzed through repeated probit regression analysis defined by [23, 24] which is based on TT, HT and HTT models. The germination rate (GR) was calculated as the inverse of the germination time for each percentile at each T or Ψ.

2.3. Thermal time (TT)

The germination time course data of constant T at each Ψ was quantified through the thermal time (TT) concept.

At sub-optimal Ts the model was: and at supra-optimal Ts the model was:

Hence the germination rate is the reverse of the seed emergence time, the Eqs (1) and (2) can be written as Eq (3):

Where θT1 and θT2 are the thermal time constant, T is the actual temperature of germination, Tb is the base temperature for germination fraction, g is the actual time to germination fraction, GR(g) is the germination rate of the seed population.

2.4. Hydro time (HT)

Modeling of SG in response to Ψs and accelerated aging period was analyzed using the hydro time model as suggested by [17]. θH determines the relationships between solute potential and germination rate in the same way as the thermal time model. The model can be expressed as:

Where θH is the hydro time constant (MPa.h), Ψ is actual water potential, Ψb(g) is the base water potential of germination fraction g (%), tg is the time of seed population for radicle emergence, GR(g) is the germination rate is the actual time to germination fraction g. These parameters can be used as an indicator to evaluate seed vigor and quality in a seed lot.

2.5. Hydrothermal time model (HTT)

The TT and HT models can be combined into a joint hydrothermal time model to predict and describe the SG patterns in response to varied T and Ψ in a single seedbed. In terms of the HTT model, the germination time course at all Ts and Ψ in the sub-optimal T (from Tb to To) can be described as:

Where θHTT is the hydrothermal time constant (MPa h) that has a constant value of seed population. To is the predicted optimum temperature for germination fraction. kT is Boltzmann constant (slope of Cb(g) versus T when T>To).

2.6. Germination attributes

The following germination indices were calculated from the per day and cumulative germination, physical observation, radicle and plumule lengths and fresh and dry weight of the seedlings.

2.6.1. Germination percentage (G%)

G% represent the total number of seeds germinated out of the total seeds sown in each Petri dish. This germination parameter was calculated from the formula used by Onofri et al. [24].

2.6.2. Germination energy (GE)

Seed germination energy was calculated by using the formula suggested by Thriunavukkarasu and his colleagues [25].

2.6.3. Mean germination time (MGT)

The MGT index showed that how fast the seeds emerged in a population. Small MGT value means seed population has a high rate and vice versa. This was calculated by the formula of Onofri et al. [24].

2.6.4. Coefficient of velocity of germination (CVG)

The CVG represents the velocity of germination of seeds in an experiment. This will increase with an upsurge in the frequency of germinated seeds. The highest theoretical CVG value will be obtained when all sown seeds germinated on the first day. This was calculated from the formula suggested by Shah et al. [12].

2.6.5. Germination index (GI)

The Germination index tells us about the germination percentage and speed of germination. GI was calculated from the methodology of Labrie et al. [26].

2.6.6. Germination rate index (GRI)

The GRI represent the percent germination on respective day and time. It was calculated by using the method of Rashidi [27].

2.6.7. Seed vigor index-1 (SVI-1)

The length of three seedlings from each pot was measured in cm and then calculated by using the formula suggested by Chen et al. [28].

2.6.8. Seed vigor index-II (SVI-II)

The dry weight of three seedlings from each pot was determined through electrical balance and then multiply with seed germination percentage as suggested by Chen et al. [28].

2.6.9. Time to 50% germination (T50%)

This index was developed to find out the time required for 50% seed germination. T50% was calculated through a mathematical formula developed by Hao et al. [29].

2.6.10. Timson germination index (TGI)

The TGI index represents the average number of seeds germinated per day. This was measured according to the method of Hao et al. [29].

2.7. Data analysis

The investigation of Ts (thermal time), Ψs (hydro time) and their interactions (hydrothermal time model) on seed germination rate and germination attributes were analyzed through linear regression using IBM SPSS Statistics 26 and SigmaPlot Version 11.0. The basic statistical calculation was performed in excel software (S1 File). The values of the following parameters: ѱb(50), σΨb; R, SE, Sig, F and T-test were determined using linear probit regression analysis in SPSS. ORIGIN 2021 PC Corporation was used for plotting various graphs of germination fraction vs accelerated aging period and germination parameters against T and Ψ.

3. Results

3.1. Germination responses to fluctuating temperatures (TT model)

Initially, the increase in temperature amplitude endorsed germination rate and percentage of seeds but decreased as T exceeds certain limit. Table 1 showed that temperature had significant (*P≤0.05) effects on germination rate (GR = 1/t50) and percentage of Cicer arietinum var NIFA-1995. Under optimum moisture (0 MPa) the highest G% was recorded at 28°C and lowest at 7 and 42°C (Fig 1A and 1F). In general, the minimum germination (10 and 16.3%) was reported at 7 and 42°C under -0.8 MPa and maximum (86.7%) at 28°C under -0.2 MPa in comparison with control (Fig 1A and 1F). It means germination increased from 40% to 93.3% with increasing temperature up to 28°C, then decreased again to 40% as the temperature exceeds from 28°C (optimum T) to 42°C. In general germination percentage increased with AAP and significantly (*P≤0.05) decreased with high T (Fig 1A–1F). According to the results a substantially high θT1 value was observed at 28°C in -0.2 MPa and decreases with decreasing Ψ (-0.8 MPa) irrespective of species investigated (Table 1). In comparison with control, θT2 value was also documented highest in (-0.2 MPa) at 28°C. The TT concept is well fitted to germination fraction data in distilled water with R value increasing 0.972 (Table 2). Plotting the germination rate against different T percentiles exhibited that linear increase was observed in GR(g) pattern above and below the To (Table 1). Using the same pattern but in opposite direction, the GR(g) values showed significant (**P≤0.01) increment with decreasing Ψ (more negative) at all Ts. The base water potential at 50 percentile (ѱb(50)) showed an irregular pattern with increasing temperature. Similarly, the F and T-test also showed a lop-sided behavior having no linear pattern, except that both values were recorded maximum at 28°C (Table 2). Initially, these GR(g) responses are applied to compute the base, optimum and ceiling temperature values.

Table 1

The estimated parameters of the hydro and thermal time model to describe Hordeum vulgare L. seed germination under different temperatures (Ts) and water potentials (ѱs).

T	Ψ (MPa)	TTsub (θT1)	TTsupra (θT2)	θH (MPa h)	θHTT (MPa h)	Hydro time GR(g)	Thermal time GR(g)
15°C	0	768	1920	38.4	384	0.013	0.013
	-0.5	544	1360	27.2	272	0.018	0.018
	-1.0	448	1120	22.4	224	0.022	0.022
	-1.5	448	1120	22.4	224	0.022	0.022
	-2.0	96.0	240.0	4.8	48.0	0.104	0.104
20°C	0	896	2240	44.8	448	0.011	0.011
	-0.5	736	1840	36.8	368	0.014	0.014
	-1.0	640	1600	32.0	320	0.016	0.016
	-1.5	448	1120	22.4	224	0.022	0.022
	-2.0	128	320.0	6.40	64.0	0.078	0.078
25°C	0	640	1600	32.0	320	0.016	0.016
	-0.5	448	1120	22.4	224	0.022	0.022
	-1.0	320	800.0	16.0	160	0.031	0.031
	-1.5	320	800.0	16.0	160	0.031	0.031
	-2.0	96.0	240.0	4.80	48.0	0.104	0.104
30°C	0	576	1440	28.8	288	0.017	0.017
	-0.5	448	1120	22.4	224	0.022	0.022
	-1.0	352	880.0	17.6	176	0.028	0.028
	-1.5	224	560.0	11.2	112	0.045	0.045
	-2.0	96.0	240.0	4.80	48.0	0.104	0.104
35°C	0	256	640.0	12.8	128	0.039	0.039
	-0.5	416	1040	20.8	208	0.024	0.024
	-1.0	320	800.0	16.0	160	0.031	0.031
	-1.5	320	800.0	16.0	160	0.031	0.031
	-2.0	96.0	240.0	4.80	48.0	0.104	0.104
40°C	0	224	560.0	11.2	112	0.045	0.045
	-0.5	96.0	240.0	4.80	48.0	0.104	0.104
	-1.0	96.0	240.0	4.80	48.0	0.104	0.104
	-1.5	64.0	160.0	3.20	32.0	0.156	0.156
	-2.0	32.0	80.0	1.60	16.0	0.313	0.313

Temperatures (T); Water potential (ψ); Thermal time constant at sub-optimal temperature (TTsub); Thermal time constant at supra-optimal temperature (TTsupra); Hydrotime constant (θH); Hydrothermal time constant (θHTT); Germination rate (GR).

Fig 1

Cumulative germination fraction for Cicer arietinum at (a) 7°C, (b) 14°C, (c) 21°C, (d)28°C, (e)35°C and (f) 42°C having different water potentials (0, -0.2, -0.4, -0.6, -0.8 MPa). Symbols indicate water potential and lines indicate cumulative germination fraction predicted by hydrothermal time model.

Table 2

Prediction of the hydrotime model parameters for chickpea using non-linear regression at each temperature.

Temperature	ѱb(50) (MPa)	σψb (MPa)	R 2	SE	F	T	Sig.
7°C	-0.91	0.457	0.960	1.431	72.00	18.47	0.003b
14°C	-0.58	0.328	0.959	1.937	69.81	19.42	0.003b
21°C	-1.28	0.174	0.893	3.648	24.92	13.36	0.015b
28°C	-1.10	0.166	0.972	2.186	103.7	27.78	0.002b
35°C	-1.27	0.290	0.661	6.686	5.860	7.161	0.094b
42°C	-0.31	0.201	0.870	1.915	20.16	11.64	0.021b

Base water potential at 50 percentile (ѱb(50)); Standard deviation in Ψb (σψb); Coefficient of determination (R); Standard error (SE); Variability between different means (F); Test (T); Level of significance (Sig).

3.2. Germination responses to water potentials (ѱs) (HT model)

The variation in seed germination time courses against water potential was scrutinized separately at each T (R ranges 0.661–0.972) using the hydro time model. θH, Ψ, ѱb and GR(g) parameters for our experimental data at each constant T and various ѱ were analyzed by this HT concept. The minimum G% of 10% was recorded at 7°C in -0.8 MPa and the maximum 86.3% in -0.8 MPa at 28°C (Fig 1A and 1D). Generally, the highest G% was observed in -0.2 MPa and lowest in -0.8 at all T (Fig 1A–1F).

It is observed that decreasing osmotic potential of the imbibition solution significantly reduced and delayed germination percentage and this inhibition effect was more severe at a temperature above and below optimum T. Both of these values showed minute increment with accelerated aging periods. The highest hydro time constant (θH) (41.6 MPa h) value was recorded in -0.2 MPa at 28°C and lowest at 7°C in -0.8 MPa in comparison with control (Table 1). The data set of θH resulted from water potentials and germination fractions of seed population were plotted against constant T. The median base water potential (ѱb(50)) values were irregularly varied with increasing temperature having values ranging from -1.28 to -0.58 MPa (Table 2). The standard deviation (σΨb) of the base water potential at 50 percentiles was also recorded lowest (0.166 MPa) at 28°C and highest (0.457 MPa) at 7°C. The GR(g) of the HT concept showed a remarkable high value at 7°C in -0.8 MPa (Table 2).

3.3. Germination responses to temperature and water potential (HTT model)

The seed germination responses to integrating the effect of temperature and water potential above the thermal threshold (Tb) and the hydro threshold (ѱb) can be quantified using the hydrothermal time model. The HTT concept predictability was maximum (R = 0.960 at 7°C) at suboptimal temperatures (T

Table 3

Estimated variable values using the hydrothermal time model for describing seed germination and cardinal temperatures of Cicer arietinum L. at six constant Ts at each of the following four ψs.

Variables		Cicer arietinum var. NIFA 1995
Hydrothermal time model parameters
Ѱb (50) (MPa)		-1.34
σψb (MPa)		2.65
θHTT (MPa°Ch-1)		34.56
kT (MPa°Ch-1)		0.104
Cardinal temperatures
Tb (°C)		4.7
To (°C)		23
Tc (°C)		44.2
R 2		0.96

Boltzmann constant (kT); Coefficient of determination (R2), Base temperature (Tb); Optimum temperature (To); Ceiling temperature (Tc).

Data of the germination attributes were presented in 3D graphs plotted against T and ѱ. Statistical analysis and graphical presentation revealed a significant change at (*P≤0.05) in radicle length, plumule length, G%, GE, MGT, CVG, GI, GRI, SVI-I and II, TGI and T50% in comparison with control treatment (Figs 2–4). The parameters which were affected negatively by increasing water potential (more negative) and temperature includes radicle length, plumule length, G%, GE, CVG, GI, GRI, SVI-I, SVI-II and TGI (Figs 2A–2D, 3B–3D and 4A–4C). These indices were reported highest in -0.2 MPa at 28°C. On the contrary, the parameters MGT and T50% were reported maximum in -0.8 MPa at 42°C (Figs 3A and 4D). The increasing pattern in these two indices is opposite with osmotic potential and temperature in comparison with above.

Fig 2

Interactive effect of water potential and temperature on (A) Radicle length (B) Plumule length (C) Germination percentage (D) Germination energy of chickpea var. NIFA 1995.

Fig 4

Interactive effect of water potential and temperature on (A) Seed vigor index-I (B) Seed vigor index-II (C) Timson germination index (D) Time to 50% germination of chickpea var. NIFA 1995.

Fig 3

Interactive effect of water potential and temperature on (A) Mean germination time (B) Coefficient of velocity of germination (C) Germination energy (D) Germination rate index of chickpea var. NIFA 1995.

4. Discussion

Finding a suitable geographic location, where a species can germinate and be established successfully, required studying germination patterns under the influence of various abiotic factors. In this aspect mathematical model (TT, HT and HTT model) aids to determine and quantify the effect of these abiotic factors on seed germination time courses in seed lot [30]. Among these abiotic factors, T is one of the devastating stress affecting seed germinations in several plants [31, 32]. Stress related to water (ѱ) is also major environmental factor limiting early seedling and seed germination [33, 34]. Our results also demonstrated that seed germination was significantly affected by T and water stress (ѱ).

Our research findings showed that in Cicer arietinum G% significantly decreased at a temperature above and below To (28°C) (Fig 2C). The decreased in G% is due to the thermal denaturation of essential amino acids required for seed germination [35]. Similarly, the decreasing pattern of G% continued with decreasing water potential. The highest G% was recorded in -0.2 MPa as compared to control and lowest in -0.8 MPa at all the six constant temperatures (Fig 1A–1F). Decreasing ѱ resulted in the consumption of water potential energy and as a result, the supply of water is limited to seed [36]. Our germination findings against ѱ can be validated with the studies of [16] and [19] for watermelon and zucchini. The GR(g) showed a linear decreasing correlation with T up to Ts≤To at constant ѱ, which is in agreement with the TT data on Hordeum sponataneum [37]. The Tb obtained (4.7°C) for chickpea in our experiment is lower than the given Tb (7°C) (Table 3). The Tb is an essential cardinal temperature required in developing a crop simulation model and suitable growing time [38]. The To calculated in our study was 23°C which is in agreement with [16]. Generally, seeds are incubated at a constant T in the laboratory, but they practice an inclusive range of T variations during the emergence time in the field. Seeds under changing T accumulated less thermal time than under constant T conditions [39]. The Tc estimated (44.2°C) in our study was probably equal to [40]. Based on the model behavior the cardinal temperature values were unaffected by ѱ in our experiment, which inversed with Mesgaran (Daucus carota) [39], (Retama raetam) [41] and corroborated with Bakhshandeh [8]. The amount θH resulted from water potentials and germination fractions increased with increasing T at sub-optimal T. The GR(g) values plotted against T also showed a slight decline with increasing T at constant ѱ (Table 1). The θH and GR(g) results are in contrast with the findings of [16] in Sesamum indicum and [31] in Allium tenuissimum. However, with reducing water potential the GR(g) values increased results of our experiment are in line with the findings of [42] for lemon balm and [20] for watermelon. In research studies and breeding programs, the θH values were used to categorize cultivars and varieties in terms of their sensitivity to ѱ.

The values of base water potential at 50 percentiles ѱb(50) showed an irregular pattern and were minimum (-1.28 MPa) at 21°C and maximum at 42°C (Table 2). Due to thermo-inhibition [20] also reported that ѱb(50) values were minimal at sup optimal T and become positive (increasing) at supra optimal T. Results indicated that σΨb values followed a liner probit trend of decreasing with increasing T up to To and then irregular pattern at supra optimal T. This can be associated to a reduction in the activity of enzymes and oxygen demand during SG time. The σΨb is used as an indicator to represent uniform changes in seed germination in seed lot [43]. However, based on estimated hydro time parameters (θH, Ψb(50) and σΨb) we can easily forecast whole germination time courses at any T and Ψ.

The TT and HT concepts are successfully applied in many types of researches to explain SG behaviors at T (sub and supra) and Ψ. But the TT concept showed an error at suboptimal T by not predicting the decline in GR when Ts>To [30]. As a result, the HTT model was developed by Bradford to overcome the problem [44]. Now the HTT concept is a robust method to study how the interaction of environmental factors (T and Ψ) influence SG in seed lot [20 and 30]. The hydrothermal time constant (θHTT) estimated for chickpea was 34.56 (MPa°Ch-1) (Table 3). Reduction in the seed germination characteristics such as radicle, plumule length, G%, GRI, GI, CVG, GE, SVI-I and II and TGI against high T and low ѱ have also been reported. High T and low Ψ cause these reductions due to thermo-inhibition of cellular mechanisms and chemical reactions in the seed [44 and 45]. The influence of these stresses is most prominent in crop agronomy because these attributes signify the component of highest concern to farmers, as well as consumers [46, 47]. Based on the statistical analysis, cardinal temperatures, θHTT and germination findings the HTT give an insight into the interactive effect of T and Ψ on seed germination populations.

5. Conclusions and novelty perspectives

The results of our findings indicated that G% and GR were significantly affected by T, Ψ and their interactions with accelerated aging periods. The HTT model developed has a clear physiological meaning and characterizes the response of C. arietinum SG behavior at all Ts and Ψs. The GR and its attributes notably reduced across all the high T (35 and 42°C) and reduced Ψ (-0.8 MPa). Based on the TT, HT and models the highest θT1 and θT2 values were observed in -0.2 MPa at 28°C, lowest and highest θH values at -0.8 MPa at 7°C and -0.2 MPa at 28°C, for HTT model predicted θHTT average value is 34.56 (MPa°Ch-1), Ѱb(50) is -1.34 MPa and σΨb value 2.65 MPa at kT 0.104 MPa°Ch-1 and cardinal Ts (Tb = 4.7°C, To = 23°C and Tc = 44.2°C. According to available literature, no specific seed germination patterns research has been reported from Pakistan to date for Cicer arietinum using the hydrothermal time model. This is the first detailed study on any mathematical model to describe germination patterns of chickpea. While the germination parameters were also described for the first time through our study for chickpea under water stress and temperature. Eventually, the HTT model provides a detailed quantitative description of C. arietinum SG to develop the physiological status of chickpea seed populations.

List of all the statistical calculations and germination indices that were performed in the experiment.

(XLSX)

Click here for additional data file.

4 Nov 2021

PONE-D-21-32942Using mathematical models to evaluate germination rate and seedlings length of chickpea seed (Cicer arietinum L.) to osmotic stress at cardinal temperaturesPLOS ONE

Dear Dr. Ullah,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process. Please submit your revised manuscript by Dec 19 2021 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.

A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.

An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: https://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols. Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols.

We look forward to receiving your revised manuscript.

Kind regards,

Shah Fahad, Ph.D

Academic Editor

PLOS ONE

Journal Requirements:

When submitting your revision, we need you to address these additional requirements.

1. Please ensure that your manuscript meets PLOS ONE's style requirements, including those for file naming. The PLOS ONE style templates can be found at

https://journals.plos.org/plosone/s/file?id=wjVg/PLOSOne_formatting_sample_main_body.pdf and

https://journals.plos.org/plosone/s/file?id=ba62/PLOSOne_formatting_sample_title_authors_affiliations.pdf

2. Thank you for stating the following financial disclosure:

"No"

At this time, please address the following queries:

a) Please clarify the sources of funding (financial or material support) for your study. List the grants or organizations that supported your study, including funding received from your institution.

b) State what role the funders took in the study. If the funders had no role in your study, please state: “The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.”

c) If any authors received a salary from any of your funders, please state which authors and which funders.

d) If you did not receive any funding for this study, please state: “The authors received no specific funding for this work.”

Please include your amended statements within your cover letter; we will change the online submission form on your behalf.

3. In your Data Availability statement, you have not specified where the minimal data set underlying the results described in your manuscript can be found. PLOS defines a study's minimal data set as the underlying data used to reach the conclusions drawn in the manuscript and any additional data required to replicate the reported study findings in their entirety. All PLOS journals require that the minimal data set be made fully available. For more information about our data policy, please see http://journals.plos.org/plosone/s/data-availability.

"Upon re-submitting your revised manuscript, please upload your study’s minimal underlying data set as either Supporting Information files or to a stable, public repository and include the relevant URLs, DOIs, or accession numbers within your revised cover letter. For a list of acceptable repositories, please see http://journals.plos.org/plosone/s/data-availability#loc-recommended-repositories. Any potentially identifying patient information must be fully anonymized.

Important: If there are ethical or legal restrictions to sharing your data publicly, please explain these restrictions in detail. Please see our guidelines for more information on what we consider unacceptable restrictions to publicly sharing data: http://journals.plos.org/plosone/s/data-availability#loc-unacceptable-data-access-restrictions. Note that it is not acceptable for the authors to be the sole named individuals responsible for ensuring data access.

We will update your Data Availability statement to reflect the information you provide in your cover letter.

4. Please include a copy of Table 5 which you refer to in your text on page 13.

5. Please review your reference list to ensure that it is complete and correct. If you have cited papers that have been retracted, please include the rationale for doing so in the manuscript text, or remove these references and replace them with relevant current references. Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript. If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice.

[Note: HTML markup is below. Please do not edit.]

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

**********

2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: Yes

**********

3. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

**********

4. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

**********

5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: For Author

1. Make all the T and ψ signs italic.

2. Please rephrase the first sentence in the abstract.

3. In subheading 2.5; Please provide citation for this model.

4. Remove figure 2 as information already present in table 1. This will provide attractive look to the MS.

5. Suggestion to proofread the results and discussion section to remove any possible grammatical mistakes.

6. In figures 3-5 make the A, C and D alphabets on one side.

7. Crosscheck all the citations and references.

8. Avoid use of unintended abbreviations.

9. Enclosed brackets are missing with few references.

10. Discuss the first sentence of Section 4 in detail.

11. Avoid use of commas after each table.

In conclusion the manuscript need minor corrections and I looking forward to see this manuscript review again.

Reviewer #2: I have carefully read your manuscript and I found it a very interesting and important study in the field of mathematical models’ application with seed germination of C. arietinum.

However, I have some questions and suggestions which the authors have to addressed in the manuscript in the revision.

1. As the work is very interesting, various statistical and graphical tools are used therefore I suggested to provide supplementary files of the calculations.

2. In the material and methods section, heading 2.3; The authors used the TT concept but have not cited the reference why? Please cite the reference here. Similarly in subheading 2.4.

3. In subheading 2.4 please provide a citation for HTT.

4. Through which instrument you checked the water potentials at each T on each day.

5. The manuscript has mostly 12 germination parameters graphs (Figure 3-5) but has very little discussion on it in the abstract portion why?

6. I would suggest the authors enhance theoretical discussion and arrive at their argument.

7. Grammatical mistakes must be removed from some sections please check the manuscript.

8. Please crosscheck all the references

Conclusion: I recommend this manuscript for publication in this journal and I will be happy to review it again after incorporation of minor mistake/suggestions.

Thank you for sharing your work.

**********

6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.

Submitted filename: Review Report PONE-D-21-32942.docx

Click here for additional data file.

Submitted filename: Review Report PONE-D-21-32942.docx

Click here for additional data file.

11 Nov 2021

Editor comments Justification

1. This is a typographical mistake Table 5 is basically Table 1. Which is now corrected throughout the manuscript.

2. All citations and references were cross-checked and formatted as per PLOS guidelines. References that are retracted were replaced with relevant and up to date references.

Reviewer 1 Comments Justification

3. Changes were made as suggested by the worthy reviewer.

4. The sentence is rephrased as suggested by the esteemed reviewer.

5. Citation is provided where necessary.

6. As proposed by a worthy reviewer Figure 2 was removed.

7. The whole manuscript was critically proofread to remove all the possible mistakes.

8. As per suggestion of the reviewer, the alphabets were moved to one specific side.

9. All the citations and references were cross-checked.

10. As suggested by the reviewer the inadvertent abbreviations were removed.

11. Now each citation is enclosed in a bracket.

12. The first sentence of the results was modified and elaborated in a precise way.

13. Commas were removed after each table.

14. The conclusion is modified and enhanced now.

Reviewer 2 Comments Justification

15. As suggested by worthy reviewer supplementary files was provided.

16. As proposed by a respected reviewer citations and references were added in the required subheadings where necessary.

17. The Citation was added.

18. Water potentials were measured with the help of

19. Figures 3-5 represent the seedlings attributes which are our secondary experiment, due to which we cannot discuss it in detail.

20. The discussion section was now modified and enhanced.

21. The manuscript was proofread for all the grammatical mistakes

22. All the references were cross-checked.

Submitted filename: Response to Reviewers.docx

Click here for additional data file.

22 Nov 2021

Using mathematical models to evaluate germination rate and seedlings length of chickpea seed (Cicer arietinum L.) to osmotic stress at cardinal temperatures

PONE-D-21-32942R1

Dear Dr. Ullah,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

An invoice for payment will follow shortly after the formal acceptance. To ensure an efficient process, please log into Editorial Manager at http://www.editorialmanager.com/pone/, click the 'Update My Information' link at the top of the page, and double check that your user information is up-to-date. If you have any billing related questions, please contact our Author Billing department directly at authorbilling@plos.org.

If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they’ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org.

Kind regards,

Shah Fahad, Ph.D

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: All comments have been addressed

Reviewer #2: All comments have been addressed

**********

2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: Yes

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

**********

6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: In my previous review, I found the manuscript written in a comprehensive way with suitable presentation of the data included in tables and graphs related to crop models via hydrothermal time models in Pakistan. However, I suggested minor edits including some abbreviations, rephrasing, corrections in headings and sub-headings, improvement of results and discussion part, changes in graphs and conclusion of the manuscript.

Presently after re-reviewing the manuscript entitled “Using mathematical models to evaluate germination rate and seedlings length of chickpea seed (Cicer arietinum L.) to osmotic stress at cardinal temperatures”. The suggestions were successfully incorporated in the revised manuscript and there is no need to further evaluate the manuscript.

In conclusion, I recommend this revised manuscript for publication in your esteemed journal in its present form.

Reviewer #2: Comments for Editor

During my last revision I observed the manuscript entitled as “Using mathematical models to evaluate germination rate and seedlings length of chickpea seed (Cicer arietinum L.) to osmotic stress at cardinal temperatures” was very interesting and important in respect of utilizing mathematical models. The manuscript written in an organized way and lies within the scope of your prestigious journal. However; previously I recommended minor edits and corrections in some parts of the manuscript like material methods, subheadings, discussion and conclusion.

Currently, after reviewing the manuscript again I found that all of my suggestions and recommendations were successfully incorporated in the revised manuscript and there is no need of further revisions in the manuscript.

Conclusion: I recommend this manuscript for publication in its present condition in your valued journal.

Thank you

**********

7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: Yes: Laurent Kamel

Reviewer #2: Yes: Jalal Ahmed

Submitted filename: Review Report PONE-D-21-32942R1.docx

Click here for additional data file.

Submitted filename: Final Review Report PONE-D-21-32942 (1).docx

Click here for additional data file.

25 Nov 2021

PONE-D-21-32942R1

Using mathematical models to evaluate germination rate and seedlings length of chickpea seed (Cicer arietinum L.) to osmotic stress at cardinal temperatures

Dear Dr. Ullah:

I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department.

If your institution or institutions have a press office, please let them know about your upcoming paper now to help maximize its impact. If they'll be preparing press materials, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information please contact onepress@plos.org.

If we can help with anything else, please email us at plosone@plos.org.

Thank you for submitting your work to PLOS ONE and supporting open access.

Kind regards,

PLOS ONE Editorial Office Staff

on behalf of

Dr. Shah Fahad

Academic Editor

PLOS ONE