A Population-based Threshold Model Describing the Relationship

Journal of Experimental Botany, Vol. 44, No. 264, pp. 1225-1234, July 1993

A Population-based Threshold Model Describing the Relationship Between Germination Rates and Seed Deterioration KENT J. BRADFORD 1 - 3 , ANA M. TARQUIS 2 and JOSE M. DURAN 2 1

Department of Vegetable Crops, University of California, Davis, California 95616-8631, USA

2

ET.S. Ing. Agronomos, Universidad Politecnica de Madrid, Ciudad Umversitaria, 28040 Madrid, Spain

Received 5 March 1993; Accepted 27 April 1993

Key words: Lettuce, Lactuca sativa L., germination rate, seed deterioration, seed viability.

INTRODUCTION A seed has a finite lifetime that is dependent primarily upon the temperature and moisture content at which it is stored. Seed deterioration occurs progressively during storage and it is generally assumed that, as damage accumulates on a cellular or biochemical level, germination will first be delayed, then abnormal seedlings will begin to appear and, eventually, even the ability to initiate growth will be lost (Delouche and Baskin, 1973; Heydecker, 1972). The occurrence of deaths in a seed population is normally distributed in time, and Roberts and Ellis (Ellis, 1988; Ellis and Roberts, 1980a, b, 1981; Roberts, 1986; Roberts and Ellis, 1989) have elegantly illustrated how probit analysis can be used to quantify the initial seed quality and the rate of loss of viability in 3

To whom correspondence should be addressed.

© Oxford University Press 1993

a given storage environment. Their model proposes that individual seeds have maximum lifetimes and will begin to display the various symptoms of deterioration at specific times prior to the complete loss of viability. Thus, within a population of seeds, the percentage germinating within a given time period, the percentage developing into normal seedlings, and the percentage capable of radicle emergence will be described by a series of parallel declining sigmoid curves offset toward progressively longer storage periods (Ellis and Roberts, 1981). The time required for germination is an important component of seed vigour and it increases as seeds age prior to the loss of viability (Dell'Aquila, 1987). In fact, there is a linear relationship between the logarithm of the

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ABSTRACT The time required for germination increases prior to the loss of viability as seeds deteriorate during siorage. We have developed a population-based threshold model that can quantify and predict seed germination times and percentages after various ageing periods under constant conditions. The model assumes that each seed has a maximum potential lifetime, the values of which vary in a normal distribution among individual seeds, and that the time to germination of a particular seed is inversely proportional to the remaining difference between the accumulated ageing period and the maximum lifetime of that seed. This model described with reasonable accuracy the germination time-courses of lettuce (Lactuca saliva L.) seeds after increasing periods of controlled deterioration at 10% moisture content (fresh weight basis) and 40 °C. In seeds of high initial quality, two phases of deterioration were detected, a relatively slow phase before significant loss of viability occurred and a more rapid phase once viability began to decline. Prehydration and redrying treatments that shortened the time to germination also reduced or eliminated the initial lag phase before the loss of viability began. Seed germination rates after different ageing periods can be normalized on a common 'ageing-time' scale, emphasizing the continuous and progressive nature of deteriorative processes in seeds. The model predicted, and the data confirmed, that there was a critical imbibition time after which no additional normal seedlings would germinate. This critical imbibition time for a given seed lot was independent of the ageing period. The maximum lifetime threshold model, in conjunction with previous population-based models of seed viability during storage, can provide a quantitative description of seed germination rates and normal or abnormal seedling percentages throughout the storage life of a seed lot.

1226 Bradford et al.—Threshold Model of Seed Deterioration

Despite this cogent analysis of seed germination rates in relation to seed deterioration, we are unaware of any attempts to apply this concept directly in order to describe quantitatively the germination time-courses actually observed in a population of ageing seeds. The log-linear relationship between mean germination time and probit viability has been empirically verified, but is not a direct consequence of the viability equations used to quantify seed longevity (Ellis and Roberts, 1980a). This relationship also does not account for the increase in mean time to germination prior to the time when viability is lost by some fraction of the population. In addition, calculating the mean time to germination on the basis of the remaining viable seeds uses a changing fraction of the initial population to estimate germination rate. For example, when 100% of the seeds are viable, the median time to germination will coincide with the time to 50% germination of the entire population. However, if only 50% of the seeds are viable, the median time to germination will coincide with the time when the 25th percentile of the original population germinated, and the actual time to 50% germination would be the time when the last viable seed germinated. A strict application of the

principles outlined by Ellis and Roberts (1981) should be able to account for the progressive delay in germination of any percentile in the original population in relation to the normally distributed maximum lifetimes within that population. Failure to germinate, or death, of a particular fraction of the population would be equivalent to an indefinitely long time to radicle emergence, at least, longer than the duration of the germination test. Many mathematical models have been developed to describe the cumulative seed germination time-course as a function of imbibition time (Brown and Mayer, 1988; Scott et al, 1984). These approaches are useful for specific purposes, and can give curves that match very closely to actual data. However, although physiological significance can sometimes be attributed to the parameters of the equations, they remain empirical functions that are not based on biological principles (Brown and Mayer, 1988). The equations must be fit to individual time-courses using as many as four variables and do not readily allow the effects of a change in a given quantitative factor (such as storage time) to be predicted. They also do not explicitly account for the population variation in germination times among individual seeds that is the basis of the sigmoidal shape of the cumulative germination time-course. Recognizing the variation inherent in seed populations, Janssen (1973) applied cumulative normal distributions to germination data. However, unlike the normal distribution, germination time-courses are generally not symmetric, but are skewed toward longer times as maximum germination percentage is approached (Brown and Mayer, 1988). Expressing the time axis on a logarithmic scale is one method to normalize cumulative germination curves (Dahal et al., 1990). Alternatively, Campbell and Sorensen (1979) showed that the inverse of time to germination (germination rate) is normally distributed within a seed population. Thus, cumulative germination time-courses can be linearized by plotting probit of germination percentage versus either the inverse or the logarithm of imbibition time (Campbell and Sorensen, 1979; Dahal et al., 1990). A population-based threshold model incorporating these concepts has been used to describe and quantify the responses of germination to water potential and plant growth regulators (Bradford, 1990; Dahal and Bradford, 1990; Gummerson, 1986; Ni and Bradford, 1992, 1993). This model assumes that each seed has a threshold, or base, response level for a given factor, and that the thresholds vary in a normal distribution among individual seeds. The time to germination for a given seed fraction or percentage g is inversely proportional to the difference between the actual level of the factor and the factor threshold level. If we consider a given factor X that influences germination rate, we can define the expression

ex=(x-xb(g))t.

(i)


mean time to germination of the remaining viable seeds and the probit of per cent viability after various storage periods (Argerich et al., 1989; Ellis and Roberts, 19806, 1981; Roberts, 1986; Tarquis and Bradford, 1992). That is, as viability is lost in a seed population, the time to germination of the remaining viable seeds increases exponentially. In seed lots with very high initial quality, the mean time to germination may increase considerably before a significant loss in viability can be detected in standard germination tests (Argerich et al., 1989; DelPAquila, 1987; Tarquis and Bradford, 1992). Thus, an increase in the time to radicle emergence is an early indication of declining seed vigour. The relationship of germination rate to seed viability was postulated by Ellis and Roberts (1981): '[T]he pattern of deterioration with regard to increasing time taken to germinate is the same for all seeds. Of course at any one time during storage the seeds, if tested, will take different periods to germinate, because their remaining lifespans differ. It is clear that within a given storage environment each seed progresses through an identical pattern of deterioration with regard to the time taken to germinate which culminates in death. Within a population this end-point is normally distributed in time and differences between populations can be simply described by a measure of the proximity and variation of the population to this end point.' The time to germination of an individual seed should, therefore, increase exponentially as the accumulated storage period approaches the seed's maximum lifetime, and the times to germination of a population of seeds would be determined by the mean and standard deviation of the normally distributed maximum lifetimes of all the seeds.

Bradford et al.—Threshold Model of Seed Deterioration where 6X is a time constant, X is the actual factor level, Xb(g) represents the normal distribution of threshold or base factor levels among seeds in the population, and tg is the time to germination of percentage g (Bradford, 1990; Gummerson, 1986). If Bx is a constant, then tg will increase as the difference between X and Xb(g) decreases. Rearranging equation 1,

i It

=(x-xb(g))/ex

(2)

probit(g) = [X- (6x/tg) - Xb(50)]/oXb.

(3)

This approach has been successful in describing the effects of water potential, abscisic acid and gibberellic acid on germination and dormancy of tomato (Lycopersicon esculentum Mill.) and lettuce (Lactuca sativa L.) seeds (Bradford, 1990; Dahal and Bradford, 1990; Ni and Bradford, 1992, 1993). Once the values of 6X, Xb(50), and (aXb) are determined for a seed lot, complete germination time-courses at any factor level can be predicted simply by changing the value of X in equation 3. These parameters have obvious biological significance, as 6X is a time constant reflecting the rate of progress toward germination, Xb(50) is the mean sensitivity of the seed population to the given factor, and (aXb) represents the range of variation in sensitivity among individual seeds (Bradford et al., 1993; Ni and Bradford, 1993). A unique aspect of this model is that although it is based on a symmetric normal distribution of thresholds among individual seeds, it automatically accounts for the skewness in germination time-courses. For example, if the difference between a given factor level and the individual seed threshold is halved, the time to germination is doubled. As the factor level further approaches the threshold, the time to germination will increase geometrically, rather than linearly. Since Xb(g) is normally distributed, the difference between X and Xb(g) will also vary in a normal distribution among individual seeds. Those seeds with thresholds nearer the actual factor level, however, will have much longer times to germination than those with a greater difference between A'and Xb(g), accounting for the skewness in the germination time-course. In addition, if the factor level exceeds the threshold values of some seeds, those seeds will be prevented from germinating. The model therefore predicts both the delay in

germination time and the decline in total germination percentage as the level of an inhibitory factor increases (Bradford et al., 1993). It is apparent that the analysis of Ellis and Roberts (1981) proposing a range of maximum lifetimes for individual seeds and a proportionate increase in time to germination as ageing period approaches the maximum seed lifetime is consistent with the population-based threshold model that has been successful in describing the effects of other factors on germination rate. In this case, the factor level (X) would be storage period (/?), the maximum lifetime threshold distribution would be Pmax(g)> a n d the ageing time constant (9age) would indicate the proportionality between p — pmaxig) ar>d the increase in time to germination. The objective of the present work was to test whether this model adequately describes the relationship between seed storage period and germination rates and percentages. We conclude that it does, and extend the analysis to account for the appearance of abnormal seedlings at a critical time after imbibition. This approach should also provide an avenue for incorporating seed germination rates, a sensitive indicator of seed vigour, into the general viability equation describing seed longevity under different temperature and moisture conditions (Ellis and Roberts, 1980a). MATERIALS AND METHODS Pretreatment, ageing and germination conditions The data used here were collected in conjunction with experiments reported previously on the effects of seed prehydration and priming treatments on seed longevity (Tarquis and Bradford, 1992). Experimental details can be found there. Briefly, lettuce (cv. Empire) seeds were hydrated in water at 20 °C for 0, 0-5, 1, 2, 4, 8 or 10 h before redrying. These treatments will be labelled CTL, H0-5, HI, H2, H4, H8, and H10, respectively. The germination and longevity characteristics of the HO-5 seeds were essentially identical to those of untreated seeds (CTL) and are considered as the control for the prehydration effects. Seeds were equilibrated to 10% moisture content (fresh weight basis) in 82% RH at 3 °C, then sealed in glass containers and incubated at 40 °C for various durations. After each ageing period, three replicates of 40 seeds each were germinated on moistened blotters in covered Petri dishes at 20 CC under fluorescent light. Radicle protrusion to 1 mm was scored at frequent intervals, and germinated seeds were transferred to blotters on slant boards to continue growth for normal seedling evaluations (International Seed Testing Association, 1985). This allowed determination of the times to germination of successive fractions of the seed population and whether they developed into normal or abnormal seedlings. Threshold model of seed ageing

The ageing model is derived from a hydrotime model of germination rates described previously (Bradford, 1990; Gummerson, 1986). These models assume that the time to germination is inversely proportional to the difference between a given quantitative factor and a threshold, or base, level of that factor. Individual seeds in the population may vary in the threshold or base value of the factor, resulting in different


which shows that the germination rate (GRg=\/tg) is proportional to a normal distribution of threshold values for a given factor level, X. A plot of \jtg versus X for a given g should be linear with a slope of \/9x and an intercept of Xb{g). To model the complete germination time-courses for all g, repeated probit regression analyses can be used to estimate the values of 8X and the mean (Xb(50J) and standard deviation (oXb) of the threshold distribution from a series of cumulative germination timecourses at different factor levels (Bradford, 1990; Dahal and Bradford, 1990), according to the probit equation

1227

1228

Bradford et al.—Threshold Model of Seed Deterioration

germination rates for a given factor level. In this case, we assume that there is a maximum potential lifetime (pmax) for each seed, and that there is a normal distribution of maximum lifetimes (/'mox(^)) among different germination fractions or percentages (g) in the population. An 'ageing time constant' (fiage) can then be defined by 0oge = (/>-/W(g))' g (4) where p is the accumulated ageing period and tg is the time to germination of percentage g. If dage is constant, the time to germination will increase in inverse proportion to the difference between p and p^xig)- If Pmaxig) is normally distributed, a probit equation can be written to describe the relationship between tg and p under a given constant storage condition based upon the mean {pmax(50)) and standard deviation (oPmax) of Pmaxig)probit(g) = [p- (9aJt.) -pmax(50)]/Op (5)

RESULTS Untreated lettuce seeds or seeds only briefly hydrated (H0-5) maintained maximum viability for up to 180 h of controlled deterioration (Fig. 1; Tarquis and Bradford, 1992). Deaths subsequently occurred in a normal distribution over time, and the declines in probit percentage normal seedlings and probit percentage radicle emergence were parallel. The percentage of seedlings represented by the vertical difference between these lines at any time would be classified as abnormal. Prehydrating seeds in water progressively decreased the time to 50% germination (tso), but also markedly decreased the mean normal

100

200

300

Ageing period (h) FIG. 1. Probit normal seedling (closed symbols) and radicle emergence (open symbols) viabilities of 0-5 h preimbibed (H0-5, circles) and 10 h preimbibed (H10, squares) lettuce seeds after controlled deterioration at 10% moisture content and 40 °C. The regression equations of the linear phases of viability loss, expressed as v=Kl-p/o (Ellis and Roberts, 1981), are: H0-5 normal seedlings, v = 5-22-/>/35-5 ( « 2 = 0-98); 2 HO-5 radicle emergence, v= 5-92-^/35-3 (R = 09S); H10 normal seedlings, v = 2-31-/)/19-8 ( « 2 = 1 0 0 ) ; H10 radicle emergence, v = 3-32-/>/19-2 ( « 2 = 0-97).

seedling viability period (pnorm(50)) (Table 1; Tarquis and Bradford, 1992). The decline in viability began much sooner and the rate of loss was more rapid (a was smaller) after prehydration for 10 h (H10), but the parallel relationship between radicle emergence capacity and normal seedling development was maintained (Fig. 1). A basic condition of the Ellis and Roberts (1981) model, that the 1. Parameters describing seed germination responses to ageing period during controlled deterioration TABLE

Seeds were prehydrated in water for 0-5 to 10 h (H0-5 to H10) before drying and subjecting them to controlled deterioration at 10% moisture content and 40 °C. The ageing time constant (0of,e), the mean maximum lifetime (pmax(50)) and the standard deviation in maximum lifetimes among seeds in the population (a P m o J are derived by fitting the model in equation 5 to germination time-courses at 20 °C after a series of ageing periods. The coefficient of determination (R2) indicates the fraction of the variance accounted for by the model. The median time germination before ageing (tso) and the mean normal seedling viability period (pnorm(50)) are taken from Tarquis and Bradford (1992). Seed treatment

Ageing period (h)

HO-5

0-192 10500 652 220-292 2050 302 0-292 9750 621 9500 635 0-59 96-119 2000 152 0-40 2300 184 64-90 375 82 0-56 1150 108 0-56 875 96

HI H2 H4 H8 H10

(h-h)

P (50') (h)

°P™*

R2

(h) 88 25 71 56 22 18 8 20 21

0-82 0-90 0-78 0-93 0-93 0-97 0-86 0-86 0-86

Pm>rm(50)

(h)

(h)

15-5

250

14-6 15-4

310 153

12-6

52

112 9-5

54 46


Repeated probit regressions of [p — (0age/tg)] versus probit(g) are conducted, combining the germination time-course data after all ageing periods and varying the value of 8age until the optimum fit is obtained. The values of pmax{50) and aPmax are then determined from the midpoint (where probit(g) = 0) and the slope (= \/aPmaJ of the probit regression line (Bradford, 1990). The repeated probit regressions can be performed by the PROC PROBIT program of the SAS Statistical Package (SAS Institute Inc., 1988). Alternatively, a convenient practical approach to performing the regression analysis is to use the logistic [In (g/(100 — g))] rather than the probit transformation of germination percentage (Hewlett and Plackett, 1978). Since the maximum likelihood regression used in probit analysis gives the data near 50% much greater weight than data at the extremes (Finney, 1971), we include only data points less than 95% of the final germination percentage in a standard linear regression analysis of logit(g) versus \p-(Oage/tg)]. This analysis can be easily performed in a computer spreadsheet program, and the values of 6age can be incremented manually by copying the revised formula into the complete column of data and the regression repeated until the maximum R2 is obtained. The midpoint of this regression (where logit (g) = 0), or the population mean, will coincide with that obtained from probit analysis, and the slope of the logit regression line is related to the standard deviation of the corresponding normal distribution by a= 1 /[slope*-nI^/T,] (Hewlett and Plackett, 1978). For practical purposes, the estimates of the model parameters obtained by the probit and logit approaches are identical. For plotting predicted cumulative germination time-courses and normal distributions, we have found the CoPlot program (CoHort Software, P.O. Box 1149, Berkeley, CA 94701 USA) to be very convenient and flexible.

Bradford et al.— Threshold Model of Seed Deterioration 1229

o o

0.1 '

A •

i

•

0.08.

•

(

0.06

L \,

A

\

0.04

> &

CTL H0.5 HI H2 H4 H8 H10

germination timing to be linked to a distribution of maximum lifetimes, as shown below. Data from complete germination time-courses were used to fit the model of equation 5 for each pretreatment across ageing periods. In the repeated probit regression procedure, it became evident that a single set of constants was adequate to fit the entire ageing period only for the HI, H8 and H10 treatments. For the remaining seed lots examined, a change in germination rate behaviour with respect to ageing was apparent that distinguished the initial phase of deterioration from that during which viability was being rapidly lost, and no single set of constants could adequately fit the entire range of ageing periods. In these cases, the data were divided and separate constants were derived for the two phases of the deterioration time-course. Since longevity was actually extended somewhat by the HI treatment, those seeds did not enter phase II during the ageing durations used in these experiments. In the H8 and H10 treatments, on the other hand, there was no lag period before viability began to be lost, so only phase II was present. The values of 9age, /?mox(50), and