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Plant and Soil

, Volume 298, Issue 1–2, pp 81–98 | Cite as

A dynamic model for the combined effects of N, P and K fertilizers on yield and mineral composition; description and experimental test

  • Kefeng Zhang
  • Duncan J. Greenwood
  • Philip J. White
  • Ian G. Burns
Regular Article

Abstract

This paper describes an integrated model for calculating the interactive effects of N, P and K fertilizers on crop response by combining routines from separate N, P and K models which used readily available inputs. The new model uses the principle of the ‘Law of the Minimum’ to calculate actual daily increments in plant weight and uptake of each nutrient based on the nutrient least able to meet the plant requirements, although account is also taken of soil factors such as the dependence of soil solution K on the level of mineral N. The validity of the model was tested against the results of 4 field experiments with different combinations of crop species, times of harvest, and levels of N, P and K fertilizers. The integrated model gave good overall predictions of the plant dry weight (excluding fibrous roots) and %N of the dry weight. However, predictions of its %P and %K in the dry weight were less satisfactory, especially in the luxury range. Simulation studies with low levels of nutrients showed that, while most interactive effects on final yield conformed to the Law of the Minimum type of response, the inter-dependence of K and nitrate concentrations in the soil solution resulted in responses to K at different levels of N that were better represented by the Mitscherlich equation or the Multiple Limitation Hypothesis. Thus the adaptability of the model allowed it to reproduce crop responses predicted by three quite different non-mechanistic static equations previously used in the literature to summarise nutrient interaction data. This suggests that the model has the potential to provide a mechanistic basis for interpreting factorial NPK fertilizer trials. Opportunities for improving the model were provided by the experimental findings that %P was strongly correlated with %N throughout the entire range of treatments; that K fertilizers failed to increase %K when %N was low; that fertilizer N increased plant %K when the level of K fertilizer was substantial but not otherwise; and that fertilizer-P depressed plant %K. The model validation also showed that there is a need to improve the parameterization for major crops.

Keywords

Crop response Fertilizer Interaction Model Law of the minimum Multiple limitation hypothesis 

Abbreviations

β

coefficient defining the dependence of N crit on W

D90

depth of soil containing 90% of roots

D1D2D3 and D4

different statistical methods for assessing discrepancies between measured and simulated parameters

K1 and K2

coefficients in a growth rate equation

KF

fertilizer-K

%K

weight of plant K as a percentage of W

Kcrit

critical %K

Kr

a term for the depressive effect in growth associated with N fertilizer

Lw

root length when plant weight is W

LM

Law of the Minimum

MLH

Multiple Limitation Hypothesis

MTS

Mitscherlich Growth Hypothesis

N_ABLE

nitrogen response model

NF

fertilizer-N

NR

fertilizer-N equivalent supplied by Rhizobium

%N

weight of plant N as a percentage of W

Ncrit

critical %N

%P

weight of plant P as a percentage of W

Pcrit

critical %P

PF

Fertilizer-P

PHOSMOD

phosphate response model

Pmin

%P at which growth ceases

POTAS

potassium response model

RNRP and RK

the daily increments in W calculated from N_ABLE, PHOSMOD and POTAS respectively

RNPK

the daily increment in W after taking account of R N R P and R K

W

dry weight of the entire plant excluding fibrous roots

Notes

Acknowledgment

The authors would like to thank the UK Department for Environment, Food and Rural Affairs who financed this work through project HH3507SFV.

References

  1. Barber SA (1995) Soil nutrient bioavailability, 2nd edn. Wiley, New York, p 398Google Scholar
  2. Barber SA, Cushman JH (1981) Nitrogen uptake model from agronomic crops. In: Iskander JK (ed) Modelling waste water renovation land treatment. Wiley, New York, pp 382–409Google Scholar
  3. Barnes A, Greenwood DJ, Cleaver TJ (1976) A dynamic model for the effects of potassium and nitrogen fertilizers on the growth and nutrient uptake of crops. J Agric Sci (Camb) 86:225–244Google Scholar
  4. Bar-Yosef B (2003) Phosphorus dynamics. In: Benbi DK, Nieder R (eds) Handbook of processes and modeling in soil–plant system. Haworth Reference Press, New York, pp 483–523Google Scholar
  5. Benbi DK, Richter J (2003) Nitrogen dynamics. In: Benbi DK, Nieder R (eds) Handbook of processes and modelling in the soil plant system. Haworth Reference Press, New York, pp 409–481Google Scholar
  6. Bloom AJ, Chapin FS, Mooney HA (1985) Resource limitation in plants—an economic analogy. Ann Rev Ecolog Syst 16:363–392Google Scholar
  7. Bohonak AJ (2004) Software for reduced major axis regression. http://www.biosdsu.edu/pub/ansy/ram.html.
  8. Broadley MR, Bowen HC, Cotterill HL, Hammond JP, Meacham MC, Mead A, White PJ (2004) Phylogenetic variation in the shoot mineral concentration of angiosperms. J Exp Bot 55:321–336PubMedCrossRefGoogle Scholar
  9. Burns IG (1974) A model for predicting the redistribution of salts applied to fallow soils after excess rainfall or evaporation. J Soil Sci 25:165–178CrossRefGoogle Scholar
  10. Claassen N, Steingrobe B (1999) Mechanistic simulation models for a better understanding of nutrient uptake from soil. In: Rengel Z (ed) Mineral nutrition of crops: fundamental mechanisms and implications. Haworth Press Binghampton, USA, pp 327–367Google Scholar
  11. Cleaver TJ, Greenwood DJ, Wood JT (1970) Systematically arranged fertilizer experiments. J Hortic Sci 45:457–469Google Scholar
  12. Ericsson T (1995) Growth and shoot:root ratios in relation to nutrient availability. Plant Soil 168–169:205–214Google Scholar
  13. Evangelou VP, Wang J, Phillips RE (1994) New developments and perspectives on soil potassium quantity/intensity relationships. Adv Agron 52:173–227Google Scholar
  14. Fraiser DM (1983) Effects of N and K applied to two maize/soybean no-tillage cropping systems on yields, profitability, growth, and soil acidity. M.S. thesis, University of Florida, Gainesville, FLGoogle Scholar
  15. Goodall DW, Grant Lipp AE, Slater WG (1955) Nutrient interactions and deficiency diagnosis in the lettuce. 1. Nutritional interactions and growth. Aust J Biol Sci 8:301–329Google Scholar
  16. Goodlass G, Rahn C, Shepherd MA, Chalmers AG, Seeney FM (1997) The nitrogen requirement of vegetables: comparisons of yield response models and recommendation systems. J Hortic Sci 72:239–254Google Scholar
  17. Greenwood DJ, Draycott A (1989a) Experimental validation of an N-response model for widely different crops. Fertil Res 18:153–174CrossRefGoogle Scholar
  18. Greenwood DJ, Draycott A (1989b) Quantitative relationships for growth and N-content of different vegetable crops grown with and without ample fertilizer-N on the same soil. Fertil Res 18:175–188CrossRefGoogle Scholar
  19. Greenwood DJ, Karpinets TV (1997a) Dynamic model for the effects of the K-fertiliser on crop growth, K-uptake, and soil-K in arable cropping. 1. Description of the model. Soil Use Manage 13:178–183CrossRefGoogle Scholar
  20. Greenwood DJ, Karpinets TV (1997b) Dynamic model for the effects of the K-fertiliser on crop growth, K-uptake, and soil-K in arable cropping. 2. Field test of the model. Soil Use Manage 13:184–189CrossRefGoogle Scholar
  21. Greenwood DJ, Stone DA (1998) Prediction and measurement of the decline in the critical-K, the maximum-K and total cation plant concentrations during the growth of field vegetable crops. Ann Bot (London) 82:871–881CrossRefGoogle Scholar
  22. Greenwood DJ, Wood JT, Cleaver TJ, Hunt J (1971) A theory of fertilizer response. J Agric Sci Camb 77:511–523Google Scholar
  23. Greenwood DJ, Cleaver TJ, Loquens SHM, Niendorf KB (1977) Relationships between plant weight and growing period for vegetable crops in the UK. Ann Bot (London) 41:987–997Google Scholar
  24. Greenwood DJ, Gerwitz A, Stone DA, Barnes A (1982) Root development of vegetable crops. Plant Soil 68:75–92CrossRefGoogle Scholar
  25. Greenwood DJ, Neeteson JJ, Draycott A (1985) Response of potatoes to N-fertilizer: dynamic model. Plant Soil 85:185–203CrossRefGoogle Scholar
  26. Greenwood DJ, Rahn CR, Draycott A, Vaidyanathan LV, Paterson CD (1996) Modelling and measurement of the effects of fertilizer-N and crop residue incorporation on N-dynamics in vegetable cropping. Soil Use Manage 12:13–24CrossRefGoogle Scholar
  27. Greenwood DJ, Karpinets TV, Stone D (2001a) Dynamic model for the effects of soil P and fertilizer P on crop growth, P uptake and soil P in arable cropping: model description. Ann Bot (London) 88:279–291CrossRefGoogle Scholar
  28. Greenwood DJ, Stone DA, Karpinets TV (2001b) Dynamic model for the effects of soil P and fertiliser P on crop growth, P uptake and soil P on arable cropping: experimental test of the model for field vegetables. Ann Bot (London) 88:293–306CrossRefGoogle Scholar
  29. Hoogenboom G, Wilkens PW, Tsuji GY (Eds) (1999) Decision support system for agrotechnology transfer (DSSAT) version 3, volume 4. Honolulu, HI: University of HawaiiGoogle Scholar
  30. Huffman EC, Yang JH, Gameda S, de Jong R (2001) Using simulation and budget models to scale-up nitrogen leaching from field to region in Canada. Sci World 1:699–706Google Scholar
  31. Karpinets TV, Greenwood DJ, Sams CE, Ammons JT (2006) RNA: protein ratio of the unicellular organism as a characteristic of phosphorus and nitrogen stoichiometry and of the cellular requirement of ribosomes for protein synthesis. BMC Biology 4:30PubMedCrossRefGoogle Scholar
  32. Knecht MF, Goransson A (2004) Terrestrial plants require nutrients in similar proportions. Tree Physiol 24:447–460PubMedGoogle Scholar
  33. Kramer PJ (1949) Plant and soil water relationships. McGraw Hill, New York, p 236Google Scholar
  34. Kristoffersen AO, Greenwood DJ, Sogn TA, Riley H (2006) Assessment of the dynamic phosphate model PHOSMOD using data from field trials with starter fertilizer to cereals. Nutr Cycl Agroecosyst 74:75–89CrossRefGoogle Scholar
  35. Leigh RA, Johnston AE (1986) An investigation into the usefulness of phosphorus concentrations in tissue water as indicators of phosphorus status in of field grown spring barley. J Agric Sci Camb 107:329–333Google Scholar
  36. Marschner H (1995) Mineral nutrition of higher plants, 2nd edn. Academic, London, p 889Google Scholar
  37. Mengel K, Kirkby EA (2001) Principles of plant nutrition, 5th edn. Kluwer, Dordrecht, pp 849Google Scholar
  38. Moss P (1969) A comparison of potassium activity ratios derived from equilibrium procedures and from measurements on displaced soil solution. J Soil Sci 20:297–306CrossRefGoogle Scholar
  39. Niklas KJ (2006) Plant allometry, leaf nitrogen and phosphorus stoichiometry and interspecific trends in annual growth rates. Ann Bot (London) 97:155–163PubMedCrossRefGoogle Scholar
  40. Olsen SR, Cole CV, Watanabe FS, Dean LA (1954) Estimation of available phosphorus by extraction with sodium bicarbonate (Circular 39). USDA, Washington, DCGoogle Scholar
  41. Paris Q (1992) The return of von Liebig’s “Law of the minimum”. Agron J 84:1040–1046CrossRefGoogle Scholar
  42. Poorter H, Nagel O (2000) The role of biomass allocation in the growth response of plants to different light levels of light, CO2, nutrients and water: a quantitative review. Aust J Plant Physiol 27:595–607CrossRefGoogle Scholar
  43. Register of Ecological Models 2007 http://eco.wiz.uni-kassel.de/ecobas.html
  44. Riley D, Barber SA (1971) Effect of ammonium and nitrate fertilization on phosphorus uptake as related to root induced pH changes at the root–soil interface. Proc Soil Sci Soc Am 35:301–306CrossRefGoogle Scholar
  45. Riley H, Guttormsen G (1993) N requirements of cabbage plants grown on contrasting soils. 2 Model verification and predictions. Nor J Agric Sci 8:99–113Google Scholar
  46. Rubio G, Zhu J, Lynch JP (2003) A critical test of two prevailing theories of plant response to nutrient availability. Am J Bot 90:143–152Google Scholar
  47. Ruhlmann J (1999) Calculation of net mineralization from the decomposable soil organic matter pool. Acta Hortic 506:167–173Google Scholar
  48. Russell EW (1973) Soil conditions and plant growth, 10th Edn. Longman, London, pp 849Google Scholar
  49. Scaife MA (1968) Maize fertilizer experiments in Western Tanzania. J Agric Sci Camb 70:209–222Google Scholar
  50. Sterner RW, Elser J (2002) Ecological stoichiometry. The biology of elements from molecules to the biosphere. Princeton University Press, Princeton, pp 439Google Scholar
  51. Taylor JD, Day JM, Dudley CL (1983) The effect of Rhizobium inoculation and nitrogen fertiliser on nitrogen fixation and seed yield of dry beans (Phaseolus vulgaris). Ann Appl Biol 103:419–429CrossRefGoogle Scholar
  52. Tinker PB, Nye PH (2000) Solute movement in the rhizosphere. Oxford University Press, Oxford, pp 444Google Scholar
  53. Whitfield WAD (1974) The soils of the National Vegetable Research Station, Wellesbourne. In: Report of the National Vegetable Research Station for 1973. The British Society for the promotion of vegetable research, Wellesbourne, UK, pp 21–30Google Scholar
  54. Williams JR, Jones CA, Dyke PT (1993) The Epic model. In: Sharpley AN, Williams JR (eds) Epic–erosion productivity impact calculator. 1. Model documentation. US Department of Agriculture Technical Bulletin no. 1768. USDA: Washington, DC, pp 92Google Scholar
  55. Wood JT, Greenwood DJ, Cleaver TJ (1972) Interaction between the beneficial effects of nitrogen, phosphate and potassium on plant growth. J Agric Sci Camb 78:389–391CrossRefGoogle Scholar
  56. Wright IJ et al (2004) The worldwide leaf economics spectrum. Nature 428:821–827PubMedCrossRefGoogle Scholar
  57. Yang J, Wadsworth GA, Rowell DL, Burns IG (1999) Evaluating a crop nitrogen simulation model, N_ABLE using a field experiment with lettuce. Nutr Cycl Agroecosyst 55:221–230CrossRefGoogle Scholar
  58. Yang J, Rowell DL, Burns IG, Guttormsen G, Riley H, Wadsworth GA (2002) Modification and evaluation of the crop nitrogen model N_ABLE using Norwegian field data. Agric Syst 72:241–261CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  • Kefeng Zhang
    • 1
  • Duncan J. Greenwood
    • 1
  • Philip J. White
    • 1
    • 2
  • Ian G. Burns
    • 1
  1. 1.Warwick HRIThe University of WarwickWellesbourneUK
  2. 2.Scottish Crop Research InstituteInvergowrieUK

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