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A Model of Growth and Nutrient Uptake by Tobacco
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Title: A Model of Growth and Nutrient Uptake by Tobacco
Physical Description: Memoir
Creator: Overman, Allen R.
Brock, Kelly H.
Publication Date: 2012
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Abstract: This memoir is focused on a model of plant growth and nutrient uptake by the broad leaf crop tobacco (Nicotiana tabacum L.). Types of tobacco include shade-grown wrapper and Virginia flue-cured. Mathematical analysis utilizes the expanded growth model and the extended logistic model published previously. The growth model describes accumulation of biomass by photosynthesis based on the three basic processes of (1) seasonal distribution of solar energy, (2) partitioning of biomass between light-gathering (leaf) and structural (stems and stalks) components, and (3) an aging function. Plant nutrients are coupled to biomass through a hyperbolic phase relation for the mineral elements nitrogen, phosphorus, potassium, calcium, and magnesium. The logistic model describes response of the plant to levels of applied nutrients. Biomass is coupled to applied nutrients through hyperbolic phase equations. Previous work has focused on annuals such as corn (Zea maize L.) and forage grasses such as bermudagrass (Cynodon dactylon L.) and bahiagrass (Paspalum notatum Flügge). This document expands the analysis to a broad-leafed crop.
Acquisition: Collected for University of Florida's Institutional Repository by the UFIR Self-Submittal tool. Submitted by Allen Overman.
Publication Status: Unpublished
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A MEMOIR ON A Model of Growth and Nutr ient Uptake by Tobacco Allen R. Overman Agricultural and Biological Engineering Department University of Florida and Kelly H. Brock City of Casselberry, Florida Copyright 2012 Allen R. Overman

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Overman and Brock Growth of Tobacco i Key words : Mathematical model, plant growt h, plant nutrient uptake, tobacco This memoir is focused on a model of plant gr owth and nutrient uptake by the broad leaf crop tobacco ( Nicotiana tabacum L.). Types of tobacco include sh ade-grown wrapper and Virginia flue-cured. Mathematical analysis utilizes the expanded growth model and the extended logistic model published previously. The growth m odel describes accumulation of biomass by photosynthesis based on the three ba sic processes of (1) seasonal distribution of solar energy, (2) partitioning of biomass between light-gathering (leaf) and structural (stems and stalks) components, and (3) an aging function. Plant nutrients are coupled to biomass through a hyperbolic phase relation for the mineral elemen ts nitrogen, phosphorus, potassium, calcium, and magnesium. The logistic model desc ribes response of the plant to levels of applied nutrients. Biomass is coupled to applied nutrients through hyperbolic phase equatio ns. Previous work has focused on annuals such as corn ( Zea maize L.) and forage grasses such as bermudagrass ( Cynodon dactylon L.) and bahiagrass ( Paspalum notatum Flgge). This document expands the analysis to a broad-leafed crop. Acknowledgements : The authors thank Amy G. Buhler, E ngineering Librarian, Marston Science Library, University of Florida, for assist ance with preparation of this memoir. At the time of this analysis Kelly Brock wa s a National Science Foundation PhD fellow in the UF/ABE Department. He is presently Assistant P ublic Works Director/City Engineer for the City of Casselberry, Florida

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Overman and Brock Growth of Tobacco 1 Coupling of Biomass and Plant Nutrient A ccumulation by a Broad Leaf Annual Crop I. Above Ground Plant Allen R. Overman Agricultural and Biological Engineering Department University of Florida, Gainesville, Florida, USA Kelly H. Brock City of Casselberry, Florida, USA Abstract : The expanded growth model has been used to describe accumulation of biomass and plant nutrients (N, P, K, Ca, Mg, Cl) for broad leaf plant shade wrapper tobacco ( Nicotiana tabacum L.). Biomass accumulation with calendar tim e is described rather well by the model. Linear correlation between biomass yield ( Y ) and the growth quantifier ( Q ) is demonstrated. Plant nutrients and biomass are coupled throug h a hyperbolic phase rela tion. Data conform to this relationship quite closely, particularly for nitrogen, potassium, and calcium. It is concluded that the rate limiting process in the system is biomass accumulation by photosynthesis, and that plant nutrient accumulation follows in virtual equilibrium with biomass. The model appears transferable among various experi mental conditions (site, time crop, and cultural practices). Keywords : Growth model, nitrogen, phosphorus, pota ssium, calcium, magnesium, chloride, tobacco. Introduction The expanded growth model has been develope d to describe accumulation of biomass with calendar time by photosynthesis (Overman and Sc holtz, 2002). Accumulati on of plant nutrients has been coupled to accumulation of bioma ss through a hyperbolic phase relation (Overman, 1998). Application of the model to flue-cured to bacco has been discussed (Overman, 1999). In this document the model is applied to shade wra pper tobacco. Data from a field study in Dinhata, West Bengal, India are used in the analysis. Model Description The mathematical model includes two com ponents: (1) accumulati on of biomass with calendar time and (2) coupling of plant nutrients to biomass. The expanded growth model is used to describe biomass accumulation by photosynthesis as Q A Y (1) in which Y is accumulated biomass, Mg ha-1; A is the yield factor, Mg ha-1; and Q is the growth quantifier defined by i i i icx x x k x x kx Q2 exp exp exp erf erf 12 2 (2)

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Overman and Brock Growth of Tobacco 2 with dimensionless time, x linked to calendar time, t (referenced to Jan. 1) by 2 2 2 c t x (3) in which is calendar time to the mean of solar en ergy distribution (referenced to Jan. 1), wk; 2 is time spread of the en ergy driving function, wk; and c is the coefficient for the aging function, wk-1; and k is the partition coefficient betw een light-gathering and structural components of the system. The value of x = xi in Eq. (2) corresponds to t = ti = time of initiation of significant plant growt h. The error function, erf x in Eq. (2) is defined by xdu u x0 2) exp( 2 erf (4) in which u is the variable of integration. Values of the error function can be found in mathematical tables (cf. Abramowitz and Stegun, 1965). Nutrient and biomass accumulation are assumed to be coupled by the hyperbolic phase relation Y K Y N Ny um u (5) in which Nu is accumulated plant nutrient uptake (N, P, K, Ca, Mg, or Cl), kg ha-1; Num is potential maximum plant nutrient uptake, kg ha-1; and Ky is the yield response coefficient, Mg ha-1. Equation (5) can be rearra nged to the linear form Y N N K N Yum um y u1 (6) Equation (6) provides a conve nient test of the phase relation from field data. Data Analysis Data for this analysis are taken from a field study by Srivastava, Rao, and Gopalachari (1984) with shade wrapper tobacco at Dinhata, We st Bengal, India. Whol e-plant (leaf + stalk) samples were collected on a 10-day interval for a period of 120 d after plan ting in late October ( t = 43.0 wk). Nutrient application rate s were: N-P-K-Ca = 275-75-310-97 kg ha-1 from inorganic fertilizer and farmyard manure. Experiments were conducted on an entisol with four replicates taken at each sampling date. Results are listed in Table 1 and shown in Figure 1 for biomass and plant N accumulation. Visual inspection of Figure 1 leads to the choice of ti = 48.2 wk and = 56 wk. Following Overman and Woodard (2005) it is next assumed that xi = 0, which leads from Eq. (3) to

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Overman and Brock Growth of Tobacco 3 0 2 2 2 c t xi i 8 7 2 48 562 it c wk (7) After several tries, c = 0.10 wk-1 is selected as the best choice, which leads from Eq. (7) to = 8.83 wk. From previous work k = 5 is chosen (Overman, 1999). These values then lead to the time transformation 0 5 12 2 48 625 0 5 12 56 2 2 2 ix t t c t x (8) The growth quantifier now becomes 000 1 1 exp 821 2 0 erf 000 12 x x Q (9) Values for x and Q along with biomass yields Y are listed in Table 2 for each sampling time t Linear regression of Y vs. Q leads to Q Y 65 3 011 0 ˆ r = 0.9960 (10) with a correlation coefficient of r = 0.9960, which is shown in Figur e 2. The intercept in Eq. (10) can be taken as the error term and can be made arbitrarily close to zero by proper choice of ti. Regression analysis of data in Ta ble 1 leads to th e phase equations Y Y N r Y N Yu u 39 8 357 ˆ 985 0 0280 0 0235 0 (11) Y Y P r Y P Yu u 0 13 0 47 ˆ 842 0 0213 0 277 0 (12) Y Y K r Y K Yu u 79 8 571 ˆ 987 0 00175 0 0154 0 (13) Y Y a C r Y Ca Yu u 6 11 200 ˆ 974 0 00499 0 0578 0 (14) Y Y g M r Y Mg Yu u 7 39 331 ˆ 708 0 00302 0 120 0 (15) Y Y l C r Y Cl Yu u 7 29 156 ˆ 990 0 00642 0 191 0 (16)

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Overman and Brock Growth of Tobacco 4 which are shown in Figures 3 thr ough 8, with the lines and curves drawn from Eqs. (11) through (16). Values at t = 48.7, 50.1, and 51.6 wk have been omitted from regression for chloride. While there is some scatter in the plots, the results are consistent with the hyperbolic phase relations. Curves in Figure 1 are drawn from Eqs. (10) and (11) for biomass and plant N uptake, respectively. Plant N concentration, Nc, is calculated from Y Y N Nu c 39 8 357 ˆ ˆ ˆ (17) Accumulation curves for phosphorus and potassium are shown in Figure 9, where the curves are drawn from Eqs. (12) and (13). Correspondin g results for calcium and magnesium are shown in Figure 10, where the curves are drawn from Eqs. (14) and (15). Discussion The expanded growth model has been used to simulate accumulation of biomass with calendar time for shade wrapper tobacco (Figure 1). Linear relationship between biomass and the growth quantifier has been c onfirmed (Figure 2). A hyperbolic relationship between plant nutrient uptake and biomass has also been confirmed for nitrogen, phosphorus, potassium, calcium, magnesium, and chloride (Figures 3 th rough 8). Similarity of the yield coefficient Ky for nitrogen and potassium should be noted, as well as between phosphorus and calcium. The hyperbolic phase relations imply that the rate limiting process is biomass accumulation from photosynthesis, with plant nutrient accumulati on in virtual equilibrium with biomass. Plant nitrogen concentration declines with time for the whole plant due to the increase in structural component (low N) re lative to the light-gathering com ponent (high N) in plant biomass (Overman and Brock, 2003). Plant N concentration, Nci = 357/8.39 = 42.6 g kg-1, represents concentration at the time of initiation of significant growth, t = ti = 48.2 wk. At the time of the last sampling plant N concen tration has dropped to 20 g kg-1 (Figure 1). It may be noted that of the six mineral elements included in this analysis, all are classified as macronutrients with the exception of chorine, wh ich is considered a micronutrient (Marschner, 1986).

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Overman and Brock Growth of Tobacco 5 References Abramowitz, M. and I.A. 1965. Handbook of Mathematical Functions Dover Publications. New York. Marschner, H. 1986. Mineral Nutrition of Higher Plants. Dover Publications. New York. Overman, A.R. 1998. An expanded growth model for grasses. Communications in Soil Science and Plant Analysis 29:67-85. Overman, A.R. 1999. Model for accumulation of dry matter and plant nutrients by tobacco. Journal of Plant Nutrition 22:81-92. Overman, A.R. and K.H. Brock. 2003. Confirma tion of the expanded growth model for a warmseason perennial grass. Communications in Soil Science and Plant Analysis 34:1105-1117. Overman, A.R. and R.V. Scholtz III. 2002. Mathematical Models of Crop Growth and Yield Taylor & Francis. New York. Overman, A.R. and K.R. Woodard. 2006. Simulati on of biomass partiti oning and production in elephantgrass. Communications in Soil Sc ience and Plant Analysis 37:1999-2010. Srivastava, R.P., D.S. Rao, and N.C. Gopalach ari. 1984. Nutrient and dry matter accumulation of Dixie shade wrapper tobacco at different stages of growth. Tobacco Science 28:99-101.

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Overman and Brock Growth of Tobacco 6 Table 1. Accumulation of biomass yield ( Y ) and plant nitrogen ( Nu), phosphorus ( Pu), potassium ( Ku), calcium ( Cau), magnesium ( Mgu), and chloride ( Clu) with calendar time ( t ) by shade wrapper tobacco at Dinhata, West Bengal, India.a t Y Nu Pu Ku Cau Mgu Clu wk Mg ha-1 kg ha-1 kg ha-1 kg ha-1 kg ha-1 kg ha-1 kg ha-1 43.0 --------------------------------45.9 0.032 1.5 0.1 2.2 0.6 0.4 0.2 47.3 0.135 5.6 0.5 8.7 2.5 1.3 0.7 48.7 0.469 16.5 1.9 29.7 8.1 3.7 1.9 50.1 1.14 42.7 4.5 68.0 17.7 8.9 4.6 51.6 1.74 60.6 5.5 92.2 24.9 12.4 7.0 53.0 2.46 87.4 7.0 123 35.5 20.1 12.0 54.4 3.81 114 8.9 163 48.0 28.2 17.9 55.9 5.29 133 11.3 199 60.3 39.9 23.1 57.3 6.83 160 16.4 261 70.7 50.2 29.7 58.7 8.36 180 19.9 285 90.8 52.6 33.9 60.1 9.15 185 21.1 294 88.6 66.1 36.7 aData adapted from Srivastava et al. (1984). Table 2. Correlation of biomass accumulation ( Y ) and the growth quantifier ( Q ) with calendar time ( t ) by shade wrapper tobacco at Dinhata, West Bengal, India.a t x erf x 2exp x Q Y wk Mg ha-1 48.2 0.000 0.000 1.0000 0.000 ----48.7 0.040 0.045 0.9984 0.050 0.469 50.1 0.152 0.170 0.977 0.235 1.14 51.6 0.272 0.299 0.929 0.499 1.74 53.0 0.384 0.413 0.863 0.799 2.46 54.4 0.496 0.517 0.782 1.13 3.81 55.9 0.616 0.616 0.684 1.51 5.29 57.3 0.728 0.697 0.589 1.86 6.83 58.7 0.840 0.765 0.494 2.19 8.36 60.1 0.952 0.822 0.404 2.50 9.15 aYield data adapted from Sr ivastava et al. (1984).

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Overman and Brock Growth of Tobacco 7 Table 3. Simulation of biomass yield ( Y ), plant nitrogen uptake ( Nu), and plant nitrogen concentration ( Nc) with calendar time ( t ) by shade wrapper tobacco at Dinhata, West Bengal, India. t x erf x 2exp x Q Y ˆ uN ˆ cN ˆ wk Mg ha-1 kg ha-1 g kg-1 48.2 0.000 0.000 1.0000 0.000 0.000 0.0 42.6 49 0.079 0.089 0.9937 0.107 0.380 15.5 40.7 50 0.159 0.178 0.975 0.249 0.899 34.6 38.4 51 0.238 0.264 0.945 0.419 1.52 54.8 36.0 52 0.317 0.346 0.904 0.617 2.24 75.2 33.6 53 0.397 0.425 0.854 0.837 3.05 95.2 31.2 54 0.476 0.500 0.797 1.07 3.90 113 29.0 55 0.556 0.569 0.734 1.32 4.81 130 27.0 56 0.635 0.631 0.668 1.57 5.72 145 25.3 57 0.714 0.687 0.600 1.82 6.64 158 23.8 58 0.794 0.739 0.533 2.06 7.51 169 22.5 59 0.873 0.783 0.467 2.29 8.35 178 21.3 60 0.952 0.822 0.404 2.50 9.12 186 20.4 61 1.032 0.855 0.345 2.70 9.85 193 19.6 62 1.111 0.884 0.291 2.88 10.5 198 18.9 63 1.190 0.908 0.242 3.05 11.1 203 18.4 64 1.270 0.928 0.199 3.19 11.6 207 17.9 65 1.349 0.944 0.162 3.31 12.1 211 17.4

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Overman and Brock Growth of Tobacco 8 Table 4. Simulation of biomass yield ( Y ), plant uptake of nitrogen ( Nu), phosphorus ( Pu), potassium ( Ku), calcium ( Cau), magnesium ( Mgu), and chlorine ( Clu) with calendar time ( t ) by shade wrapper tobacco at Dinhata, West Bengal, India. t Y ˆ uP ˆ uK ˆ ua C ˆ ug M ˆ ul C ˆ wk Mg ha-1 kg ha-1 kg ha-1 kg ha-1 kg ha-1 kg ha-1 48.2 0.000 0.00 0.0 0.00 0.00 0.00 49 0.380 1.33 23.7 6.34 3.14 1.97 50 0.899 3.04 53.0 14.4 7.33 4.58 51 1.52 4.92 84.2 23.2 12.2 7.60 52 2.24 6.91 116 32.4 17.7 10.9 53 3.05 8.93 147 41.6 23.6 14.5 54 3.90 10.8 175 50.3 29.6 18.1 55 4.81 12.7 202 58.6 35.8 21.7 56 5.72 14.4 225 66.1 41.7 25.2 57 6.64 15.9 246 72.8 47.4 28.5 58 7.51 17.2 263 78.6 52.7 31.5 59 8.35 18.4 278 83.7 57.5 34.2 60 9.12 19.4 291 88.0 61.8 36.6 61 9.85 20.3 302 91.8 65.8 38.9 62 10.5 21.0 311 95.0 69.2 40.7 63 11.1 21.6 319 97.8 72.3 42.4 64 11.6 22.2 325 100 74.8 43.8 65 12.1 22.7 331 102 77.3 45.2

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Overman and Brock Growth of Tobacco 9 List of Figures Figure 1. Accumulation of biomass ( Y ), plant nitrogen uptake ( Nu), and plant nitrogen concentration ( Nc) with calendar time ( t ) for shade wrapper tobacco at Dinhata, West Bengal, India. Data adapted from Srivastava et al. (198 4). Curves drawn from Eqs. (10), (11), and (17). Figure 2. Correlation of biomass ( Y ) with the growth quantifier ( Q ) for shade wrapper tobacco at Dinhata, West Bengal, India. Data adapted from Srivastava et al. (1984) Line drawn from Eq. (10). Figure 3. Phase relation betw een plant nitrogen uptake ( Nu) and biomass yield ( Y ) for shade wrapper tobacco at Dinhata, West Bengal, India. Data adapted from Srivastava et al. (1984). Line and curve drawn from Eq. (11). Figure 4. Phase relation betw een plant phosphorus uptake ( Pu) and biomass yield ( Y ) for shade wrapper tobacco at Dinhata, West Bengal, India. Data adapted from Srivastava et al. (1984). Line and curve drawn from Eq. (12). Figure 5. Phase relation betw een plant potassium uptake ( Ku) and biomass yield ( Y ) for shade wrapper tobacco at Dinhata, West Bengal, India. Data adapted from Srivastava et al. (1984). Line and curve drawn from Eq. (13). Figure 6. Phase relation betw een plant calcium uptake ( Cau) and biomass yield ( Y ) for shade wrapper tobacco at Dinhata, West Bengal, India. Data adapted from Srivastava et al. (1984). Line and curve drawn from Eq. (14). Figure 7. Phase relation betw een plant magnesium uptake ( Mgu) and biomass yield ( Y ) for shade wrapper tobacco at Dinhata, West Bengal, India. Data adapted from Srivastava et al. (1984). Line and curve drawn from Eq. (15). Figure 8. Phase relation between plant chloride uptake ( Clu) and biomass yield ( Y ) for shade wrapper tobacco at Dinhata, West Bengal, India. Data adapted from Srivastava et al. (1984). Line and curve drawn from Eq. (16). Figure 9. Accumulation of plant phosphorus ( Pu) and potassium ( Ku) with calendar time ( t ) for shade wrapper tobacco at Dinhata, West Bengal, India. Data adapted from Srivastava et al. (1984). Curves drawn from Eqs. (12) and (13). Figure 10. Accumulation of plant calcium ( Cau) and magnesium ( Mgu) with calendar time ( t ) for shade wrapper tobacco at Dinhata, West Bengal, India. Data adapted from Srivastava et al. (1984). Curves drawn from Eqs. (14) and (15).

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Overman and Brock Growth of Tobacco 10 Figure 1. Accumulation of biomass ( Y ), plant nitrogen uptake ( Nu), and plant nitrogen concentration ( Nc) with calendar time ( t ) for shade wrapper tobacco at Dinhata, West Bengal, India. Data adapted from Srivastava et al. (198 4). Curves drawn from Eqs. (10), (11), and (17).

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Overman and Brock Growth of Tobacco 11 Figure 2. Correlation of biomass ( Y ) with the growth quantifier ( Q ) for shade wrapper tobacco at Dinhata, West Bengal, India. Data adapted from Srivastava et al. (1984) Line drawn from Eq. (10).

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Overman and Brock Growth of Tobacco 12 Figure 3. Phase relation betw een plant nitrogen uptake ( Nu) and biomass yield ( Y ) for shade wrapper tobacco at Dinhata, West Bengal, India. Data adapted from Srivastava et al. (1984). Line and curve drawn from Eq. (11).

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Overman and Brock Growth of Tobacco 13 Figure 4. Phase relation betw een plant phosphorus uptake ( Pu) and biomass yield ( Y ) for shade wrapper tobacco at Dinhata, West Bengal, India. Data adapted from Srivastava et al. (1984). Line and curve drawn from Eq. (12).

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Overman and Brock Growth of Tobacco 14 Figure 5. Phase relation betw een plant potassium uptake ( Ku) and biomass yield ( Y ) for shade wrapper tobacco at Dinhata, West Bengal, India. Data adapted from Srivastava et al. (1984). Line and curve drawn from Eq. (13).

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Overman and Brock Growth of Tobacco 15 Figure 6. Phase relation betw een plant calcium uptake ( Cau) and biomass yield ( Y ) for shade wrapper tobacco at Dinhata, West Bengal, India. Data adapted from Srivastava et al. (1984). Line and curve drawn from Eq. (14).

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Overman and Brock Growth of Tobacco 16 Figure 7. Phase relation betw een plant magnesium uptake ( Mgu) and biomass yield ( Y ) for shade wrapper tobacco at Dinhata, West Bengal, India. Data adapted from Srivastava et al. (1984). Line and curve drawn from Eq. (15).

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Overman and Brock Growth of Tobacco 17 Figure 8. Phase relation between plant chloride uptake ( Clu) and biomass yield ( Y ) for shade wrapper tobacco at Dinhata, West Bengal, India. Data adapted from Srivastava et al. (1984). Line and curve drawn from Eq. (16).

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Overman and Brock Growth of Tobacco 18 Figure 9. Accumulation of plant phosphorus ( Pu) and potassium ( Ku) with calendar time ( t ) for shade wrapper tobacco at Dinhata, West Bengal, India. Data adapted from Srivastava et al. (1984). Curves drawn from Eqs. (12) and (13).

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Overman and Brock Growth of Tobacco 19 Figure 10. Accumulation of plant calcium ( Cau) and magnesium ( Mgu) with calendar time ( t ) for shade wrapper tobacco at Dinhata, West Bengal, India. Data adapted from Srivastava et al. (1984). Curves drawn from Eqs. (14) and (15).

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Overman and Brock Growth of Tobacco 20 Coupling of Biomass and Plant Nutrient A ccumulation by a Broad Leaf Annual Crop II. Leaf Fracction Allen R. Overman Agricultural and Biological Engineering Department University of Florida, Gainesville, Florida, USA Kelly H. Brock City of Casselberry, Florida, USA Abstract: In part I of this sequen ce it was demonstrated that the expanded growth model described accumulation of biomass yield and plant nutrient uptake with time for the broad leaf crop tobacco ( Nicotiana tabacum L.) for above ground biomass. A linear relationship between biomass ( Y ) and the growth quantifier ( Q ) was confirmed. Hyperbol ic phase relationships between plant nutrients (N, P, K, Ca, Mg, and Cl ) and biomass were also demonstrated. In this document the model is applied to tobacco data for accumulation of biomass and plant nutrients (N, P, K, Ca, and Mg) in the leaf fracti on of the plant. Linear correlation between Y and Q for leaf data is established The yield factor ( A ) exhibits strong dependen ce on water availability. However, the phase relations now become linear, i ndicating that concentrati ons of plant nutrients remain essentially constant as the leaf develops When leaves and stalks are combined, the phase relation becomes hyperbolic due to an increase in the proportion of biomass in the structural component (lower nutrients) vs. the light-gatheri ng component (higher nutrients) as the plant ages. This work continues the effort to generali ze the growth model to de scribe various species of plants and to connect components of plants. Keywords: Growth model, nitrogen, phosphorus, pot assium, calcium, magnesium, tobacco. Introduction In part I of this sequence the expanded growth model is applied to da ta for the broad leaf plant tobacco. The model is used to describe accumulation of biomass and plant nutrients with time for above ground plant (leaf + stalk). In the pr esent document the model is used to describe biomass and plant nutrient accumulation with cal endar time for tobacco leaves. The growth model remains the same as for whole plant. Howe ver, the phase relation is modified to conform to data Y N Nc u (1) in which Y is accumulated biomass in leaves, Nu is accumulated plant nutrient (N, P, K, Ca, or Mg) in leaves, and Nc is plant nutrient concentration in the leaves. In this analysis Nc is shown to remain constant for each element during growth. Data Analysis Data for this analysis are taken from a field study by Bruns and McIntosh (1988) with Maryland tobacco at Upper Marlboro, MD in 1983 and 1984. Plants were transplanted on 31

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Overman and Brock Growth of Tobacco 21 May 1983 ( t = 24.5 wk) and 6 June 1984 ( t = 25.5 wk). Leaf samples were collected on a weekly interval for 10 weeks. Plots were replicated three times on Monmouth fine sandy loam (fine, mixed, active, mesic Typic Hapludult). Ni trogen was applied at a rate of 100 kg ha-1 as ammonium nitrate. Irrigation of 2.5 cm was applied in 1983 to relieve severe drought stress. Results are averages for two cultivars (‘MD 609’ and ‘MD 341’) and are reported as mass per plant. Results for accumulation of leaf biomass and nutrients are listed in Table 1 (1983) and Table 2 (1984). The first step is to estimate the gr owth quantifier with cal endar time for each year. Model parameters are chosen as: 5 wk 10 0 wk, 00 8 2 wk, 0 261 k c From the plot of leaf biomass ( Y ) vs. calendar time ( t ) in Figure 1 for 1983, time of initiation of significant growth is chosen as ti = 25.2 wk. The plot of data for 1984 in Figure 2 leads to ti = 25.4 wk. Dimensionless time ( x ) and growth quantifier ( Q ) are calculated from 1983: 300 0 00 8 8 22 400 0 00 8 26 ix t t x (2) 271 1 914 0 exp 821 2 329 0 erf 500 02 x x Q (3) 1984: 325 0 00 8 8 22 400 0 00 8 26 ix t t x (4) 297 1 900 0 exp 821 2 354 0 erf 625 02 x x Q (5) Values for Q along with leaf biomass ( Y ) are listed in Table 3 (1983) and Table 4 (1984). Linear regression of Y vs. Q leads to the estimation equations 1983: 9812 0 6 62 82 0 ˆ r Q Y (6) 1984: 9897 0 0 78 63 0 ˆ r Q Y (7) with correlation coefficients of r > 0.98. Lines in Figure 3 are drawn from Eqs. (6) and (7). The second step is to relate nutrient accumu lation to biomass accumulation for each element and each year. Results are shown in Figures 4 an d 5 for 1983, which suggest linear correlations. This leads to the regression equations between plant nutrients and biomass of 1983: 2 37 9923 0 0372 0 048 0 ˆ c uN r Y N g kg-1 (8) 89 2 9972 0 00289 0 0077 0 ˆ c uP r Y P g kg-1 (9) 2 41 9885 0 0412 0 026 0 ˆ c uK r Y K g kg-1 (10) 1 26 9909 0 0261 0 090 0 ˆ c uCa r Y a C g kg-1 (11)

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Overman and Brock Growth of Tobacco 22 15 8 9963 0 00815 0 012 0 ˆc uMg r Y g M g kg-1 (12) Average nutrient concentrations are also listed. The corresp onding regression equations for 1984 are given by 1984: 8 34 9975 0 0348 0 0011 0 ˆ c uN r Y N g kg-1 (13) 49 2 9804 0 00249 0 0057 0 ˆ c uP r Y P g kg-1 (14) 2 35 9770 0 0352 0 137 0 ˆ c uK r Y K g kg-1 (15) 7 16 9957 0 0167 0 030 0 ˆ c uCa r Y a C g kg-1 (16) 86 5 9250 0 00586 0 045 0 ˆc uMg r Y g M g kg-1 (17) The final step is to relate the yield factor ( A ) to water availability ( W ), in which W is the sum of rainfall + irrigation during the growing season. Results are show n in Figure 6, with the curve drawn from 10 15 exp 1 95 ˆ W A (18) The yield factor for 1983 and 1984 reached 66% and 82%, respectively, of estimated maximum of 95 g plant-1. This illustrates dependence of plant yi eld on water availability, as pointed out by Bruns and McIntosh (1988). Figure 6 is intended for illustration only, since there are only two data points. Equation (18) is si milar to the one proposed by Overma n and Scholtz (2002) for corn response to water. This completes analysis of the data. Discussion The expanded growth model describes the growth curves of Maryland tobacco leaves reasonably well (Figures 1 and 2). Biomass accumulation appeas to follow linear dependence on the growth quantifier, as assumed in the grow th model (Figure 3). Ph ase plots between plant nutrient and biomass accumulation follow straight lin es (Figures 4 and 5), indicating that plant nutrient concentrations remain essentially constant during leaf development. Th is is in contrast to the hyperbolic phase relations for leaf + stalks discussed in part I. Overman and Scholtz (2004) observed similar results for coastal bermudagra ss grown at Tifton, GA, USA by Burton et al. (1963). It appears reasonable to assume expone ntial dependence of the yield factor ( A ) in the growth model on water availability (rainfall + irrigation). This is consistent with results obtained by Overman and Scholtz (2002) for corn grown at Bushland, TX, USA by Tolk et al. (1998).

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Overman and Brock Growth of Tobacco 23 References Bruns, H.A. and M.S. McIntosh. 1988. Growth ra tes and nutrient concen trations in Maryland tobacco. Tobacco Science 32:82-87. Burton, G.W., J.E. Jackson and R.H. Hart. 1963. Effects of cutting frequency and nitrogen on yield, in vitro digestibility, and protein, fiber, and carotene content of coastal bermudagrass. Agronomy J. 55:500-502. Overman, A.R. and R.V. Scholtz III. 2002. Corn response to irrigation and applied nitrogen. Communications in Soil Sc ience and Plant Analysis. 33:3609-3619. Overman, A.R. and R.V. Scholtz III. 2004. Model of dry matter a nd plant nitrogen partitioning between leaf and stem for coastal bermudagrass. J. Plant Nutrition 27:1585-1592. Tolk, J.A., T.A. Howell, and S.R. Evett. 1998. Evapotranspiration and yield of corn grown on three high plains soils. Agronomy J. 90:447-454.

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Overman and Brock Growth of Tobacco 24 Table 1. Accumulation of biomass ( Y ) and plant nitrogen ( Nu), phosphorus ( Pu), potassium ( Ku), calcium ( Cau), and magnesium ( Mgu) with calendar time ( t ) by Maryland tobacco leaves (1983).a t Y Nu Pu Ku Cau Mgu wk g plant-1 g plant-1 g plant-1 g plant-1 g plant-1 g plant-1 21.7 1.24 0.0317 0.0042 0.0457 0.0087 0.0063 22.7 1.26 0.0292 0.0045 0.0352 0.0060 0.0049 23.7 1.60 0.0513 0.0046 0.0562 0.0224 0.0106 24.7 3.91 0.136 0.0097 0.156 0.0717 0.0285 25.7 8.34 0.281 0.0194 0.327 0.174 0.0679 26.7 23.1 0.707 0.0503 0.866 0.393 0.169 27.7 46.3 1.53 0.106 1.92 0.946 0.400 28.7 54.6 1.80 0.148 2.00 1.13 0.357 29.7 75.2 3.06 0.212 2.84 2.13 0.590 30.7 91.2 3.63 0.268 4.41 2.46 0.744 31.7 132 4.63 0.372 5.16 3.26 1.08 aData adapted from Bruns and McIntosh (1988). Table 2. Accumulation of biomass ( Y ) and plant nitrogen ( Nu), phosphorus ( Pu), potassium ( Ku), calcium ( Cau), and magnesium ( Mgu) with calendar time ( t ) by Maryland tobacco leaves (1984).a t Y Nu Pu Ku Cau Mgu wk g plant-1 g plant-1 g plant-1 g plant-1 g plant-1 g plant-1 22.6 0.52 0.0191 0.0026 0.0201 0.0024 0.0029 23.6 0.92 0.0287 0.0028 0.0287 0.0060 0.0049 24.6 1.73 0.0534 0.0049 0.0752 0.0222 0.0097 25.6 5.07 0.155 0.0117 0.197 0.0942 0.0290 26.6 17.9 0.599 0.0391 0.728 0.323 0.151 27.6 31.7 1.16 0.117 1.28 0.596 0.259 28.6 68.6 2.53 0.184 2.95 1.33 0.635 29.6 93.2 2.99 0.252 4.42 1.60 0.772 30.6 122 4.35 0.274 4.03 2.16 0.635 31.6 149 4.37 0.329 4.89 2.35 0.636 32.6 143 4.37 0.424 6.74 3.23 1.07 aData adapted from Bruns and McIntosh (1988).

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Overman and Brock Growth of Tobacco 25 Table 3. Correlation of biomass ( Y ) with the growth quantifier ( Q ) over calendar time ( t ) for Maryland tobacco leaves (1983).a t x erf x 2exp x Q Y wk g plant-1 25.2 0.300 0.329 0.914 0.000 ------25.7 0.362 0.391 0.877 0.093 8.34 26.7 0.488 0.510 0.788 0.337 23.1 27.7 0.612 0.613 0.687 0.633 46.3 28.7 0.738 0.704 0.580 0.959 54.6 29.7 0.862 0.777 0.475 1.29 75.2 30.7 0.988 0.838 0.377 1.60 91.2 31.7 1.112 0.884 0.290 1.88 132 aYield data adapted from Bruns and McIntosh (1988). Table 4. Correlation of biomass ( Y ) with the growth quantifier ( Q ) over calendar time ( t ) for Maryland tobacco leaves (1984).a t x erf x 2exp x Q Y wk g plant-1 25.4 0.325 0.354 0.900 0.000 25.6 0.350 0.379 0.885 0.035 5.07 26.6 0.475 0.499 0.798 0.256 17.9 27.6 0.600 0.604 0.698 0.536 31.7 28.6 0.725 0.695 0.591 0.854 68.6 29.6 0.850 0.771 0.486 1.18 93.2 30.6 0.975 0.832 0.386 1.49 122 31.6 1.100 0.880 0.298 1.78 149 32.6 1.225 0.917 0.223 2.02 143 aYield data adapted from Bruns and McIntosh (1988).

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Overman and Brock Growth of Tobacco 26 List of Figures Figure 1. Accumulation of biomass ( Y ), plant nitrogen uptake ( Nu), and plant nitrogen concentration ( Nc) with calendar time ( t ) for tobacco leaves at Upper Marlboro, MD, USA (1983). Data adapted from Bruns and McIntosh (1988). Curves drawn from Eqs. (6) and (8). Figure 2. Accumulation of biomass ( Y ), plant nitrogen uptake ( Nu), and plant nitrogen concentration ( Nc) with calendar time ( t ) for tobacco leaves at Upper Marlboro, MD, USA (1984). Data adapted from Bruns and McIntosh (1988). Curves drawn from Eqs. (7) and (13). Figure 3. Correlation of biomass ( Y ) with the growth quantifier ( Q ) for tobacco leaves at Upper Marlboro, MD, USA (1983 and1984). Yield data adapted from Bruns and McIntosh (1988). Lines drawn from Eqs. (6) and (7). Figure 4. Correlation of plant nitrogen ( Nu), plant phosphorus ( Pu), and plant potassium ( Ku) with biomass ( Y ) accumulation for tobacco leaves at Uppe r Marlboro, MD, USA (1983). Data adapted from Bruns and McIntosh (1988). Line s drawn from Eqs. (8) through (10). Figure 5. Correlation of plant calcium ( Cau), and plant magnesium ( Mgu) with biomass ( Y ) accumulation for tobacco leaves at Upper Marlboro, MD, USA ( 1983). Data adapted from Bruns and McIntosh (1988). Lines draw n from Eqs. (11) and (12). Figure 6. Dependence of yield factor ( A ) on water availability ( W ) for tobacco leaves at Upper Marlboro, MD, USA. Curv e drawn from Eq. (18).

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Overman and Brock Growth of Tobacco 27 Figure 1. Accumulation of biomass ( Y ), plant nitrogen uptake ( Nu), and plant nitrogen concentration ( Nc) with calendar time ( t ) for tobacco leaves at Upper Marlboro, MD, USA (1983). Data adapted from Bruns and McIntosh (1988). Curves drawn from Eqs. (6) and (8).

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Overman and Brock Growth of Tobacco 28 Figure 2. Accumulation of biomass ( Y ), plant nitrogen uptake ( Nu), and plant nitrogen concentration ( Nc) with calendar time ( t ) for tobacco leaves at Upper Marlboro, MD, USA (1984). Data adapted from Bruns and McIntosh (1988). Curves drawn from Eqs. (7) and (13).

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Overman and Brock Growth of Tobacco 29 Figure 3. Correlation of biomass ( Y ) with the growth quantifier ( Q ) for tobacco leaves at Upper Marlboro, MD, USA (1983 and1984). Yield data adapted from Bruns and McIntosh (1988). Lines drawn from Eqs. (6) and (7).

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Overman and Brock Growth of Tobacco 30 Figure 4. Correlation of plant nitrogen ( Nu), plant phosphorus ( Pu), and plant potassium ( Ku) with biomass ( Y ) accumulation for tobacco leaves at Uppe r Marlboro, MD, USA (1983). Data adapted from Bruns and McIntosh (1988). Line s drawn from Eqs. (8) through (10).

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Overman and Brock Growth of Tobacco 31 Figure 5. Correlation of plant calcium ( Cau), and plant magnesium ( Mgu) with biomass ( Y ) accumulation for tobacco leaves at Upper Marlboro, MD, USA ( 1983). Data adapted from Bruns and McIntosh (1988). Lines drawn from Eqs. (11) and (12).

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Overman and Brock Growth of Tobacco 32 Figure 6. Dependence of yield factor ( A ) on water availability ( W ) for tobacco leaves at Upper Marlboro, MD, USA. Curv e drawn from Eq. (18).

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Overman and Brock Growth of Tobacco 33 Coupling of Biomass and Plant Nutrient Accu mulation by a Broad Leaf Annual Crop III. Coupling of Tops and Roots Allen R. Overman Agricultural and Biological Engineering Department University of Florida, Gainesville, Florida, USA Kelly H. Brock City of Casselberry, Florida, USA Abstract: In part I of this sequen ce the linear relationship betw een biomass and the growth quantifier of the expanded growth model was confirmed for tobacco ( Nicotiana tabacum L.). The hyperbolic phase relationship between plan t nutrient and biomass accumulation was also confirmed. In part II an indepe ndent set of data was used to c onfirm the growth model for leaf development, and a linear relationship establis hed between nutrient and biomass accumulation. In this document a third set of data is used to further confirm findings in part I and II, and to demonstrate a linear relationship between root and top development with calendar time. Conclusions from this study are consistent w ith earlier modeling of growth of corn ( Zea mays L.) and bermudagrass ( Cynodon dactylon L.). The basic structure of th e growth model and the phase relations appear to be well established. Detailed procedures for parameter estimation from field data are included in this sequence. Keywords: Growth model, nitrogen, phosphorus, pot assium, calcium, magnesium, chloride, tobacco. Introduction In part I of this sequence the expanded growth model was applied to data for the broad leaf plant tobacco. The model is used to describe accumulation of biomass and plant nutrients with calendar time for above ground plant (leaf + stalk). In part II fi ndings in part I were further confirmed and a linear phase relationship betw een plant nutrient and biomass accumulation in the leaf fraction was established. In part III additional data are analy zed to further confirm findings in parts I and II, and to show a lin ear relationship between root and top biomass accumulation. The equations are the same as in parts I and II and are not repeated here. Data Analysis Data for this analysis are adapted from a field study by Bertinuson et al. (1970) with Connecticut shadegrown wrapper tobacco at Hartford, CT, USA during 1966 through 1968. Plants were transpla nted around June 1 ( t = 21.9 wk). Samples were collected on a weekly interval between 4 and 12 weeks after transplanting. Plots were replicated four times on unspecified soil. Nitrogen, phosphor us, and potassium were applied at rates of 208, 112, and 175 kg ha-1, respectively. Water was by rainfall only. Yield data are listed in Table 1 for tops ( Yt) and roots ( Yr) with calendar time ( t ) for the three years of the experiment. For this analysis tops include leaves and stalks. Correlation of root yield with top yield is shown in Figure 1 for the aver age of the three years. The line is drawn from

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Overman and Brock Growth of Tobacco 34 9985 0 142 0 005 0 ˆ r Y Yt r (1) The high correlation coefficient ( r = 0.9985) indicates that ro ot growth follows a linear relationship with top growth. Therefore, focus is on modelin g top growth by photosynthesis. Accumulation of top biomass with calendar time is shown in Figure 2. Model parameters are chosen as in part II of this sequence: 5 wk 10 0 wk, 00 8 2 wk, 0 261 k c Time of initiation of significant growth is chosen from Figure 2 as ti = 27.1 wk. Dimensionless time ( x ) and growth quantifier ( Q ) become 538 0 00 8 8 22 400 0 00 8 26 2 2 2 ix t t c t x (2) 537 1 749 0 exp 821 2 554 0 erf 688 1 2 exp exp exp erf erf 12 2 2 x x cx x x k x x kx Qi i i i (3) Values of Q are listed in Table 2 alon g with top yields. According to the expanded growth model there should be a linear correlation between Yt and Q Results are shown in Figure 3, where the line is drawn from 9969 0 92 3 019 0 ˆ r Q Yt (4) which confirms the linear relationship. The grow th curve in Figure 2 is drawn from Eqs. (2) through (4). The next step is to relate plant nutrient a nd biomass accumulation for tops. Data are listed in Table 3 for top biomass ( Yt) and plant uptake of nitrogen ( Nut), phosphorus ( Put), potassium ( Kut), calcium ( Caut), and magnesium ( Mgut). Phase relations between plant nutrient uptake and biomass is expected to follo w the hyperbolic relationship t yt t umt utY K Y N N (5) in which Numt is potential maximum plant nutrient uptake for tops, kg ha-1 and Kyt is yield response coefficient for tops, Mg ha-1. Equation (5) can be rearra nged to the linear form t umt umt yt ut tY N N K N Y 1 (6) Results are shown in Figures 4 through 8. Analys is of the data in Table 3 leads to the phase relations

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Overman and Brock Growth of Tobacco 35 t t ut t ut tY Y N r Y N Y 86 9 393 ˆ 9971 0 00255 0 0251 0 (7) t t ut t ut tY Y P r Y P Y 72 6 8 16 ˆ 9566 0 0595 0 400 0 (8) t t ut t ut tY Y K r Y K Y 68 9 598 ˆ 9940 0 00167 0 0162 0 (9) t t ut t ut tY Y a C r Y Ca Y 4 32 481 ˆ 9376 0 00208 0 0673 0 (10) t t ut t ut tY Y g M r Y Mg Y 3 14 1 67 ˆ 9686 0 0149 0 213 0 (11) Lines and curves in Figure 4 th rough 8 are drawn from Eqs. (7) through (11). This confirms the hyperbolic phase relations for all five mineral elements. Data for biomass and plant nutrients contained in the leaves are given in Table 3 and plotted in Figures 9 and 10. Following the results in part II, a linear rela tionship is assumed for the leaf fraction, which leads to the estimation equations 9993 0 7 37 64 1 ˆ r Y Nt uL (12) 9961 0 57 1 340 0 ˆ r Y Pt uL (13) 9945 0 6 40 19 9 ˆ r Y Kt uL (14) 9975 0 4 26 70 5 ˆ r Y a Ct uL (15) 9922 0 39 6 83 0 ˆ r Y g Mt uL (16) Lines in Figures 9 and 10 are drawn from Eq s. (12) through (16). On intuitive grounds the intercepts in Eqs. (12) through (16) are expected to be zero. If this cons traint is imposed, then plant nutrients concentrations in the leaves become NcL = 38.5, PcL = 1.73, KcL = 45.0, CacL = 23.5, and MgcL = 5.97 g kg-1, compared to the slopes in Eqs. (12) through (16). These values are considerably higher than for tops (stalks + leaves ) at maturity which can be estimated from Eqs. (7) through (11). The structural component of plants is known to have lower mineral concentrations than the leaves. Discussion

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Overman and Brock Growth of Tobacco 36 These results show a close corr elation of biomass for roots ( Yr) with biomass for tops ( Yt) for Connecticut data (Figure 1). Growth of top biomass with calendar time ( t ) is described rather closely with the expanded growth model (Figure 2), with high correlation between top biomass and growth quantifier ( Q ). Coupling between plan t nutrient accumulation and biomass for tops is described rather well by th hyperb olic phase relations (Figures 4 through 8). This is in agreement with results for flue-cured tobacco discussed in pa rt I. Equations (7) through (11) can be used to estimate change in plant nutrient between time of initiation ( ti = 27.1 wk) and final sampling ( t = 33.9 wk). Results are listed in Table 4. This d ecline occurs from the increase in structural component (stalks, with lower concentrations ) over light-gathering co mponent (leaves, with higher concentrations) as the plant develops. Similar coupling for leaves is described by linear phase relations (Figures 9 and 10), which is in agreement with results for Maryland tobacco di scussed in part II. All of these results from three independent studies with tobacco confirm the utility of the phase relations in coupling accumulation of plant nutrients with biomass. All of these results suggest that the rate limiting process in plant growth is biomass accumulation by photosynthesis. This conclusion is in agreement previous results Overman and Brock, 2003) based on field expe riments at Tifton, GA, USA (Burton and Hart, 1961) with coastal bermudagrass. A similar conclusion has been reached for biomass and plant nutrient accumulation corn (Overman and Scholtz, 1999) as well as by flue-cured tobacco (Overman, 1999). References

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Overman and Brock Growth of Tobacco 37 Bertinuson, T.A., E. Larsen, B. Tereris, M-G Comfort, and M. Petersen. 1970. Nutrient uptake and dry matter accumulation of Connecticut shadegrown wrapper tobacco for three consecutive years. Tobacco Science 14:155-157. Burton, G.W. and R.H. Hart. 1961. Grass and Turf Investigations Annual Report, Georgia Coastal Plain Experiment Stat ion. Tifton, GA., 1961; 231,236. Overman, A.R. 1999. Model for accumulation of dry matter and plant nutrients by tobacco. J. Plant Nutrition 22:81-92. Overman, A.R. and K.H. Brock. 2003. Confirma tion of the expanded growth model for a warmseason perennial grass. Commun. Soil Science and Plant Analysis 34:1105-1117. Overman, A.R. and R.V. Scholtz III. 1999. M odel for accumulation of dry matter and plant nutrients by corn. Commun. Soil Science and Plant Analysis 30:2059-2081. Table 1. Accumulation of biomass for tops ( Yt) and roots ( Yr) with calendar time ( t ) for Connecticut shadegrown wrapper to bacco grown at Harford, CT, USA.a

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Overman and Brock Growth of Tobacco 38 t Yt Yr wk Mg ha-1 Mg ha-1 1966 1967 1968 avg 1966 1967 1968 avg 21.9 -----------------------------------25.9 0.13 0.09 0.10 0.11 0.016 0.011 0.010 0.012 26.9 0.45 0.31 0.19 0.32 0.057 0.037 0.024 0.039 27.9 0.92 0.55 0.52 0.66 0.115 0.078 0.067 0.087 28.9 2.12 1.49 1.14 1.58 0.244 0.239 0.187 0.223 29.9 2.76 2.25 1.80 2.27 0.432 0.365 0.274 0.357 30.9 4.34 3.55 3.18 3.69 0.612 0.519 0.500 0.544 31.9 5.45 4.80 4.06 4.77 0.775 0.711 0.588 0.691 32.9 5.91 5.62 5.22 5.58 0.808 0.821 0.688 0.772 33.9 6.47 6.03 5.68 6.06 0.828 0.951 0.800 0.860 aData adapted from Ber tinuson et al. (1970). Table 2. Correlation of biomass for tops ( Yt) with the growth quantifier ( Q ) for Connecticut shadegrown wrapper tobacco grown at Hartford, CT, USA.a t x erf x 2exp x Q Yt wk Mg ha-1 27.1 0.538 0.554 0.749 0.000 ----27.9 0.638 0.633 0.666 0.155 0.66 28.9 0.762 0.719 0.559 0.396 1.58 29.9 0.888 0.790 0.455 0.662 2.27 30.9 1.012 0.847 0.359 0.931 3.69 31.9 1.138 0.892 0.274 1.183 4.77 32.9 1.262 0.926 0.203 1.402 5.58 33.9 1.388 0.950 0.146 1.587 6.06 aYield data adapted from Be rtinuson et al. (1970). Table 3. Accumulation of biomass for leaves ( YL) and plant nutrients for leaves ( NuL, PuL, KuL, CauL, MguL) with calendar time ( t ) for Connecticut shadegrown wrapper tobacco grown at Hartford, CT, USA.a t Yt Nut Put Kut Caut Mgut wk Mg ha-1 kg ha-1 kg ha-1 kg ha-1 kg ha-1 kg ha-1 21.9 --------------------27.9 0.468 19 1.1 25 8.8 2.4 28.9 0.948 39 2.0 50 19 5.5 29.9 1.27 50 2.2 62 27 7.2 30.9 1.87 72 3.1 87 41 11 31.9 2.21 83 3.9 104 53 12 32.9 2.46 94 4.1 105 59 15 33.9 2.65 103 4.6 114 66 17 aData adapted from Ber tinuson et al. (1970).

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Overman and Brock Growth of Tobacco 39 Table 4. Decline in plant nutrient concentr ations with time from time of initiation ( ti = 27.1 wk) to final sampling ( t = 33.9 wk) for tops for Connecticut shadegrown wrapper tobacco grown at Hartford, CT, USA. Element N P K Ca Mg Concentration ( ti = 27.1 wk), g kg-1 39.9 2.50 61.8 14.8 4.69 ( t = 33.9 wk), g kg-1 24.7 1.31 38.0 12.5 3.30

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Overman and Brock Growth of Tobacco 40 List of Figures Figure 1. Correlation of biomass accumulation roots ( Yr) and tops ( Yt) for Connecticut shadegrown wrapper tobacco grown at Hartford, CT. Data adapted from Bertinuson et al. (1970). Line drawn from Eq. (1). Figure 2. Accumulation of top biomass ( Yt) with calendar time ( t ) for Connecticut shadegrown wrapper tobacco grown at Hartford, CT. Data adapted from Bertinuson et al. (1970). Curves drawn from Eqs. (2) through (4). Figure 3. Correlation of top biomass ( Yt) with the growth quantifier ( Q ) for Connecticut shadegrown wrapper tobacco grown at Hartford, CT. Data adapted from Bertinuson et al. (1970). Line from Eq. (4). Figure 4. Phase plots between plant N uptake ( Nut) and biomass ( Yt) of tops for Connecticut shadegrown wrapper tobacco grown at Hartford, CT. Data adapted from Bertinuson et al. (1970). Line and curve drawn from Eq. (7). Figure 5. Phase plots between plant P uptake ( Put) and biomass ( Yt) of tops for Connecticut shadegrown wrapper tobacco grown at Hartford, CT. Data adapted from Bertinuson et al. (1970). Line and curve drawn from Eq. (8). Figure 6. Phase plots between plant K uptake ( Kut) and biomass ( Yt) of tops for Connecticut shadegrown wrapper tobacco grown at Hartford, CT. Data adapted from Bertinuson et al. (1970). Line and curve drawn from Eq. (9). Figure 7. Phase plots between plant Ca uptake ( Caut) and biomass ( Yt) of tops for Connecticut shadegrown wrapper tobacco grown at Hartford, CT. Data adapted from Bertinuson et al. (1970). Line and curve drawn from Eq. (10). Figure 8. Phase plots between plant Mg uptake ( Mgut) and biomass ( Yt) of tops for Connecticut shadegrown wrapper tobacco grown at Hartford, CT. Data adapted from Bertinuson et al. (1970). Line and curve drawn from Eq. (11). Figure 9. Phase plots between plant N uptake ( Nut), P uptake ( Put), and K uptake ( Kut) and biomass ( YL) of leaves for Connecticut shadegrown wrapper tobacco grown at Hartford, CT. Data adapted from Bertinuson et al. (1970) Lines drawn from Eqs. (12) and (14). Figure 10. Phase plots between plant Ca uptake ( Caut) and Mg uptake ( Mgut) and biomass ( YL) of leaves for Connecticut shadegrown wrapper tob acco grown at Hartford, CT. Data adapted from Bertinuson et al. (1970) Lines drawn from Eqs. (15) and (16).

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Overman and Brock Growth of Tobacco 41 Figure 1. Correlation of biomass accumulation roots ( Yr) and tops ( Yt) for Connecticut shadegrown wrapper tobacco grown at Hartford, CT. Data adapted from Bertinuson et al. (1970). Line drawn from Eq. (1).

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Overman and Brock Growth of Tobacco 42 Figure 2. Accumulation of top biomass ( Yt) with calendar time ( t ) for Connecticut shadegrown wrapper tobacco grown at Hartford, CT. Data adapted from Bertinuson et al. (1970). Curves drawn from Eqs. (2) through (4).

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Overman and Brock Growth of Tobacco 43 Figure 3. Correlation of top biomass ( Yt) with the growth quantifier ( Q ) for Connecticut shadegrown wrapper tobacco grown at Hartford, CT. Data adapted from Bertinuson et al. (1970). Line from Eq. (4).

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Overman and Brock Growth of Tobacco 44 Figure 4. Phase plots between plant N uptake ( Nut) and biomass ( Yt) of tops for Connecticut shadegrown wrapper tobacco grown at Hartford, CT. Data adapted from Bertinuson et al. (1970). Line and curve drawn from Eq. (7).

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Overman and Brock Growth of Tobacco 45 Figure 5. Phase plots between plant P uptake ( Put) and biomass ( Yt) of tops for Connecticut shadegrown wrapper tobacco grown at Hartford, CT. Data adapted from Bertinuson et al. (1970). Line and curve drawn from Eq. (8).

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Overman and Brock Growth of Tobacco 46 Figure 6. Phase plots between plant K uptake ( Kut) and biomass ( Yt) of tops for Connecticut shadegrown wrapper tobacco grown at Hartford, CT. Data adapted from Bertinuson et al. (1970). Line and curve drawn from Eq. (9).

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Overman and Brock Growth of Tobacco 47 Figure 7. Phase plots between plant Ca uptake ( Caut) and biomass ( Yt) of tops for Connecticut shadegrown wrapper tobacco grown at Hartford, CT. Data adapted from Bertinuson et al. (1970). Line and curve drawn from Eq. (10).

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Overman and Brock Growth of Tobacco 48 Figure 8. Phase plots between plant Mg uptake ( Mgut) and biomass ( Yt) of tops for Connecticut shadegrown wrapper tobacco grown at Hartford, CT. Data adapted from Bertinuson et al. (1970). Line and curve drawn from Eq. (11).

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Overman and Brock Growth of Tobacco 49 Figure 9. Phase plots between plant N uptake ( Nut), P uptake ( Put), and K uptake ( Kut) and biomass ( YL) of leaves for Connecticut shadegrown wrapper tobacco grown at Hartford, CT. Data adapted from Bertinuson et al. (1970) Lines drawn from Eqs. (12) and (14).

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Overman and Brock Growth of Tobacco 50 Figure 10. Phase plots between plant Ca uptake ( Caut) and Mg uptake ( Mgut) and biomass ( YL) of leaves for Connecticut shadegrown wrapper tob acco grown at Hartford, CT. Data adapted from Bertinuson et al. (1970) Lines drawn from Eqs. (15) and (16).