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Yield-densityequations and their application for agronomic research: a review

Review Paper | October 1, 2011

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Ibrahim Yahuza

Key Words: Yield-density equations, Asymptotic response, Parabolic response

Int. J. Biosci.1( 5), 1-17, October 2011


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Plant population density (density) trials are time consuming, repetitive and cost intensive. The literatures indicate that density trials are more effectively and efficiently described when meaningful yield-density equations such as reciprocal linear and/or parabolic equations are applied to quantify data. Several of these types of equations and their derivatives such as competitive indices have been proposed. It is generally agreed that where response to density deviated from linearity, equations based on linear reciprocal of yield per plant and density can satisfactorily describe an asymptotic response. In certain cases when the harvest index is substantially affected by density and/or due to unfavorable growth conditions, equations that assumed parabolic responses may be more valid. The review by Willey and Heath (1969) on the quantitative response of yield to density appears to have remained a useful resource up to date. However, more recently, several investigations based on reciprocal quantitative relationships between yields and density and how this may be influenced by other agronomic practices were carried out. Yet, most of these substantial knowledge and progress on yield-density investigations appear to be scattered in published or unpublished works as no attempt has been made to collate them together. This paper reviews more recent progress on yield-density equations research and their application, and highlights needs for the applications of some of these equations for agronomic research with more emphasis given to intercropping.


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Yield-densityequations and their application for agronomic research: a review

Azam-Ali SN, Squire GR. 2002. Principles of Tropical Agronomy. Wallingford, UK: CABI.

Azam-Ali SN, Nageswara RC, Craigon J, Wadia KDR, Williams JH. 1993. A method for calculating the population/yield relations of groundnut (Arachis hypogeae) in semi-arid climates. Journal of Agricultural Sciences 121, 213-222.

Baumann DT, Bastiaans L, Kropff MJ. 2001. Competition and crop performance in a leek-celery intercropping system. Crop Science 41, 764-774.

Bleasdale JKA. 1966a. Plant growth and crop yield. Annals of Applied Biology 57, 173-182.

Bleasdale JKA. 1966b. The effects of plant spacing on the yield of bulb onions (Allium cepa L.) grown from seed. Journal of Horticultural Science 41, 145-153.

Bleasdale JKA. 1967. The relationship between the weight of a plant part and total weight as affected by plant density. Journal of Horticultural Science 42, 51-58.

Bleasdale JKA. 1984. Plant Physiology in Relation to Horticulture, 2nd edition. London: MacMillan.

Bleasdale JKA, Nelder JA. 1960. Plant population and crop yield. Nature 188, 342.

Bulson HAJ. 1991. Intercropping wheat with field beans in organic farming systems. PhD Thesis, University of Reading, United Kingdom.

Bulson HAJ, Snaydon RN, Stopes CE. 1997. Effects of plant density on intercropped wheat and field beans in an organic farming system. Journal of Agricultural Sciences 128, 59-71.

Connolly J. 1987. On the use of response models in mixture experiments. Oecologia 72, 95-103.

Counce PA. 1987. Asymptotic and parabolic yield and linear nutrient content responses to rice population density. Agronomy Journal 79, 864-869.

Craufurd PQ. 1996. Effects of plant population density on dry matter partitioning and yield in a short-duration cultivar of cowpea (Vigna unguiculata) grown in the tropics. Journal of Agricultural Science 127, 89-96.

Craufurd PQ. 2000. Effect of plant density on the yield of sorghum-cowpea and pearl millet-cowpea intercrops in northern Nigeria. Experimental Agriculture 36, 379-395.

Dolman G. 1985. Density trials with systematic designs on intercropped carrots and onions. PhD Thesis, University of Reading, United Kingdom.

Ellis RH, Salahi M. 1997. Optimizing inputs for contrasting cultivars: Quantifying the effects of plant population density and nitrogen fertilizer on the yield of four cultivars of spring wheat. Aspects of Applied Biology 50, 139-146.

Ellis RH, Salahi M, Jones SA. 1999. Yield-density equations can be extended to quantify the effect of applied nitrogen and cultivar on wheat grain yield. Annals of Applied Biology 134, 347-352.

Farazdaghi H, Harris PM. 1968. Plant competition and crop yield. Nature 217, 289-290.

Firbank LG, Watkinson AR. 1985. On the analysis of competition within two-species mixtures of plants. Journal of Applied Ecology 22, 503–517.

Francis CA. 1989. Biological efficiencies in multiple-cropping systems. Advances in Agronomy 42, 1-42.

Fukai S, Trenbath BR. 1993. Processes determining intercrop productivity and yields of component crops. Field Crops Research 34, 247-271.

Giunta F, Pruneddu G, Motzo R. 2009. Radiation interception, biomass and nitrogen accumulation in different cereal and grain legume species. Field Crops Research 110, 76-84.

Gooding MJ., Pinyosinwat A, Ellis RH. 2001. The response of wheat grain nitrogen concentration to plant population density. Aspects of Applied Biology 64, 157-162.

Gooding MJ, Pinyosinwat A, Ellis RH. 2002. Responses of wheat grain yield and quality to seed rate. Journal of Agricultural Science 138, 317-331.

Heath SB. 1970. An examination of the biological significance, which can be attributed to the quantitative relationships between plant population and crop yield. PhD Thesis, University of Reading, United Kingdom.

Helenius J, Jokinen K. 1994. Yield advantage and competition in intercropped oats (Avena sativa L.) and faba bean (Vicia faba L.): application of the hyperbolic yield-density model. Field Crops Research 37, 85-94.

Holliday R. 1960a. Plant population and crop yield: part I: Field Crop Abstracts 13, 159-167.

Holliday R. 1960b. Plant population and crop yield: part II: yield and plant population in British crops. Field Crop Abstract 13, 247-254.

Holliday R. 1960c. Plant population and crop yield. Nature 186, 22-24.

Innis D. 1997. Intercropping and the scientific basis of traditional agriculture. London, UK: Intermediate Technology publication.

Khah EM, Roberts EH, Ellis RH. 1989. Effect of seed ageing on growth and yield of spring wheat at different plant-population densities. Field Crops Research 20, 175-190.

Kindred DR, Gooding MJ. 2005. Heterosis for yield and its physiological determinants in wheat. Euphytica 142, 149-159.

Law R, Watkinson AR. 1987. Response-surface analysis of two species competition: An experiment on Phleum arenarium and Vulpia fasciculata. The Journal of Ecology 75, 871-886.

Li B, Watkinson AR. 2000. Competition along a nutrient gradient: A case study with Daucus carota and Chenopodium album. Ecological Research, 15, 293-306.

Mead R. 1970. Plant density and crop yield. Applied Statistics 19, 64-81.

Mead R. 1979. Competition experiments. Biometrics 35, 41-54.

Mligo JK, Craufurd PQ. 2007. Productivity and optimum plant density of pigeonpea in different environment in Tanzania. Journal of Agricultural Science 145, 343-351.

Neumann A, Werner J, Rauber R. 2009. Evaluation of yield-density relationships and optimization of intercrop compositions of field grown pea-oat intercrops using the replacement series and the response surface design. Field Crops Research 114, 286-294.

Ofori F, Stern WR. 1987. Cereal-legume intercropping systems. Advances in Agronomy 41, 41-90.

Park SE, Benjamin LR, Watkinson AR. 2002. Comparing biological productivity in cropping systems: A competition approach. The Journal of Applied Ecology 39, 416-426.

Pinyosinwat A. 2001. The effect of seed rate on the yield and quality of wheat and its interaction with other agronomy practices. PhD Thesis, University of Reading, United Kingdom.

Rejmanek M, Robinson GR, Rejmankova E. 1989. Weed-crop competition: experimental designs and models for data analysis. Weed Science 37, 276-284.

Salahi MM. 2002. Yield and quality of cereals in response to input and spatial variability. PhD Thesis, University of Reading, United Kingdom.

Shainsky LJ, Radosevich SR. 1992. Mechanisms of competition between Douglas-fir and red alder seedlings. Ecology 73, 30-45.

Shinozaki K, Kira T. 1956. Intraspecific competition among higher plants. VII. Logistic theory of the C-D effect. Journal of the Institute Polytechnic Osaka City , University Series D7, 35-72.

Shirtliffe SJ, Johnston AM. 2002. Yield-density relationships and optimum plant populations in two cultivars of solid-seeded dry bean (Phaseolus vulgaris L.) grown in Saskatchewan . Canadian Journal of Plant Science 82, 521-529.

Spitters CJT. 1983. An alternative approach to the analysis of mixed cropping experiments. 1. Estimation of competition effects. Netherlands Journal of Agricultural Science 31, 1-11.

Tollenaar H. 1992. Reinterpretation and evaluation of some simple descriptive models for weed-crop interference in terms of one-sided and two-sided competition. Oikos 65, 256-264.

Vandermeer J. 1989. The Ecology of intercropping. Cambridge, UK: Cambridge University press.

Watkinson AR. 1981. Interference in pure and mixed populations of Agrostemma githago . Journal of Applied Ecology 18, 967-976.

Watkinson AR, Freckleton RP. 1997. Quantifying the impact of arbuscular mycorrhiza on plant competition. Journal of Ecology 85, 541–545.

Weigelt A, Schumacher J, Walther T, Bartelheimer M, Steinlein T, Beyschlag W. 2007. Identifying mechanisms of competition in multi-species communities. Journal of Ecology 95, 53-64.

Willey RW. 1985. Evaluation and presentation of intercropping advantages Experimental Agriculture 21, 119-133.

Willey RW, Heath SB. 1969. The quantitative relationship between plant population and crop yield. Advances in Agronomy 21, 281-321.

Wright AJ. 1981. The analysis of yield-density relationship in binary mixtures using inverse polynomials. Journal of Agricultural Science 96, 561-567.