- Email: [email protected]
Dynamic Simulating to the Accumulation and Distribution of Dry Matter for Black Walnut (Juglans hindsii) Seedlings
Agricultural Sciences in China
January 2010
2010, 9(1): 56-63
Dynamic Simulating to the Accumulation and Distribution of Dry Matter for Black Walnut (Juglans hindsii) Seedlings ZHANG Ji-xiang1, MAO Zhi-quan1, SHU Huai-rui1 and WEI Qin-ping2 State Key Laboratory of Crop Biology, College of Horticultural Science and Engineering, Shandong Agricultural University, Tai’an 271018, P.R.China 2 Institute of Forestry & Pomology, Beijing Academy of Agriculture & Forestry Sciences, Beijing 100093, P.R.China 1
Abstract It is very important to study eco-physiological processes of plants and to determine quantitative relations between accumulation, distribution of dry matter and environmental factors for regionalization, standardization and precision agriculture. Meanwhile, global changes, e.g., atmospheric CO2 concentration rising, global warming, and climate abnormity, have been effecting on agricultural productivity. This study provides a theoretical basis for predicting productive potentials and development trends in different agricultural regions. One-year-old black walnut (Juglans hindsii) seedlings were employed as subjects for setting up the dynamic models of dry matter accumulation and distribution, based on mechanistic models of photosynthesis, matter conservation and concentration gradient. Under optimum conditions of soil moisture and mineral nutrient, during the period of the canopy construction, the dry matter accumulation of the canopy conformed to logistic curves; but the accumulation of both total biomass and dry matter of stem-root could be divided into two phases: the first phase was exponential increase, the second was linear increase. The total biomass, dry matter of canopy and stem-root all presented a fluctuant increase, which was affected by the environmental factors. Ratio of daily increase of dry matter in the canopy and the steem-root (dWl/dWs) was changeable along with growth periods and environmental factors. At the initial stage of the canopy forming, dWl/dWs was larger, about 3.2 on average, which indicated that the photosynthetic product was mainly used to develop leaves; in the midterm, it was about 1.9, which indicated that the distribution of dry matter in the canopy and in the stem-root was relatively balanced; when the plant tended to stop growing, dWl/dWs decreased linearly, and the main distribution of dry matter moved to the roots. Key words: black walnut, dry matter, accumulation and distribution, dynamic model
INTRODUCTION During the growth and development of plants, the accumulation and distribution of dry matter among roots, stems, fruit and leaves are decided by their genotypes and environmental factors (Cruz 1986). The latter influence on the accumulation and distribution of the dry matter has qualitatively reported (Calion and Yu 1984;
Chung and Sinba 1981; Thornley 1972). Generally, dry matter is favor of the above-ground, rather than the under-ground in the conditions of weak light, high temperature or ample soil moisture (Fang et al. 2000; Molles 2000); and under disadvantageous surroundings, for example, drought stress or poor nutrition, dry matter accumulation not only decrease, but also its distribution among different organs is biased toward the under-ground (Cai 2002; Zhang et al. 2004a, b, 2006).
Received 21 May, 2009 Accepted 16 September, 2009 ZHANG Ji-xiang, Professor, Ph D, Tel: +86-538-8249953, E-mail: [email protected]; Correspondence WEI Qin-ping, Porfessor, E-mail: [email protected]
© 2010, CAAS. All rights reserved. Published by Elsevier Ltd. doi:10.1016/S1671-2927(09)60067-5
Dynamic Simulating to the Accumulation and Distribution of Dry Matter for Black Walnut (Juglans hindsii) Seedlings
Many studies (de Wit 1978; Liu et al. 2001; Yu et al. 2001) have showed that the accumulation and distribution of dry matter respond to a single environmental factor, for example, Thornley (1972) set up a distribution model of dry matter between the above-ground and the under-ground in the conditions of different nitrogen-nutritional levels. Liu et al. (2001) reconstructed FAO productivity model, which provided theoretical basis for estimating crop productivity accurately under doubled CO2 concentration. But it was rarely reported how the accumulation and distribution of dry matter quantitatively respond to more than two environmental factors. The reasons are: 1) the accumulation and distribution of dry matter cover many complicated processes, such as, photosynthesis, respiration, transportation and transformation of assimilates, and so on. The quantitative or simulative studies on these processes have to involve many functions to describe them. At present, it was difficult to set up these functions because the physiological mechanism of the processes was not completely clear; 2) environmental factors not only synchronously influence the accumulation and distribution of dry matter, but also act one another. So it was too difficult to design and actualize the experiments on the physiological processes of the accumulation and distribution of dry matter to respond to environmental factors. Based on the past works, a dynamic model of the accumulation and distribution of the dry matter of 1-year-old American walnut (J. hindsii) seedlings responding to environmental factors was presented. Some experiential functions or hypotheses were applied in setting up the model, but the simulated results by these function as a whole accorded with the field tested data.
57
managed with conventional methods. The field was fertilized with 8 000 kg ha-1 organic manure and 900 km ha-1 bi-ammonium phosphate respectively in March and June, 2005. The soil relative moisture was always controlled over 60%.
Methods To measure both fresh and dry weight of the plants The 5 standing plants were stochastically selected to be wholly dug up every 5 days during the whole test period, and their leaf area, leaf area index, leaf area radio, the fresh and dry weights of the leaves, stems and roots were respectively measured (Zhang et al. 2004b, 2006). To measure the meteorological data The solar radiant flux densities of diffusive, direct and global radiation were respectively measured during the plant growing period, using the automatic aerograph at the Yucheng Comprehensive Experimental Station. To set up and validate models By summarizing the previous and relevant studies, and based on the diffusive laws, conservation laws of matter and the relationship between source and sink, the dynamic model frameworks to simulate accumulation and distribution of black walnut seedlings were set up. Then the computer programs to run the models were compiled, applying Fortran 90 under the background of Fortran PowerStation 4.0. The all models were parameterized, applying a math Software, Origin 6.0 (Hao and Shi 2000). Finally, the models were validated with the measured data in farm field.
MATERIALS AND METHODS
RESULTS
Materials
Courses to set up the models
The subject was 1-year-old seedlings of J. hindsii, whose seeds were offered by Black Walnut Experimental Station of Chinese Academy of Forests in Luoyang of Henan Province, China. The field tests were implemented at Yucheng Comprehensive Experimental Station of Institute of Geography, Chinese Academy of Sciences from Oct. 2003 to Oct. 2004. The seedlings were planted at 60 cm × 40 cm, and
To set up the models of the accumulative and distributive models of dry matter The organs of the tested seedlings were divided into two parts: “productive organ” (the canopy) and “consumptive organ” (the stems-roots), as showed in Fig.1. Based on the diffusive laws, conservation laws of matter, and the relationship of source and sink, the following functions were set up (Stutzel and Beech 1988):
© 2010, CAAS. All rights reserved. Published by Elsevier Ltd.
58
ZHANG Ji-xiang et al.
Fig. 1 Relation diagram for accumulation and distribution of assimilate between productive and consumptive organs.
dWl = Y(Pcd - Kl - Ml) - DlWl
(1)
dWs = Y(Kl - Ms) - DsWs
(2)
Where Wl and W s represent the dry matter of the productive and consumptive organs, respectively; dWl and dWs, the daily production of both organs; Pcd , the daily photosynthetic yield of the productivity organ; Kl , the daily flux of the dry matter from the productive organ to the consumptive organ; Ml and Ms, the maintenance respiratory capacities of the organs, respectively; Y, the transforming coefficient of dry matter in the organs, which indicates the ratio of the plant growth and respiratory cost; Dl and Ds, the mortalities of the productive and consumptive organs. To ascertain the daily photosynthetic yield of the canopy Firstly, a sing leaf photosynthetic rate (mol m-2 s-1) was simulated by means of uniting biochemical model of photosynthesis introduced by Farquhar (Farquhar et al. 1980) with B-B model of stomatal conductance (Collatz et al. 1991; Leuning 1990; Zhang et al. 2004a, b); secondly, on the basis of Ross and Nilson’s models (Ross and Nilson 1966) of leaf declination distribution and mathematization of geometric structure of canopies, the highly distinguishable models of canopy structures and the transmissive submodels of direct and diffusive radiation in the canopy were set up and the leaf photosynthetic rates of the canopies
were calculated (Ross and Nilson 1966; Monsi and Saeki 1995); Zhang et al. 2006); finally, the daily photosynthetic yield of the productive organ, and the daily assimilation product in unit land area (mol CO2 m-2 d-1), were ascertained (Zhang et al. 2004a, b). The daily assimilated CO2 was transformed into carbohydrate (kg CH 2O m-2 d-1), which transformation coefficient was 33/40, and the dry matter of the whole canopy leaves (Wl) was transformed into leaf area index (LAI): (3) LAI = SLA Wl Where SLA representes the special leaf area (m2 g-1), indicating the leaf area per gram of the leaf dry matter. Under the condition of water and fertilizer optimum and during certain periods of the plant growth and development, the photosynthetic rate was mainly decided by atmosphere factors, for example, solar radiation flux density, temperature and air humidity, and so on. The daily flux of the dry matter responds to environmental factors The assimilate product of photosynthesis above all accumulated in the mesophyllous cells and increased the assimilate concentration of cytoplasm. According to the diffusive law of matter, the assimilate transports from leaves to stem-root when the assimilate concentration in the leaves was higher than in the stem-root. Here it was assumed that the assimilate flux (Kl) from leaves to stem-root was determined by the concentration difference of assimilate between leaves and stem-root. Kl could be showed as: Kl = Gc(T )Wl (Cl - Cst) (4) Where Gc(T) represents the assimilate conductivity from the leaves to the stem-root, which mainly depended upon the environmental temperature (T) (Thornley 1991a): Gc(T) = (a0 + a1T + a2T2) (G) (20) (5) Where a 0, a 1 and a 2 were coefficients, showed as (Thornley 1991a, b): (6)
(7)
(8)
© 2010, CAAS. All rights reserved. Published by Elsevier Ltd.
Dynamic Simulating to the Accumulation and Distribution of Dry Matter for Black Walnut (Juglans hindsii) Seedlings
Where G (20) was the assimilate conductivity at 20°C, being assumed as 5.0 kg d-1; T0 and Tm, the minimum and maximum effective temperature, under which the assimilate could conduct, being assumed as 5.0 and 30.0°C, respectively (Thornley 1991a, b); Cl and Cst, the concentrations of the assimilate in the leaves and the stem-root, respectively. Here it was assumed that the concentrations of the assimilate in the leaves and the stem-root amounted to the ratio of their receiving matter to their total dry weight: (9)
(10) Function 9 and 10 are inserted to function 4, the following function is gotten: (11) The maintenance respiration responds to the environmental factors Here it was assumed that temperature was only an environmental factor. Q10 was applied to the response of the maintenance respiration to temperature, which value generally was 10. The rate of maintenance respiration doubled when temperature increaseed by 10°C (Thornley 1972). The rates were converted to the cost of carbohydrate (CH2O), and the rates of the leaves and the stem-root were 0.015 and 0.010 kg kg-1d-1 at 25°C (Thornley 1991a). Both at any temperature (T) could be described as (Thornley 1991b): Ml = 0.015Wl 2(0.1T - 2.5)
(12)
Ms = 0.010Ws 2(0.1T - 2.5)
(13)
Where Ml and Ms represent maintenance respiratory rates of the leaves and the stem-root, respectively. The growing respiration responds to environmental factors The plant growth not only needs part of assimilate to form structural matter of the organ, but also costs some assimilate by respiration, which is named as the growing respiration. The transformation coefficient, the structural matter produced per gram assimilate consumed, averagely was 0.72 kg kg-1.
59
Developmental rate responds to environmental factors The developmental rate (DVR) determines the length of plant developmental phase. The greater the developmental rate is, the shorter the developmental phrase (DVS) last: (14) or
(15)
The annual growth period of the tested seedlings was divided into two phases. The first phase covered from the germination of the epigeal cotyledon (DVS = 0) to stopping growth of the seedlings (the effective leaf area index reached to maximal value; DVS = 1). The second phase covered from the end of the first phase to the beginning of dormancy stage (the effective leaf area reached to zero; DVS = 2). The developmental rate could be described as the function of temperature (Stutzel and Beech 1988):
(16)
Where Ti represents daily mean temperature of some day (i) during the seedling growth; n, the needed days to complete certain developmental phase. In addition, the coefficient (Dl) of the death rate of the leaves could be described as the function of the developmental period (DVS), but the coefficient (Ds) of the stem-root could not change with the seedling development: Dl = 0.05sin( DVS3) and Ds = 0.01
(17)
To paramerize and validate the models The initialization values to run the model could be gotten from the experiment. The dry matter of the “productive” and “consumptive” organs was measured at the spreading period of the first euphylla (at early May, 2004) as the initialization values (Wl0 = 0.006 kg m-2 and Ws0 = 0.012 kg m-2) to run the model. The needed meteorological data to run the models were gained from Yucheng Comprehensive Experimental Station. The daily photosynthesis yield could be obtained by Zhang et al. (2006). Fig.2 showed the accumulative processes of the dry
© 2010, CAAS. All rights reserved. Published by Elsevier Ltd.
60
matter respectively in the whole plant, the leaf and the stem-root of 1-year-old J. hindsii seedlings. As a whole, the whole plant and the stem-root grew with the similar rhythm, which growing processes were generally divided into two phases: the prophase, in which both grew in conformity to exponential curves; the anaphase, in conformity to straight lines. But the dry matter accumulation in the canopy as a whole presented a logistic curve. Meanwhile, the growth of the whole plant, the leaves and the stem-root all presented wavy increase, which was induced by the wavy change of the environmental factors day by day. In addition, the results running the models fitted to the experimental data to a great extent. Fig.3 showed that dWl /dWs (the daily matter ratio between all leaves in capony and stem-root) responded to daily average temperature day by day from the plant emergence. The change of dWl /dWs over time presented 3 phases based on its dimension. In the first phase (010 days after the emergence), dWl /dWs was the great-
Fig. 2 The simulated and measured dry biomass of leaf and stemroot for J. hindsii at 1-year-old. WT, WS , and W1 are respectively total biomass, dry leaf and stem-root weight.
Fig. 3 The ratio of daily accumulative weight between leaf and stem-root of J. hindsii in the period of leaf formation at 1-yearold.
ZHANG Ji-xiang et al.
est (the average was about 3.2), which indicated that the assimilate produced by the leaves was mainly used to the construction of the canopy. The values of dWl / dWs kept about 1.9 for long time in the second phase (10-55 days after the emergence), which showed the dry matter distribution between the leaves and the stemroot displayed a relatively balanced status. The dimension of dWl /dWs abruptly decreased in the third phase (55-90 days after the emergence), which indicated the dry matter was mainly distributed to promote stem and root growth, and to speed up matter reposition; yet leaf growth gradually stopped. Both Figs.2 and 3 showed that the total trend of the plant growth and the distribution of dry mater among the different organs generally kept to phonological cycle. But the wavy change of the growth and the distribution responded to the instant change of environmental factors. In the favorable soil water and nutrition condition, the distribution of the dry matter was mainly regulated by air temperature and solar radiation flux density, and so on. Dry matter export flux (K l, kg m-2 d-1) out of plant canopy is not only determined by genotypes, development stages, but also by environmental factors. Fig.4 showed that the dry matter export flux out of the canopy to stem and root responded to air temperature in 1year-old J. hindsii seedlings. At a certain developmental stage and under the condition of other environmental factors keeping unchanging, the response of the dry matter flux from the canopy to temperature presented a conic curve. The flux was 0 kg m-2 d-1 at 5.0°C, which sharply increased along with the increase of temperature. When temperature exceeded 20°C, the increasing trend of the flux went slow. The flux reached to maximum at about 30°C. Then it slowly decreased. Fig.5 displayed that the dry matter export flux responded to daily photosynthesis yield (Pcd , kg m-2 d-1). The flux linearly increased with the daily photosynthesis yield. In fact, the daily photosynthesis yield was synthetically effected by plant varieties, canopy structure (for example, planted density, leaf area index, and its spacial distribution, etc.) developmental stage, and environmental factors. Under the conditions of the certain plant variety, the certain developmental phase and under the condition of favorable soil water and nutrition, the daily photosynthesis yield was mainly de-
© 2010, CAAS. All rights reserved. Published by Elsevier Ltd.
Dynamic Simulating to the Accumulation and Distribution of Dry Matter for Black Walnut (Juglans hindsii) Seedlings
Fig. 4 Response of canopy dry mass export flux to air temperature about 1-year-old J. hindsii.
Fig. 5 Response of canopy dry matter export flux to daily photosynthesis value in the J. hindsii canopy.
termined by environmental factors. Meanwhile among all of environmental factors, solar radiation was the most main factor and played a driving role, because it was not only energy sources for leaf photosynthesis, but also effected the spatial and temporal distribution of air temperature, air humidity, leaf temperature within the canopy, and also effected a series of eco-physiological processes, for example, transpiration and stomatal openness and closeness. So Fig.5 also reflected relationship between dry matter export flux out of the canopy and daily solar radiation flux received by the canopy leaves.
DISCUSSION The accumulation and distribution of dry matter among different organs and the growth and development of plants are decided by the plant genotypes and environmental factors (Bruchou 1999). The genotypes deter-
61
mine the annual period rhythm of plant growth and development; but the seasonal and stochastic changes of the environmental factors affect the process of plant growth and development (Bruchou 1999; Cai 2000). The studies ( Chung and Sinba 1981; Schwintzer and Lancelle 1983; Calion and Yu 1984; Hodgkinson and Becking 1987; Penning de Vries and Jonsen 1989; Shu 1993; Shi 1993; Liu et al. 2001) showed that during the reproductive growth phase the assimilate was preferentially provided to reproductive organs under the condition of limited nutritious supply; and so was it under the vegetative growth phase, in which the ratio of the dry matter distribution between the canopy and the stemroot was often adjusted to adapt to the changeful environment and to make the function of the plant balanced. Here the dynamic models was set up to analyze the influence of environmental factors on the accumulation and distribution of the dry matter among the different organs during a contain growth and development phase with 1-year-old J. hindsii seedlings. In this study, along with the lowering of solar radiation flux densities, the photosynthetic rate of the canopy decreased to make the growth rate of the canopy and the stem-root lower. Generally, root growth is most limited among all the organs, so dW l /dW s becomes greater. By contraries, when solar radiation flux densities become weak, the photosynthetic rate goes down, the roots limits getting more assimilate, and dWl/dWs decreases, which accords with the handy distribution principle of assimilate (Thornley 1972; Zhang et al. 2004a). The influence of temperature on the accumulation and distribution of dry matter among the organs is more complicated, because temperature not only affects the photosynthetic rate of the canopy, but also affects the accumulation, transportation and distribution of assimilate and the respiration. In addition, leaves or roots always stand in distinct temperature gradients. The differences of temperature in leaves or roots at the different layers will affect the response of the accumulation and distribution of dry matter to temperature (Stutzel and Beech 1988). Here it was showed that under the other environmental factors keeping constant, the assimilate exporting from the canopy increased, or dWl / dWs decreased at the lower temperature. Along with the increase of temperature the exporting assimilate
© 2010, CAAS. All rights reserved. Published by Elsevier Ltd.
62
ZHANG Ji-xiang et al.
gradually decreased, or dWl /dWs increased. Soil moisture and mineral nutrient affect the plant growth and development and the distribution of the dry matter, similar to the atmospheric factors. Our study was carried in the optimum conditions of soil moisture and mineral nutrient. But in the natural environment, the soil moisture and nutrient is not often meet for the need of the plant growth and development. When the soil water or mineral nutrient is lacking, assimilate is favor of the roots. The canopy cannot obtain enough assimilate to make leaf growth stop, or partly perish, which is the plant adaptability to the stress environment. In addition, agricultural techniques also affect the accumulation and distribution of dry matter and plant growth and development. For example, the pruning or thinning can make the root growth become weak, and the dead rate of roots go up.
periods and environmental factors. At the initial stage of the canopy forming, dWl /dWs was larger, which indicated that the photosynthetic product was mainly used to develop leaves; and when the plant tended to stop growing, dWl /dWs decreased linearly, and the main distribution of dry matter moved to the roots. The dWl / dWs was also restricted by the phase of the growth and development and the environmental factors, which was adjusted along with the physiological demands of the total plant in order to make itself at the best in the different environments.
CONCLUSION
References
Acknowledgements This work was in part funded by the Superior Cultivars Program of Shandong Province Government and Open Foundation Program of Chinese Academy of Sciences, China.
Bruchou C, Genard M. 1999. A space-time model of carbon
The models of the accumulation and distribution of the dry matter were set up under the optimum conditions of the soil moisture and mineral nutrient, according to the laws of energy balance and the theories of concentration gradient. Presumed that the assimilate concentration in the different organs was in the proportion of their gained dry matter at the same time, the relational function (the function 11) of the assimilate flux from the canopy to the stem-root was deduced, by which the estimated values comparatively accorded with the experimental results. During a certain phase of growth and development for 1-year-old J. hindsii, the dry matter accumulations of the canopy, stem-root and total plant as a whole increased with the stated rules. Under the favorable conditions of soil moisture and mineral nutrient, during the period of the canopy construction, the dry matter accumulation of the canopy conformed to logistic curves; but the accumulation of both total biomass and dry matter of stem-root could be divided into two phases: The first phase was exponential increase, the second was linear increase. The total biomass, dry matter of canopy and stem-root all presented a fluctuant increase, which was affected by the environmental factors. Ratio of daily increase of dry matter in the canopy and the stem-root (dWl /dWs) was changeable along with growth
translocation along a shoot bearing fruits. Annals of Botany, 84, 565-576. Cai X M. 2000. Ecology on Ecosystem. Science Press, Beijing. (in Chinese) Calion M, Yu O. 1984. Analysis of the time course of change in nitrogen content in Daclylis glomerata L. and on the kinetics of growth in the vegetative phase. Annals of Botany, 26, 6976. Chung H H, Sinba M J. 1981. C14 distribution and utilization in blue grama as affected by temperature, water potential and defoliation regimes. Oecologia, 47, 190-195. Collatz G J, Ball J T, Grivet C, Berry J A. 1991. Physiological and environmental regulation of stomatal conductance, photosynthesis and transpiration: A model that includes a laminar boundary layer. Agricultural and Forest Meteorology, 54, 107-136. Cruz R T. 1986. Shoot and root response to water deficits in rainfed lowland rice. Australian Journal of Plant Physiology, 13, 567-575. Drew A P, Ledig F T. 1980. Episodic growth and relative shoot: Root balance in loblolly pine seedlings. Annals of Botany, 45, 143-148. Fang J Y, Tang Y H, Lin J D. 2000. Global Ecology - Climate Change and Ecological Responses. Higher Education Press, Beijing. (in Chinese) Farquhar G D, von Caemmerer S, Berry J A. 1980. A biochemical model of photosynthetic CO2 assimilation in leaves C3 species. Planta, 149, 78-90.
© 2010, CAAS. All rights reserved. Published by Elsevier Ltd.
Dynamic Simulating to the Accumulation and Distribution of Dry Matter for Black Walnut (Juglans hindsii) Seedlings
63
Chinese Press of Electric Power, Beijing, China. (in Chinese)
Beijing, China. (in Chinese) Stutzel H, Beech D F. 1988. A model of the partitioning of new
Hodgkinson K C, Becking H G. 1977. Effect of defoliation on root growth of some arid zone perennial plants. Australian
above-ground dry matter. Annals of Botany, 61, 481-487. Thornley J H M. 1972. A balanced quantitative model for root:
Journal of Agricultural Research, 29, 31-42. Leuning R. 1990. Modeling stomatal behavior and photosynthesis
shoot ratios in vegetative plants. Annals of Botany, 36, 431441.
of Eucalyptus grandis. Australian Journal of Plant Physiology,
Thornley J H M. 1991a. A model of leaf tissue growth, acclimation and senescence. Annals of Botany, 67, 219-228.
Hao H W, Shi G W. 2000. A Practical Course on Origin 6.0.
17, 159-175. Liu J D, Wang S L, Yu Q. 2001. Simulation of impacts of doubled CO2 on the climatic productivity in Huang-Huai-Hai plain. Journal of Natural Disasters, 10, 17-23. (in Chinese)
Thornley J H M. 1991b. A transport-resistance model of forest growth and partitioning. Annals of Botany, 68, 211-226. de Wit C T. 1978. Simulation of Assimilation, Rrespiration and
Molles M C. 2000. Ecology: Concepts and Applications. McGraw-Hill Companies, Inc. USA & China Science Press,
Transpiration of Crops. Pudoc., Wageningen, The
Beijing, China. Monsi M, Saeki T. 1953. Uber den Lictfaktor in den
Yu Q, Hengdijk J D, Liu J D. 2001. Application of a progressive-
Pflanzengesellschaften und sein Bedeutung fur die Stoffproduktion. Japan Journal of Botany, 14, 22-52. Penning de Vries F W T, Jonsen D M. 1989. Simulation of Ecophysiological Processes of Growth in Several Annual Crops. vol. 34. Pudoc. Wageningen, The Netherland. pp. 7382. Ross J K. 1981. The Radiation Regime and Architecture of Plant Stands. Dr W. Junk Publisher. The Hague, The Netherlands. Schwintzer C R, Lancelle S A. 1983. Effects of water-table depth on shoot growth and nodulation of Myrica gale seedlings. Journal of Ecology, 71, 89-101. Shi J Z. 1993. Studies on the assimilate models and the water use efficiency of the leaves at the different layers in the wheat canopy. Ph D thesis, Shanghai Institute of Plant Physiology, Chinese Academy of Sciences. pp. 20-52. (in Chinese) Shu H R. 1993. Pomicultural Physiology. Agricultural Press,
Netherland. pp. 1-112. difference method to identify climatic factors causing variation in the rice yield in the Yangtze Delta. International Journal of Biometeorology, 25, 258-267. Zhang J X, Wei Q P, Lu P L. 2004a. Mathematically modeling ecophysiological process response to environmental factors for American black walnut seedlings (II): Dynamic models of the accumulation and distribution for black walnut’s dry matter. Journal of Biomathematics, 19, 109-116. (in Chinese) Zhang J X, Mao Z Q, Wei Q P. 2004b. Establishment and verification of an ecophysiological model for the leaf photosynthesis of American black walnut seedlings. Journal of Biomathematics, 19, 213-218. (in Chinese) Zhang J X, Mao Z Q, Wei Q P. 2006. Mathematically modeling ecophysiological process response to environmental factors for American black walnut seedlings (III): The mathematical models of the canopy photosynthesis. Journal of Biomathematics, 21, 401-411. (in Chinese) (Managing editor ZHANG Yi-min)
© 2010, CAAS. All rights reserved. Published by Elsevier Ltd.
January 2010
2010, 9(1): 56-63
Dynamic Simulating to the Accumulation and Distribution of Dry Matter for Black Walnut (Juglans hindsii) Seedlings ZHANG Ji-xiang1, MAO Zhi-quan1, SHU Huai-rui1 and WEI Qin-ping2 State Key Laboratory of Crop Biology, College of Horticultural Science and Engineering, Shandong Agricultural University, Tai’an 271018, P.R.China 2 Institute of Forestry & Pomology, Beijing Academy of Agriculture & Forestry Sciences, Beijing 100093, P.R.China 1
Abstract It is very important to study eco-physiological processes of plants and to determine quantitative relations between accumulation, distribution of dry matter and environmental factors for regionalization, standardization and precision agriculture. Meanwhile, global changes, e.g., atmospheric CO2 concentration rising, global warming, and climate abnormity, have been effecting on agricultural productivity. This study provides a theoretical basis for predicting productive potentials and development trends in different agricultural regions. One-year-old black walnut (Juglans hindsii) seedlings were employed as subjects for setting up the dynamic models of dry matter accumulation and distribution, based on mechanistic models of photosynthesis, matter conservation and concentration gradient. Under optimum conditions of soil moisture and mineral nutrient, during the period of the canopy construction, the dry matter accumulation of the canopy conformed to logistic curves; but the accumulation of both total biomass and dry matter of stem-root could be divided into two phases: the first phase was exponential increase, the second was linear increase. The total biomass, dry matter of canopy and stem-root all presented a fluctuant increase, which was affected by the environmental factors. Ratio of daily increase of dry matter in the canopy and the steem-root (dWl/dWs) was changeable along with growth periods and environmental factors. At the initial stage of the canopy forming, dWl/dWs was larger, about 3.2 on average, which indicated that the photosynthetic product was mainly used to develop leaves; in the midterm, it was about 1.9, which indicated that the distribution of dry matter in the canopy and in the stem-root was relatively balanced; when the plant tended to stop growing, dWl/dWs decreased linearly, and the main distribution of dry matter moved to the roots. Key words: black walnut, dry matter, accumulation and distribution, dynamic model
INTRODUCTION During the growth and development of plants, the accumulation and distribution of dry matter among roots, stems, fruit and leaves are decided by their genotypes and environmental factors (Cruz 1986). The latter influence on the accumulation and distribution of the dry matter has qualitatively reported (Calion and Yu 1984;
Chung and Sinba 1981; Thornley 1972). Generally, dry matter is favor of the above-ground, rather than the under-ground in the conditions of weak light, high temperature or ample soil moisture (Fang et al. 2000; Molles 2000); and under disadvantageous surroundings, for example, drought stress or poor nutrition, dry matter accumulation not only decrease, but also its distribution among different organs is biased toward the under-ground (Cai 2002; Zhang et al. 2004a, b, 2006).
Received 21 May, 2009 Accepted 16 September, 2009 ZHANG Ji-xiang, Professor, Ph D, Tel: +86-538-8249953, E-mail: [email protected]; Correspondence WEI Qin-ping, Porfessor, E-mail: [email protected]
© 2010, CAAS. All rights reserved. Published by Elsevier Ltd. doi:10.1016/S1671-2927(09)60067-5
Dynamic Simulating to the Accumulation and Distribution of Dry Matter for Black Walnut (Juglans hindsii) Seedlings
Many studies (de Wit 1978; Liu et al. 2001; Yu et al. 2001) have showed that the accumulation and distribution of dry matter respond to a single environmental factor, for example, Thornley (1972) set up a distribution model of dry matter between the above-ground and the under-ground in the conditions of different nitrogen-nutritional levels. Liu et al. (2001) reconstructed FAO productivity model, which provided theoretical basis for estimating crop productivity accurately under doubled CO2 concentration. But it was rarely reported how the accumulation and distribution of dry matter quantitatively respond to more than two environmental factors. The reasons are: 1) the accumulation and distribution of dry matter cover many complicated processes, such as, photosynthesis, respiration, transportation and transformation of assimilates, and so on. The quantitative or simulative studies on these processes have to involve many functions to describe them. At present, it was difficult to set up these functions because the physiological mechanism of the processes was not completely clear; 2) environmental factors not only synchronously influence the accumulation and distribution of dry matter, but also act one another. So it was too difficult to design and actualize the experiments on the physiological processes of the accumulation and distribution of dry matter to respond to environmental factors. Based on the past works, a dynamic model of the accumulation and distribution of the dry matter of 1-year-old American walnut (J. hindsii) seedlings responding to environmental factors was presented. Some experiential functions or hypotheses were applied in setting up the model, but the simulated results by these function as a whole accorded with the field tested data.
57
managed with conventional methods. The field was fertilized with 8 000 kg ha-1 organic manure and 900 km ha-1 bi-ammonium phosphate respectively in March and June, 2005. The soil relative moisture was always controlled over 60%.
Methods To measure both fresh and dry weight of the plants The 5 standing plants were stochastically selected to be wholly dug up every 5 days during the whole test period, and their leaf area, leaf area index, leaf area radio, the fresh and dry weights of the leaves, stems and roots were respectively measured (Zhang et al. 2004b, 2006). To measure the meteorological data The solar radiant flux densities of diffusive, direct and global radiation were respectively measured during the plant growing period, using the automatic aerograph at the Yucheng Comprehensive Experimental Station. To set up and validate models By summarizing the previous and relevant studies, and based on the diffusive laws, conservation laws of matter and the relationship between source and sink, the dynamic model frameworks to simulate accumulation and distribution of black walnut seedlings were set up. Then the computer programs to run the models were compiled, applying Fortran 90 under the background of Fortran PowerStation 4.0. The all models were parameterized, applying a math Software, Origin 6.0 (Hao and Shi 2000). Finally, the models were validated with the measured data in farm field.
MATERIALS AND METHODS
RESULTS
Materials
Courses to set up the models
The subject was 1-year-old seedlings of J. hindsii, whose seeds were offered by Black Walnut Experimental Station of Chinese Academy of Forests in Luoyang of Henan Province, China. The field tests were implemented at Yucheng Comprehensive Experimental Station of Institute of Geography, Chinese Academy of Sciences from Oct. 2003 to Oct. 2004. The seedlings were planted at 60 cm × 40 cm, and
To set up the models of the accumulative and distributive models of dry matter The organs of the tested seedlings were divided into two parts: “productive organ” (the canopy) and “consumptive organ” (the stems-roots), as showed in Fig.1. Based on the diffusive laws, conservation laws of matter, and the relationship of source and sink, the following functions were set up (Stutzel and Beech 1988):
© 2010, CAAS. All rights reserved. Published by Elsevier Ltd.
58
ZHANG Ji-xiang et al.
Fig. 1 Relation diagram for accumulation and distribution of assimilate between productive and consumptive organs.
dWl = Y(Pcd - Kl - Ml) - DlWl
(1)
dWs = Y(Kl - Ms) - DsWs
(2)
Where Wl and W s represent the dry matter of the productive and consumptive organs, respectively; dWl and dWs, the daily production of both organs; Pcd , the daily photosynthetic yield of the productivity organ; Kl , the daily flux of the dry matter from the productive organ to the consumptive organ; Ml and Ms, the maintenance respiratory capacities of the organs, respectively; Y, the transforming coefficient of dry matter in the organs, which indicates the ratio of the plant growth and respiratory cost; Dl and Ds, the mortalities of the productive and consumptive organs. To ascertain the daily photosynthetic yield of the canopy Firstly, a sing leaf photosynthetic rate (mol m-2 s-1) was simulated by means of uniting biochemical model of photosynthesis introduced by Farquhar (Farquhar et al. 1980) with B-B model of stomatal conductance (Collatz et al. 1991; Leuning 1990; Zhang et al. 2004a, b); secondly, on the basis of Ross and Nilson’s models (Ross and Nilson 1966) of leaf declination distribution and mathematization of geometric structure of canopies, the highly distinguishable models of canopy structures and the transmissive submodels of direct and diffusive radiation in the canopy were set up and the leaf photosynthetic rates of the canopies
were calculated (Ross and Nilson 1966; Monsi and Saeki 1995); Zhang et al. 2006); finally, the daily photosynthetic yield of the productive organ, and the daily assimilation product in unit land area (mol CO2 m-2 d-1), were ascertained (Zhang et al. 2004a, b). The daily assimilated CO2 was transformed into carbohydrate (kg CH 2O m-2 d-1), which transformation coefficient was 33/40, and the dry matter of the whole canopy leaves (Wl) was transformed into leaf area index (LAI): (3) LAI = SLA Wl Where SLA representes the special leaf area (m2 g-1), indicating the leaf area per gram of the leaf dry matter. Under the condition of water and fertilizer optimum and during certain periods of the plant growth and development, the photosynthetic rate was mainly decided by atmosphere factors, for example, solar radiation flux density, temperature and air humidity, and so on. The daily flux of the dry matter responds to environmental factors The assimilate product of photosynthesis above all accumulated in the mesophyllous cells and increased the assimilate concentration of cytoplasm. According to the diffusive law of matter, the assimilate transports from leaves to stem-root when the assimilate concentration in the leaves was higher than in the stem-root. Here it was assumed that the assimilate flux (Kl) from leaves to stem-root was determined by the concentration difference of assimilate between leaves and stem-root. Kl could be showed as: Kl = Gc(T )Wl (Cl - Cst) (4) Where Gc(T) represents the assimilate conductivity from the leaves to the stem-root, which mainly depended upon the environmental temperature (T) (Thornley 1991a): Gc(T) = (a0 + a1T + a2T2) (G) (20) (5) Where a 0, a 1 and a 2 were coefficients, showed as (Thornley 1991a, b): (6)
(7)
(8)
© 2010, CAAS. All rights reserved. Published by Elsevier Ltd.
Dynamic Simulating to the Accumulation and Distribution of Dry Matter for Black Walnut (Juglans hindsii) Seedlings
Where G (20) was the assimilate conductivity at 20°C, being assumed as 5.0 kg d-1; T0 and Tm, the minimum and maximum effective temperature, under which the assimilate could conduct, being assumed as 5.0 and 30.0°C, respectively (Thornley 1991a, b); Cl and Cst, the concentrations of the assimilate in the leaves and the stem-root, respectively. Here it was assumed that the concentrations of the assimilate in the leaves and the stem-root amounted to the ratio of their receiving matter to their total dry weight: (9)
(10) Function 9 and 10 are inserted to function 4, the following function is gotten: (11) The maintenance respiration responds to the environmental factors Here it was assumed that temperature was only an environmental factor. Q10 was applied to the response of the maintenance respiration to temperature, which value generally was 10. The rate of maintenance respiration doubled when temperature increaseed by 10°C (Thornley 1972). The rates were converted to the cost of carbohydrate (CH2O), and the rates of the leaves and the stem-root were 0.015 and 0.010 kg kg-1d-1 at 25°C (Thornley 1991a). Both at any temperature (T) could be described as (Thornley 1991b): Ml = 0.015Wl 2(0.1T - 2.5)
(12)
Ms = 0.010Ws 2(0.1T - 2.5)
(13)
Where Ml and Ms represent maintenance respiratory rates of the leaves and the stem-root, respectively. The growing respiration responds to environmental factors The plant growth not only needs part of assimilate to form structural matter of the organ, but also costs some assimilate by respiration, which is named as the growing respiration. The transformation coefficient, the structural matter produced per gram assimilate consumed, averagely was 0.72 kg kg-1.
59
Developmental rate responds to environmental factors The developmental rate (DVR) determines the length of plant developmental phase. The greater the developmental rate is, the shorter the developmental phrase (DVS) last: (14) or
(15)
The annual growth period of the tested seedlings was divided into two phases. The first phase covered from the germination of the epigeal cotyledon (DVS = 0) to stopping growth of the seedlings (the effective leaf area index reached to maximal value; DVS = 1). The second phase covered from the end of the first phase to the beginning of dormancy stage (the effective leaf area reached to zero; DVS = 2). The developmental rate could be described as the function of temperature (Stutzel and Beech 1988):
(16)
Where Ti represents daily mean temperature of some day (i) during the seedling growth; n, the needed days to complete certain developmental phase. In addition, the coefficient (Dl) of the death rate of the leaves could be described as the function of the developmental period (DVS), but the coefficient (Ds) of the stem-root could not change with the seedling development: Dl = 0.05sin( DVS3) and Ds = 0.01
(17)
To paramerize and validate the models The initialization values to run the model could be gotten from the experiment. The dry matter of the “productive” and “consumptive” organs was measured at the spreading period of the first euphylla (at early May, 2004) as the initialization values (Wl0 = 0.006 kg m-2 and Ws0 = 0.012 kg m-2) to run the model. The needed meteorological data to run the models were gained from Yucheng Comprehensive Experimental Station. The daily photosynthesis yield could be obtained by Zhang et al. (2006). Fig.2 showed the accumulative processes of the dry
© 2010, CAAS. All rights reserved. Published by Elsevier Ltd.
60
matter respectively in the whole plant, the leaf and the stem-root of 1-year-old J. hindsii seedlings. As a whole, the whole plant and the stem-root grew with the similar rhythm, which growing processes were generally divided into two phases: the prophase, in which both grew in conformity to exponential curves; the anaphase, in conformity to straight lines. But the dry matter accumulation in the canopy as a whole presented a logistic curve. Meanwhile, the growth of the whole plant, the leaves and the stem-root all presented wavy increase, which was induced by the wavy change of the environmental factors day by day. In addition, the results running the models fitted to the experimental data to a great extent. Fig.3 showed that dWl /dWs (the daily matter ratio between all leaves in capony and stem-root) responded to daily average temperature day by day from the plant emergence. The change of dWl /dWs over time presented 3 phases based on its dimension. In the first phase (010 days after the emergence), dWl /dWs was the great-
Fig. 2 The simulated and measured dry biomass of leaf and stemroot for J. hindsii at 1-year-old. WT, WS , and W1 are respectively total biomass, dry leaf and stem-root weight.
Fig. 3 The ratio of daily accumulative weight between leaf and stem-root of J. hindsii in the period of leaf formation at 1-yearold.
ZHANG Ji-xiang et al.
est (the average was about 3.2), which indicated that the assimilate produced by the leaves was mainly used to the construction of the canopy. The values of dWl / dWs kept about 1.9 for long time in the second phase (10-55 days after the emergence), which showed the dry matter distribution between the leaves and the stemroot displayed a relatively balanced status. The dimension of dWl /dWs abruptly decreased in the third phase (55-90 days after the emergence), which indicated the dry matter was mainly distributed to promote stem and root growth, and to speed up matter reposition; yet leaf growth gradually stopped. Both Figs.2 and 3 showed that the total trend of the plant growth and the distribution of dry mater among the different organs generally kept to phonological cycle. But the wavy change of the growth and the distribution responded to the instant change of environmental factors. In the favorable soil water and nutrition condition, the distribution of the dry matter was mainly regulated by air temperature and solar radiation flux density, and so on. Dry matter export flux (K l, kg m-2 d-1) out of plant canopy is not only determined by genotypes, development stages, but also by environmental factors. Fig.4 showed that the dry matter export flux out of the canopy to stem and root responded to air temperature in 1year-old J. hindsii seedlings. At a certain developmental stage and under the condition of other environmental factors keeping unchanging, the response of the dry matter flux from the canopy to temperature presented a conic curve. The flux was 0 kg m-2 d-1 at 5.0°C, which sharply increased along with the increase of temperature. When temperature exceeded 20°C, the increasing trend of the flux went slow. The flux reached to maximum at about 30°C. Then it slowly decreased. Fig.5 displayed that the dry matter export flux responded to daily photosynthesis yield (Pcd , kg m-2 d-1). The flux linearly increased with the daily photosynthesis yield. In fact, the daily photosynthesis yield was synthetically effected by plant varieties, canopy structure (for example, planted density, leaf area index, and its spacial distribution, etc.) developmental stage, and environmental factors. Under the conditions of the certain plant variety, the certain developmental phase and under the condition of favorable soil water and nutrition, the daily photosynthesis yield was mainly de-
© 2010, CAAS. All rights reserved. Published by Elsevier Ltd.
Dynamic Simulating to the Accumulation and Distribution of Dry Matter for Black Walnut (Juglans hindsii) Seedlings
Fig. 4 Response of canopy dry mass export flux to air temperature about 1-year-old J. hindsii.
Fig. 5 Response of canopy dry matter export flux to daily photosynthesis value in the J. hindsii canopy.
termined by environmental factors. Meanwhile among all of environmental factors, solar radiation was the most main factor and played a driving role, because it was not only energy sources for leaf photosynthesis, but also effected the spatial and temporal distribution of air temperature, air humidity, leaf temperature within the canopy, and also effected a series of eco-physiological processes, for example, transpiration and stomatal openness and closeness. So Fig.5 also reflected relationship between dry matter export flux out of the canopy and daily solar radiation flux received by the canopy leaves.
DISCUSSION The accumulation and distribution of dry matter among different organs and the growth and development of plants are decided by the plant genotypes and environmental factors (Bruchou 1999). The genotypes deter-
61
mine the annual period rhythm of plant growth and development; but the seasonal and stochastic changes of the environmental factors affect the process of plant growth and development (Bruchou 1999; Cai 2000). The studies ( Chung and Sinba 1981; Schwintzer and Lancelle 1983; Calion and Yu 1984; Hodgkinson and Becking 1987; Penning de Vries and Jonsen 1989; Shu 1993; Shi 1993; Liu et al. 2001) showed that during the reproductive growth phase the assimilate was preferentially provided to reproductive organs under the condition of limited nutritious supply; and so was it under the vegetative growth phase, in which the ratio of the dry matter distribution between the canopy and the stemroot was often adjusted to adapt to the changeful environment and to make the function of the plant balanced. Here the dynamic models was set up to analyze the influence of environmental factors on the accumulation and distribution of the dry matter among the different organs during a contain growth and development phase with 1-year-old J. hindsii seedlings. In this study, along with the lowering of solar radiation flux densities, the photosynthetic rate of the canopy decreased to make the growth rate of the canopy and the stem-root lower. Generally, root growth is most limited among all the organs, so dW l /dW s becomes greater. By contraries, when solar radiation flux densities become weak, the photosynthetic rate goes down, the roots limits getting more assimilate, and dWl/dWs decreases, which accords with the handy distribution principle of assimilate (Thornley 1972; Zhang et al. 2004a). The influence of temperature on the accumulation and distribution of dry matter among the organs is more complicated, because temperature not only affects the photosynthetic rate of the canopy, but also affects the accumulation, transportation and distribution of assimilate and the respiration. In addition, leaves or roots always stand in distinct temperature gradients. The differences of temperature in leaves or roots at the different layers will affect the response of the accumulation and distribution of dry matter to temperature (Stutzel and Beech 1988). Here it was showed that under the other environmental factors keeping constant, the assimilate exporting from the canopy increased, or dWl / dWs decreased at the lower temperature. Along with the increase of temperature the exporting assimilate
© 2010, CAAS. All rights reserved. Published by Elsevier Ltd.
62
ZHANG Ji-xiang et al.
gradually decreased, or dWl /dWs increased. Soil moisture and mineral nutrient affect the plant growth and development and the distribution of the dry matter, similar to the atmospheric factors. Our study was carried in the optimum conditions of soil moisture and mineral nutrient. But in the natural environment, the soil moisture and nutrient is not often meet for the need of the plant growth and development. When the soil water or mineral nutrient is lacking, assimilate is favor of the roots. The canopy cannot obtain enough assimilate to make leaf growth stop, or partly perish, which is the plant adaptability to the stress environment. In addition, agricultural techniques also affect the accumulation and distribution of dry matter and plant growth and development. For example, the pruning or thinning can make the root growth become weak, and the dead rate of roots go up.
periods and environmental factors. At the initial stage of the canopy forming, dWl /dWs was larger, which indicated that the photosynthetic product was mainly used to develop leaves; and when the plant tended to stop growing, dWl /dWs decreased linearly, and the main distribution of dry matter moved to the roots. The dWl / dWs was also restricted by the phase of the growth and development and the environmental factors, which was adjusted along with the physiological demands of the total plant in order to make itself at the best in the different environments.
CONCLUSION
References
Acknowledgements This work was in part funded by the Superior Cultivars Program of Shandong Province Government and Open Foundation Program of Chinese Academy of Sciences, China.
Bruchou C, Genard M. 1999. A space-time model of carbon
The models of the accumulation and distribution of the dry matter were set up under the optimum conditions of the soil moisture and mineral nutrient, according to the laws of energy balance and the theories of concentration gradient. Presumed that the assimilate concentration in the different organs was in the proportion of their gained dry matter at the same time, the relational function (the function 11) of the assimilate flux from the canopy to the stem-root was deduced, by which the estimated values comparatively accorded with the experimental results. During a certain phase of growth and development for 1-year-old J. hindsii, the dry matter accumulations of the canopy, stem-root and total plant as a whole increased with the stated rules. Under the favorable conditions of soil moisture and mineral nutrient, during the period of the canopy construction, the dry matter accumulation of the canopy conformed to logistic curves; but the accumulation of both total biomass and dry matter of stem-root could be divided into two phases: The first phase was exponential increase, the second was linear increase. The total biomass, dry matter of canopy and stem-root all presented a fluctuant increase, which was affected by the environmental factors. Ratio of daily increase of dry matter in the canopy and the stem-root (dWl /dWs) was changeable along with growth
translocation along a shoot bearing fruits. Annals of Botany, 84, 565-576. Cai X M. 2000. Ecology on Ecosystem. Science Press, Beijing. (in Chinese) Calion M, Yu O. 1984. Analysis of the time course of change in nitrogen content in Daclylis glomerata L. and on the kinetics of growth in the vegetative phase. Annals of Botany, 26, 6976. Chung H H, Sinba M J. 1981. C14 distribution and utilization in blue grama as affected by temperature, water potential and defoliation regimes. Oecologia, 47, 190-195. Collatz G J, Ball J T, Grivet C, Berry J A. 1991. Physiological and environmental regulation of stomatal conductance, photosynthesis and transpiration: A model that includes a laminar boundary layer. Agricultural and Forest Meteorology, 54, 107-136. Cruz R T. 1986. Shoot and root response to water deficits in rainfed lowland rice. Australian Journal of Plant Physiology, 13, 567-575. Drew A P, Ledig F T. 1980. Episodic growth and relative shoot: Root balance in loblolly pine seedlings. Annals of Botany, 45, 143-148. Fang J Y, Tang Y H, Lin J D. 2000. Global Ecology - Climate Change and Ecological Responses. Higher Education Press, Beijing. (in Chinese) Farquhar G D, von Caemmerer S, Berry J A. 1980. A biochemical model of photosynthetic CO2 assimilation in leaves C3 species. Planta, 149, 78-90.
© 2010, CAAS. All rights reserved. Published by Elsevier Ltd.
Dynamic Simulating to the Accumulation and Distribution of Dry Matter for Black Walnut (Juglans hindsii) Seedlings
63
Chinese Press of Electric Power, Beijing, China. (in Chinese)
Beijing, China. (in Chinese) Stutzel H, Beech D F. 1988. A model of the partitioning of new
Hodgkinson K C, Becking H G. 1977. Effect of defoliation on root growth of some arid zone perennial plants. Australian
above-ground dry matter. Annals of Botany, 61, 481-487. Thornley J H M. 1972. A balanced quantitative model for root:
Journal of Agricultural Research, 29, 31-42. Leuning R. 1990. Modeling stomatal behavior and photosynthesis
shoot ratios in vegetative plants. Annals of Botany, 36, 431441.
of Eucalyptus grandis. Australian Journal of Plant Physiology,
Thornley J H M. 1991a. A model of leaf tissue growth, acclimation and senescence. Annals of Botany, 67, 219-228.
Hao H W, Shi G W. 2000. A Practical Course on Origin 6.0.
17, 159-175. Liu J D, Wang S L, Yu Q. 2001. Simulation of impacts of doubled CO2 on the climatic productivity in Huang-Huai-Hai plain. Journal of Natural Disasters, 10, 17-23. (in Chinese)
Thornley J H M. 1991b. A transport-resistance model of forest growth and partitioning. Annals of Botany, 68, 211-226. de Wit C T. 1978. Simulation of Assimilation, Rrespiration and
Molles M C. 2000. Ecology: Concepts and Applications. McGraw-Hill Companies, Inc. USA & China Science Press,
Transpiration of Crops. Pudoc., Wageningen, The
Beijing, China. Monsi M, Saeki T. 1953. Uber den Lictfaktor in den
Yu Q, Hengdijk J D, Liu J D. 2001. Application of a progressive-
Pflanzengesellschaften und sein Bedeutung fur die Stoffproduktion. Japan Journal of Botany, 14, 22-52. Penning de Vries F W T, Jonsen D M. 1989. Simulation of Ecophysiological Processes of Growth in Several Annual Crops. vol. 34. Pudoc. Wageningen, The Netherland. pp. 7382. Ross J K. 1981. The Radiation Regime and Architecture of Plant Stands. Dr W. Junk Publisher. The Hague, The Netherlands. Schwintzer C R, Lancelle S A. 1983. Effects of water-table depth on shoot growth and nodulation of Myrica gale seedlings. Journal of Ecology, 71, 89-101. Shi J Z. 1993. Studies on the assimilate models and the water use efficiency of the leaves at the different layers in the wheat canopy. Ph D thesis, Shanghai Institute of Plant Physiology, Chinese Academy of Sciences. pp. 20-52. (in Chinese) Shu H R. 1993. Pomicultural Physiology. Agricultural Press,
Netherland. pp. 1-112. difference method to identify climatic factors causing variation in the rice yield in the Yangtze Delta. International Journal of Biometeorology, 25, 258-267. Zhang J X, Wei Q P, Lu P L. 2004a. Mathematically modeling ecophysiological process response to environmental factors for American black walnut seedlings (II): Dynamic models of the accumulation and distribution for black walnut’s dry matter. Journal of Biomathematics, 19, 109-116. (in Chinese) Zhang J X, Mao Z Q, Wei Q P. 2004b. Establishment and verification of an ecophysiological model for the leaf photosynthesis of American black walnut seedlings. Journal of Biomathematics, 19, 213-218. (in Chinese) Zhang J X, Mao Z Q, Wei Q P. 2006. Mathematically modeling ecophysiological process response to environmental factors for American black walnut seedlings (III): The mathematical models of the canopy photosynthesis. Journal of Biomathematics, 21, 401-411. (in Chinese) (Managing editor ZHANG Yi-min)
© 2010, CAAS. All rights reserved. Published by Elsevier Ltd.