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SEED PHYSIOLOGY, PRODUCTION & TECHNOLOGY

An Alternative Model to Predict Corn Seed Deterioration during Storage

^a RiceTec, Inc., P.O. Box 1305, Alvin, TX 77512 USA
^b Dep. of Agronomy, University of Kentucky, Lexington, KY 40546-0091 USA

dtekrony{at}ca.uky.edu

	ABSTRACT

TOP NOTES ABSTRACT INTRODUCTION Model Development Materials and methods Results Discussion Appendix REFERENCES

 
An assumption of the Ellis-Roberts viability equation, that all seed lots of a species deteriorate at the same rate in the same storage environment, was not valid for hybrid corn (Zea mays L.) seed. Thus, an alternative model was developed that used a potential storability index (P_G, the time for germination to decline to a level G) and a storage environment coefficient (SEC, the factor by which seed longevity is altered by a change in storage temperature and seed moisture content) to predict deterioration of hybrid corn seed. The alternative model was derived from the ratio of seed longevity of the same seed lot in two storage environments. The P_G in the storage environment was estimated as the product of P_G in a rapid-aging test and SEC, which was determined with a regression model based on the differences in temperature and moisture between the two environments. The model was evaluated by predicting the time to 90 and 50% germination (P₉₀ and P₅₀) for high- and medium-quality seed lots stored under a range of constant conditions. There was generally good agreement between predicted and observed P₉₀ and P₅₀, with many of the predicted values within 10% of observed values across five seed lots. The storage conditions in the rapid-aging test had no effect on the predictive ability of the model. This model provides an effective approach to predicting corn seed longevity that may be useful in managing seed storage.

Abbreviations: E, environment • SEC, storage environment coefficient

	INTRODUCTION

TOP NOTES ABSTRACT INTRODUCTION Model Development Materials and methods Results Discussion Appendix REFERENCES

 
THE PREDICTION of corn seed deterioration depends on understanding the quantitative relationships between seed longevity and initial seed quality, seed moisture content, and storage temperature. Seed longevity can be described as the time until a certain proportion of a seed lot or seed population is dead. For example, the half viability period, P₅₀, is the time taken for 50% of the seeds to die (Roberts, 1972). Attempts to quantify the relationship between seed longevity and the three factors affecting seed deterioration have produced numerous qualitative or quantitative prediction equations (Goodspeed, 1911; Grove, 1917; Hutchinson, 1944; Roberts, 1960, 1972, 1973; Harrington, 1963; Ellis and Roberts, 1980a, 1981).

Qualitative models (Harrington, 1963; Delouche and Baskin, 1973; Egli et al., 1979) only deal with relative effects of initial seed quality and environmental conditions on seed longevity. Although they may provide practical recommendations for favorable combinations of moisture content and temperature for seed storage, such qualitative statements regarding seed longevity have limited use in the design and management of seed storage systems (Ellis and Roberts, 1981).

Quantitative models, in contrast, are designed to provide accurate predictions of seed viability after storage in any environment. The development of quantitative models culminated with the viability equation (Eq. [1]) of Ellis and Roberts (1980a)

(1)

where v is the probit or standard normal equivalent deviate of germination (%), K_i is the initial seed lot constant (on the probit scale), p is the storage period (days), m is moisture content (%, fresh weight basis), t is temperature (°C), and K_E, C_W, C_H, and C_Q are constants having common values for all seed lots of a species. The significant characteristics of this equation are the inclusion of initial seed quality, storage temperature and seed moisture. Equation [1] has been evaluated in a number of crop species (Ellis and Roberts, 1980b, 1981; Ellis et al., 1982; Kraak and Vos, 1987; Ellis, 1988; Te-Krony et al., 1993; Fabrizius et al., 1999) and is dependent on two key assumptions: normality of distribution of seed deaths with time and a constant rate of seed deterioration for all seed lots within a species stored in identical conditions.

The failure of seed survival to be normally distributed has been reported for several crop species (Moore and Roos, 1982; Wilson et al., 1989; Fabrizius et al., 1999). However, 80% of the corn seed survival curves evaluated by Tang et al. (1999a) were symmetrical sigmoids and could generally be described by a negative cumulative normal or near-normal distribution.

Corn seed lots of several hybrids with variation in initial quality did not deteriorate at the same rate in the same storage environment (Tang et al., 1999b) suggesting that the second assumption may not be valid. Bruggink (1989) also reported variable rates for corn as did Fabrizius et al. (1999) for soybean [Glycine max (L.) Merrill].

The hypothesis proposed to derive the alternative model developed in this paper is that differences in the rates of deterioration among seed lots may result from a difference in the constant K_E in Eq. [1]. All available evidence indicates that within a species (Roberts and Ellis, 1977; Ellis and Roberts, 1980a), and even among species (Ellis et al., 1988, 1989; Dickie et al., 1990), the values of the temperature constants, C_H and C_Q [Eq. 1], are not affected by genotype, seed quality, or species. Likewise, within a species, the value of C_W, when moisture content was expressed as a percentage, was not affected by genotype or seed quality (Ellis et al., 1988, 1989, 1990; Dickie et al., 1990). Furthermore, C_W had a common value among species when moisture content was expressed as equilibrium relative humidity (Ellis et al., 1989). Consequently, the difference in seed deterioration rate among seed lots is best explained by differences in K_E, as reported by Ellis et al. (1989) for two timothy (Phleum pratense L.) seed lots. Elimination of K_E from Eq. [1] would allow development of an alternative equation to predict corn seed longevity.

	Model Development

TOP NOTES ABSTRACT INTRODUCTION Model Development Materials and methods Results Discussion Appendix REFERENCES

 
Seed deaths during time in storage can be described by constructing a seed survival curve that could follow a normal or logistic distribution (Finney, 1971). Other distributions, such as the Weibull curve, have also been used (Moore and Jolliffe, 1987). Regardless of the distribution underlying the seed survival curve, the viability period indices (P₈₀, P₅₀, P₃₀) can be estimated, where P_G is the time for germination to decline to a level G.

Suppose G₁ = F₁(P) is a cumulative distribution function that accurately describes the distribution of seed survival (germination after time P in storage) for a seed lot in a specific environment, E₁. Similarly, define G₂ for storage environment E₂. Assume that G₁ and G₂ have the same mathematical form but differ with respect to parameter values so as to model seed death events during storage in the two environments, that is, 0 G₁ 1, and 0 G₂ 1.

If the distribution of seed survival times has a density function f(P), then

(2)

the density function f, apart from having to be non-negative for all P and such that it integrates to unity across the entire domain of the function, is completely arbitrary, but is often taken to be normal with unknown mean µ and standard deviation (probit model) or logistic (logit model) (Prentice, 1976).

The inverse of the probability function F(P) provides the corresponding time period, that is, P_G = F^-1(G), for the seed lot to deteriorate to germination level G. For example, the P₅₀ is calculated as F^-1(0.50). Thus, we define P_1,50 = F₁^-1 (0.50) as the half viability period in E₁, and P_2,50 = F₂^-1(0.50) in E₂.

From the relationship between seed longevity and storage conditions proposed by Roberts (1972) (Eq. [3]),

(3)

where K_v is a seed lot constant, C₁ and C₂ are constants that express the effects of seed moisture content (m) and storage temperature (t) on seed longevity, we have log₁₀P_1,50 = K_v - C₁m₁ - C₂t₁ for E₁, while log₁₀P_2,50 = K_v - C₁m₂ - C₂t₂ for E₂.

For a seed lot stored in two different environments, the ratio between the P₅₀ values is

(4)

where is a function of temperature and seed moisture content. The operator denotes the difference between the two sets of storage conditions with respect to the variable or function which follows, for example, t = t₁ - t₂, m = m₁ - m₂. From Eq. [4], we can write Eq. [5], which can then be rewritten as a general formula, that is,

(5)

if any viability period is a function of temperature, moisture content, and a seed lot constant K, (i.e., log₁₀P_G = K - C₁m - C₂t), then

(6)

Thus, one storability index (P_1,G ) can be used to predict another index (P_2,G) provided the temperatures and seed moisture contents in both environments are known. The only relevant differences between the two environments are temperature and seed moisture content. Thus, the function (m, t), defined as the ratio of seed longevity in one environment to seed longevity in another environment, constitutes a factor by which seed longevity is altered by changes in storage temperature and seed moisture content. Hereafter, we will refer to (m, t) as the storage environment coefficient (SEC) and P_2,G as the potential storability index. Thus, P_2,50 is a special case of P_2,G. Equation [6] can also be derived directly from Eq. [1] or by assuming that the seed survival curve follows other distributions, such as the Weibull distribution (See Appendix).

Previous studies (Ellis and Roberts, 1980a, 1980b, 1981; Ellis et al., 1982) indicated that the simple relationship between seed longevity and storage environment given by -C₁m - C₂t was applicable only to a narrow range of storage environments. A logarithmic relationship between longevity and moisture content, and a quadratic temperature term were needed to cover a wider range of storage environments. Therefore, the exponent in the function (m, t) probably needs to contain an ln m term instead of m, and a quadratic temperature term as shown in Eq. [7], where C_W, C_H, and C_Q are constants.

(7)

The relationship between the SEC and seed moisture content and storage temperature in Eq. [7] could be expanded to provide more flexibility for fitting data from diverse species as shown in Eq. [8], where C₁ to C₆ are constants and ln m = (ln m₁ - ln m₂), (tm) = (t₁m₁ - t₂m₂), and (t ln m) = (t₁ln m₁ - t₂ln m₂).

(8)

Regression analysis of data from a series of storage studies with constant temperatures and seed moisture contents can be used to select the best model from Eq. [8] for a given species. Obviously, Eq. [7] is one model obtainable from Eq. [8] by such selection. Once the best model has been determined, it should be possible to predict seed longevity accurately for all seed lots within that species.

	Materials and methods

TOP NOTES ABSTRACT INTRODUCTION Model Development Materials and methods Results Discussion Appendix REFERENCES

 
Data from storage experiments described by Tang et al. (1999a) were used to select the best model from Eq. [8] and to validate the model. The initial germination percentage of the 10 seed lots was high (>89%), but there was a range in vigor (high, medium, and low), based on accelerated-aging and cold-test germination (Tang et al., 1999a). Seed samples conditioned to desired moisture contents were heat sealed into aluminum foil packets and stored in an incubator (long-term storage) or a water bath (short-term storage). Survival of the seeds was determined by removing samples from storage at regular intervals and determining standard germination as described by International Seed Testing Association (1993). A completely randomized design was used with two replications of each seed lot in each storage environment.

The seed lots were stored in two experiments at different times with slightly different procedures for moisture adjustment and equilibration (Tang et al., 1999a). In Exp. 1, each seed lot was first divided into two replications that were conditioned to the desired levels at different times. In Exp. 3, each seed lot was conditioned to the desired moisture level before it was divided into replications and sealed into aluminum foil packets (Tang et al., 1999a). Data from four seed lots (Lots 1–4, Tang et al., 1999a) from four hybrids in Exp. 1 and six seed lots (Lots 6–11, Tang et al., 1999a) from two hybrids stored in various combinations of constant temperatures (30, 40, 50°C) and seed moisture contents (120, 140, 160 g kg^-1) were used to derive the constants and test the model.

Previous analysis of the survival curves from these experiments confirmed that they were generally normally or near-normally distributed (Tang et al., 1999a). Thus, it was appropriate to use probit analysis (Finney, 1971) to analyze the survival curves. The PROBIT procedure (SAS Institute, 1988) was used to calculate P₅₀ from the full data set for each seed lot in each storage environment in Exp. 3, and then the P₅₀ ratio between any two environments for a seed lot was calculated. Analysis of variance was used to determine if there were significant differences in P₅₀ or P₅₀ ratios among seed lots. The P₅₀ values were transformed to log₁₀P₅₀, and the transformed data subjected to regression analysis with m, ln m, t, t², tm, and tln m as candidate regressor variables in a joint regression across seed lots, allowing different intercepts for different seed lots, but constant regression coefficients for the regressor variables. This analysis was accomplished using the Maximum R² Improvement (MAXR) method in SAS Procedure Reg (SAS Institute, 1988) with indicator variables for seed lots forced into the model to provide for distinct intercepts. When using such a fitted model to predict a log₁₀P₅₀ ratio for two sets of moisture and temperature conditions for the same seed lot, the intercept for the specific seed lot vanishes and the regression coefficients are multiplied by the variables (m, ln m, t, t², tm, and/or t ln m) corresponding with the regressor variables retained in the final chosen regression model. Thus, the exponent in Eq. [8] is obtained from the regression analysis by putting the C_j, j = 1, ..., 6, equal to the regression coefficients reversed in sign for those terms retained in the chosen model (and the C_j put equal to zero for terms omitted). The sign reversal compensates for the conventional prefixing of the C_j with a negative sign in Eq. [8]. The resulting model was obtained with the intent that it should be useful for prediction in practice and not with intent to achieve meaningful biological interpretation of the individual regression coefficients.

	Results

TOP NOTES ABSTRACT INTRODUCTION Model Development Materials and methods Results Discussion Appendix REFERENCES

 
Estimates of P₅₀
The estimates of P₅₀ ranged from 0.14 d for Seed Lot 6 at 50°C and 160 g kg^-1 seed moisture content to 505 d for Seed Lot 1 at 30°C and 120 g kg^-1 (data not shown). There were significant differences in P₅₀ among seed lots and across storage environments. The P₅₀ for seed lots with high initial vigor, as indicated by high accelerated-aging and cold-test germination, was larger than the P₅₀ for seed lots with low initial vigor, and this ranking was generally consistent across storage environments. The correlation between P₅₀ and initial levels of accelerated-aging or cold-test germination within a storage environment was usually significant (n = 10, P = 0.05) and greater than 0.65, demonstrating that P₅₀ is related to initial seed vigor.

Storage Environment Coefficient
The storage environment coefficient (ratio of P₅₀ for any two storage environments) for several combinations of temperature and moisture content was generally similar among Seed Lots 8, 9, 10, and 11 in Exp. 3, which included only lots with high and medium initial seed vigor (Table 1) , although there were a few comparisons that were significantly different. Constant SECs imply that the relative response of seed longevity (i.e., the ratio of P₅₀) to changes in the storage environment is the same for all high- and medium-vigor seed lots. In contrast, the rate of seed deterioration in these constant environments differed significantly among seed lots (Tang et al., 1999b). The SECs of seed lots with low initial vigor levels (Lots 6 and 7) were usually much higher than for other seed lots (significant at P = 0.05). Thus, seed lots with low initial quality were excluded from further analysis.

(9)

was used to predict corn seed deterioration. A regression analysis using a model allowing the constants C₁, C₃, C₅, and C₆ to vary with seed lot showed sums of squares of 31.917 [F = 8132.57, df = (4,43)] due to the common regression and 0.043 [F = 3.68, df = (12,43)] due to differences in regression. Although statistically significant, the latter seems, for practical purposes, to be negligibly small. Therefore, we considered it expedient to derive a set of common constants representing high- and medium-vigor seed lots for the four-variable model as illustrated in Table 3 . Either of these sets of coefficients should prove useful in predicting corn seed longevity.

View larger version (23K): [in this window] [in a new window]   Fig. 1 Comparison of observed and predicted storage environment coefficients (SEC). Predicted SECs were calculated with Eq. [9] and constants developed with data from Seed Lot 8. Data from Exp. 3. The solid line represents the 1:1 line and the dashed lines represent ± 10% of the 1:1 line

View larger version (16K): [in this window] [in a new window]   Fig. 2 Comparison of observed and predicted P50 for Seed Lots 1 and 4 stored at a range of temperatures (30–50°C) and seed moisture contents (120–160 g kg-1). Data from the 40°C–160 g kg-1 and 50°C–120 g kg-1 storage environments were used as the rapid-aging test and the constants used in Eq. [9] were developed using data from Seed Lots 8 to 11 (Table 3)

View larger version (15K): [in this window] [in a new window]   Fig. 3 Comparison of observed and predicted P90 for Seed Lots 1 and 4 stored at a range of temperatures (30–50°C) and seed moisture contents (120–160 g kg-1). Data from the 40°C–160 g kg-1 and 50°C–120 g kg-1 storage environments were used as the rapid-aging test and the constants used in Eq. [9] were developed using data from Seed Lots 8 to 11 (Table 3)

View larger version (23K): [in this window] [in a new window]   Fig. 4 Comparison of observed and predicted P90 for Seed Lots 1, 4, 9, 10, and 11 stored at a range of temperatures (30–50°C) and seed moisture contents (120–160 g kg-1). Data from the 40°C–160 g kg-1 storage environment were used as the rapid-aging test and the constants used in Eq. [9] were developed using data from Seed Lot 8 (Table 3)

	Discussion

TOP NOTES ABSTRACT INTRODUCTION Model Development Materials and methods Results Discussion Appendix REFERENCES

The model was validated using two environments (40°C and 160 g kg^-1 and 50°C and 120 g kg^-1) as the rapid-aging test and predicting P₉₀ and P₅₀. The P₉₀ may be of greater practical interest because seed lots with a germination percentage of 50% usually have little commercial value. Both sets of constants (i.e., from Seed Lots 8 and 8–11) provided excellent predictions of P₉₀ and P₅₀ for five high- and medium-vigor seed lots. In some situations, larger deviations were observed at larger values of P₉₀ and P₅₀ (>300 and 500 d, respectively). As expected from the derivation of the model, both rapid-aging environments provided good predictions. Theoretically, any storage conditions can be used for the rapid-aging test, so the choice of conditions rests on the practical considerations of routinely conducting the test in a seed laboratory while obtaining a valid survival curve.

We believe that this alternative model will be useful to predict seed deterioration, although further validation with more seed lots is needed. The model should work on other crop species, although the constants in Eq. [9] may be species specific. The inaccurate predictions of large values of P₅₀ and P₉₀ may be a result of the limited data from low-temperature and low-moisture environments (i.e., temperatures below 30°C and moisture contents below 120 g kg^-1) used to derive the constants. Data from such environments are needed to extend the model to conditions normally encountered in routine seed storage; however, seed deterioration is slow under these conditions making the construction of survival curves very time-consuming.

The prediction accuracy should be independent of the storage environment used for the rapid-aging test, but a carefully constructed complete survival curve is needed to provide a good estimate of P_G. The 40°C–160 g kg^-1 environment required 11.6 d, averaged across seed lots, to construct a complete survival curve (i.e., germination declining below 50%). The decline in germination was faster in the 50°C–120 g kg^-1 environment (average of 6.4 d) (Tang, 1998), a desirable characteristic for a routine laboratory test.

This model has a threefold advantage over previously published models. First, it does not require a constant rate of deterioration of all seed lots of a species when stored in the same environment. This is important since there is now evidence that the rate of deterioration does vary among seed lots in corn (Bruggink, 1989; Tang et al., 1999b) and soybean (Fabrizius et al., 1999). Secondly, this model does not require that seed deterioration follows a normal distribution. Other distributions, such as logistic or the Weibull curve can be used providing, of course, that the distribution applies to deterioration in both environments. Finally, an estimate of initial quality (K_i in Eq. [1]) is not directly involved in the prediction of deterioration, avoiding the problem of obtaining an accurate estimate of initial quality (Fabrizius et al., 1999). Thus, the assumptions underlying this model are not as restrictive as those associated with the Ellis and Roberts (1980a) viability equation (Eq. [1]), which requires both a constant rate of deterioration among seed lots of the same species and a survival curve that follows a normal distribution.

There are some limitations to the use of this model. The model is dependent on a seed survival curve generated in a rapid-aging test, and no single germination or vigor test can replace the rapid-aging test. The characteristics of the curve are somewhat dependent on the conditions of the test environment. If the curve does not represent the deterioration characteristics of the seed lot, the model will not provide accurate predictions. Perhaps the biggest problem, especially at high temperatures and moisture contents, is arranging the sampling interval to provide an adequate number of samples during the rapid decline in germination while, at the same time, maintaining the total number of samples at a manageable level. Temperature and seed moisture must be kept constant during the test to obtain valid deterioration curves.

Accurate measurements of seed moisture and temperature in the rapid-aging test and storage environment are also essential to accurately estimate storability. Small changes in seed moisture content can have dramatic effects on storability when moisture constants are between 120 and 160 g kg^-1. Recommended procedures (International Seed Testing Association, 1993) must be followed carefully to obtain accurate estimates of seed moisture contents. The rapid-aging test is tedious and time-consuming, but, fortunately, with care most seed laboratories should be able to obtain the necessary data.

This model does not seem to be applicable to seed lots with low initial quality. Perhaps no model can predict seed longevity of low-vigor seed lots because the longevity of these seed lots seems to respond to changes in temperature and seed moisture content differently than medium- or high-quality seed lots (Tang, 1998). Fortunately, commercial seed lots with low initial quality are usually not stored for long periods, thus, predictions of seed longevity are not needed.

In summary, the model described here provides an effective approach to accurately predicting corn seed longevity. In particular, it overcomes many of the limitations of other models. Because the constants in Table 3 were derived from data obtained in temperatures ranging from 30 to 50°C, they cannot be used to reliably predict seed longevity at temperatures below 30°C. Data from storage experiments at lower temperatures are needed to extend the model to temperatures likely to be encountered in controlled and natural storage in many environments where corn seed is produced.

	NOTES

TOP NOTES ABSTRACT INTRODUCTION Model Development Materials and methods Results Discussion Appendix REFERENCES

 
Contribution from Kentucky Agric. Exp. Stn. no. 98-06-206.

Received for publication December 21, 1998.

	Appendix

TOP NOTES ABSTRACT INTRODUCTION Model Development Materials and methods Results Discussion Appendix REFERENCES

 
Mathematically, the alternative model can also be derived directly from the improved viability equation (Eq. [1]) (Ellis and Roberts, 1980a) when the seed survival curve conforms to a normal distribution. The equation, , can be used to calculate P₅₀ or P₈₀ by probit analysis,

If the longevity of a seed lot in two environments is P_1,50 and P_2,50, respectively, the ratio of the two longevity indices is independent of initial seed quality (K_i) and the species constant K_E,

substituting ,

Therefore, P_1,50 = P_2,50(m, t). This is the same as Eq. [6].

Similarly, , then . More generally, , then .

When the seed death curve conforms to the two-parameter Weibull distribution , the inverse of the survival function (Eq. [10]) (Evans et al., 1993)

(10)

can be used to calculate the half viability period or any other period. Here b is a scale parameter, c is a shape parameter, and G is germination expressed as a proportion. Similar to the case for a normal distribution,

if c₁ = c₂

where (m, t) is analogous to (m, t), a function of moisture content and temperature, that is, a storage environment coefficient. Other distributions that use the inverse to calculate the viability period will probably give rise to equations similar to Eq. [6].

	REFERENCES

TOP NOTES ABSTRACT INTRODUCTION Model Development Materials and methods Results Discussion Appendix REFERENCES

 

• Bruggink H. Evaluation and improvement of vigor test methods. I. An alternative procedure for the controlled deterioration test. Acta Hort. 1989;253:143-151.
• Delouche J.C., Baskin C.C. Accelerated aging techniques for predicting the relative storability of seedlots. Seed Sci. Technol. 1973;1:427-452.
• Dickie J.B., Ellis R.H., Kraak H.L., Ryder K., Tompsett P.B. Temperature and seed storage longevity. Ann. Bot. 1990;65:197-204.[Abstract/Free Full Text]
• Egli D.B., White G.M., TeKrony D.M. Relationship between seed vigor and storability of soybean seed. J. Seed Technol. 1979;3:1-11.
• Ellis R.H. The viability equation, seed viability nomographs, and practical advice on seed storage. Seed Sci. Technol. 1988;16:29-50.
• Ellis R.H., Hong T.D., Roberts E.H. A low moisture content limit to logarithmic relationship between seed moisture content and longevity. Ann. Bot. 1988;61:405-408.[Abstract/Free Full Text]
• Ellis R.H., Hong T.D., Roberts E.H. A comparison of the low moisture content limit to the logarithmic relationship between moisture and longevity in twelve species. Ann. Bot. 1989;63:601-611.[Free Full Text]
• Ellis R.H., Hong T.D., Roberts E.H. Moisture content and the longevity of seeds of Phaseolus vulgaris. Ann. Bot. 1990;66:341-348.[Abstract/Free Full Text]
• Ellis R.H., Osi-Bonsu K., Roberts E.H. The influence of genotype, temperature and moisture on seed longevity in chickpea, cowpea and soya bean. Ann. Bot. 1982;50:69-82.[Abstract/Free Full Text]
• Ellis R.H., Roberts E.H. Improved equations for the prediction of seed longevity. Ann. Bot. 1980;45:13-30 a.[Abstract/Free Full Text]
• Ellis R.H., Roberts E.H. The influence of temperature and moisture on seed viability period in barley (Hordeum distichum L.). Ann. Bot. 1980;45:31-37 b.[Abstract/Free Full Text]
• Ellis R.H., Roberts E.H. The quantification of aging and survival in orthodox seeds. Seed Sci. Technol. 1981;9:373-409.
• Evans M., Hastings N., Peacock B. Statistical distributions, 2nd ed New York: John Wiley and Sons, 1993.
• Fabrizius E., TeKrony D.M., Egli D.B., Rucker M. Evaluation of a viability model for predicting soybean seed germination during warehouse storage. Crop Sci. 1999;39:194-201.[Abstract/Free Full Text]
• Finney D.J. Probit analysis, 3rd ed Cambridge, UK: Cambridge University Press, 1971.
• Goodspeed T.H. The temperature coefficient of the duration of life of barley grains. Bot. Gazette 1911;51:220-224.
• Grove J.F. Temperature and life duration of seeds. Bot. Gazette. 1917;63:169-189.
• Harrington J.F. Practical instructions and advice on seed storage. Proc. Int. Seed Test Assoc. 1963;28:989-994.
• Hutchinson J.B. The drying of wheat. III. The effect of temperature on germination capacity. J. Soc. Chem. Industry London 1944;63:104-107.
• International Seed Testing Association. 1993. International rules for seed testing. Seed Sci. and Technol. 21 Suppl. ISTA, Zurich, Switzerland.
• Kraak H.L., Vos J. Seed viability constants for lettuce. Ann. Bot. 1987;59:343-349.[Abstract/Free Full Text]
• Moore F.D., III, Jolliffe P.A. Mathematical characterization of seed mortality in storage. J. Am. Soc. Hort. Sci. 1987;112:681-686.
• Moore F.D., Roos E.E. Determining differences in viability loss rates during seed storage. Seed Sci. Technol. 1982;10:283-300.
• Prentice R.L. A generalization of the probit and logit methods for dose response curves. Biometrics 1976;32:761-768.[ISI][Medline]
• Roberts E.H. The viability of cereal seed in relation to temperature and moisture. Ann. Bot. 1960;24:12-31.[Abstract/Free Full Text]
• Roberts E.H. Storage environment and control of viability. In: Roberts E.H., ed. Viability of seed. Syracuse, NY: Syracuse Univ. Press, 1972:14-58.
• Roberts E.H. Predicting the storage life of seeds. Seed Sci. Technol. 1973;1:499-514.
• Roberts E.H., Ellis E.H. Prediction of seed longevity at sub-zero temperatures and genetic resources conservation. Nature (London) 1977;268:431-433.
• SAS Institute. 1988. SAS/STAT user's guide. Version 6.03. SAS Inst., Cary, NC.
• Tang, S. 1998. Survival characteristics of hybrid corn seed during constant storage. Ph.D. diss. (Diss. Abstr. 99-07726). Univ. of Kentucky, Lexington.
• Tang S., TeKrony D.M., Egli D.B., Cornelius P.L. Survival characteristics of corn seed during storage. II. Rate of seed deterioration. Crop Sci. 1999;39:1400-1406 b.[Abstract/Free Full Text]
• Tang S., TeKrony D.M., Egli D.B., Cornelius P.L., Rucker M. Survival characteristics of corn seed during storage. I. Normal distribution of seed survival. Crop Sci. 1999;39:1394-1400 a.[Abstract/Free Full Text]
• TeKrony D.M., Nelson C., Egli D.B., White G.M. Predicting soybean seed germination during warehouse storage. Seed Sci. Technol. 1993;21:127-137.
• Wilson D.O., Jr., McDonald M.B., Jr., St. Martin S.K. A probit planes method for analyzing seed deterioration data. Crop Sci. 1989;29:471-476.[Abstract/Free Full Text]

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