Journal of Experimental Botany, Vol. 50, No. 334, pp. 655–664, May 1999
Modelling the effects of water stress and temperature on
germination rate of Orobanche aegyptiaca seeds
E. Kebreab and A.J. Murdoch1
Department of Agriculture, The University of Reading, Earley Gate, P.O. Box 236, Reading RG6 6AT, UK
Received 8 September 1998; Accepted 7 January 1999
Abstract
Orobanche aegyptiaca seeds were germinated at a
range of water potentials and temperatures and the
progress of germination within the seed population
was modelled. Base water potentials (at which the rate
of progress towards germination is zero) varied
between individual seeds according to a normal distribution with a mean of −1.96 MPa and standard deviation of 0.33 MPa at 20 °C. Contrary to the underlying
assumption of the hydrothermal time model in the
literature, the median base water potential varied
significantly with temperature, being c. −2 MPa at
14–23 °C and increasing at both higher and lower temperatures. Thermal times to germination also varied
according to a normal distribution between individual
seeds with a mean of 49 °Cd and standard deviation
of 18 °Cd in water. The median thermal time to germination varied with water potential. Again, however,
an assumption of the hydrothermal time model was
found to be invalid since the base temperature for rate
of germination also varied significantly with water
potential. The relationships of both base temperature
and thermal time to water potential were linear such
that germination progress curves in 33 different hydrothermal environments (8–26 °C and 0 to −1.2 MPa)
could be described according to a new modified
thermal time model which accounted for 78% of the
variation in the data.
Key words: Water stress, temperature, Orobanche aegyptiaca, germination rate, hydrothermal time models.
and in the field, water stress often limits germination
(Benech-Arnold and Sanchez, 1995). At an optimum
temperature for germination with water and oxygen freely
available, the uptake of water by seeds has three phases
(Ching, 1972). During the first phase, dry seeds with
water potentials generally between −350 and −50 MPa
(Roberts and Ellis, 1989) imbibe rapidly when placed in
contact with free water. This imbibition is a purely
physical process that occurs equally in live or dead seeds
(Hegarty, 1978). During the second or lag phase, major
metabolic events take place in live seeds in preparation
for radicle emergence and can be considered to be the
period of germination sensu stricto which is terminated
by the initiation of growth (Bewley and Black, 1978).
Water uptake sharply increases in the third phase which
is concurrent with radicle elongation (Bewley and
Black, 1994).
Imbibition at reduced water potential lowers the rate
of water uptake and final seed water content during the
first phase, extends the length of the second phase and
delays entry into the third phase (Bradford, 1986).
Gummerson (1986) and Bradford and co-workers
(Bradford, 1990; Bradford et al., 1993a, b; Dahal et al.,
1996) have researched the relationship between germination rate, temperature and reduced water potential in
sugar beet (Beta vulgaris L.), tomato (Lycopersicon esculentum Mill.) and lettuce (Lactuca sativa L.). This paper
tests some of their hypotheses on seeds of Orobanche
aegyptiaca and proposes an alternative model to overcome
acknowledged shortcomings of the existing hydrothermal
time model.
Thermal time
Introduction
Temperature and moisture are important factors that
determine the rate of germination of non-dormant seeds
At suboptimal temperatures for the rate of germination,
the rate of progress towards germination of fraction g of
a seed population is a linear function of mean temperature
1 To whom correspondence should be addressed: Fax: +44 118 935 2421. E-mail [email protected]
© Oxford University Press 1999
656 Kebreab and Murdoch
(T, °C ), that is,
1/t =K+mT
(1)
g
where the rate of germination is the reciprocal of the time
(t , days) from the start of the germination test and K
g
and m are constants (Labouriau, 1970; Bradford, 1995).
The base temperature T , at which the germination rate
b
is by definition zero, is −K/m. The reciprocal of the
slope (1/m) is the thermal time (h , °Cd ) above T
T(g)
b
which must be accumulated to achieve g% germination
(Garcia-Huidobro et al., 1982). The equation can therefore be rearranged as follows,
1/t =(T−T )/h
(2)
g
b T(g)
The base temperature is a seed lot and probably a species
characteristic ( Ellis and Butcher, 1988) while thermal
time varies within the seed lot according to a normal
distribution (Covell et al., 1986; Ellis et al., 1986). The
germination time-course in terms of thermal time is
therefore quantified as:
probit (g)=K +(h /s )
(3)
T
T(g) hr
where K is a constant and s is the standard deviation
T
h
of the frequency distribution r of thermal times in the
population. Since by definition probit (50%) is zero when
expressed in normal equivalent deviates, it follows that
K =−h
/s where h
is the median thermal time
T
T(50) h
T(50)
to germination rin water, that is, for the 50th percentile.
Substituting for h
from equation (2), equation (3)
T(g)
can be rearranged as follows,
probit (g)=[(T−T )t −h
]/s
b g
T(50) hr
(4)
Hydrotime
Bradford (1990) introduced the idea of hydrotime where
seed germination can be predicted in terms of the delaying
effects of reduced water potential on germination at a
single constant temperature. The rate of progress towards
germination of fraction g of a seed population is a linear
function of water potential, y (MPa), that is,
1/t =K+my
(5)
g
where K and m are constants. In an analogous way to
the thermal time analysis, the base water potential (y ),
b(g)
where the rate of germination of fraction g is by definition
zero, is −K/m. The reciprocal of the slope (1/m) is the
‘hydrotime’ (h , MPa d), which must be accumulated
H
above the base water potential to achieve g% germination.
The equation can therefore be rearranged as follows,
1/t =(y−y )/h
(6)
g
b(g) H
Most importantly, Gummerson (1986) found that the
slope of the relationship between germination rate and
water potential was the same for all fractions of the sugar
beet seed populations he studied. The hydrotime was
therefore, constant for all seeds in the population at a
single temperature. It therefore follows that the variation
in times to germination among seeds in the population is
a direct consequence of variation in base water potentials
within each seed lot (Gummerson, 1986; Bradford, 1990;
Dahal and Bradford, 1990). This variation in base water
potentials approximates to a normal or Gaussian distribution and, in theory, germination of the gth seed in the
seed population occurs when that seed has accumulated
h hydrotime units above its base water potential (y ).
H
b(g)
The germination time-course can therefore be described
according to the following equation,
probit (g)=K +y /s
(7)
y
b(g) yb
where s is the standard deviation of y
values in the
hb
b(g)
population.
From equation (6),
=y−h /t
(8)
b(g)
H g
Substituting in equation (7) and rearranging in a similar
form to equation (4),
y
probit (g)=[y−(h /t )−y
]/s
(9)
H g
b(50) yb
The parameter estimates in this equation, however, vary
with temperature.
Hydrothermal time
Gummerson (1986) proposed that the effects of temperature and water potential on germination rate might be
combined on a hydrothermal time-scale such that rates
in thermal time depend on water potential rather than
rates in actual time as in equation (6), that is,
=(y−y )/h
(10)
T(g)
b(g) HT
where h
is the hydrothermal time (MPa °Cd).
HT
Substituting the value of h
from equation (2) in
T(g)
equation (10),
1/h
h =(y−y ) (T−T )t
(11)
HT
b(g)
b g
Rearranging equation (11) in terms of y , substituting
b(g)
for y in equation (7) and rearranging in a similar form
b(g)
to equation (9), the germination time-course can be
described as follows:
probit (g)=[y−(h /(T−T )t )−y
]/s
(12)
HT
b g
b(50) yb
Since h and h are assumed constant for all fractions
HT
H
of the population (Gummerson, 1986), the ratio of h /t
T(g) g
must be constant. Mathematically, this ratio can only be
constant if the base temperature is constant. Equation
(11) therefore implies that the base temperature is the
same at each water potential and that the base water
potential is the same at each temperature. Dahal et al.
(1993) reported that they found the general model
Germination of Orobanche seeds 657
(equation 12) explained 75% of the variation in germination of tomato seeds. They also found that the assumptions might not always be true but apart from pointing
out the better accuracy of the models when each temperature and water potential were analysed separately, they
failed to offer an alternative model that would account
for the observed variation.
Objectives
The objectives of this paper are therefore to (a) test and
quantify the validity of the hydrotime and thermal time
models (equations 1–6) in relation to the effects of water
potential and temperature on germination of O. aegyptiaca, (b) test the hypotheses that base water potential and
temperature are independent and that base temperature
and water potential are independent, i.e. to test the
assumptions of the hydrothermal time model, and (c)
develop a new model to predict the progress of germination of O. aegyptiaca at different water potentials and
temperatures.
The species used in this study, O. aegyptiaca, is a smallseeded (0.25 mm long) root-holoparasitic plant that
attacks mainly solanaceous plants such as tomato and
tobacco among other horticultural crops ( Teryokhin,
1997). The seeds have an absolute requirement for germination of an imbibition period known as conditioning
followed by exposure to a stimulant which, in the natural
environment, is produced by the roots of the host plant
(Sahai and Shivana, 1982). Studies on the effect of water
stress on germination of parasitic weeds especially
Orobanche are noticeably lacking in the literature. Those
that mention water potential were in an attempt to explain
the effect of nitrogen on germination (Abu-Irmaileh,
1981; Nandula et al., 1996).
Materials and methods
O. aegyptiaca seeds were collected at the Newe-Yaar Research
Centre in Israel in June 1995 from plants parasitizing tomato.
The seeds were stored in black plastic containers and immediately dispatched to Reading where they were stored in the dark
at 3–5 °C before use. All water was deionized and then
autoclaved before use. Filter papers and seeds were sterilized as
described in Kebreab and Murdoch (1999).
A range of osmotic potentials was produced using aqueous
solutions of polyethylene glycol (PEG 6000, Merck) prepared
according to Michel and Kaufmann (1973). Contact of seeds
with PEG 6000 solution does not inhibit seed germination
(Emmerich and Hardegree, 1990). The water used in preparing
the solutions contained 3 ppm GR24 to stimulate germination.
Storage and handling of this artificial stimulant are described
in Kebreab and Murdoch (1999).
The experiment was conducted on a temperature gradient
plate (Murdoch et al., 1989) in an air-conditioned dark room.
The plate operated in one direction and provided 13 constant
temperature regimes between 5 °C and 40 °C.
The seeds were placed between 9 mm diameter glass fibre
filter discs ( Whatman GF/A). These discs were placed in 9 cm
Petri dishes on top of two layers of filter paper ( Whatman
No. 1, 9 cm circles). The dishes were moistened with 5 ml water
in order to condition the seeds for 2 weeks at 20 °C. The discs
containing the seeds were then placed on a non-sterile filter
paper to remove excess moisture. Polystyrene boxes
(4.5×4.5×1.9 cm) were used for germinating seeds on the
temperature gradient plate. The boxes were sterilized with 1%
NaOCl solution for 10 min and rinsed thoroughly. The boxes
were then dried and lined with two layers of filter paper
( Whatman No. 1, 4.4×4.4 cm) and one upper layer of glass
fibre filter ( Whatman GF/A, 4.4×4.4 cm). Three millilitres of
the appropriate solution of PEG with GR24 were added to
each box. The boxes were left to stabilize for 2 h on the
temperature gradient plate, after which the discs were placed
on top of the glass fibre paper and the boxes were covered with
their lids. The boxes were sealed with parafilm to avoid moisture
loss, but were opened daily for aeration.
Treatments were replicated twice and lasted for up to 80 d.
Germination was counted periodically. When counting, one
box at a time was taken from the plate and germinated seeds
were counted and removed in an adjacent room at a temperature
of about 20 °C. The box was sealed again and immediately put
back to its original place. Each count took less than 5 min
per box.
Statistical analysis
A germination progress curve was constructed for each of the
temperature regimes by taking the average of the replicates.
Estimates of the times taken for germination to reach 10, 20,
30, 40, 50, 60, 70, 80, and 90% (where applicable) were
interpolated from the graphs. The germination rate (1/t ) was
g
then calculated for each percentile. At suboptimal temperatures
for the rate of germination, linear models of rate of
germination as a function of temperature were fitted for each
percentile.
To test the hypothesis that the base temperature (T ) was
b
common to all percentiles, it was necessary to get an initial
estimate of T by semi-manual iteration using GENSTAT
b
(Genstat 5 Committee, 1994). Models were fitted which
constrained the lines for each percentile (6–9 depending on
water potential ) through a common value. The resultant base
temperature was incremented by 0.5 °C and ultimately narrowed
to a resolution of 0.1 °C. The value of T which produced the
b
lowest residual deviance was accepted. Another model in which
the base temperature was allowed to vary for the different
percentiles was then tested and compared with the common
base temperature model. A common base temperature for all
the water potentials was also compared with a model that
allowed separate base temperatures. A consequence of this
method is that standard errors are not available for T .
b
To fit the hydrotime model, straight lines were fitted to
explain the relationship between water potential and germination
rate and regressions of models for separate and common slopes
at each temperature were compared. Using probit analysis, the
variation of the base water potential was tested to see if it was
normally distributed among the seed population. Using the
method of repeated probit analysis developed by Ellis et al.
(1986), the hydrotime constant that best described the relationship was estimated. In the same procedure, parameters for the
mean and standard deviation of the distribution were estimated.
The analysis was repeated for all the temperature regimes
tested. The expected germination was then calculated using the
parameters estimated. It should be noted that the last 10% of
seeds to germinate were not included in the final analysis.
658 Kebreab and Murdoch
Fig. 1. Germination rate of O. aegyptiaca at (A) 0, (B) −0.2, (C ) −0.6, (D) −0.9, and ( E ) −1.2 MPa. The germination percentages analysed
were 10% (%), 20% (+), 30% (O), 40% (,), 50% (6), 60% (&), 70% (( ), 80% ($) and 90% ()). Lines were fitted according to equation (2).
Results
Effect of water potential on base temperature and thermal
time
Germination rates of each percentile derived from germination time-courses of O. aegyptiaca were linear functions of temperature up to 26 °C at 0 to −0.6 MPa and
up to 23 °C at −0.9 and −1.2 MPa (Fig. 1). No seeds
germinated above 32 °C (data not shown). The base
temperatures did not differ significantly between percentiles (P<0.05) at given water potentials ( Fig. 1). At 5 °C
for 0 to −0.6 MPa, some seeds (<10%) germinated,
giving an apparent inconsistency with the predicted base
temperatures (Fig. 1B, C ).
The base temperature did, however, increase significantly (F-ratio=19.2 on 4 and 236 df ) with decrease in
water potential (Fig. 2). This dependence of base temperature on water potential means that the assumption of
independence in the hydrothermal time model is not valid
at least in O. aegyptiaca.
Thermal time (the inverse of the slopes of the lines in
Fig. 1) was also modified by water potential. The thermal
time model (equations 3 and 4) fitted the data well such
that seed to seed variation corresponded to a normal
distribution provided each water potential was analysed
separately ( Fig. 3). Separate analyses are required partly
because the base temperature varied with water potential
and partly because the seed to seed variation in thermal
time increased with decrease in water potential. Thus the
standard deviation of the distribution of thermal time
within the seed population increased with decrease in
water potential ( Table 1, cf. slopes in Fig. 3).
Gummerson, Bradford and co-workers’ model vis-á-vis
Orobanche
The hypothesis that there is a linear relationship between
germination rate and water potential (equation 6) was
tested at 8 temperatures ( Fig. 4 shows an example at
20 °C ). Between 8 °C and 29 °C, statistical analysis showed
that there was no evidence for non-parallelism among the
lines for each percentile at any temperature and the
common slope models had R2 values of more than 90%.
In order to estimate the parameters in equation (9),
probit (g) was regressed as a function of y−h /t (which
H g
is the base water potential, equation 8). The median base
Fig. 2. Base temperatures of O. aegyptiaca seeds at different water
potentials calculated from the common base temperature models of
Fig. 1 (equation 2).
Germination of Orobanche seeds 659
Fig. 3. Thermal time for progress of germination of O. aegyptiaca seeds at water potentials of (A) 0, (B) −0.2, (C ) −0.6, (D) −0.9, and (E )
−1.2 MPa and temperatures of 5 (%), 8 (+), 11 (O), 14 (,), 17 (6), 20 (&), 23 (( ), 26 ($) and 29 °C ()). Lines were fitted by probit analysis
according to equation (4).
Table 1. The effect of water potential on the standard deviation
(s ) of the thermal time for germination in O. aegyptiaca
hT
The standard deviation is the reciprocal of the slope of the regression
of probit germination against thermal time ( Fig. 3, equation (3)).
Estimated slopes and standard errors (s.e.) are shown.
Water potential
(MPa)
s
hT
(°Cd)
Slope (s.e.)
0
−0.2
−0.6
−0.9
−1.2
12.18
13.67
17.21
24.96
36.81
0.082
0.073
0.058
0.040
0.027
(0.0024)
(0.0022)
(0.0017)
(0.0014)
(0.0014)
water potential was then calculated as the value where
probit (g) equals zero and s as the inverse of the slope.
y
Figure 5 shows an example ofb the fitted line at 20 °C and
the parameter estimates for all temperatures are summarized in Table 2. The goodness of fit of the hydrotime
model (equation 9) exceeded 90% when each temperature
was analysed separately ( Table 2). The attempt, however,
to extend the analysis to all temperatures and water
potentials using the hydrothermal time model (equation
12) was unsuccessful because the residual variance
exceeded the variance in observed germination.
The reasons for failure of the hydrothermal time model
to fit the data are clear. The median base water potential
decreased up to an optimum of about 14 −23 °C and
then it increased again ( Table 2). The interaction of
temperature and water stress is clearer when both temper-
Fig. 4. The effect of water potential on germination rates of O.
aegyptiaca seeds at 20 °C. Germination percentiles illustrated are 10%
(%, 20% (+), 30% (O), 40% (,), 50% (6), 60% (&), and 70% (( ).
Lines with common slopes were fitted according to equation (5).
Dotted lines are extrapolations of the data down to the base water
potential for each percentile.
ature and water potential are plotted against germination
rate ( Fig. 6). When the germination rates are extrapolated
to zero, the base temperature, increased approximately
linearly with decrease in water potential while the base
water potentials show a curvilinear relationship with
660 Kebreab and Murdoch
Fig. 5. Probit analysis of germination time-courses of O. aegyptiaca as
a function of base water potential, equation (9). Seeds were germinated
at 20 °C in water potentials of 0 (%), −0.2 (+), −0.6 (O), −0.9 (,),
and −1.2 MPa (6). The parameter estimates of the fitted line are
in Table 2.
Fig. 6. Germination rate to 50% (1/t ) of O. aegyptiaca seeds incubated
50
at water potentials of 0 to −1.2 MPa and a range of temperature from
5–29 °C (O). Solid lines were fitted according to equation (14) and
broken lines represent extrapolated base water potentials. The base
water potentials calculated by equation (8) are indicated by solid
symbols ($).
Table 2. Parameter estimates for predicting germination time-courses of O. aegyptiaca at different temperatures according to equation (9)
The standard deviation (s ) is the reciprocal of the slope of the regression of probit germination against base water potential (equations 8 and 9;
yb
Fig. 5). Estimated slopes and
standard errors (s.e.) are shown.
Temperature
(°C )
Hydrotime
(h , MPa d)
H
Median base water
potential
(y
, MPa)
b(50)
8
11
14
17
20
23
26
29
16.30
11.33
11.08
7.43
6.66
4.93
3.32
3.06
−1.34
−1.62
−2.08
−1.99
−1.96
−1.98
−1.60
−1.51
temperature (Fig. 6). Thus the underlying assumptions
of the hydrothermal time model are invalid for this
dataset.
Modelling the hydrothermal effect on germination
Assuming T and h both vary linearly with water potenb
T
tial, equation (2) can be rewritten as
1/t =(T−T −m y)/(h −m y)
(13)
g
b(0)
b
T(g)
T
where T
is the base temperature in water and m and
b(0)
b
m are the rates of change in T (°C MPa−1) and h
T
b
T
(°Cd MPa−1), respectively, due to water potential.
When each percentile was analysed separately, this new
model (equation 13) explained more that 98% of the
variation in each case. The variation in parameter estimates between percentiles ( Table 3) was then used to
Standard deviation
of base water potential
(s , MPa)
yb
0.287
0.293
0.351
0.319
0.334
0.381
0.325
0.384
Slope (s.e.)
3.49
3.41
2.85
3.13
3.03
2.62
3.12
2.67
(0.14)
(0.11)
(0.10)
(0.12)
(0.12)
(0.11)
(0.16)
(0.15)
develop an overall model for the progress of germination.
There was no significant variation in the estimated T as
b
would be expected after introduction of a correction
factor for each water potential ( Table 3) while m and
b
m appear to be randomly distributed among the percentT
iles (Table 3). However, the variation in estimated h
T
appeared to be approximately normally distributed in the
population of seeds ( Fig. 7) as might be predicted from
equation (3).
From equation (13), the thermal time for germination
of fraction g as modified by water potential is
=t (T−T −m y)+m y
(14)
T(g) g
b(0)
b
T
Substituting for h
in equation (3), the overall proT(g)
gress of germination at different temperatures and water
potentials could be explained in terms of the modified
h
Germination of Orobanche seeds 661
Table 3. Parameter estimates using equation (13) at different germination percentages; standard errors are given in brackets
Percentile
Base
temperature in water
(T , °C )
b(0)
Effect of water
potential on T (m )
b b
Thermal time
in water (h , °Cd )
T
Effect of water
potential on h
T
(m )
T
10
20
30
40
50
60
70
80
3.8
3.7
3.8
4.0
4.2
4.2
4.1
4.4
−2.7
−2.5
−2.0
−1.7
−2.9
−3.5
−3.8
−4.2
38.6
41.4
42.9
43.6
45.3
47.3
49.5
52.9
17.3
21.9
28.1
34.7
26.3
22.8
27.6
19.1
(0.34)
(0.35)
(0.43)
(0.57)
(0.50)
(0.52)
(0.70)
(0.66)
(0.62)
(0.66)
(0.85)
(1.15)
(1.01)
(1.02)
(1.54)
(2.14)
Fig. 7. Variation in expected thermal time in water at various percentiles
of germination. Each data point is the result of individual analysis of
the percentiles according to equation (13).
thermal time being normally distributed among the
population.
probit (g)=K +(t (T−T −m y)+m y)/s
T
g
b(0)
b
T
hT
(15)
This model explained 78.1% of the variation in the
observed values (Fig. 8).
Equation (15) can be further rearranged to be compared more easily with equation (9) and its relation to
equation (4) is clearer.
probit (g)=[t (T−T −m y)+m y−h
]/s
g
b(0)
b
T
T(50) hT
(16)
where h
is the median thermal time to germination in
T(50)
water. Parameter estimates for equation (16) are shown
in Table 4.
Discussion
Gummerson (1986) developed a general model which
combined the thermal time and hydrotime models. While
this paper supports the hypotheses that base water potentials are distributed normally within seed populations and
(0.91)
(0.99)
(1.29)
(1.74)
(1.52)
(1.68)
(2.32)
(2.36)
(2.39)
(2.76)
(3.87)
(5.67)
(5.10)
(5.60)
(8.40)
(11.3)
that hydrotime is a seed lot constant, two crucial assumptions of the hydrothermal time model have been shown
to be incorrect in O. aegyptiaca.
First of all the current experiment categorically showed
that in O. aegyptiaca, base temperature increased with
decrease in water potential (Figs 1, 2, 6). Other workers
have also found that temperature and water potential
were not independent of each other. Fyfield and Gregory
(1989) found that base temperature increased as the
water potential decreased in mung bean indicating that
the greater the water stress, the less capable were the
seeds of germinating at low temperatures. El-Sharkawi
and Springuel (1977) found a significant interaction
between temperature and water potential. Gummerson
(1986) cited research where results were better accommodated by slight changes in base temperature (Akeson
et al., 1980) or a large variation in base temperature
( Williams and Shaykewich, 1971) and speculated that
the hydrothermal time to germination might not be
constant.
Secondly, although the base water potential values were
found to be normally distributed, the median base water
potential varied systematically with temperature ( Table 2;
Fig. 6). Interestingly, it was lowest at about 14–23 °C
( Fig. 6) which is the optimum germination temperature
for O. aegyptiaca ( Kebreab and Murdoch, 1999). This
indicates that the seeds are capable of germinating with
higher levels of water stress at optimal temperatures.
The optimum temperature for rate of germination is
therefore higher (26–29 °C, Fig. 1) than the optimum
temperature with respect to the final germination percentage. Even though fewer seeds may germinate at 29 °C,
those which do may be germinating in rapidly drying
soils. So a difference in optima for rate of germination
compared to total germination is beneficial to seedling
survival. Orobanche seeds as in most parasitic plants are
at their most vulnerable between initiation and attachment to host roots; particularly just after radicle emergence and before formation of the haustorium. Therefore,
in order to minimize the time taken during this vulnerable
stage, rapid germination is necessary once stimulant has
been detected.
662 Kebreab and Murdoch
Fig. 8. Germination progress curves of O. aegyptiaca seeds incubated in water potentials of 0 (%), −0.2 (+), −0.6 (#), −0.9 (,), and −1.2 MPa
(6) at constant temperatures of 8–26 °C (data at 5 °C and 29 °C are not shown because most seeds failed to germinate at these temperatures). The
lines were fitted according to equation (16). Note that the x-axis is extended for 8 °C and 11 °C compared to 14–23 °C.
Germination of Orobanche seeds 663
Table 4. Parameter estimates in equation (16) to fit germination
progress curves of O. aegyptiaca in different hydrothermal
environments
Parameter
Base temperature (T , °C )
b(0)
Effect of water potential on
T (m , °C MPa−1)
b b
Effect of water potential on
h (m , °Cd MPa−1)
T T
Median thermal time
(h
, °Cd )
T(50)
Standard deviation of h
T
(s , °Cd)
hT
Estimate
Standard error
with water potential and base water potential with
temperature could be quantified and were essential to
account for these data. The overall goodness of fit was
without systematic bias and the five parameter model
(equation 16) proved capable of describing the progress
of germination of O. aegyptiaca in 33 hydrothermal
environments ( Fig. 8).
3.55
−2.44
0.24
0.31
33.60
2.75
49.12
1.70
Acknowledgements
17.89
1.12
Our thanks to Dr D Joel for kindly providing the seeds, to
Professor RH Ellis for helpful discussions, to Dr A Hodge for
statistical advice and to Colin Bishop for advice on computing.
We are also grateful to the following organizations which have
provided partial financial support to EK: The Society for
Protection of Science and Learning, The Africa Educational
Trust, The Heinz and Anna Kroch Foundation, The Sir Richard
Stapley Educational Trust, The Maximillian Trust, The Sidney
Perry Foundation, The Churches Commission for Overseas
Students, The Leonard Sutton Scholarship Fund of the
University of Reading, The Julius Silman Trust and The
Leche Trust.
Although the hydrotime model predicts seed germination times well across a range of water potentials at a
given single constant temperature (Fig. 5), the significant
interactions of temperature and base water potential
observed in cereals ( El-Sharkawi and Springuel, 1977)
diminishes the value of considering hydrotime and
thermal time independently. Other workers have also
reported variation of y
at different temperatures
b(50)
(Sharma, 1976; Welbaum and Bradford, 1991; Battaglia,
1993). On the other hand, some studies have found no
interaction between temperature and water potential
( Khah et al., 1986), but since the latter experiment was
carried out in the field with a limited range of hydrothermal environments, the conclusion must be treated
with caution.
In O. aegyptiaca, the hydrotime model fitted the data
quite well when the data were analysed separately for
each temperature ( Table 2). The introduction of the
‘hydrothermal constant’ with its associated assumptions
meant that the hydrothermal time model could not
satisfactorily explain the variation observed in O. aegyptiaca to the extent that it proved impossible to fit the
model (equation 12) to the data. The ability of the new
model to explain only 78% of the variation compared to
98% when the percentiles were analysed separately could
probably be due to the variations observed in m and
b
m ( Table 3). Future work may therefore be needed to
T
investigate why there is so much variation in m and m .
b
T
While accepting that the hydrothermal time model
developed by Gummerson and applied by Bradford and
co-workers may be found satisfactory in some species
and in some datasets, there is also substantial evidence
that temperature and base water potential can depend
on each other. The inability of this model to account for
the results of this study in seeds of O. aegyptiaca has
therefore led to the development of a new and more
general model that allows for an interaction of temperature and base water potential. The present model was
developed using a dataset with a wider range of water
potentials and temperatures than previous work which
might help to explain why variations in base temperature
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