Journal of Experimental Botany, Vol. 52, No. 364, pp. 2187–2197, November 2001
Seed reserve-dependent growth responses
to temperature and water potential in
carrot (Daucus carota L.)
W.E. Finch-Savage1,3, K. Phelps1, J.R.A. Steckel1, W.R. Whalley2 and H.R. Rowse1
1
2
Horticulture Research International, Wellesbourne, Warwick CV35 9EF, UK
Silsoe Research Institute, Wrest Park, Silsoe, Bedford MK45 4HS, UK
Received 18 June 2001; Accepted 26 June 2001
Abstract
Introduction
Both temperature and soil moisture vary greatly in
the surface layers of the soil through which seedlings
grow following germination. The work presented
studied the impact of these environmental variables
on post-germination carrot growth to nominal
seedling emergence. The rapid pre-crook downward
growth of both the hypocotyl and root was consistent
with their requirement for establishment in soil drying
from the surface. At all temperatures, both hypocotyl
and root growth rates decreased as water stress
increased and there was a very distinct temperature
optimum that tended to occur at lower temperatures
as water stress increased. A model based on the
thermodynamics of reversible protein denaturation
was adapted to include the effects of water potential
in order to describe these growth rate responses.
In general, the percentage of seedlings that reached
the crook stage (start of upward hypocotyl growth)
decreased at the extremes of the temperature range
used and was progressively reduced by increasing
water stress. A model was developed to describe
this response based on the idea that each seedling
within a population has lower and upper temperature
thresholds and a water potential threshold which
define the conditions within which it is able to grow.
This threshold modelling approach which applies
growth rates within a distribution of temperature
and water potential thresholds could be used to
simulate seedling growth by dividing time into
suitable units.
The distribution of seedling emergence in time, as well
as the number of seedlings that become established has
a major influence on the dynamics of plant communities
and subsequent competition between individual plants in
crop, weed and natural populations. The emergence time
of individual seedlings is the result of a complex interaction of ambient weather conditions, soil, seed and seedling characteristics that influence their germination and
subsequent reserve-dependent growth. Finch-Savage et al.
have shown that delays in the mean time to seedling
emergence were due largely to delays in germination, but
that seedling losses and variation in the spread of seedling
emergence times within the population occurred largely
during the post-germination growth phase (Finch-Savage
et al., 1998).
Significant progress has been made in the prediction
of germination times from a population of seeds under
variable conditions of temperature and soil moisture
(Gummerson, 1986; Finch-Savage and Phelps, 1993; Dahal
and Bradford, 1994; Bradford, 1995; Finch-Savage et al.,
1998; Rowse et al., 1999). However, knowledge of preemergence seedling growth is more limited, especially in
relatively small dicot seeds. Of the wide range of factors
that can influence pre-emergence growth, three are ubiquitous: temperature, moisture and mechanical impedance. If the effect of these variables can be explained and
modelled then more meaningful studies of the impact
of intermittent problems such as soil crusting can be
made. Whalley et al. studied the impact of mechanical
impedance at a limited range of water potentials and suboptimal temperatures (Whalley et al., 1999). The present
work considers how this phase of reserve-dependent
growth is affected by water potential at temperatures
covering both the sub- and supra-optimal range.
Key words: Daucus carota, seedling growth threshold models,
water stress, temperature, seedling establishment.
3
To whom correspondence should be addressed. Fax: q44 789 470552. E-mail: [email protected]
ß Society for Experimental Biology 2001
2188
Finch-Savage et al.
A number of studies have been made of the response of
pre-emergence seedling growth to temperature (Wanjura
et al., 1970; Blacklow, 1972; Hsu et al., 1984; Wheeler and
Ellis, 1991; Weaich et al., 1996, and references therein).
Different methods have been used to describe growth
data from different species, but in many cases a thermal
time approach has been adopted which assumes growth
rate is linearly related to temperature. This approach
can provide useful predictions of the timing of seedling
emergence for some applications. However, linearity usually occurs over a limited temperature range. In addition,
soil moisture varies greatly in the surface layers of the soil
through which seedlings grow. The utility of thermal time
for seedling emergence prediction is therefore limited in
practice. Fewer studies have been made on the interaction
of temperature and water potential on pre-emergence
seedling growth (Fyfield and Gregory, 1989; Choinski
and Tuohy, 1991).
The kinetics of development in response to temperature is similar in many organisms (animal and plant)
whose temperature is dependent on ambient conditions
(poikilotherms). In these organisms development can be
described using models based on the thermodynamics of
reversible protein denaturation (Sharpe and DeMichele,
1977). Within these models, rate of development is determined by the reversible inactivation, at high and low
temperatures, of developmental control enzymes. This
approach accommodates the linearity in response over
a limited temperature range that has been adopted
in thermal time models. However, it also accommodates the non-linearity often observed outside that range
(Hsu et al., 1984). The present work describes the adaptation of an improved model formulation derived by
Schoolfield et al. to include the response to water
potential (Schoolfield et al., 1981).
The mechanisms that determine the timing of seed
germination in many species under variable soil conditions are such that germination occurs only when sufficient moisture is available for the initial seedling growth
(Ross and Hegarty, 1979; Finch-Savage and Phelps,
1993). Near the soil surface germination therefore tends
to occur most often after rainfall. Following germination,
initial growth of both the root and hypocotyl of epigeal
seedlings is downwards, arguably as an adaptation to
maintain contact with soil moisture in the surface layers
of the soil which dry rapidly. A crook then forms in the
hypocotyl to facilitate upward growth. Further growth
is by extension of the hypocotyl to pull the cotyledons
to the soil surface. In the present work carrot has been
used as a representative epigeal seedling with the limited
reserves of a small seed. However, the success of seedling emergence in carrot crops has immediate practical
relevance because it directly influences both their yield
and monetary value (Finch-Savage, 1995). For example,
although it is plant density that determines both total
yield and mean root size in carrot crops (Bleasdale,
1967), the variation in seedling emergence times can
greatly influence the uniformity of plant size at harvest
(Benjamin, 1982). This in turn determines the proportion
of the crop in the higher-value size grades specified by
markets. An understanding of the causes of variation in
seedling emergence both within and between sowing
occasions is therefore necessary to determine efficient
crop production practices in carrot and to predict their
outcome.
The approach taken in the present work furthered the
aim to develop the components of a simulation model
for seedling emergence in the variable environmental
conditions of surface soil layers.
Materials and methods
Carrot (Daucus carota L; F1 hybrid; cv. Narman) seeds were
size graded to 1.6–2 mm. Before use in experiments they
were soaked in a 3.2% aqueous solution of sodium dichloroisocyanurate (Sigma-Aldrich Co. Ltd, Poole, UK) for 6 min to
surface-sterilize them, then rinsed five times in distilled water
and redried to their initial moisture content of 8.5% (wet weight
basis). After treatment, their viability in germination tests
(% normal seedlings, ISTA, 1996) was 93%.
In the following experiments, either dry, ungerminated seeds
or seeds selected with emerged radicles (- or ¼ 1 mm) were laid
on a single layer of moist absorbent tinted paper (T300,
Papierfabriek Schut bv., Heelsum, Holland) in transparent
polystyrene boxes (20 3 80 3 125 mm) in the dark. There were
five replicate boxes per treatment, each containing 12 seeds
on which seedling growth was recorded. The seeds were in a row
40 mm from the base end of a sloping box held in racks contained in a plastic propagator. The whole assembly was placed
in a polyethylene bag to prevent moisture loss and covered with
thick black polyethylene sheet to exclude light. Seedlings were
exposed to light from a single fluorescent tube during measurement only. The assemblies were held in cabinets with temperature control that varied by less than 0.5 8C. Temperature
was monitored continuously by thermistors placed, like seeds,
on moist paper.
Following germination, all growth measurements were made
from the hypocotyluroot join to the tip of the root or the tip of
the crook using digital calipers (Helios-Mebtechnik, Germany).
Experiment 1
The time of germination (radicle emerged), crook formation and
daily measurements of root and hypocotyl growth were recorded
from individual dry seeds placed on moist absorbent paper at
20 8C until growth ceased.
Experiment 2
Germinated seeds were selected at 66 h and 96 h of imbibition
(the times when the 25th and 75th quartiles germinated in preliminary experiments) from separate bulks of seeds placed on
moist absorbent paper towels in plastic trays (75 3 400 3 700 mm)
in the dark at 20 8C. The two seed bulks were placed to
germinate at appropriate times that allowed the selection of 66 h
and 96 h samples at the same time. As seeds were selected with
radicles - or ¼ 1 mm (i.e. just germinated) the 66 h and 96 h
Seedling growth models 2189
samples were considered to represent the 25th and 75th quartiles
of the seed population only. Thus representative percentiles of
the bulk of the population could be compared and seed from
the tails of the distribution of germination rates were avoided.
Following selection, seeds were kept moist and placed in boxes
with their radicles in contact with the moist paper. In this way,
seeds were placed in all combinations of eight temperatures
between 3 8C and 35 8C and six water potentials between 0 and
1.2 MPa. These treatments were set up on different occasions,
but on each occasion both fractions of the seed population
were used. The experimental design therefore comprised five
replicates of an 8 3 6 3 2 factorial. Seedlings were observed at
least daily and more frequently in near optimal conditions for
growth. The root and hypocotyl length was measured on each
individual seedling on two occasions, as the crook formed and
when the hypocotyl length was approximately 15 mm (nominal
seedling emergence).
Water potentials were established using aqueous solutions of
polyethylene glycol (PEG 20 000, Merck, Munchen, Germany).
This was preferred to a moist solid matrix as it allowed
continuous monitoring of seedlings growth and enabled seedling
exposure to accurate and constant values of water potential.
This is not possible in a matrix, because steep potential profiles
can develop at the surface of the seedlings as they take up water.
When seedlings are submerged in PEG solutions they can
become oxygen stressed. This is unlikely in the present system
where seedling roots are, at most, covered by a thin film of PEG.
Thus the surface area of the PEG exposed to oxygen compared
to its volume is very large.
PEG solution (12.5 ml) was placed in the box laying flat. The
box was then placed at an angle in the rack when the paper was
fully moist, excess solution drained to the base of the box and
then germinated seeds were placed on the paper. In germination
experiments it is common practice to move seeds to new
filter paper and solution at regular intervals. However, growing
seedlings could be damaged by moving them. Therefore to
maintain constant conditions, at each observation the box was
laid flat to wash the solution over the seedlings. In addition, at
weekly intervals the excess solution in the box was replaced.
Calibration curves of PEG concentration and water potential
were constructed. The water potential measured was that of
a filter paper disc placed at the position of the seed on filter
paper in a box as used for seedling growth measurements.
Measurement was made 48 h after setting up the box. The filter
paper disc was placed into the chamber of a sealed Peltier-type
thermocouple psychrometer unit (C52 units connected to an
HR-33T dewpoint microvoltmeter; Wescor Inc, Logan, UT,
USA.) and water potential was measured at the required
temperatures. The values determined were used to make up
solutions used in experimental treatments. Calibration curves
and experiments were carried out with the same batch of PEG.
The problem of exclusion of PEG from the absorbent paper
(pointed out by Hardegree and Emmerich, 1990) was taken into
account by having an excess of solution and by measuring water
potential using moist paper discs in the psychrometer.
Statistical methods
Rates of growth for roots and hypocotyl, before and after crook
formation, were estimated for each seedling based on an initial
root length of 1 mm. To allow for either linear or exponential
growth they were calculated from both the raw data and the
logarithms of the raw data. Preliminary inspection of these data
was by a stratified analysis of variance based on a factorial set of
seven temperatures (3, 7, 10, 15, 20, 25, and 30 8C), three water
potentials (0, 0.21 and 0.59 MPa) and two germination
quartiles (25% and 75%) chosen to exclude treatments where
few seeds had germinated.
Model for seedling growth rates: Sharpe and DeMichele proposed a model to describe how the rate of a biological process
is affected by temperature (Sharpe and DeMichele, 1977).
Their model is derived from the following assumptions: (1) at
all temperatures, the development rate of a poikilotherm
population is determined by a single rate-controlling enzyme
reaction; and (2) this rate-controlling enzyme is reversibly
inactivated at high and low temperatures, but a constant total
concentration (activeqinactive) is maintained independent of
temperature. Their model was later reformulated (Schoolfield
et al., 1981) by replacing three of its six parameters by three
new thermodynamic parameters with more intuitive biological
interpretations. Parameter estimation was better under the
new formulation because there was less correlation between
parameters and initial estimates could be obtained by visual
inspection of graphs.
The Schoolfield et al. model used in this paper is:
"
#
HA6¼ 1
T
1
exp
rð25 CÞ
298
298 T
R
rðTÞ ¼
HL
1
1
HH
1
1
1 þ exp
þ exp
T1=2L T
T1=2H T
R
R
(1)
where r(T ) is growth rate at temperature T(K), r(25 8C) is
the development rate at the standard reference temperature
of 25 8C assuming no enzyme inactivation (298 K ¼ 25 8C),
R is the universal gas constant (1.987 cal deg1 mol1), DHA/
is the enthalpy of activation of the reaction that is catalysed
by the enzyme (cal mol1), DHL, DHH are the changes in
enthalpy associated with lowuhigh temperature inactivation of
the enzyme (cal mol1), T1u2L , T1u2H are the temperatures (K)
at which the enzyme is 12 active and 12 lowuhigh temperature
inactive (Schoolfield et al., 1981).
This model was chosen because it has a physical basis and was
developed to describe growth processes. Although the original
nomenclature is retained no attempt is made to interpret the
coefficients in terms of the reaction processes that determine
seedling growth. However, the coefficients are expressed as
functions of water potential thus allowing the model to be
applied under all conditions of temperature and water potential.
These functions were derived by inspection of the data, although
in practice there were insufficient data points to propose anything more complex than linear or exponential functions. As
suggested by Schoolfield et al. specification of the model was
facilitated by the study of Arrhenius plots where logarithms
of rate are plotted against the inverse of temperature (K)
(Schoolfield et al., 1981). These plots provide guidance as to
where there is high or low temperature inactivation; in addition
they showed which parameters were affected by water stress.
Once a model had been proposed, preliminary estimates of the
parameters were made from the Arrhenius plots and model (1)
was fitted to the data from the 25th and 75th germination
quartiles using the FITNONLINEAR command of Genstat
(Genstat 5 Committee, 1993).
Model for the percentage of seedlings reaching the crook
stage: The model developed is based on the idea that each
seedling within a population has lower and upper thresholds
which define the temperature range within which it is able to
grow and reach the crook stage. Likewise it has a water potential threshold below which it cannot grow and reach the crook
stage. In the model it is assumed that these thresholds are normally distributed within the seedling population so that the
2190
Finch-Savage et al.
final percentage of seedlings reaching the crook stage at any
given temperature or water potential can be predicted. This
general approach is explained at length by Grundy et al. who
used it to model percentage germination within seed populations (Grundy et al., 2000). They estimated the parameters of
the model using a generalized linear model (McCullough and
Nelder, 1989) with a binomial error distribution and a probit
link function. Inspection of the percentage of seedlings that
formed a crook in the present work suggested that the same
form of generalized linear model was appropriate to describe
these data.
Results
Experiment 1
Lengths of roots and shoots of a sample of individual
seedlings were plotted against time and the pattern of
growth of the seedling with median germination time is
shown in Fig. 1. Following germination, both the root
and hypocotyl contribute downward growth (Fig. 1b, c),
a crook then forms (Fig. 1d) and all subsequent hypocotyl
growth is upward while all root growth is downward
Fig. 1. The pattern of carrot seed germination and early seedling
growth. (a) downward growth (h, hypocotyl; j, root plus hypocotyl)
and upward growth (m) following germination of the median seed in the
population. (b–f ) Schematic representation of seedling growth stages.
(g) Cumulative germination (solid), crook formation (dotted) and
nominal seedling emergence (15 mm upward growth, dashed) of the
seed population at 20 8C in the dark.
(Fig. 1e, f ). This pattern of growth is the same for all
individuals in the population. However, post-crook
growth was sometimes linear and sometimes exponential
across the population. No abnormal seedling growth
(Bekendam and Grob, 1979) was recorded in this seed lot.
Figure 1g shows the distribution of times taken within
the population to germinate, form a crook and to achieve
15 mm of upward growth (nominal seedling emergence).
In general, the earliest germinating seeds tended to have
faster seedling growth (first decile of the population to
germinate, 7.1 mm d1) than the latest germinating
seeds (last decile to germinate, 5.2 mm d1) resulting in
a greater spread of nominal emergence times than germination times. However, growth rate was similar in the
bulk of the population.
Experiment 2
Seedling growth rates: Henceforth seedling growth rates
are referred to as (1) root pre-crook, (2) root post-crook,
(3) hypocotyl pre-crook, (4) hypocotyl post-crook.
Analyses of variance using logarithmic transformation
indicated that all four growth rates were affected by
temperature and water potential (P-0.05), but there was
no significant difference between the 25th and 75th
quartiles. Using untransformed data all four rates showed
a significant (P-0.001) interaction between temperature
and water potential, but again there was no evidence
of a difference between the quartiles. The two germination quartiles were therefore treated as replicates in
subsequent studies on growth rates. Subsequently, rates
were used based on linear growth of the hypocotyl before
crook formation and exponential growth otherwise.
The reasons for this are discussed later.
Frequency distributions of the four rates were characterized to investigate their utility for building models
of seedling populations. Histograms were drawn based
on the 120 seedlings from each combination of temperature and water potential and the means, standard
deviations and skewness were inspected. Few of the
distributions showed evidence of skewness and for each
of the rates there was a strong correlation between the
standard deviation and the mean. Normal distributions were fitted to all of the distributions with more than
10 recorded seedlings. These fitted well with only 3 of
33, 8 of 30, 3 of 33, 5 of 30 for rates 1 to 4, respectively,
showing a significant lack of fit (P-0.01) according to
a chi-squared test.
Means and standard deviations for each combination
of temperatures and water potentials were calculated
from the mean rates of the seedlings in 10 (5 replicates
3 2 quartiles) boxes of each combination. The standard
deviations were linearly related to the means. This
indicates that the frequency distributions for all combinations of each rate had the same coefficient of variation.
Seedling growth models 2191
Regression analysis provided estimates of these
coefficients (14.2%, 16.9%, 24.0%, 13.8% for rates 1 to
4, respectively) and a measure of goodness of fit (r2 ¼ 0.78,
0.84, 0.90, 0.69 on 32 df for rates 1 to 4, respectively).
These coefficients of variation measure the variation
between seedlings placed in different boxes rather than
just variation between seedlings. These were thought
more appropriate to the situation in field soil.
Comparison of rates 2, 3 and 4 with rate 1 indicated that
the four rates were highly intercorrelated (r2 ¼ 0.913,
0.951 and 0.917 for rates 2, 3 and 4, respectively). The
close relationship between hypocotyl and root growth
rates for the pre- and post-crook stages is illustrated in
Fig. 2. These results show that the root : shoot ratio was
unaffected by environment.
The rates of growth of individual seedlings were examined to see whether seeds with slower rates pre-crook were
also slower post-crook and whether seeds with slow
growing roots tended to have slow growing hypocotyls.
Seeds from a relatively slow-growing treatment combination (15 8C and 0.2 MPa) were classified according to
the four quartiles of each of the four rates and contingency tables constructed to make the comparisons
(Tables 1, 2). In the absence of an association very similar
numbers of observations would have been expected in
each cell of the table. A chi-squared test on 9 df was used
to determine the significance of any association. No
association was found with pre-crook hypocotyl growth
rate, but there was an association between root rates
pre- and post-crook (P-0.001, Table 1) and between
root rates post-crook and hypocotyl rates post-crook
(P-0.001, Table 2). A similar effect was observed in the
other treatment combinations.
Fig. 2. The relationship between the pre-crook root growth rate and
(k) pre-crook hypocotyl growth rate (mm d1), and (%) post-crook
hypocotyl and (m) post-crook root growth rates (loge mm d1). Data
are means across all treatments.
r (25 C) ¼ exp(b0qb1(W ));
Modelling seedling growth rates: The five replicates of
each quartile were combined so that temperature and
water potential effects could be quantified, but data
from the two quartiles were kept separate to give some
indication of the variability in the data. A clear pattern
emerged when rates were plotted against temperature
and water potential (Fig. 3). At all temperatures rates
decreased as water stress increased. There was a very
distinct rate optimum that tended to occur at lower
temperatures as water stress increased.
When these data were drawn as Arrhenius plots
(Fig. 4) a consistent effect of water potential became
apparent. It is proposed that the approximately linear
region between 283 and 303 K (Fig. 4) is the range where
there is neither low nor high temperature inactivation.
Increasing the amount of water stress reduced the growth
rate, but it did not affect the slope of the line. Water stress
also affected the temperature at which inactivation
occurred. Based on this interpretation, equation (1)
was reformulated so that some of the parameters were
functions of water potential. The consistent response to
water potential at central temperatures implied that DHA/
remained the same at all water potentials. Of the remaining parameters only the relationship of r (25 8C) to water
potential could be readily determined; graphs of logarithm of rate versus water potential at each temperature show that they form a set of straight lines. In the
absence of other evidence, T1u2L and T1u2H were assumed
to be linearly related to water potential whilst D HL and
D HH remained constant. Thus equation (1) was modified
to include
T1u2L ¼ b2qb3(W ) and
T1u2H ¼ b4qb5(W )
Table 1. Contingency table showing the relationship between pre-crook and post-crook root growth rates at 15 8C and 0.2 Mpa
Each cell contains the corresponding number of observations in each quartile of the population.
Root post-crook
Fourth quartile
Third quartile
Second quartile
First quartile
Root pre-crook
Median rates
0.28
0.35
0.38
0.41
Fourth quartile
Third quartile
Second quartile
First quartile
0.46
0.54
0.57
0.62
11
6
3
4
6
4
11
4
5
11
5
3
2
4
5
14
2192
Finch-Savage et al.
Table 2. Contingency table showing the relationship between post-crook hypocotyl and post-crook root growth rates at 15 8C
and 0.2 Mpa
Each cell contains the corresponding number of observations in each rate quartile of the population.
Hypocotyl
post-crook
Fourth
quartile
Third
quartile
Second
quartile
First
quartile
Root post-crook
Median rates
1.31
1.52
1.68
1.88
Fourth quartile
Third quartile
Second quartile
First quartile
0.28
0.35
0.38
0.41
16
5
2
1
2
7
9
7
4
8
4
8
2
5
9
9
Fig. 3. The effect of temperature and water potential on seedling growth rates. (a) Pre-crook root, (b) pre-crook hypocotyl, (c) post-crook root,
(d) post-crook hypocotyl. Curves according to Equation 1 are fitted to data collected at each nominal water potential; (k) water, (u) 0.2 MPa,
(n) 0.5 MPa, (\) 0.6 MPa, and (e) 0.8 MPa. The curves are drawn for the water potentials listed in the headings of Table 4, but where appropriate the parameter estimates are based on values in the footnote of that table. Note different scales, growth rates assume exponential growth
except for pre-crook hypocotyl (b) see text.
The model parameters were estimated separately for
the pre-crook and post-crook stages (Table 3). At both
stages the parameters of the model were constrained to be
the same for root and hypocotyl growth rates. However,
root rates were multiplied by a further parameter that
estimated the ratio of the root rates to the hypocotyl
rates. The model fitting procedure was weighted by the
number of recorded seedlings. Additional weighting by
the reciprocal of the rate values (suggested by Schoolfield
et al., 1981), was tried but this gave too much emphasis to
the fit of low rate values. To reduce errors in predicting
seedling emergence under field conditions, good estimation of faster rates is more important than that of slower
rates. For both pre-crook and post-crook the fitting
Seedling growth models 2193
Table 4. Percentage of seeds from the 25th germination percentile
that reach the crook formation stage
Values in parenthesis are fitted using the model described in the text
(Equation 2).
Temperature
(8C)
Water potential (MPa)
0
3
7
10
15
20
25
30
35
Fig. 4. Arrhenius plots for pre-crook root growth rate at a range of
water potentials. Symbols as for Fig. 3.
Table 3. Parameters of seedling growth rate models
Parameter
Pre-crook
estimate
SE
Post-crook
estimate
SE
b0
b1
b2
b3
b4
b5
DHA/
DHL
DHH
Rootuhypocotyl ratio
0.7131
1.293
276.31
0
304.84
6.86
15035
57595
46244
0.9006
0.0944
0.115
1.68
–
1.57
1.35
2458
36794
4459
0.0103
0.075
1.1515
278.85
0
304.85
2.49
10729
37562
45571
1.0676
0.113
0.0887
3.95
–
2.49
1.57
4838
17109
5780
0.0119
procedure failed unless b3 was set to 0 suggesting that
T1u2L did not interact with water potential. In general, the
curves generated from the model fitted the data well
(Fig. 3).
Modelling seedling numbers reaching crook formation:
The percentage of seedlings that reached the crook formation stage was greatly influenced by temperature and
water potential (Table 4). In general, the percentage
decreased at the extremes of the temperature range and
was progressively reduced by increasing water stress. This
effect was greater with the slower germinating seeds
(75th percentile; data not shown) than with the faster
germinating seeds (25th percentile). This pattern of
results clearly shows the impact of the distribution of
temperature and water potential thresholds for growth
within the population.
Several stages of scrutinizing graphs (not shown) were
used to develop an empirical model to describe the distribution of temperature and water potential thresholds
for growth: (1) Graphs of normal equivalent deviates
(probits) of the percentages against water potential produced parallel straight lines for all temperatures of each
a
93
97
98
100
98
95
97
97
(100)
(100)
(100)
(100)
(100)
(100)
(99)
(92)
0.21
0.48
0.59
0.77
96
98
95
90
97
95
93
93
80
98
97
92
97
78
75
0
48
73
85
95
88
75
15
0
0
0
20
37
47
0
0
0
(94)
(98)
(99)
(99)
(99)
(98)
(91)
(62)
(80)
(76)
(83)
(88)
(85)
(91)a
(72)a
(34)a
(35)
(56)
(66)
(73)
(69)
(53)
(26)
(5)
(7)
(17)
(30)
(37)
(33)
(16)
(4)
(0)
Water potential, 0.35 MPa.
of the two germination percentiles. (2) For each percentile, plotting intercepts for each temperature against the
corresponding temperature values produced quadratic
curves. (3) When these quadratic curves were compared
for the two quartiles they were parallel. Therefore a
model was fitted that incorporated terms for the quartiles
thus:
s ¼ nW 1 (2:675 0:02144pq0:1912T
0:006083T 2 qQy )
(2)
where s is the number of seedlings reaching the crook
stage, n is the number sown, p is the germination
percentile (25 or 75), T is the temperature (8C), y is
the water potential (MPa). W1 is the inverse of the
normal probability function. Q ¼ 5.151 and 3.896 for
the 25th and 75th percentiles, respectively. The residual
mean deviance was 9.5 on 90 df. The model provided
a relatively simple description of the main features of
the data (Fig. 5). Fitted values from the model for the
25th percentile in each treatment combination are given
in Table 4.
Analysis of variance of the lengths of the roots and the
hypocotyls at the time of crooking showed a statistically
significant (P-0.001 and P-0.01, respectively) interaction between temperature and water potential, but
these effects were small relative to those amongst the
rates. The overall mean values of 10.8 and 2.8 mm
determined for root and hypocotyl lengths, respectively,
were therefore considered to be sufficiently accurate for
simulation purposes. The relatively constant value of the
lengths at crook formation and the major effects of
temperature and water potential on the pre-crook growth
rates led to a substantial range of times to crook
formation. For example, times ranged from 0.96 d at
25 8C in water, through 10 d at 7 8C in water to 57.8 d
at 3 8C and 0.77 MPa.
2194
Finch-Savage et al.
Fig. 5. The effect of water potential and temperature on the numbers of
seedlings that reach the stage of crook formation. The response surface
shown is the output from Equation 2 describing data in Table 4 for the
25th percentile.
Discussion
Seedling growth
There is a reversible moisture-sensitive block to germination that prevents germination in drying soils (Ross
and Hegarty, 1979; Finch-Savage and Phelps, 1993;
Finch-Savage et al., 1998) and therefore seeds tend
to germinate following rain or irrigation. In the absence
of subsequent rain, only a brief opportunity for the
completion of germination and seedling growth may
be presented before the surface soil layers dry again, but
the seedsuseedlings appear adapted to this. Seed ‘priming’
in the soil (Rowse et al., 1999, and references therein)
means that germination can be rapid when water becomes
available and then the initial rapid downward growth
of both the root and hypocotyl, described here, will
contribute to maintaining contact with soil moisture as
the surface layers dry. The hydraulic conductivity of soil
in the surface layer quickly falls to a very low value as
drying continues and this will tend to reduce the rate of
water loss from deeper layers (Lascano and van Bavel,
1986). The seedling root will therefore grow into
increasingly wet soil and may not subsequently become
severely water stressed. This same scenario is likely for
seeds in the surface layers of soil under natural conditions. The initial period of downward seedling growth
following germination is therefore critical to successful
seedling establishment.
Both temperature and water potential had large predictable effects on seedling growth and these will interact
under variable conditions. For example, seedling growth
rate increased as sub-optimal temperature increased, however in soil, higher temperature is associated with more
rapid drying of the surface layers. Consequently, the rate
of growth will decrease as the soil around the seedling
starts to dry. For example, growth rate in the present
work was reduced to c. 50% at –0.5 MPa compared to
that in water. Thus soil moisture can rapidly become a
limiting factor during post-germination seedling growth.
Whalley et al. show that elongation rates of pea seedlings
were similar when subjected to either a soil matric potential or to an osmotic potential in a PEG 20 000 solution
(Whalley et al., 1998). It is therefore reasonable to consider that the results collected in the present work will
represent seedling growth in the soil in the absence of
significant impedance to growth.
Even at optimum temperatures growth ceased so that
most seedlings failed to reach crook formation at water
potentials between 0.6 and 0.8 MPa, which could
explain the data presented by Hegarty of percentage
carrot seedling emergence in soils of different water
potentials. In that work, there was a sharp decline from
c. 70% to 10% seedling emergence at approximately
0.6 MPa (Hegarty, 1976). In other work carrot seedling
growth immediately after germination was completely
arrested in 50% of the population at 0.87 MPa (Ross
and Hegarty, 1979). In preliminary work germinated
onion seeds were grown alongside germinated carrot
seeds on polyethylene glycol solutions in the same box. At
0.8 MPa carrot growth was prevented, but onions
continued to grow past crook formation (data not
presented). This indicated that threshold water potentials
for growth differ between these two species and that, as
suggested by Lawlor, there is no toxic effect of high
molecular weight polyethylene glycol (PEG 20 000)
(Lawlor, 1970). Therefore, growth arrest is a result of
water stress not some property of PEG (20 000). In
addition, carrot seedlings that did not grow at 0.8 MPa
subsequently grew when transferred to water (data not
shown). However, if they were held for a long time
at 0.8 MPa the radicle tip turned brown and regrowth
appeared to result from a secondary initial. This has
a practical consequence, because partial drying of the
newly-germinated root can result in the production of
split roots with consequent impact on the value of the
carrot crop when harvested (Globerson and Feder, 1987).
In practice, models of germination and subsequent seedling growth could be used to time water applications to
avoid interrupted progress to seedling emergence and
prevent root damage. This approach has so far been used
to time a single irrigation for improved germination
(Finch-Savage and Steckel, 1994).
Pre-emergence seedling growth is seed reservedependent and in carrots the final length of seedlings
depends on the initial seed weight (Tamet et al., 1994),
although relative growth rate is not directly influenced by
initial seed weight (Tamet et al., 1996). In the absence of
a crust, carrot seedlings can emerge through 45–50 mm
Seedling growth models 2195
of soil without significant reduction in the percentage of
seedlings that emerge (Tamet et al., 1996). However,
extension of the hypocotyl to more than c. 10 mm before
emergence resulted in reduced subsequent growth and a
reduced ability to penetrate soil crusts. Delayed seedling
emergence also reduced post emergence growth as a result
of reduced efficiency for photosynthesis (Tamet et al.,
1996). Accurate seedling emergence models could be used
to time irrigation events to limit these effects of delayed
emergence and reduce the impact of time-dependent
seedbed deterioration.
There are differences in the rate of seedling growth
within the seedling population that can be directly
related to germination rate in carrots (Finch-Savage and
McQuistan, 1988). Results from experiment 1 confirm
this result and show that at the extremes of the population the fastest and slowest germinating seeds had
the fastest and slowest post-germination growth rates,
respectively. However, both experiments 1 and 2 show
that although growth rates vary in the bulk of the
population (at least within those selected as 25th to 75th
percentiles) these differences are not associated with
germination time. After germination, seedlings with the
fastest pre-crook growth rates had the fastest post-crook
root and hypocotyl growth rates. This correlation did not
extend to pre-crook hypocotyl growth and it is possible
that this part of seedling growth may result from cell
elongation only, in line with the seedlings’ ability for
rapid downward growth when water is available in the
surface layers of the soil. An absence of cell division in
early growth may account for the relatively constant
mean pre-crook length of the hypocotyl and of the root
across temperature and water potential treatments.
Hypocotyl growth can result from both cell division and
elongation or from elongation only depending on the
species (Galli, 1988). In Arabidopsis thaliana elongation is
initiated at the base of the hypocotyl (Gendreau et al.,
1997) consistent with the initial rapid downward growth
observed here before crook formation in carrot.
Modelling seedling growth
In onion (Allium cepa L.), pre-crook cotyledon growth
was linearly related to time and thereafter increased
exponentially with time (Wheeler and Ellis, 1991). Exponential pre-emergent seedling growth has also been
reported in a wide range of species (Wanjura and Buxton,
1972; Hsu et al., 1984; Wheeler and Ellis, 1991; Weaich
et al., 1996) and was thought to end when seed reserves
became exhausted (Wanjura and Buxton, 1972). In the
present work with carrot, both pre- and post-crook
hypocotyl growth could be adequately described by a
linear or exponential model. This may be because seedling
growth was recorded to 15 mm only, a nominal sowing
depth commonly used by commercial growers, so that
above this length seedlings would emerge in practice.
Using the same seed lot as in the present work Whalley
et al. grew seedlings for longer than those recorded here,
and then seedling growth could be described more accurately by an exponential model (Whalley et al., 1999).
Therefore a linear model was used for pre-crook hypocotyl growth and an exponential model for the other three
growth stages. This is consistent with growth by cell
elongation only in the hypocotyl before crook formation
and by cell division and expansion in the other growth
phases. Elsewhere, in Vicia faba the exponential phase of
growth was associated with the onset of cell division
(Rogan and Simon, 1975).
In
germination
studies,
hydrothermal
time
(Gummerson, 1986; Bradford, 1995) has been widely
adopted to describe the seeds’ response to water potential
and temperature. This approach uses linear rate relationships within temperature and water potential thresholds.
The non-linear nature of the data presented here makes
this model unacceptable, as it has in some germination
studies (Marshall and Squire, 1996). However, the
widespread use of computers enables more complex
approaches to rate data feasible, when this can be
justified. Thus threshold models can be developed to
provide a more accurate description of the data while
retaining a similar general approach. In the present work
the utility of such a model to describe the impact of
temperature and water potential on the growth rates of
seedlings within thresholds for growth has been shown.
The rates at all stages of development were correlated,
except pre-crook hypocotyl growth. Furthermore the
studies on the frequency distribution of the growth rates
suggested that they were normally distributed with
constant coefficients of variation. Thus a simulation
could be built, from the model presented, to describe the
growth of a whole population by selecting a random
normal deviate for each seedling then calculating rates
according to the organ (root or hypocotyl) and development stage. This model could also indicate the time of
crook formation. It is important to have this information
in a simulation of seedling emergence as it defines the
point when upward growth starts with the associated
impact of soil impedance to growth, a factor that is also
dependent on soil water potential (Whalley et al., 1999).
The crook formation model provides thresholds for
pre-crook downward growth. The central importance
of rapid pre-crook growth to the successful completion of
seedling emergence in variable soil conditions has been
discussed above. Currently, as far as these authors are
aware, this initial downward growth of both the root and
hypocotyl is not considered in any models of seedling
emergence. The work presented, provides a quantitative
basis for including this growth pattern into simulations of
seedling emergence. It extends understanding of seedling
growth from small seeds and can be combined with the
2196
Finch-Savage et al.
growth rate model into a simulation by dividing time into
suitable units. The full seedling emergence simulation
would include other models that describe seed germination (Rowse et al., 1999) and the impact of soil impedance
to growth (Whalley et al., 1999) in the same species.
Seedling emergence simulation has obvious application
for indicating best establishment practices, not least the
timing of irrigation to give maximum effect on germination and growth with minimum impact on seedbed
deterioration. In a wider context the simulation could
be adapted to describe the establishment of weeds and of
natural plant communities.
Acknowledgements
We thank the Ministry of Agriculture Fisheries and Food for
funding this work and Margaret Jones for drawing Figure 1.
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