Model of Dry Matter and Plant Nitrogen Partitioning between Leaf and Stem for Coastal Bermudagrass. I. Dependence on Harvest Interval

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1 JOURNAL OF PLANT NUTRITION Vol. 27, No. 9, pp , 2004 Model of Dry Matter and Plant Nitrogen Partitioning between Leaf and Stem for Coastal Bermudagrass. I. Dependence on Harvest Interval A. R. Overman* and R. V. Scholtz III Agricultural and Biological Engineering Department, University of Florida, Gainesville, Florida ABSTRACT Forage production depends on factors such as applied nutrients, available water, and harvest interval (for perennials). It has been shown that seasonal yield of Coastal bermudagrass (Cynodon dactylon L. Pers.) and Pensacola bahiagrass (Paspalum notatum Flu gge) are dependent on harvest interval. A growth model has been developed which describes this dependence quite well. This analysis explains the response in terms of partitioning between leaves and stems. It accounts for the strong decrease in leaf dry matter fraction with increase in harvest interval. Data from Tifton, GA for Coastal *Correspondence: A. R. Overman, Agricultural and Biological Engineering Department, University of Florida, Gainesville, FL ; aoverman@agen.ufl.edu DOI: /PLN Copyright & 2004 by Marcel Dekker, Inc (Print); (Online)

2 1586 Overman and Scholtz bermudagrass are used to show that at a harvest interval of 4 wk the leaf fraction is approximately 78%. Peak dry matter production of 20.3 Mg ha 1 is estimated to occur at a harvest interval of 10.4 wk, with a corresponding leaf fraction of 51%. Key Words: Model; Forage; Partitioning. INTRODUCTION Field experiments [1,2] with Coastal bermudagrass have shown that yields and forage quality are strongly related to harvest interval, and that partitioning of dry matter shifts from leaves at short intervals toward stems at long intervals. A linear growth model to describe this partitioning was developed. [3] It appeared to work well for intervals up to 6 wk, but proved inadequate for longer intervals. The growth model was expanded to a linear-exponential form, [4] which proved more adequate for the purpose. A mathematical theorem was proved, [5] which established linear-exponential dependence of seasonal dry matter yield on harvest interval. In this article field data are used to describe partitioning of dry matter between leaf and stem for Coastal bermudagrass at harvest intervals up to 24 wk. The model is given by [4,5] Y ¼ð þ tþ expð tþ MODEL DESCRIPTION where Y ¼ seasonal dry matter yield, Mg ha 1 ; t ¼ harvest interval, wk; ¼ intercept parameter for dry matter, Mg ha 1 ; ¼ slope parameter for dry matter, Mg ha 1 wk 1 ; ¼ aging coefficient, wk 1. If it is assumed that dependence of plant nitrogen uptake on harvest interval follows a similar relationship, then it can be written N u ¼ð n þ n tþ expð tþ where N u ¼ seasonal plant N uptake, kg ha 1 ; n ¼ intercept parameter for plant N uptake, kg ha 1 ; n ¼ slope parameter for plant N uptake, kg ha 1 wk 1. It follows from Eqs. (1) and (2) that plant N concentration ð1þ ð2þ

3 Dry Matter and Plant N Partitioning between Leaf and Stem Part I 1587 (N c ) is given by N c ¼ N u Y ¼ n þ n t þ t Since above ground dry matter can be partitioned into leaves (Y L )and stems (Y S ), it follows that Y ¼ Y L þ Y S At this point, it is hypothesized that leaf and stem dry matter can be described by relations similar to Eq. (1), so that Y L ¼ð L þ L tþ expð tþ Y S ¼ð S þ S tþ expð tþ where subscripts L and S refer to leaves and stems, respectively. Now it is further hypothesized that plant N uptake can be written as the sum of uptake by leaves and by stems N u ¼ N cl Y L þ N cs Y S where N cl ¼ leaf N concentration, g kg 1 ; N cs ¼ stem N concentration, gkg 1. Substitution of Eqs. (5) and (6) into Eq. (7) leads to N u ¼½ð L N cl þ S N cs Þþð L N cl þ S N cs ÞtŠ expð tþ which provides a rational basis for Eq. (2). By equating like terms in Eqs. (2) and (8), the following two relations are obtained: L N cl þ S N cs ¼ n L N cl þ S N cs ¼ n ð3þ ð4þ ð5þ ð6þ ð7þ ð8þ ð9þ ð10þ Since there are two equations in two unknowns (N cl and N cs ), it should be possible to estimate the concentrations of nitrogen in the leaves and stems. DATA ANALYSIS Data for this analysis are taken from a field study by Burton et al. [2] 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. The data are listed in Table 1 and Fig. 1.

4 1588 Overman and Scholtz Table 1. Dependence of dry matter (Y ) partitioning between leaves (Y L ) and stems (Y S ) on harvest interval (t) for Coastal Bermudagrass grown at Tifton, GA. a t Y Y L Y S Y* Y L Y S (wk) (Mg ha 1 ) f L (Mg ha 1 ) (Mg ha 1 ) (Mg ha 1 ) (Mg ha 1 ) (Mg ha 1 ) a Yield data adapted from Burton et al. (1963). [2] Figure 1. Dependence of seasonal dry matter yield (Y ) on harvest interval (t) for Coastal bermudagrass grown at Tifton, GA. Yield adapted from Burton et al. [2] Lines drawn from Eqs. (13), (15), and (16); curves drawn from Eqs. (18) (20).

5 Dry Matter and Plant N Partitioning between Leaf and Stem Part I 1589 The first step in the analysis is to standardize (linearize) response data (Y* and Nu ) according to the equations Y Y expðtþ ¼ þ t N u ¼ N u expðtþ ¼ n þ n t ð11þ ð12þ It has previously been shown [6] that the best choice is ¼ wk 1 for these data, which led to Y Y expð0:077tþ ¼ þ t ¼ 8:91 þ 3:49t N u ¼ N u expð0:077tþ ¼ n þ n t ¼ 422 þ 33:0t ð13þ ð14þ Following this same procedure for leaves and stems, with ¼ wk 1, leads to Y L Y L expð0:077tþ ¼ L þ L t ¼ 14:8 þ 0:778t r ¼ 0:982 ð15þ Y S Y S expð0:077tþ ¼ S þ S t ¼ 5:84 þ 2:71t r ¼ 0:999 ð16þ while Eqs. (15) and (16) lead to high correlation coefficients (r), we arrive at two rather startling conclusions: first, that the intercept in Eq. (16) is negative and second, that it appears that leaf mass is greater than total mass for t! 0. Obviously this poses a dilemma. The answer to this dilemma can be seen in Fig. 2 for the plot of leaf fraction ( f L ) vs. harvest interval (t), where the curve is described by f L ¼ Y L Y ¼ 14:8 þ 0:778t 8:91 þ 3:48t ð17þ which shows that f L! 1ast! 2 wk. In fact the intersection occurs at t ¼ 5.84/2.71 ¼ 2.15 wk. This suggests that the first two weeks of regrowth consists almost entirely of leaves, and that Eqs. (15) and (16) only apply for t 2 wk. Yield curves for leaf and stem in Fig. 1 are drawn from Y L ¼ð L þ L tþ expð tþ ¼ð14:8 þ 0:778tÞ expð 0:077tÞ Y S ¼ð S þ S tþ expð tþ ¼ð 5:84 þ 2:71tÞ expð 0:077tÞ ð18þ ð19þ

6 1590 Overman and Scholtz Figure 2. Dependence of dry matter leaf fraction ( f L ) on harvest interval (t) for Coastal bermudagrass grown at Tifton, GA. Data adapted from Burton et al. [2] Curve drawn from Eq. (17). for t 2 wk. The yield curve for total dry matter is given by Y ¼ð þ tþ expð tþ ¼ð8:91 þ 3:49tÞ expð 0:077tÞ ð20þ Equations (9) and (10) can now be used to estimate N concentration for leaves and stems. Substitution of the various parameters leads to 14:8N cl 5:84N cs ¼ 422 ð21þ 0:778N cl þ 2:71N cs ¼ 33:0 ð22þ Solution of these two simultaneous equations gives N cl ¼ 29.9 g kg 1 and N cs ¼ 3.6 g kg 1. SUMMARY AND CONCLUSIONS The expanded growth model appears to describe partitioning of dry matter between leaves and stems reasonably well for Coastal bermudagrass. Equations (18) and (19) describe dependence of leaf and stem dry matter on harvest interval satisfactorily. According to Eq. (17) dry matter is comprised of approximately 78% leaves at a harvest interval of 4 wk, 65% leaves at 6 wk, and 48% leaves at 12 wk. Since the stem

7 Dry Matter and Plant N Partitioning between Leaf and Stem Part I 1591 fraction contains considerably less nitrogen than leaves (3.6 g kg 1 compared to 29.9 g kg 1 ), longer harvest intervals represent lower forage quality. Digestibility of the forage also declines with age. [2] Now it can be shown that peak harvest interval (t p ) and peak dry matter yield (Y p ) are given by t p ¼ 1 ¼ 1 8:91 ¼ 10:4 wk ð23þ 0:077 3:49 Y p ¼ð8:91 þ 3:49t p Þ expð 0:077t p Þ¼20:3 Mgha 1 ð24þ It follows from Eq. (17) that the corresponding leaf fraction at peak is 0.51, and plant N uptake is N u ¼ð422 þ 33:0t p Þ expð 0:077t p Þ¼344 kg ha 1 ð25þ It should be noted that peak harvest interval and peak plant N uptake (N up ) are given by t p ¼ 1 n ¼ ¼ 0:2 0wk ð26þ n 0:077 33:0 N up ¼ð422 þ 33:0t p Þ expð 0:077t p Þ¼422 kg ha 1 ð27þ In part II of this series application of the model to partitioning of dry matter between leaves and stems with time as plants age will be discussed. Preliminary work along these lines is also underway for alfalfa (Medicago sativa L.). REFERENCES 1. Prine, G.M.; Burton, G.W. The effect of nitrogen rate and clipping frequency upon the yield, protein content and certain morphological characteristics of Coastal bermudagrass (Cynodon dactylon (L) Pers.). Agron. J. 1956, 48, Burton, G.W.; Jackson, J.E.; Hart, R.H. Effects of cutting frequency and nitrogen on yield, in vitro digestibility, and protein, fiber, and carotene content of Coastal bermudagrass. Agron. J. 1963, 55, Overman, A.R.; Wilkinson, S.R. Partitioning of dry matter between leaf and stem in Coastal bermudagrass. Agric. Sys. 1989, 30,

8 1592 Overman and Scholtz 4. Overman, A.R. An expanded growth model for grasses. Commun. Soil Sci. Plant Anal. 1998, 29, Overman, A.R. A mathematical theorem to relate seasonal dry matter to harvest interval for the expanded growth model. Commun. Soil Sci. Plant Anal. 2001, 32, Overman, A.R.; Scholtz, R.V. Mathematical Models of Crop Growth and Yield; Marcel Dekker, Inc.: New York, 2002; 328.