Development of combined imbibition and hydrothermal threshold models to simulate maize (Zea mays) and chickpea (Cicer arietinum) seed germination in variable environments


Author for correspondence: W. E. Finch-Savage Tel: +44 (0)24 7657 4968 Fax: +44 (0)24 7657 4500 Email:


  • • The ability of hydrothermal time (HTT) and virtual osmotic potential (VOP) models to describe the kinetics of maize (Zea mays) and chickpea (Cicer arietinum) seed germination under variable conditions of water potential was investigated with a view to gaining an improved understanding of the impact of on-farm seed priming on seedling establishment through simulation.
  • • Germination and/or imbibition time courses were recorded over a wide range of constant temperatures and water potentials and simple stepwise changes in water potential.
  • • Both models adequately described germination under constant environmental conditions, but not conditions of water potential that varied. To test the hypothesis that this inaccuracy resulted from the use of ambient water potential, a parsimonious model of seed imbibition was developed to calibrate the HTT and VOP models (IHTT and IVOP) and drive them with estimates of seed water potential.
  • • The IHTT and IVOP models described germination during stepwise changes in water potential more accurately than the conventional models, and should contribute to improved predictions of germination time in the field.


Hydro- and hydrothermal threshold models have been widely used on small-seeded species to describe the influence of temperature and water potential on germination under constant conditions (e.g. Gummerson, 1986; Bradford, 1990; Dahal & Bradford, 1994; Bradford, 1995; Rowse et al., 1999; Allen et al., 2000; Alvarado & Bradford, 2002; Rowse & Finch-Savage, 2003). Very few studies have extended this modelling approach to conditions that vary (Finch-Savage & Phelps, 1993; Finch-Savage et al., 1998, 2000; Roman et al., 1999; Shrestha et al., 1999; Allen, 2003; Finch-Savage, 2004). However, there is a great need to develop these models for use in variable environments, as this has wide relevance to understanding the relative timing of germination in crop, weed and wild species in the field (Allen, 2003). Relative timing of germination plays a key role in the development of subsequent competition between individuals and species, and therefore the dynamics of plant community establishment in both agricultural and natural settings. The main objective of the present work was to develop a new approach to facilitate the use of hydrothermal threshold models in variable environments. The approach is developed in the context of gaining an improved understanding of the effect of ‘on-farm’ seed priming which is commonly used by resource-poor farmers in the semiarid tropics to improve germination of larger agricultural seeds. The species selected for study, maize (Zea mays) and chickpea (Cicer arietinum), are of great agricultural importance and their field establishment has the potential to be improved by priming. This contribution is part of a larger programme with the aim of developing better understanding of the conditions under which maximum benefit can be derived from this seed treatment (Finch-Savage et al., 2004; Murungu et al., 2004).

The practice of on-farm seed priming (henceforth called priming) involves soaking the seeds from overnight to 24 h (Harris et al., 1999); 10–18 h has been recommended depending on the crop (D. Harris, personal communication). Following soaking, the seeds are surface dried and sown in the imbibed state. This practice has been promoted to improve establishment (Harris et al., 1999) in the semiarid tropics where crop failure is frequent (Stewart & Kashasha, 1984). Under these conditions priming has been shown to increase emergence and lead to better plant stands, more vigorous plants, better drought tolerance, earlier flowering, earlier harvest and higher grain yield (Harris et al., 1999, 2001, 2002). However, the reasons for these improvements are not well understood, nor is the reason for the variable response to priming that can be experienced (Murungu et al., 2004). The considerable benefits that can be achieved from priming have led to speculation that priming may result in a major physiological change that persists throughout growth to influence yield, and recent results have indicated that priming can result in resistance to or avoidance of disease infections (Rashid et al., 2004). A further objective of the present work was therefore to develop a simulation of seed germination, to help investigate the hypothesis that the main effects of priming could be achieved simply by loading the seed with water. Benefits from priming then result from earlier and improved plant establishment in drying seedbeds compared with establishment from sowing dry seeds.

The present work contrasts germination in the monocot seeds of maize and the dicot seeds of chickpea. The germination response of seeds from both species to temperature has been extensively studied and can be adequately described (maize, Itabari et al., 1993; chickpea, Covell et al., 1986; Ellis et al., 1986) using the principles of thermal time analysis (Garcia-Huidobro et al., 1982). However, germination is also influenced by moisture availability (Bradford, 1990, 1995), and soil moisture is of major importance in semiarid conditions. Sowings made into moist soil often receive no further rain for several days. Obtaining sufficient water for large seeds, such as those of maize and chickpea, to imbibe and germinate can be a particular problem under these conditions. To date no analysis has been carried out to extend the threshold modelling approach to the effects of water potential on germination in these large-seeded species.

Two population-based threshold-modelling approaches, the hydrothermal time (HTT) model and the virtual osmotic potential (VOP) model, are considered here to describe seed responses to water potential and temperature. In both approaches it is assumed that seeds germinate in a set order unaffected by germination conditions, so that each seed can be assigned a value G, the percentage of the population at which it germinates.

Hydrothermal time (HTT) model

Gummerson (1986) developed a theory in which germination time t(G) is a function of the extent to which the constant water potential (Ψ) and constant suboptimal temperature (T) of each seed (G) exceed thresholds (bases; Ψb, Tb) below which germination will not occur:

image((Eqn 1))

HTT (θHT) required for germination and the base temperature (Tb) are assumed constant for all seeds. Only the base water potential (Ψb) varies with (G), so the distribution of the germination times of individual seeds within the population are determined by the distribution of this parameter. This approach has been shown adequately to describe germination curves produced in a wide range of suboptimal constant temperatures and water potentials (Gummerson, 1986; Dahal & Bradford, 1994; Finch-Savage et al., 1998; Roman et al., 1999; Shrestha et al., 1999; Allen et al., 2000). Accepting these assumptions, it is possible to describe the response of the whole seed population in a single equation by incorporating a suitable distribution (usually a normal distribution) of base water potentials within the population (Gummerson, 1986; Dahal et al., 1993; Dahal & Bradford, 1994; Bradford, 1995; Cheng & Bradford, 1999; Rowse & Finch-Savage, 2003).

Virtual osmotic potential (VOP) model

The VOP model is being developed to assist simulation of germination response under variable seedbed conditions (Rowse et al., 1999; Rowse & Finch-Savage, 2003). When developing the model, germination of an imbibed seed was considered to result from further water uptake and growth of the radicle. It was assumed that the growth was driven by an increase in turgor pressure exceeding the yield threshold pressure (Y) caused by an accumulation of solutes and a consequent decrease in osmotic potential (Ψπ). The model used changes in Ψπ to integrate the history of water potential experienced by the seed. For simplicity, Y was considered as a constant for every seed in the population. However, growth could also result from a decrease in Y. This necessarily means that values of Ψπ used in the model are empirical, and to avoid confusion with real measurable osmotic potentials the term VOP with the symbol Ψπν was used.

The VOP model utilizes the concepts of Ψb and Tb, but also incorporates progress towards germination at water potentials below Ψb and above the minimum for metabolic advancement Ψmin (Tarquis & Bradford, 1992) that is not included in the basic HTT model. It is at these water potentials that osmotic priming occurs. Thus germination time of a seed fraction was described by Rowse & Finch-Savage (2003) as:

image((Eqn 2))

where Ψ, Ψb, Ψmin, T and Tb are as described above, and Y and the rate constant k are determined by fitting.

Models used for simulation

When using the HTT model to simulate the effects of a varying environment, advancement towards germination can be determined by integrating changes in θ that are proportional to the history of temperature and water potential experienced by the seed relative to Tb, and Ψb. The increase in θHT during each finite step of the simulation is given by:

image((Eqn 3))

and germination of a specific percentile of the population (G) occurs when θHT(G) = θHT required for germination.

The equivalent VOP model integrates changes in Ψπν that are proportional to the history of temperature and water potential experienced by the seed relative to Tb, Ψmin and Ψb. The increase in Ψπν during each finite step of the simulation is given by:

image((Eqn 4))

and germination of a specific percentile of the population (G) occurs when Ψπν(G) = (Ψ − Y).

Both the HTT and VOP models can be extended to include supraoptimal temperatures by incorporating a progressive linear upward shift (with slope m) in the distribution of Ψb, beginning at a temperature Td near to (Rowse & Finch-Savage, 2003) or at (Alvarado & Bradford, 2002) the temperature optimum. At temperatures above Td, effective Ψb for any percentile of the seed population is given by Ψb(G)d + m(T − Td), where Ψb(G)d is the uncorrected base water potential for that percentile. Ψb continues to increase with temperature to 0 MPa at the ceiling temperature above which germination no longer takes place.

The threshold models described above were applied to maize and chickpea seeds under conditions of constant water potential, and the problems of applying them to variable conditions were explored using simple stepwise changes in water potential. However, both models assume that seed and soil are at the same water potential, and cannot readily be used to investigate the effects of loading the seed with water and therefore the impact of on-farm priming. Consequently, an approach is developed using an imbibition model to calibrate the HTT and VOP models so that they are driven from estimates of seed water potential rather than ambient water potential. Simulations of germination from on-farm primed and untreated seeds are then constructed from published seedbed environment measurements made in the semiarid tropics (Townend et al., 1996).

Materials and Methods

Seed source and moisture content determination

Seeds of maize (Zea mays L.) cultivar SC403 were purchased from Seed Co. Ltd, Harare, Zimbabwe. Chickpea (Cicer arietinum L.) seeds were supplied by ICRISAT, Patancheru, India. Seeds of both species were transported by courier in sealed polyethylene bags to the UK. Seeds were then placed in fresh sealed polyethylene bags and stored in a room maintained at 4°C and 30% RH. Moisture content and viability (germination percentage) were determined according to ISTA (2003) protocols. On arrival in the UK, seed moisture content was 11.3 and 14.8% (fresh weight basis) and viability was 95 and 100% for maize and chickpea, respectively; very few abnormal seedlings were observed. Seeds were graded by eye for uniformity in size, and all experiments reported were carried out on the same seed lots within a 2 yr period. Seeds were taken directly from the store for each experiment. The seeds were surface sterilized by submerging them for 6 min in a sodium dichloroisocyanurate solution (150 mol m−3; Sigma-Aldrich, Dorset, UK), dried and then dusted with a thiram fungicide (Tripomol: 80% a.i.; Bos Chemicals Ltd) at 3 g a.i. kg−1.

Equipment used

The maintenance of accurate and constant water potentials in germination experiments is difficult. For good reasons, it is common practice to expose seeds to polyethylene glycol (PEG) solutions of known concentration and water potential. However, the results from such experiments can suffer from problems associated with concentration of the solutions as water is removed by the seed, by evaporation, and by condensation on containers resulting from small temperature gradients. Often only small volumes of PEG solutions are used, compounding these problems. If larger volumes of solution are used to buffer these effects, for example in Petri dishes, oxygen supply to the seeds may be limited. A further problem when weighing seeds to follow imbibition is the difficulty in removing PEG solution from the seeds. The following simple equipment (Fig. 1) was developed in a series of preliminary experiments (not reported here) to minimize these effects. An aluminium block (255 × 135 × 15 mm) was hollowed out to form a thick-walled rectangular box, 900 g in weight, to provide thermal mass. The inside was coated with silicone conformal coating (RS Components Ltd, Corby, UK) to avoid problems of corrosion, and filled to the brim with 220 ml of a PEG solution (mol wt 20 000 kDa; Merck, Munchen, Germany) of appropriate strength. A sheet of dialysis membrane (Cuprophan, MWCO 10 000, Medicell International Ltd, London, UK) was laid over the surface of the block containing the PEG solution and sandwiched around the edges of the block with a layer of silicone rubber (1 mm, Altec Products Ltd, Alton, UK) as a seal, and then by a further layer of the hollow aluminium block. The assembly was held together by screws securing the aluminium layers together. The membrane has a 10 000 mol wt cut-off and so should retain the PEG 20 000, but allow the passage of water. The membrane was selected because it was very thin (11.5 µm) to reduce resistance to the flow of water. Maize seeds were placed embryo-side down; chickpea seeds were placed with the embryonic axis down and the joint between the cotyledons at right angles to the membrane. A flat, transparent perspex lid (10 mm thick) with the same external dimensions as the block was placed on top of the seed. The weight of this sheet ensured good contact between seed and the membrane that was flexible enough to form around the base of the seed to increase the contact area. A gap remained between the lid and the top of the block to allow free air flow around the seed. The whole assembly was placed in a self-sealing polyethylene bag to minimize water loss.

Figure 1.

Maize and chickpea seeds placed on equipment used for imbibition and germination experiments. A flat, transparent perspex lid was placed on top of the seed, and the whole assembly was placed within a self-sealing polyethylene bag.

These units were replicates within the experimental designs used. There was a septum on the side of the block through which water could be injected to maintain the desired PEG concentration. The PEG concentration was determined from a curve of concentration and water potential constructed at 20°C using a Wescor vapour pressure osmometer (C52 unit without filter paper connected to an HR-33T dewpoint microvoltmeter; Wescor Inc., Logan, UT, USA). Before use, the water potential of each solution was checked using the same equipment. For each water potential treatment, an additional unit was assembled. At each seed weighing, during imbibition and at intervals during germination, seeds were moved from one replicate unit to the additional unit. The replicate unit was then weighed, PEG concentration adjusted by adding the appropriate amount of water to return the unit to its original weight, and the unit shaken gently to ensure uniform mixing of the solution. Seeds from the next replicate were then moved onto the adjusted unit and the procedure was repeated for all replicates.

The replicate units were arranged in randomized blocks on shelves within an aluminium cupboard held within a temperature-controlled cabinet. A fan on top of the cupboard continually moved the air in the cabinet around the outside of the cupboard to minimize temperature gradients. The cabinet was placed in a constant-temperature room set to the same temperature. The experiments were set up, units equilibrated and all measurements made inside this room.

Imbibition and germination experiments

For both species, changes in seed weight with time and germination (radicle emerged with visible extension growth) were recorded on 10 seeds on each of four replicate germination units. Measurements were made at 20°C on each of the following nominal water potentials: 0, −0.5, −0.76, −1.0, −1.24, −1.41, −1.71 MPa. For maize, measurements were also made at −2.34 and −2.67 MPa.

At the start, seed moisture content was measured on four replicates of 10 seeds, then individual seeds to be used in the experiment were weighed. At each water potential, seeds were placed on two replicate units. Two further units were set up 8 h later to provide a smooth curve of increasing weight from measurements made during imbibition. The position of all seeds relative to each other remained unchanged, and they were weighed individually approximately every 24 h (time recorded) initially and then every 48 h until they germinated. Germination was recorded more frequently when necessary, but the lids were not removed. When germinated, seeds were weighed and discarded. As described above, PEG solutions were adjusted at each measurement of seed weight. Measurements were not made more frequently than 24 h to minimize disturbance of seed contact with the membrane and to keep this disturbance the same across treatments.

Seeds were also germinated in replicate clear polystyrene boxes (17 × 11 × 5 cm). The boxes contained three sheets of filter paper on a single layer of glasshouse capillary matting (absorbency 2.5 l m−2; Vattex F, Avoncrop Ltd, UK) and 75 ml distilled water. The seeds were placed between the top two sheets. Seed orientation was as described for the germination units above.

Determination of Ψmin

For both species, 20 seeds were placed on each of four replicate germination units at each water potential and held at 20°C. The following water potentials were used for chickpea: –1.92, −2.42, −2.72, −3.02, −3.29, −3.72, −4.74, −5.29, −6.03 MPa. For maize the following water potentials were used: −3.0, −3.72, −4.74, −5.29, −6.03, −6.92, −7.93, −8.62, −10.1 MPa. These water potentials were chosen to be around or below the mean base water potential for germination (Table 1a) and were adjusted to their initial concentration every 24 h for 6 d, then every 48 h. After 10 d imbibition, seeds were placed to germinate between filter papers on moist capillary matting at 12.5°C and germination was recorded at least twice daily. This temperature was chosen to be significantly above the base temperature for germination, but low enough to slow germination allowing detailed recordings for the calculation of rates. Four replicates of 20 untreated seeds were also placed to germinate as controls.

Table 1.  Parameters determined for use in hydrothermal time (HTT, IHTT) and virtual osmotic potential (VOP, IVOP) models
 Model parametersChickpea (Cicer arietinum)Maize (Zea mays)
  1. (a) Unmodified models driven by ambient water potential; (b) models driven by seed water potential determined from the imbibition model; (c) additional parameters to account for supraoptimal temperatures. To indicate the fit of the models, the residual sums of squares of the differences (SS) between measured and modelled germination percentages are given. A smaller SS indicates a better fit to the data.

HTTTb (°C)5.495.62
θHT (MPa °Cd)61.988.8
Ψb(50) (MPa)−2.02−2.79
σΨb (MPa)0.170.24
VOPTb (°C)5.495.62
Ψmin (MPa)−3.44−5.01
Y (MPa)9.9528.8
k (d−1)0.350.48
Ψb(50) (MPa)−1.70−2.09
σΨb (MPa)0.310.42
IHTTTb (°C)5.495.62
θHT (MPa °Cd)7.5323.4
Ψb(50) (MPa)−1.57−2.22
σΨb (MPa)0.120.24
IVOPTb (°C)5.495.62
Ψmin (MPa)−3.44−5.01
Y (MPa)0.022.42
k (d−1)0.300.33
Ψb(50) (MPa)−1.53−2.11
σΨb (MPa)0.320.40
 Td (°C)30.037.2
m (MPa °C−1)0.130.57

Stepwise changes in water potential

During imbibition, seeds were exposed to a single-step change to water following a period at lower water potential. Twenty maize and chickpea seeds were placed on each of four replicate germination units containing PEG solutions with water potentials of −3.06 and −1.95 MPa, respectively. The units were held at 20°C. As described below, these water potentials were chosen to illustrate maximum differences in the prediction of germination time between the HTT and VOP models. The solutions were adjusted to their initial concentration every 24 h, as described above. After 96 h seeds were transferred to germination units containing reverse osmosis-purified water, and germination was recorded.

Estimation of model parameters

The fitting of all model parameters was optimized by minimizing the residual sum of squares of the differences between measured and modelled values.

Results and Model Development

Determination of Ψmin

Water potentials were selected to span the range around and below the mean base water potential where maize and chickpea seeds were likely to become metabolically active. It is well understood from osmotic priming studies that seeds exposed to such water potentials will germinate more quickly on removal of the stress than seeds that have not received the treatment. This advancement is generally greater as the degree of stress is reduced and treatment time is increased, but experience has shown little increase beyond 10 d (Rowse et al., 2001). In both species, the effect of the water potential to which seeds were exposed on subsequent germination rate on moist filter paper is shown in Fig. 2, together with the fitted model. The model assumes that at water potentials below a critical value (Ψmin), germination rate was constant and was not affected by water potential. At water potentials above Ψmin, a linear increase in germination rate with water potential was assumed. For both species the model was fitted by minimizing the sum of squares of the difference between the experimental points and the two-line model. In the VOP germination model, Ψmin was assumed to be the lowest water potential at which metabolic advancement occurred, and was estimated to be −5.0 and −3.4 MPa for maize and chickpea, respectively. There was no effect of any treatment on the final percentage of seeds that germinated on moist filter paper (data not shown).

Figure 2.

Maize and chickpea seed germination rate on water-moistened filter paper following transfer from 10 d imbibition at a range of water potentials. The intercept of the two lines is taken to be Ψmin. These fitted lines accounted for 95 and 74% of the variance in maize and chickpea, respectively. Vertical bars show standard errors if ± SE is greater than symbol size. The germination rate of untreated control seeds was 0.0073 and 0.023 for maize and chickpea, respectively.

Germination experiments: effect of constant temperature and water potential conditions

Cumulative germination curves were recorded at a range of water potentials at 20°C for both maize and chickpea (Fig. 3). In both species, the rate of germination was increasingly delayed as water potential decreased. In parallel experiments, germination curves were also recorded at six temperatures between 12.5 and 40°C, and at 11 temperatures between 7 and 43°C for the same seed lots of chickpea and maize, respectively (data not shown). As reported elsewhere for these species (maize, Itabari et al., 1993; chickpea, Covell et al., 1986; Ellis et al., 1986) there was a linear relationship between rate of germination and suboptimal temperatures. Estimates of Tb (Table 1a) were determined from cumulative germination data at different temperatures in the parallel experiments. These values of Tb and values of Ψmin calculated above were used in fitting the HTT and VOP models (equations 1 and 2) to cumulative germination curves at a range of water potentials (Fig. 3). The data used were obtained from water potentials above −1.41 and −1.71 MPa in chickpea and maize, respectively, thus the water potential nearest to Ψb in each case was excluded as the least reliable. The optimized parameters of both models are shown in Table 1a. Using these parameters, both models adequately describe the germination of maize and chickpea seeds at a range of water potentials (Fig. 3). There is no formal way to compare the fit of the two models as it is dependent on the fitting procedure used. However, the residual sum of squares is shown (Table 1) as a guide to indicate the relative fit of the models, and the values should be used in conjunction with visual inspection of the appropriate figure (e.g. Figure 3). Based on the minimum residual sum of squares obtained during fitting, the HTT model provided the best fit to data in maize, but the VOP model provided the best fit to data in chickpea (Table 1a).

Figure 3.

Cumulative germination curves in a range of water potentials at 20°C for maize and chickpea. Solid lines are fitted using the HTT model (equation 1) and the VOP model (equation 2). •, 0; ○, −0.5; ▪, −0.76; □, −1.0; ▴,−1.24; ▵, −1.41; ◆, −1.71 MPa. Vertical bars show standard errors if ± SE is greater than symbol size.

Application of HTT and VOP models to stepwise changes in water potential

Simulations were run using the parameters derived from constant water potential experiments (Table 1a) to estimate germination times in conditions where water potential changed. The water potential scenarios used in experiments were chosen by running many such simulations of germination using both HTT and VOP models to identify simple regimes where there was a clear illustration of the difference in estimates made by models. Germination experiments were then carried out to validate the models for these scenarios. Seeds were held at a water potential of −3.06 or −1.95 MPa (maize and chickpea, respectively) for 96 h and then transferred onto water (0 MPa) to germinate (Fig. 4b,d). Neither model accurately predicted germination time under these conditions, although both models were effective in constant conditions of water potential (Figs 3, 4a,c). The HTT model overestimated the time taken for seeds of both species to germinate, in part because it did not take account of metabolic advancement at water potentials between Ψb and Ψmin. The VOP model did allow for this advancement, but underestimated the time taken for germination. This is probably because it assumed (as does the HTT model) that seeds transferred to 0 MPa are immediately at this potential, whereas in reality there is a delay before the seed reaches 0 MPa. This failure to predict germination time illustrates the limitations of the HTT and VOP models when used in conditions where water potential varies.

Figure 4.

Cumulative germination curves for maize and chickpea seeds at (a,c) −0.5 (•) MPa and −1.24 (○) MPa; (b,d) following 96 h at −3.06 MPa and −1.95 MPa for maize and chickpea, respectively, then transferred to water (time of transfer indicated by arrow). Simulations of germination times are shown using HTT (black dashed line); VOP (black solid line); IHTT (grey dashed line); and IVOP (grey solid line) models. ◆, recorded cumulative germination, SE smaller than symbol size. Simulation of seed water potential during imbibition is shown as a black dotted line.

Seed imbibition and the development of an imbibition model

A more accurate description of germination in variable water potentials may be achieved if the seed water potential estimates used in the HTT and VOP models were calculated from an imbibition model, instead of being set equal to the ambient water potential. This may be most important when ambient water potential changes abruptly (for example, following rain or sowing of imbibed seeds). To test this hypothesis, a parsimonious imbibition model was developed to simulate changing seed moisture content (dry weight basis) and water potential under conditions of variable ambient water potential. The model was fitted to imbibition curves recorded at a range of water potentials at 20°C (Fig. 5). In both species, the rate of imbibition decreased as water potential decreased.

Figure 5.

Imbibition curves in a range of water potentials at 20°C for maize and chickpea. Water uptake is shown as a fraction of dry weight. •, 0; ○, −0.5; ▪, −0.76; □, −1.0; ▴, −1.24; ▵, −1.41; ◆, −1.71, ◊, −2.34; ×, −2.67 MPa. Standard errors are smaller than the symbol size. Solid lines are fitted using the imbibition model (equation 7).

In the model, seed water content is expressed as a fraction (f) of the original dry weight of the seed. It is assumed that, in the absence of germination, the seed will eventually come into equilibrium with the ambient water potential. This equilibrium seed water content (fe) is assumed to be at a maximum in water and to decline as the ambient water potential declines. The major assumption of the model is that, during imbibition, the rate of change of f is proportional to the difference between it and the equilibrium water content, fe. Thus:

image((Eqn 5))

Note that equation 5 is concerned with the rate of change of f rather than the rate of water uptake. This means that L (proportionality constant) is likely to depend on seed size, but this will have little consequence when dealing with comparatively uniform crop seeds. Integration of equation 5 leads to:

image((Eqn 6))

During imbibition, the seed water content does not start from zero, but from some fixed value (fp). When t = 0 then f = fp, and when t = infinity then f = fe. Thus equation 6 becomes:

image((Eqn 7))

Values of fe and L were determined by fitting equation 7 separately to imbibition data collected from each water potential treatment. The results showed that there was no consistent change in L with ambient water potential but, as anticipated, fe decreased as water potential decreased (Fig. 6). The model was therefore refitted with a common value of L (Table 2) and the following relationship between the equilibrium seed water content fe and ambient water potential Ψa:

Figure 6.

Change in equilibrium seed water content (fe, ○) and the proportionality constant L (•) with water potential in maize and chickpea. Values of fe and L were determined by fitting equation 7 separately to imbibition data collected from each water potential treatment by minimizing the residual sum of squares between the experimental and fitted water contents. A horizontal line is fitted to values of L and equation 8 was used to fit a line to values of fe.

Table 2.  Parameters determined for use in the imbibition model
Imbibition parametersChickpea (Cicer arietinum)Maize (Zea mays)
image((Eqn 8))

where f0 is the equilibrium water content in water (assuming no germination) and c is a water release constant. This equation can be transposed to give Ψa in terms of water content:

image((Eqn 9))

As equation 9 applies to equilibrium conditions, so the equilibrium seed water potential Ψs is equal to the ambient water potential Ψa, and hence it can be used to give a relationship between equilibrium seed water content fe and seed water potential. Further, by considering the imbibition process to be a series of equilibrium states (use f rather than fe), equation 9 may be modified to estimate the seed water potential as a function of seed water content at any stage during imbibition:

image((Eqn 10))

Equation 10 assumes a one-to-one relationship between seed water content and water potential (no hysteresis), and that there are no gradients of water potential within the seed, neither of which is likely. It also suggests that the relationship does not vary during imbibition. We cannot envisage an experimental technique that would allow this relationship to be measured at different instants during imbibition, but it seems probable that the breakdown of complex storage molecules and consequent increase in osmotic potential during germination would alter the relationship. Despite these difficulties, the theory is likely to give a much better estimate of seed water potential than simply assuming it to be equal to the ambient water potential.

Equation 7 gives the water content of an imbibing seed at any time in terms of the eventual equilibrium water content fe. Equation 8 gives this equilibrium water content as a function of the ambient water potential. So substitution for fe in equation 7 from equation 8 yields:

image((Eqn 11))

This equation gives the seed water content at any time t after it is placed in a constant water potential of Ψa MPa as a function of four constants: fp, f0, c and L. The constant fp was determined experimentally, the other three were determined by fitting equation 10 to the data (Table 2). Using these constants, the model adequately described the increase in both maize and chickpea seed moisture content when they were exposed to water potentials (0 to −2.67 MPa) used in the present experiments (Fig. 5).

Combined imbibition and germination models

When imbibition is considered independently, it is not possible to develop simple equations (equivalent to equations 1 and 2) to model germination data collected from single fixed potentials (as in Fig. 3). Instead, models that included imbibition (IHTT and IVOP) were fitted using a numerical method to calculate changes in θ (IHTT) and Ψπν (IVOP) during a number of small time steps (0.02 d). At each step, the seed water fraction (f) calculated from equation 11 was used in equation 10 to calculate seed water potential. Equations 3 and 4 were then used to update the θ and Ψπν values for each percentile of the seed population and hence to determine whether germination had been completed. The predetermined values of Tb and Ψmin were used, together with initial estimates of Ψb, σΨb and θHT (for HTT; equation 3) and Ψb, σΨb, Y and k (for VOP; equation 4). An optimization procedure was used to determine the values of the estimated parameters that gave the minimum sum of squares of the difference between the experimental and the calculated germination times (Table 1b).

Based on the minimum sum of squares obtained during fitting, the IHTT and IVOP models fitted these data, collected at constant water potential, better than the respective HTT and VOP models in maize, but not in chickpea (Table 1b; Fig. 4a,c). By the same criteria, the IHTT model provided a better fit than the IVOP model. However, it can be seen from the examples of two constant water potentials shown in Fig. 4a,c that all four models gave very similar predictions of germination time at higher water potentials, but tended to differ more at lower water potentials closer to Ψb (−1.24 MPa is closer to Ψb in chickpea than in maize). In contrast, when the models were used in situations where there was a step change in water potential, both IHTT and IVOP models more accurately described the data than conventional HTT and VOP models (Fig. 4b,d).

The algorithm used to calculate germination time in variable water potentials was similar to that used in the fitting process outlined above for constant water potential. However, equation 11 can be used only in constant conditions of water potential. Therefore at each step equation 8 was used to calculate equilibrium seed water content (fe) as a function of ambient water potential (Ψa), then equation 5 was used to calculate the change in seed water content, and finally (as above) equation 10 was used to calculate seed water potential.

Simulation of germination under field conditions in the semiarid tropics

The IHTT and IVOP models were extended to include the effect of supraoptimal temperatures according to the methods of Rowse & Finch-Savage (2003). For this the parameters Td and m were determined from data collected in the parallel experiments on the effects of temperature on germination, mentioned above (Table 1c). The resulting models were used to simulate the effect of sowing primed and nonprimed seed under seedbed conditions characteristic of the semiarid tropics. Detailed regular measurements of soil temperature and soil matrix potential at a range of depths in the surface layers of seedbeds in Hombolo, Tanzania have been published (Townend et al., 1996). Linear interpolation of these data was used to provide estimates of all combinations of temperature, water potential, sowing depth and time. In practice, seeds are often sown at different depths (4–10 cm are used), both within and between sowings. Therefore simulations of seed germination from primed and untreated seeds of maize and chickpea were run following sowing at different depths and in different irrigation regimes. Within the simulation, primed seeds were imbibed for 17 and 10 h before sowing for maize and chickpea, respectively, reflecting treatments used in practice. Figure 7 shows simulations run in the scenario of a drying seedbed following 10 mm irrigation before sowing. Although predictions of percentage germination differ between the IVOP and IHTT models, the general pattern of results was the same and so output from the IVOP model only is shown. In both species, a greater percentage of seeds germinated more rapidly from primed seeds than from untreated seeds. However, the extent of this benefit diminishes with increasing sowing depth and consequent higher soil matrix potentials (higher soil moisture) as the seedbed dries out from the surface. In general, maize seed germination is less affected by the dryer conditions (lower matrix potentials) at more shallow sowing depths than is seed germination in chickpea.

Figure 7.

Soil temperature (a) and soil matrix potential (b) at depths of 4–10 cm, estimated by linear interpolation from original data recorded in seedbeds in Hombolo, Tanzania following 10 mm irrigation (Townend et al., 1996). Cumulative maize (c) and chickpea (d) germination curves from on-farm primed (17 and 10 h soaking, respectively; dotted black lines) and untreated seeds (solid grey lines) simulated using the IVOP model are also shown. Sowing depths in centimetres are indicated by numbers.


Two hydrothermal threshold models were fitted to cumulative germination data for maize and chickpea seeds collected at a range of constant water potentials. Estimates of Ψmin and Ψb were significantly lower for maize seeds than for chickpea seeds (Table 1), reflecting their ability to germinate at lower water potentials and the relatively smaller impact of reducing water potential on their germination rate. Both HTT and VOP models adequately described the germination response to different constant water potentials (Figs 3, 4a,c) as they have for a range of smaller-seeded species (Gummerson, 1986; Bradford, 1990; Dahal & Bradford, 1994; Rowse et al., 1999; Allen et al., 2000; Alvarado & Bradford, 2002; Rowse & Finch-Savage, 2003). The minimum residual sums of squares obtained during fitting the models indicated that the HTT model provided a better fit to data from maize, whereas the VOP model provided a better fit to chickpea data. However, neither model accurately predicted the time of seed germination when seeds were exposed to simple step changes in water potential (Fig. 4b,d). While such stepwise changes are unlikely to occur during soil drying under natural conditions, they will occur during wetting after rain, and this situation is simplified in the water potential regime illustrated in Fig. 4b,d. A step change will also occur when the moist seeds following on-farm priming are sown into nonoptimal conditions of moisture.

There is an implicit assumption in the conventional HTT and VOP models, that the seed water potential is equal to the ambient water potential, whereas in reality there is a delay before the seed equilibrates following a step change in water potential. This is of little consequence when the models are fitted to germination data collected from various constant water potentials, and used to predict germination in constant water potentials. However, the potential errors of using these models in conditions where water potential varies and seed water potential takes time to equilibrate are illustrated in Fig. 4b,d. The effect was best illustrated by simple stepwise changes in water potential, as it can be less clear in more complex environments because of compensating errors resulting from different characteristics of the models.

A logical approach to the problem described above is to use seed water potential estimates in the HTT and VOP models calculated from an imbibition model, rather than ambient water potential. Such combined IVOP and IHTT models predicted the timing of germination more accurately than the conventional models during stepwise changes in water potential (Fig. 4b,d). A further limitation of the basic HTT model also becomes apparent: unlike the VOP model, no advancement in predicted germination time is made as a result of time spent between Ψmin and Ψb when osmotic priming will occur. However, this could be addressed by the inclusion of a further model for hydrothermal priming time (Cheng & Bradford, 1999), as discussed by Bradford (1995).

The use of seed water potential rather than the ambient water potential addresses one potential inaccuracy in the use of threshold models to predict germination in variable soil conditions. However, there are other potential problems, such as the establishment of water potential gradients in the soil surrounding the seed as they imbibe. These gradients could have particular importance for larger seeds such as those of maize and chickpea, and implications when simulating a comparison of primed and untreated seeds in soil. Other complicating factors when estimating imbibition include changes at the seed–soil interface; the extent of seed–soil contact; and the relative contribution of water from vapour phase to seed imbibition (Hadas, 1970, 1982; Vertucci, 1989). The latter may be more important than previously considered (Wuest et al., 1999). Elsewhere, seed–soil contact and water uptake in the liquid and vapour phases have been considered in models for maize seed imbibition (Bruckler, 1983a, 1983b). In the present work a more parsimonious approach was adopted, in keeping with the general philosophy of threshold models in maintaining simplicity and having few parameters.

The process of imbibition has been clearly described in maize (McDonald et al., 1994). These authors suggest that water is taken up through two separate pathways, the first resulting in near full embryo hydration within 15 h, and the second resulting in endosperm hydration that can take longer than 48 h. At germination, the moisture content of the embryo was > 50%, whereas the moisture content of the endosperm was still 25–30%, and it subsequently continued to wet up. In maize the embryo is positioned to one side of the seed, and imbibition of the embryo is more rapid if that side, rather than the side containing only endosperm, is in contact with moisture. To take account of this in the experiments here, maize seeds were always placed embryo-side down in contact with the membrane. In order to reduce any additional variation in imbibition between individuals, all chickpea seeds were also placed in the same orientation with the embryonic axis in contact with the membrane.

Water uptake by the seed generally occurs in three phases: rapid initial uptake, a lag phase with limited further uptake, then a second phase of rapid water uptake associated with radicle emergence (Bewley & Black, 1994). Imbibition is identified with the first phase of water uptake and is regarded as a physical process, although metabolic activity is initiated as the seeds reach Ψmin, well before they reach full moisture content. Initial water uptake into a dry seed is driven by matric forces resulting from the hydration of cell walls, starch and protein bodies, etc. As the physiological range of water contents is approached, there is a greater dependence on osmotic potential determined by the concentration of dissolved solutes (Vertucci, 1989; Bewley & Black, 1994). There is no unique relationship between matric potential and water content in a porous material so it is likely to display hysteresis, whereas osmotic solutions do not display hysteresis and there is a single relationship between osmotic potential and solute concentration. Seed advancement and germination occur at these water potentials, and it is therefore reasonable in the models developed here to ignore any potential inaccuracy resulting from hysteresis that may occur at low seed moisture contents. A lack of hysteresis has also been assumed in other imbibition models (Bruckler, 1983a, 1983b).

Published soil environment data (Townend et al., 1996) collected in Tanzania were used with the IHTT and IVOP models to simulate seed germination and investigate potential advancement from priming under field conditions representing those found in the semiarid tropics. It was clear from the simulation that priming seeds of both species could have a major impact on the timing and, in particular, the number of seedlings emerging in a drying seedbed (Fig. 7). Subsequent rainfall, not considered in the simulation, may well trigger further germination from untreated seeds; however, seedling emergence would be significantly delayed and likely to be spread over time with the potential for uneven growth and maturity dates within the crop. Sowing depth, as it relates to moisture, was critical to the proportion of seeds that would germinate from both primed and untreated seeds, and farmers would aim to sow into moisture. Continued drying of the soil after sowing would favour seedling emergence from primed seeds. Resource-poor farmers will hand-sow, and this generally results in seeds at a range of depths and therefore soil moisture contents. In a drying seedbed, priming would clearly aid the germination of seeds sown close to the surface where the soil dries most quickly. However, the more rapid germination of the primed seeds may also aid those sown more deeply. This is because the seedbed can deteriorate with time and, in general, its negative impact increases with sowing depth and consequent delay in emergence. Increasing impedance can be a major problem under these conditions for maize (Murungu et al., 2004). Townend et al. (1996) show that, for cowpea and sorghum, emergence can be low even when germination is high as a result of increasing impedance to emergence. However, greater emergence of cowpea compared with sorghum resulted, in part, from more rapid emergence. Priming would advance germination, especially under nonoptimal conditions of moisture. The effect this can have is illustrated in Fig. 7. Germination of maize was greater than that of chickpea in the drying seedbed conditions used, and the potential benefit of priming in maize is less than in chickpea. Maize has a more negative Ψmin and Ψb than chickpea, indicating greater tolerance to dryer conditions.

This paper illustrates difficulties in the use of conventional HTT and VOP models under conditions that vary, and suggests a potential improvement. An imbibition model was used to provide estimates of seed water potential for use with the HTT and VOP models, rather than ambient water potential. The combined IVOP and IHTT models simulated the timing of germination more accurately than the conventional models during stepwise changes in water potential. This ability to simulate the effects of variable ambient environments on germination has many applications in agriculture and ecology, especially in situations where resources or costs prohibit experiments with multiple sowing dates. This potential was illustrated in a comparison of primed and untreated seeds in the semiarid tropics.


This document is an output from a project (Plant Sciences Research Programme R7440) funded by the UK Department for International Development (DFID) and administered by the Centre for Arid Zone Studies (CAZS) for the benefit of developing countries. The views expressed are not necessarily those of DFID. We thank John Townend and colleagues for generously making available to us their field environment data from Tanzania, recorded during work funded by ODA NRI grant EMC X0237. We also thank ICRISAT for supplying chickpea seeds, and Lawrence Clark and Richard Whalley for many useful discussions during this work.