Model Analysis for Growth Response of Soybean

Transcription

1 COMMUNICATIONS IN SOIL SCIENCE AND PLANT ANALYSIS Vol. 34, Nos. 17 & 18, pp , 2003 Model Analysis for Growth Response of Soybean A. R. Overman * and R. V. Scholtz III Agricultural and Biological Engineering Department, University of Florida, Gainesville, Florida, USA ABSTRACT The expanded growth model was developed to describe accumulation of dry matter and plant nutrients with time for annual and perennial crops. It incorporates an environmental driving function and an intrinsic growth function. Previous analysis has shown that the model applies to the annual corn (Zea mays L.) and the warm-season perennial bermudagrass (Cynodon dactylon L. Pers.). In this article the model is used to describe accumulation of dry matter and plant nitrogen (N) by soybean (Glycine max L. Merr.). The model describes dry matter accumulation by the vegetative component of the plant followed by accumulation of dry matter and plant N with time by seeds and pods. Strong dependence of yields and plant N uptake on seasonal rainfall is illustrated. *Correspondence: A. R. Overman, Agricultural and Biological Engineering Department, University of Florida, Gainesville, FL , USA; aoverman@ agen.ufl.edu DOI: /CSS Copyright D 2003 by Marcel Dekker, Inc (Print); (Online)

2 2620 Overman and Scholtz INTRODUCTION The expanded growth model for plant accumulation of dry matter and nutrients is the culmination of 20 years of effort. The first step was the empirical model applied to perennial grasses. [1 4] This was followed by a phenomenological model, [5,6] which incorporated a Gaussian environmental function and a linear intrinsic growth function. It worked for perennial grasses up to harvest intervals of six weeks. The intrinsic growth function was then modified with a linear exponential intrinsic growth function to form the expanded growth model, [7] which was shown to apply to annuals and perennials. [8] This article discusses application of the expanded model to data for soybean. MODEL DESCRIPTION The expanded growth model consists of two components: 1) an environmental driving function and 2) an intrinsic growth function. We assume a Gaussian environmental function, E, given by " E ¼ constant exp t p ffiffi m # 2 2 s ð1þ where t = calendar time from Jan. 1, wk; m = time to the mean of the distribution, wk; s = time spread of the distribution, wk. The intrinsic growth function is assumed to follow the linear exponential form dy 0 dt ¼ ½a þ bðt t i ÞŠ exp½ cðt t i ÞŠ where dy /dt = rate of dry matter accumulation under constant environmental conditions, Mg ha 1 wk 1 ; a = initial growth rate at t = t i,mgha 1 wk 1 ; b = coefficient of increase in the growth rate, Mg ha 1 wk 2 ; c = coefficient of aging, wk 1 ; t i = time of initiation of growth, wk. Net growth rate, dy/dt, is taken as the product of Eqs. 1 and 2, so that ð2þ dy dt ¼ constant ½a þ bðt t i ÞŠ exp½ cðt t i ÞŠ " exp t p ffiffi m # 2 2 s ð3þ

3 Model Analysis for Growth Response of Soybean 2621 It should be noted that Eq. 3 contains two reference times, viz. t i and m, related to the plant and environment, respectively. Overman [7] showed that Eq. 3 could be integrated to obtain the function Y ¼ AQ ð4þ where Y = accumulated dry matter, Mg ha 1 ; A = yield factor, Mg ha 1 ; and Q = growth quantifier defined by pffiffi Q ¼ exp 2 scxi ð1 kx i Þ½erf x erf x i Š k pffiffiffi ½expð x 2 Þ expð x 2 i p ÞŠ where k = dimensionless curvature factor in the intrinsic growth function, defined by pffiffi 2 sb k ¼ ð6þ a and x = dimensionless time variable defined by x ¼ t ffiffi m pffiffi 2 sc p þ 2 s 2 where x i = dimensionless time corresponding to the time of initiation of growth, t i. The error function in Eq. 5 is defined by ð5þ ð7þ erf x ¼ p 2 ffiffiffi p Z x 0 expð u 2 Þdu ð8þ where u is simply the variable of integration. Values for the error function can be obtained from mathematical tables. [9] DATA ANALYSIS Data for this analysis are taken from a field study by Henderson and Kamprath [10] with soybean (cv. Lee) at Clayton, NC. The soil was Norfolk loamy sand (fine-loamy, kaolinitic, thermic Typic Kandiudult). Plant samples were collected every 10 days from June through September. Planting was approximately May 10 (t = 18.7 wk). While the experiment was conducted during 1966 through 1968, our analysis will focus on 1966

4 2622 Overman and Scholtz Table 1. Accumulation of dry matter (Y ), plant N uptake (N u ), and plant N concentration (N c ) with calendar time (t) by the vegetative component of soybean grown at Clayton, NC. a Y (Mg ha 1 ) N u (kg ha 1 ) N c (g kg 1 ) t (wk) a Data adapted from Henderson and Kamprath. [10] Time is calendar weeks from Jan. 1. and 1967 since sampling in 1968 was reduced to a 20-d frequency. Starting 110 days after planting, plants were divided into plant and pods & seeds. Measurements were made of dry matter and plant nutrients [N, phosphorus (P), potassium (K), calcium (Ca), and magnesium (Mg)]. Results are given in Table 1 and shown in Figure 1 for dry matter and plant N of the vegetative component (leaves + stalks) for 1966 and Time is referenced to Jan. 1. From the intercept of the growth plots, we choose t i = 24 wk. Based on previous experience with application of the expanded growth pffiffi model for corn, [11] model parameters are chosen as: m = 26 wk, 2 s = 8 wk, c = 0.05 wk 1, k = 5. The dimensionless time variable (Eq. 7) now becomes x ¼ t ffiffi m pffiffiffi 2 sc t 26 t 24:4 p þ ¼ þ 0:2 ¼ ; x i ¼ 0:050 2 s ð9þ and the dimensionless growth quantifier (Eq. 5) becomes pffiffi Q ¼ exp 2 scxi ð1 kx i Þ½erf x erf x i Š k pffiffiffi ½expð x 2 Þ expð x 2 i p ÞŠ ¼ 0:980f1:25½erf x þ 0:0564Š 2:821½expð x 2 Þ 0:9975Šg ð10þ

5 Model Analysis for Growth Response of Soybean 2623 Figure 1. Growth response of dry matter (Y), plant N uptake (N u ), and plant N concentration (N c ) with calendar time (t) for vegetative component of soybean grown at Clayton, NC. Data adapted from Henderson and Kamprath. [10] Curves drawn from Eqs

6 2624 Overman and Scholtz Table 2. Calculations for the expanded growth model for vegetative component of soybean grown at Clayton, NC. Ŷ (Mg ha 1 ) t (wk) x erf x exp( x 2 ) Q Values of x and Q are given in Table 2. Next the model is calibrated at t = 34 wk to obtain 6: : Y ¼ Q ¼ 1:826Q ð11þ 3: : Y ¼ 10:00 Q ¼ 3:043Q ð12þ 3:286 Yield estimates in Table 2 and the curves shown in Figure 1 are calculated from Eqs. 11 and 12. Since dry matter and plant N in the vegetative component decline after t = 34 wk, model calculations after that time do not apply. Data for dry matter and plant N accumulation in the seeds and pods are listed in Table 3 and shown in Figure 2. The intercept of the plots is estimated to be t i = 33 wk. Other parameters are assumed the same as for the vegetative component, which leads to x ¼ t ffiffi m pffiffi 2 sc p þ ¼ 2 s 2 t 26 8 þ 0:2 ¼ t 24:4 ; x i ¼ 1:075 ð13þ 8

7 Model Analysis for Growth Response of Soybean 2625 Table 3. Accumulation of dry matter (Y), plant N uptake (N u ), and plant N concentration (N c ) with calendar time (t) by seeds and pods of soybean grown at Clayton, NC. a Y (Mg ha 1 ) N u (kg ha 1 ) N c (g kg 1 ) t (wk) a Data adapted from Henderson and Kamprath. [10] Time is calendar weeks from Jan. 1. pffiffi Q ¼ exp 2 scxi ð1 kx i Þ½erf x erf x i Š k pffiffiffi ½expð x 2 Þ expð x 2 i p ÞŠ ¼ 1:537f 4:375½erf x 0:871Š 2:821½expð x 2 Þ 0:315Šg ð14þ Values calculated from Eqs. 13 and 14 are listed in Table 4. Yield curves are calibrated at t = 39 wk to obtain 4: : Y ¼ AQ ¼ Q ¼ 9:76Q ð15þ 0:410 8: : Y ¼ AQ ¼ Q ¼ 20:7Q ð16þ 0:410 Curves for Y vs. t in Figure 2 are drawn from Eqs. 15 and 16. Phase plots (Y and N c vs. N u ) are shown in Figure 3, where Y = accumulated dry matter in seeds & pods, Mg ha 1 ; N u = accumulated plant N in the seeds & pods, kg ha 1 ; N c = plant N concentration in the seeds & pods, g kg 1. Based on these plots, we assume the hyperbolic phase relation Y ¼ Y mn u ð17þ K n þ N u where Y m = potential maximum yield, Mg ha 1 ; K n = nitrogen response coefficient, kg ha 1. Eq. 17 can be rearranged to relate plant N concentration and plant N accumulation N c ¼ N u Y ¼ K n Y m þ 1 Y m N u ð18þ

8 2626 Overman and Scholtz Figure 2. Growth response of dry matter (Y), plant N uptake (N u ), and plant N concentration (N c ) with calendar time (t) for soybean seeds and pods grown at Clayton, NC. Data adapted from Henderson and Kamprath. [10] Curves drawn from Eqs and Eqs

9 Model Analysis for Growth Response of Soybean 2627 Table 4. Calculations for the expanded growth model for soybean seeds and pods grown at Clayton, NC. t (wk) x erf x exp ( x 2 ) Q Ŷ (Mg ha 1 ) Nˆ u (kg ha 1 ) Nˆ c (g kg 1 )

10 2628 Overman and Scholtz Figure 3. Phase plot of dry matter and plant N concentration vs. plant N uptake (Y and N c vs. N u ) for soybean seeds and pods grown at Clayton, NC. Data adapted from Henderson and Kamprath. [10] Lines drawn from Eqs ; curves from Eqs. 20 and 22.

11 Model Analysis for Growth Response of Soybean 2629 Linear regression of N c vs. N u leads to 1966 : N c ¼ K n Y m þ 1 Y m N u ¼ 34:5 þ 0:0831N u r ¼ 0:988 ð19þ Y ¼ Y mn u K n þ N u ¼ 12:0N u 410 þ N u ð20þ 1967 : N c ¼ K n Y m þ 1 Y m N u ¼ 34:4 þ 0:0356N u r ¼ 0:969 ð21þ Y ¼ Y mn u K n þ N u ¼ 28:1N u 965 þ N u ð22þ The lines in Figure 3 are drawn from Eqs. 19 and 21, while the curves are drawn from Eqs. 20 and 22. Values of N u are calculated from Eqs. 20 and 22 corresponding to Y in Table 4, and are shown in Figure 2. Corresponding values of N c are listed in Table 4 and shown in Figure 2. DISCUSSION From this analysis we conclude that the expanded growth model provides reasonable description of dry matter accumulation by the vegetative component of soybean up to t = 34.4 wk (110 days after planting). After this time there is rapid loss of dry matter and plant N due to leaf shed (Figure 1). At t = 33.0 wk (100 days after planting) development of seeds and pods begins, which is also described by the model with the same parameters as for the vegetative component (Figure 2). A hyperbolic phase relationship couples dry matter and plant N (Figure 3). Model estimates of projected maximum dry matter are 4.86 and Mg ha 1, with corresponding plant N of 280 and 560 kg ha 1 for 1966 and 1967, respectively. Maximum plantn concentrations are 57.6 and 54.3 g kg 1 for the two years. It is apparent from Figures 1 and 2 that accumulation of plant N in the seeds and pods includes both translocation from the vegetative component and transfer from the roots. Hammond et al. [12] showed that fallen leaves are very low in nitrogen. Differences in projected maximum dry matter (Y) and plant N (N u and N c ) for seeds and pods between 1966 and 1967 can be attributed at least in part to seasonal rainfall (R), as given in Table 5 and shown in Figure 4.

12 2630 Overman and Scholtz Table 5. Model estimates of maximum dry matter (Y), plant N uptake (N u ), and plant N concentration (N c ) vs. seasonal rainfall (R) for soybean seeds and pods grown at Clayton, NC. Year R (cm) Y (Mg ha 1 ) N u (kg ha 1 ) N c (g kg 1 ) Seasonal rainfall includes the months of June through September. Overman and Scholtz [13] have shown that yield response of corn to available water (rainfall + irrigation) follows an exponential function of the form Y ¼ A 1 exp R R 0 ð23þ 30 where A = maximum value of Y at high R, Mgha 1 ; R 0 = intercept rainfall for Y = 0, cm. Analysis of the data points in Figure 4 leads to the equation R 23 Y ¼ 15:5 1 exp ð24þ 30 for yield dependence on seasonal rainfall. Assuming a similar relationship for dependence of seasonal plant N uptake, we arrive at the equation R 23 N u ¼ exp ð25þ 30 It follows from Eqs. 24 and 25 that plant N concentration is given by N c ¼ N u ¼ 55:5 ð26þ Y The curves and line in Figure 4 are drawn from Eqs Figure 4 illustrates the strong sensitivity of soybean yield to available water. PlantN concentration remains relatively constant at approximately 55 g kg 1. According to this analysis, yields and plant N uptake were 32% and 66% of potential maximum in 1966 and 1967, respectively. Obviously, further work is needed to either verify these relationships or develop better ones for dependence of yields on water availability. A reader might be curious as to the effect of planting date in the growth model. It is implicit in the time of initiation, t i. For this study we found that t i = 24 wk for the vegetative component. Since planting date was 18.7 wk (May 10), this represents a lag of 5.3 wk from planting to significant plant growth when plant cover fully captures solar radiation. A

13 Model Analysis for Growth Response of Soybean 2631 Figure 4. Dependence of estimated maximum dry matter (Y), plant N uptake (N u ), and plant N concentration (N c ) on seasonal rainfall (R) for soybean seeds and pods grown at Clayton, NC. Curves drawn from Eqs. 24 and 25; line from Eq. 26.

14 2632 Overman and Scholtz similar lag was found for corn plants. [11] The time lag for formation of pods & seeds was = 14.3 wk after planting, which was = 9 wk after formation of the vegetative component. REFERENCES 1. Overman, A.R. Estimating crop growth with land treatment. J. Env. Eng. Div., Am. Soc. Civil Eng. 1984, 110, Overman, A.R.; Angley, E.A.; Wilkinson, S.R. Empirical model of coastal bermudagrass production. Trans. Am. Soc. Agric. Eng. 1988, 31, Overman, A.R.; Angley, E.A.; Wilkinson, S.R. Evaluation of an empirical model of coastal bermudagrass production. Agric. Syst. 1988, 28, Overman, A.R.; Wilson, D.M.; Vidak, W. Extended probability model for dry matter and nutrient accumulation by crops. J. Plant Nutr. 1995, 18, Overman, A.R.; Angley, E.A.; Wilkinson, S.R. A phenomenological model of coastal bermudagrass production. Agric. Syst. 1989, 29, Overman, A.R.; Angley, E.A.; Wilkinson, S.R. Evaluation of a phenomenological model of coastal bermudagrass production. Trans. Am. Soc. Agric. Eng. 1990, 33, Overman, A.R. An expanded growth model for grasses. Commun. Soil Sci. Plant Anal. 1998, 29, Overman, A.R.; Wilson, D.M. Physiological control of forage grass yield and growth. In Crop Yield: Physiology and Processes; Smith, D.L., Hamel, C., Eds.; Springer-Verlag: New York, 1999; Abramowitz, M.; Stegun, I.A. Handbook of Mathematical Functions; Dover: New York, Henderson, J.B.; Kamprath, E.J. Nutrient and Dry Matter Accumulation by Soybeans; Tech. Bull., North Carolina Agricultural Experiment Station: Raleigh, NC, 1970; Vol. 197, Overman, A.R.; Scholtz, R.V. Model for accumulation of dry matter and plant nutrients by corn. Commun. Soil Sci. Plant Anal. 1999, 30, Hammond, L.C.; Black, C.A.; Norman, A.G. Nutrient Uptake by Soybeans on Two Iowa Soils; Bulletin, Iowa Agricultural Experiment Station: Ames, IA, 1951; Vol. 384, Overman, A.R.; Scholtz, R.V. Corn response to irrigation and applied nitrogen. Commun. Soil Sci. Plant Anal. 2002, 33,