Agronomy Journal 95:65-70 (2003)
© 2003 American Society of Agronomy
SYMPOSIUM PAPERS
Modeling Genetic Effects on the Photothermal Response of Soybean Phenological Development
Douglas W. Stewart*,a,
Elroy R. Cobera and
Richard L. Bernardb
a Eastern Cereal and Oilseed Res. Cent. (ECORC), Agric. and Agri-Food Can., Ottawa, ON, Canada K1A 0C6
b Univ. of Illinois, Urbana, IL 61801
* Corresponding author (stewartdw{at}em.agr.ca)
Received for publication May 1, 2001.
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ABSTRACT
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The identification of genes that affect plant growth and development has played a prominent role in modern plant research. Mathematical modeling can be a useful tool in this process of quantifying the effects of individual genes. In soybean [Glycine max (L.) Merr.], seven loci (E1 to E7) have been identified that condition time to flowering and maturity and photoperiod sensitivity. Twenty-nine near-isogenic lines with different combinations of alleles at six of these loci in either ‘Clark’ or ‘Harosoy’ background were used in this study. Days from planting to first flower were observed in these lines over 2 yr at two locations (Ottawa, ON, Canada, and Urbana, IL, USA) under natural daylength and a 20-h photoperiod. A mathematical model was developed to simulate the effect of average daily temperature, photoperiod, and the temperature x photoperiod interaction. A photoperiod coefficient was calculated for each isoline, which resulted in an R2 of 0.93 when calculations of times to first flower were correlated with observations. A submodel was developed to calculate photoperiod coefficients by adding contributions from each locus with dominant alleles. This reduced the 29 isoline coefficients to seven coefficients (one for each locus plus an additional value for unknown genes) but with a reduction of the R2 of from 0.93 to 0.89. The E1 coefficient was approximately twice the size of the other five allele coefficients. Time from planting to first flower can be calculated from the average daily temperatures and latitude of a given location using the gene model if the genetic makeup of the line is known.
Abbreviations: ILD, incandescent lamp daylength
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INTRODUCTION
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SOYBEAN, A SHORT-DAY PLANT, has a photoperiod response opposite to most other temperate-season crops; that is, maturity is delayed by longer photoperiods (Major, 1980). Therefore, breeding varieties for northern locations is restricted not only by cooler temperatures and shorter growing seasons, but also by longer photoperiods. The genetic control of photoperiod response is understood. However, photoperiod interaction with temperature is less well understood (Cober et al., 2001). Mathematical models that can simulate photoperiod x temperature interactions as influenced by genetic makeup would be useful in identifying adapted genotypes for plant breeding programs. The problem is how to quantify the effects of genes on the photoperiod x temperature interactions with phenological development.
There has been an extensive amount of research on developing models of phenological development based on temperature and photoperiod functions in soybean. This work supports breeding programs and can be incorporated into plant growth models such as SOYGRO (Jones et al., 1989). Some of this work involved multiplying functions together (Major et al., 1975; Grimm et al., 1993, 1994; Piper et al., 1996a, 1996b). A somewhat simpler approach has been to add temperature and photoperiod functions (Hadley et al., 1984; Constable and Rose, 1988; Summerfield et al., 1991; Upadhyay et al., 1994), resulting in simple linear equations where coefficients were solved for by linear least squares. However, simple additive equations do not capture temperature x photoperiod interactions (Cober et al., 2001). Most of this work [except for Upadhyay et al. (1994) and Cober et al. (2001)] did not incorporate direct effects of genes into the models.
Alleles at seven loci affect time from planting to first flower in soybean: E1 and E2 (Bernard, 1971), E3 (Buzzell, 1971), E4 (Buzzell and Voldeng, 1980), E5 (McBlain and Bernard, 1987), E6 (Bonato and Vello, 1999), and E7 (Cober and Voldeng, 2001). Excepting E6, which was found in tropical germplasm, in all other six loci, the dominant or partially dominant alleles (E) result in more photoperiod sensitivity and later flowering than the recessive alleles (Cober et al., 2001). Upadhyay et al. (1994) using additive equations and Cober et al. (2001) using additive equations with a temperature x photoperiod interactive term studied how combinations of these dominant alleles changed the photoperiod coefficient in their respective models. In this paper, the approach by Cober et al. (2001) will be extended so that the effect of the dominant allele at each of the six loci will be incorporated directly into the model. This model should be useful to plant breeders to develop lines of soybean for specific regions and planting dates.
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MATERIALS AND METHODS
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Experimental Procedures
Twenty-nine indeterminate near-isogenic lines developed using the recurrent parents Clark or Harosoy have been developed with combinations of recessive (e) and dominant (E) maturity alleles at six known maturity loci (Table 1). Some of these combinations are present in both Clark and Harosoy genetic backgrounds while others are present in only one background. The isolines with an L prefix were developed by R.L. Bernard, University of Illinois, Urbana, IL. The isolines with an OT prefix were developed at the Eastern Cereal and Oilseed Research Centre, Ottawa, ON, Canada.
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Table 1. Genotypes of near-isogenic lines grown in Ottawa, ON, Canada, and Urbana, IL, USA, in 1998 and 1999. In the table, e represents recessive alleles while E represents dominant alleles.
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All isolines were grown in the field in 1998 and 1999 at Ottawa (45°23' N lat) and at Urbana (40°4' N lat). Two photoperiods were provided at each location: natural daylength and natural daylength extended to 20 h using incandescent lamps [incandescent lamp daylength (ILD)]. At Ottawa, the longest day is about 16.9 h including civil twilight or 15.7 h excluding twilight, and at Urbana, the corresponding values are 16.1 and 15.0 h, respectively. Civil twilight starts and ends when the true center of the sun is 6° below the horizon. Inclusion of civil twilight is justified for daylength calculations in soybean (Summerfield and Roberts, 1987). At Ottawa, ILD was generated using 200-W incandescent bulbs suspended 2.25 m above the soil and spaced 3 m apart in ranges 3 m wide. Photosynthetic photon flux at the canopy surface was approximately 3 µmol m-2 s-1. At Urbana, a 75-W incandescent floodlight was placed about 1.5 m above each one-row plot. Lights were turned on, from emergence to killing frost, about 0.5 h before sunset until 2200 h and then turned on again at 0200 h until about 0.5 h past sunrise, leaving a 4-h dark period between 2200 and 0200 h. Under ILD, plots were single rows spaced 50 cm apart at Ottawa and 75 cm apart at Urbana and were 3 m long with 30 seeds planted per meter of row. The ILD plots were planted on 9 June 1998 and 8 June 1999 at Ottawa and on 21 May 1998 and 28 May 1999 at Urbana.
Under natural daylength, plots were single rows spaced 50 cm apart and 4 m long at Ottawa and spaced 75 cm apart and 3 m long at Urbana with 30 seeds planted per meter of row. Natural daylength plots were planted 21 May 1998 and 28 May 1999 at Ottawa. At Urbana, plots were planted 16, 28, and 29 May 1998 and 26 May 1999. Each photoperiod treatment was arranged as a randomized complete block with two replications, except for the 20-h treatment at Urbana, which had only one replication. The date of flowering was recorded when 50% of plants in a plot had an open flower.
Maximum and minimum daily air temperatures were measured at local weather stations. Average daily air temperature was the maximum plus the minimum divided by two. Day-length with twilight as defined above was calculated from astrological equations (List, 1958) for each day at each latitude.
Theoretical Considerations
Following Cober et al. (2001), phenological development can be defined as a variable D with a rate of change expressed as:
 | [1] |
which was subject to the following constraints:
where- t = time
- T = temperature
- TB = base temperature below which T had no effect on rate of development
- P = the length of photoperiod
- PB = base photoperiod below which photoperiod had no effect on rate of development
- b = a genetic coefficient
- TM = an upper temperature limit above which there was no further effect on rate of development (i.e., T was not allowed to exceed TM)
- PM = an upper photoperiod limit above which there was no further effect on rate of development (i.e., P was not allowed to exceed PM. PM was not in the original model of Cober et al., 2001)
The function CF included a photoperiod coefficient (C) and a temperature term that interacted with photoperiod (Cober et al., 2001) and was expressed as:
 | [2] |
where d is a genetic coefficient and TD is a temperature set at 28°C where C equals CF when T equals TD. The value of TD could vary from 24 to 30°C with compensatory changes in d and have no effect on model calculations. The function CF was set to zero if negative and introduced an interaction between temperature and photoperiod (Cober et al., 2001).
A common assumption is that development (D) increases from 0 to 1 during the phenological stage under study (in this case, time from planting to first flower) (Robertson, 1968). Therefore, integrating Eq. [1] resulted in:
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where N is the number of days from planting to first flower. Note that CF is the function described in Eq. [2] and not a coefficient. Integrating Eq. [3] numerically resulted in:
 | [4] |
where 
t is a time step of 1 d.
This theory was modified to be compatible with the growing degree day concept. By dividing all terms of Eq. [4] by b, a growing photo-degree day (GPDD ) was expressed as:
 | [5] |
where GPDD has the same units as growing degree days (°Cd).
Equation [5] was used to calculate N by summing GPDD each day from planting given the average daily temperature and photoperiod until the total equaled 1/b, which was at the time of first flower. Values of b, C, d, TB, TM, and PB were needed for calculating N. We assumed TB, TM, and PB were 5.78°C, 30°C, and 13.5 h, respectively, from Cober et al. (2001). Values of the other coefficients were determined by fitting Eq. [5] to the observed times from planting to first flower for the 2 yr and two locations using a nonlinear least-squares algorithm (Marquardt, 1963). Values for b and d were assumed to be constant for all isolines. However, the photoperiod coefficient (C) was calculated for each of the 29 isolines for both the natural(CN) and the 20-h daylength (C20). As well, the data for the 20-h daylength were used to solve for PM.
Because the model will be used for natural light only, further analysis was directed at the 29 values of CN. To convert from an isoline-based model (CN) to an allele-based model (CNM), we assumed that each value of the photoperiod coefficient could be calculated from components from each allele according to:
 | [6] |
where j represents the six loci (E1, E2, E3, E4, E5, and E7) plus the effect of unknown loci represented by a seventh term (E?). Each component (CNj) had a positive value when dominant alleles were present and a value of zero when recessive alleles were present, except for the seventh term, which was a simple positive number. These seven positive values were calculated from the 29 values of CN and the information on dominant and recessive alleles for each line by least squares. Therefore, the gene-based model (CNM) eliminated the need for 29 values (for the 29 isolines) of CN, replacing them instead with the seven CNj components.
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RESULTS AND DISCUSSION
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Initially, we attempted to fit the original model of Cober et al. (2001) to the above data as described in Materials and Methods. This model did not have the photoperiod limit (PM) and only one set of photoperiod coefficients (C). It was obvious from this initial analysis that there was something fundamentally different between the data with natural light and those with the 20-h daylength. Therefore, PM and the two sets of photoperiod coefficients (CN and C20) were added to the model as described above. The results of this sequence of fitting the original model, the model with PM, and the model with two sets of photoperiod coefficients plus PM are shown in Fig. 1. Substantial improvements in the model with each step are clearly indicated (e.g., R2 of 0.63, 0.87, and 0.96, respectively).
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Fig. 1. Comparison of observed and calculated days to first flower for natural and artificial light. Observations were averaged over replications. Each point represents one isoline-location-year. Calculations are based on the isoline-based model (Eq. [1] through [6]) with (a) using the original model by Cober et al. (2001), (b) the original model modified by inserting the photoperiod limit (PM), and (c) the original model modified with PM plus two sets of photoperiod coefficients.
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The model with PM and the two sets of photoperiod coefficients worked well for both natural and artificial light (Fig. 1 and 2). Values of R2 and SEE (standard error of estimate) were 0.92 and 4.85 d for natural light (Fig. 2) and 0.96 and 4.76 d for natural and artificial light (Fig. 1) when the model calculations were compared with observations although this does not represent an independent test of the model.
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Fig. 2. Comparison of observed and calculated days to first flower for natural light for soybean isolines in a Clark or Harosoy background. Observations were averaged over replications. Each point represents one isoline-location-year. Calculations are based on the isoline-based model (Eq. [1] through [6]).
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Values of all coefficients except the C's are shown in Table 2. The value for b was 0.00214 °C-1 d-1, which corresponds to 467 growing photo-degree days (GPDD) from planting to flowering. The value of d (Table 2) was the same value as in Cober et al. (2001) (0.196 h-1).
The fact that two sets of the photoperiod coefficient were solved for was an important modification of the original model. Values for the two sets of photoperiod coefficients (CN and C20, °C h-1) for each isoline are listed in Table 3 with their differences. Differences were surprisingly large for some isolines (Table 3). The difference varied with isoline and acted to delay flowering (negative values) in some cases and to speed flowering (positive values) in other cases. Therefore, for some lines, incandescent lamps had a relatively large effect on phenological development, possibly because of a differential response of these loci to light quality or to the extreme 20-h photoperiod. These results suggest that there may be hazards in studying phenological development under artificial lights. Because the model will not be used for artificial light conditions, values of C20 were of academic interest only.
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Table 3. Values of the photoperiod coefficients (C) for each isoline for natural light (C = CN) and for the 20-h daylength (c = c20) along with the differences (C = CN - C20).
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While the Cober et al. (2001) study was conducted with only Harosoy isolines, this study was conducted with Harosoy and Clark isolines, of which 12 maturity gene combinations were present in both genetic backgrounds. There did not appear to be differences between the two backgrounds because isoline background biases were not observed in the model (Fig. 2).
The emphasis in this study was on the calculation of effects of individual genes on photothermal response in soybean, which to the best of our knowledge, has never been done before. However, some parts of the model were not extensively tested because only two relatively northern locations were used. For example, many phenological models have temperature responses that reach a maximum of about 30°C and then decline (Stewart et al., 1998; Piper et al., 1996a, 1996b; Yin et al., 1995). Because average daily temperatures seldom exceeded 30°C, the simple linear model was quite adequate at the two locations used in this study but may not be adequate in locations closer to the equator. Similarly, short photoperiods were not encountered in this study, and the base photoperiod (PB) of 13.5 h needs to be tested in locations closer to the equator. We are undertaking a study where phenological observations are being made throughout eastern North America for a greater range of photoperiods. Further research will use this database to test the model for the vegetative phase and develop a model for the reproductive phase of soybean development. Another shortcoming was the use of planting date rather than emergence date for the start of the vegetative period; however, emergence data were not available in this study. No doubt some of the errors in estimating time to flowering resulted from combining the emergence phase of growth with the vegetative phase, but the common genetic backgrounds of the isolines should have minimized this source of error.
The main focus in this paper was to quantify the effect of individual genes for natural light conditions. The photoperiod coefficient for natural light (CN) was a linear function of the number of loci with dominant alleles although there was some scatter about the line (Fig. 3). This scatter was of some interest. Did it represent uneven effects of genes or effects of various combinations of genes or interactions among genes? Dividing CN into components using Eq. [7] indicated that dominant alleles at the different loci have effects of different magnitudes (Table 4). The simple additive model of CN accounted for 96% of the variation (Fig. 4). Therefore, the addition of interactions could only improve the model slightly. The main difference in magnitudes of the different loci occurred between E1 and the other loci (E2, E3, E4, E5, and E7). The average value of the components for these loci (E2 to E7) was 0.58 Cd h-1. This was approximately half of the E1 component. Upadhyay et al. (1994) also noted the large effect of E1 compared with E2 and E3. If, however, we accept the premise that all genes act equally, then E1 could represent two loci. Again, using the average effect of loci E2 to E7, the remaining photoperiod effect (E?) predicts the discovery of two or more additional genes.
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Fig. 3. Photoperiod coefficient (°C h-1) for natural daylength (CN) as related to the number of loci with dominant alleles. Genotypes for each isoline are shown in Table 1.
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Table 4. The components of the photoperiod coefficient (CN) for natural daylength for the dominant allele at each locus.
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Fig. 4. Comparison of values of the photoperiod coefficient (°C h-1) for natural daylength (CN) calculated as individual values for each isoline and by using the allele-based model (Eq. [7]).
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Moving from a line- or genotype-based model to an allele-based model by substituting the CNM submodel into the phenology model decreased the R2 from 0.92 to 0.89 and increased the standard error from 4.85 to 5.80 d (Fig. 5). However, this change decreased the number of photoperiod coefficients from 29 to 7 and made the model more useable. That is, if the genetic information (the genotype at each of the loci) was known for a soybean line, the model has the potential of being used with archived temperature data to calculate time from planting to first flower for a range of planting dates in a specific region. The model could also be used to predict the number of dominant alleles required in cultivars when a new agronomic regime (for example, earlier, later, or winter planting) or a new location is being considered for soybean production.
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Fig. 5. Comparison of observed and calculated days to first flower. Calculations were made using the allele-based model (Eq. [7]) to calculate the photoperiod coefficient.
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NOTES
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ECORC Contrib. no. 11641.
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REFERENCES
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- Bernard, R.L. 1971. Two major genes for time of flowering and maturity in soybeans. Crop Sci. 11:242–244.[Abstract/Free Full Text]
- Bonato, E.R., and N.A. Vello. 1999. E6, a dominant gene conditioning early flowering and maturity in soybeans. Genet. Mol. Biol. 22:229–232.
- Buzzell, R.I. 1971. Inheritance of a soybean flowering response to fluorescent-daylength conditions. Can. J. Genet. Cytol. 13:703–707.[ISI]
- Buzzell, R.I., and H.D. Voldeng. 1980. Inheritance of insensitivity to long daylength. Soybean Genet. Newsl. 7:26–29.
- Cober, E.R., D.W. Stewart, and H.D. Voldeng. 2001. Photoperiod and temperature responses in early-maturing near-isogenic soybean lines. Crop Sci. 41:721–727.[Abstract/Free Full Text]
- Cober, E.R., and H.D. Voldeng. 2001. A new soybean maturity and photoperiod-sensitivity locus linked to E1 and T. Crop Sci. 41:698–701.[Abstract/Free Full Text]
- Constable, G.A., and I.A. Rose. 1988. Variability of soybean phenology response to temperature, daylength and rate of change in daylength. Field Crops Res. 18:57–69.
- Grimm, S.S., J.W. Jones, K.J., Boote, and D.C. Herzog. 1994. Modeling the occurrence of reproductive stages after flowering for four soybean cultivars. Agron. J. 86:31–38.[Abstract/Free Full Text]
- Grimm, S.S., J.W. Jones, K.J. Boote, and J.D. Hesketh. 1993. Parameter estimation for predicting flowering date of soybean cultivars. Crop Sci. 33:137–144.[Abstract/Free Full Text]
- Hadley, P., E.H. Roberts, R.J. Summerfield, and F.R. Minchin. 1984. Effects of temperature and photoperiod on flowering in soya bean [Glycine max (L.) Merrill]: A quantitative model. Ann. Bot. 53:669–681.[Abstract/Free Full Text]
- Jones, J.W., K.J. Boote, G. Hoogenboom, S.S. Jagtap, and G.G. Wilkerson. 1989. SOYGRO V5.42—soybean crop growth simulation model: User's guide. Florida Agric. Exp. Stn. J. no. 8304. Univ. of Florida, Gainesville.
- List, R.J. 1958. Smithsonian meteorological tables. Smithsonian Misc. Collections Vol. 114. Smithsonian Inst., Washington, DC.
- Major, D.J. 1980. Photoperiod response characteristics controlling flowering of nine crop species. Can. J. Plant Sci. 60:777–784.
- Major, D.J., D.R. Johnson, J.W. Tanner, and I.C. Anderson. 1975. Effects of daylength and temperature on soybean development. Crop Sci. 15:174–179.[Abstract/Free Full Text]
- Marquardt, D.W. 1963. An algorithm for least squares estimation of non-linear parameters. J. Soc. Ind. Appl. Math. 11:431–441.
- McBlain, B.A., and R.L. Bernard. 1987. A new gene affecting the time of flowering and maturity in soybeans. J. Hered. 78:160–162.[Abstract/Free Full Text]
- Piper, E.L., K.J. Boote, J.W. Jones, and S.S. Grim. 1996a. Comparisons of two phenology models for predicting flowering and maturity date of soybean. Crop Sci. 36:1606–1614.[Abstract/Free Full Text]
- Piper, E.L., M.A. Smit, K.J. Boote, and J.W. Jones. 1996b. The role of daily minimum temperature in modulating the development rate to flowering in soybean. Field Crops Res. 47:211–220.
- Robertson, G.W. 1968. A biometeorological time scale for a cereal crop involving day and night temperatures and photoperiod. Int. J. Biometeorol. 12:191–223.
- Stewart, D.W., L.M. Dwyer, and L.L. Carrigan. 1998. Phenological temperature response of maize. Agron. J. 90:73–79.[Abstract/Free Full Text]
- Summerfield, R.J., and E.H. Roberts. 1987. Effects of illuminance on flowering in long- and short-day grain legumes: A reappraisal and unifying model. p. 203–223. In J.G. Atherton (ed.) Manipulation of flowering. Butterworths, London.
- Summerfield, R.J., E.H. Roberts, R.H. Ellis, and R.J. Lawn. 1991. Towards the reliable prediction of time to flowering in six annual crops: I. The development of simple models for fluctuating field environments. Exp. Agric. 27:11–31.
- Upadhyay, A.P., R.H. Ellis, R.J. Summerfield, E.H. Roberts, and A. Qi. 1994. Characterization of photothermal flowering responses in maturity isolines of soyabean [Glycine max (L.) Merrill] cv. Clark. Ann. Bot. 74:87–96.
- Yin, X., M.J. Kropff, G. McLaren, and R.M. Visperas. 1995. A nonlinear model for crop development as a function of temperature. Agric. For. Meteorol. 77:1–16.
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ABSTRACT
INTRODUCTION
