JOURNAL OF PLANT NUTRITION Vol. 27, No. 9, pp. 1593 1600, 2004 Model of Dry Matter and Plant Nitrogen Partitioning between Leaf and Stem for Coastal Bermudagrass. II. Dependence on Growth Interval A. R. Overman* and R. V. Scholtz III Agricultural and Biological Engineering Department, University of Florida, Gainesville, Florida ABSTRACT Part I of this series discussed dependence of partitioning between leaf and stem on harvest interval for Coastal bermudagrass (Cynodon dactylon L. Pers.). The expanded growth model described partitioning of both dry matter and plant nitrogen for seasonal totals. In this article the model is applied to accumulation of stem dry matter with time (growth interval) as the season progresses. A linear phase relation is established between leaf and stem dry matter. Estimates of leaf and stem nitrogen concentrations from Part I are then used to estimate accumulation of plant nitrogen with time. Model simulations describe data from Tifton, GA rather well. *Correspondence: A. R. Overman, Agricultural and Biological Engineering Department, University of Florida, Gainesville, FL 32611-0570; E-mail: aoverman@agen.ufl.edu. 1593 DOI: 10.1081/PLN-200026002 Copyright & 2004 by Marcel Dekker, Inc. 0190-4167 (Print); 1532-4087 (Online) www.dekker.com
1594 Overman and Scholtz Key Words: Model; Forage; Partitioning. INTRODUCTION In Part I of this series, [1] the expanded growth model [2] was used to describe partitioning between leaf and stem for the warm-season perennial Coastal bermudagrass as related to harvest interval. Now the question of dry matter and plant N accumulation in leaves and stems as the season progresses is addressed. The analysis gives further insight into coupling between plant components as the plant grows. The growth model is comprised of a Gaussian environmental function and a linearexponential intrinsic growth function. [2] MODEL DESCRIPTION The expanded growth model for perennial grass is given by Y ¼ AQ where Y ¼ dry matter accumulation with time, Mg ha 1 ; A ¼ yield coefficient, Mg ha 1 ;andq¼growth quantifier, defined by pffiffi Q ¼ exp 2 cxi ð1 kx i Þ½erf x erf x i Š k pffiffiffi exp x 2 exp x 2 i ð2þ in which the dimensionless time variable, x, is defined by x ¼ t ffiffi pffiffiffi 2 c p þ 2 2 where t ¼ calendar time since Jan. 1, wk; t i ¼ time of initiation of growth, wk; ¼ time to the mean of the dry matter distribution, wk; ¼ time spread of the dry matter distribution, wk; c ¼ aging coefficient in the intrinsic growth function, wk 1 ; k ¼ curvature factor in the intrinsic growth function; and x i is the value of Eq. (3) corresponding to t i. The error function in Eq. (2) is defined by erf x ¼ p 2 ffiffiffi Z x 0 exp ð u 2 Þdu where u is simply the variable of integration. ð1þ ð3þ ð4þ
Dry Matter and Plant N Partitioning between Leaf and Stem Part II 1595 It will be shown that leaf dry matter, Y L, and stem dry matter, Y S, can be related by the linear phase equation Y L ¼ a þ by S ð5þ Plant N accumulation can be estimated from N u ¼ N cl Y L þ N cs Y S ð6þ where N cl and N cs are plant N concentrations for leaf and stem, respectively. DATA ANALYSIS Data for this analysis are taken from a field study by Burton and Hart [3] at Tifton, GA. The soil was Tifton loamy sand (fine-loamy, kaolinitic, thermic Plinthic Kandiudult). Applied nitrogen was 672 kg ha 1. Harvest intervals included 3, 4, 5, 6, 8, 12, and 24 wk. Data for the first cutting of each harvest interval is used to estimate a growth curve, as described previously. [4] The data are listed in Table 1 and shown in Fig. 1. We now proceed with the estimation procedure. The first step in the analysis is to estimate pffiffiffi model parameters. From previous analysis, [4] we choose: ¼ 25 wk, 2 ¼ 12 wk, c ¼ 0.15 wk 1, k ¼ 5. From Fig. 1 the time of initiation of stem growth is chosen as t i ¼ 16.6 wk. Substitution of Table 1. Response of plant nitrogen (N u ), total dry matter (Y ), leaf fraction ( f L ), leaf mass (Y L ), and stem mass (Y S ), with calendar time (t) and harvest interval (t) for the 1st cutting of Coastal Bermudagrass at Tifton, GA (1961). a t t N u Y Y L Y S (wk) (wk) (kg ha 1 ) (Mg ha 1 ) f L (Mg ha 1 ) (Mg ha 1 ) 14.6 17.6 3 61.8 2.37 0.824 1.95 0.42 18.6 4 84.0 3.49 0.742 2.59 0.90 19.6 5 92.6 4.26 0.654 2.79 1.47 20.6 6 138 6.83 0.551 3.76 3.07 22.6 8 126 8.78 0.482 4.23 4.55 26.6 12 148 12.54 0.483 6.06 6.48 38.6 24 230 16.96 0.443 7.51 9.45 a Data adapted from Burton and Hart (1961). [3]
1596 Overman and Scholtz Figure 1. Response of stem mass (Y S ), leaf mass (Y L ), and leaf fraction ( f L ) with time (t) for Coastal bermudagrass grown at Tifton, GA (1961). Data adapted from Burton and Hart. [3] Curves drawn from Eqs. (9) (11). these values into Eq. (3) for dimensionless time leads to x ¼ t ffiffi pffiffiffi 2 c t 25 t 14:2 p þ ¼ þ 0:90 ¼, x i ¼ 0:200 ð7þ 2 2 12 12 and into Eq. (2) for the growth quantifier leads to pffiffi Q ¼ exp 2 cxi ð1 kx i Þ½erf x erf x i Š k pffiffiffi exp x 2 exp x 2 i ¼ 1:433 0:0½erf x 0:223Š 2:821 exp ð x 2 Þ 0:961 ð8þ
Dry Matter and Plant N Partitioning between Leaf and Stem Part II 1597 Table 2. Model estimates of stem mass (Y S ), leaf mass (Y L ), leaf fraction (f L ), plant N uptake (N u ), and plant N concentration (N c ) with calendar time (t) for Coastal bermudagrass grown at Tifton, GA. t (wk) x erf x exp ( x 2 ) Q Y^ S (Mg ha 1 ) Y^ L ^N u ^N c (Mg (kg (g ha 1 ) f^ L ha 1 ) kg 1 ) 16.6 0.200 0.223 0.961 0 0 1.89 1.000 56.5 29.9 18 0.317 0.346 0.905 0.226 0.576 2.24 0.795 69.0 24.5 19 0.400 0.428 0.852 0.441 1.12 2.56 0.696 80.6 21.9 20 0.483 0.505 0.792 0.683 1.74 2.93 0.627 93.9 20.1 22 0.650 0.642 0.655 1.24 3.16 3.78 0.544 124 17.9 24 0.817 0.752 0.513 1.81 4.62 4.66 0.502 156 16.8 26 0.983 0.835 0.380 2.35 6.00 5.48 0.477 185 16.1 28 1.150 0.896 0.266 2.81 7.16 6.18 0.463 211 15.8 30 1.317 0.937 0.177 3.17 8.08 6.73 0.454 230 15.5 32 1.483 0.964 0.111 3.44 8.77 7.14 0.449 245 15.4 34 1.650 0.980 0.0657 3.62 9.23 7.43 0.446 255 15.3 36 1.817 0.989 0.0369 3.74 9.54 7.60 0.443 262 15.3 38 1.983 0.9949 0.0196 3.81 9.72 7.71 0.442 266 15.3 40 2.150 0.9975 0.00983 3.85 9.82 7.77 0.442 268 15.2 Model estimates are listed in Table 2. The yield coefficient in Eq. (1) is calibrated at t ¼ 26 wk for Y S ¼ 6.00 Mg ha 1 and Q ¼ 2.35, which leads to Y^ S ¼ A S Q ¼ 6:00 Q ¼ 2:55Q ð9þ 2:35 The curve for stem mass in Fig. 1 is drawn from Eq. (9). The phase plot (Y L vs. Y S ) is shown in Fig. 2, where the line is drawn from ^ Y L ¼ a þ by S ¼ 1:89 þ 0:599Y S r ¼ 0:9945 ð10þ with a correlation coefficient of r ¼ 0.9945. Equations (9) and (10) are combined to calculate the curve for leaf mass in Fig. 1. Leaf fraction can now be estimated from the definition ^ f L ¼ ^ Y L ^ Y L þ ^Y S ð11þ as shown in Fig. 1.
1598 Overman and Scholtz Figure 2. Phase plot of leaf mass (Y L ) vs. stem mass (Y S ) for Coastal bermudagrass grown at Tifton, GA. Data adapted from Burton and Hart. [3] Line drawn from Eq. (10). The final step is to estimate plant N uptake and plant N concentration vs. time. From Part I of this analysis we obtained N cl ¼ 29.9 g kg 1 and N cs ¼ 3.6 g kg 1, which leads to ^N u ¼ N cl ^Y L þ N cs ^Y S ¼ 29:9 ^ Y L þ 3:6 ^ Y S ð12þ ^N c ¼ ^N u ^Y L þ ^Y S ð13þ and the values listed in Table 2 and shown in Fig. 3. SUMMARY AND CONCLUSIONS The expanded growth model provides excellent simulation of stem and leaf dry matter accumulation and change in leaf fraction with time (Fig. 1). Leaf and stem dry matter follow a linear phase relationship with time (Fig. 2). Dependence of plant N accumulation and plant N concentration on time is described reasonably well by the model (Fig. 3). It was shown previously [4] that the model provides satisfactory simulation of total dry matter with time.
Dry Matter and Plant N Partitioning between Leaf and Stem Part II 1599 Figure 3. Response of plant N uptake (N u ) and plant N concentration (N c ) with time (t) for Coastal bermudagrass grown at Tifton, GA. Data adapted from Burton and Hart. [3] Curves drawn from Eqs. (12) and (13). This analysis provides some insight into the growth process of Coastal bermudagrass. During the first two weeks in the spring, growth consists of leaf development. Afterwards, stem and leaf growth proceeds along together in a somewhat linear relationship. As a result, leaf fraction declines with time as the structural component of the plant develops. Since nitrogen concentration of stems is much less than that of leaves, the average nitrogen concentration of the plant declines with age. Peak dry matter production occurs for a harvest interval of about 10 wk where the leaf fraction is approximately 50%. In contrast, maximum plant N uptake occurs for very short harvest intervals where leaf fraction is near 100%. The net result is that seasonal yield increases up to about 10 wk with a corresponding reduction in forage quality. This seems to be
1600 Overman and Scholtz an inevitable consequence of change in plant morphology with age. A larger plant requires more structural material for physical support. REFERENCES 1. Overman, A.R.; Scholtz, R.V. Model of dry matter and plant nitrogen partitioning between leaf and stem for Coastal bermudagrass. I. Dependence on harvest interval. J. Plant Nutr. 2004, 27 (9); this issue. 2. Overman, A.R. An expanded growth model for grasses. Commun. Soil Sci. Plant Anal. 1998, 29, 67 85. 3. Burton, G.W.; Hart, R.H. Grass and Turf Investigations; Georgia Coastal Plain Experiment Station: Tifton, GA, 1961; Annual Report, 231, 234, 236. 4. Overman, A.R.; Brock, K.H. Confirmation of the expanded growth model for a warm-season perennial grass. Commun. Soil Sci. Plant Anal. 2003, 34, 1105 1117.