Cited by 310Crop Yield and Soil FertilityAgriculture, Soil, Plant ScienceAgronomic Practices and Intercropping Systems

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The Quantitative Relationships Between Plant Population And Crop Yield

Willey, R.W., Heath, S.B.·1969·Advances in Agronomy

DOI 10.1016/s0065-2113(08)60100-5

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A Flexible Growth Function for Empirical Use
Richards, F. (1959) · Journal of Experimental Botany · doi:10.1093/jxb/10.2.290 · Cited by 4,275
Competition Among Crop and Pasture Plants
Donald, C. (1963) · Advances in agronomy · doi:10.1016/s0065-2113(08)60397-1 · Cited by 710
Plant Population and Crop Yield
Holliday, R. (1960) · Nature · doi:10.1038/186022b0 · Cited by 285
Effect of Plant Population and Row Spacing on Soybean Development and Production1
Weber, C. R., Shibles, R. M., & Byth, D. E. (1966) · Agronomy Journal · doi:10.2134/agronj1966.00021962005800010034x · Cited by 200
Competition among wheat plants sown at a wide range of densities
Puckridge, D., & Donald, C. (1967) · Australian Journal of Agricultural Research · doi:10.1071/ar9670193 · Cited by 185
Plant Population and Crop Yield
Bleasdale, J. K. A., & Nelder, J. A. (1960) · Nature · doi:10.1038/188342a0 · Cited by 146
A Relationship between Individual Plant-spacing and Yield
Mead, R. (1966) · Annals of Botany · doi:10.1093/oxfordjournals.aob.a084076 · Cited by 120
Competition among pasture plants. I. Intraspecific competition among annual pasture plants
Donald, C. (1951) · Australian Journal of Agricultural Research · doi:10.1071/ar9510355 · Cited by 104
Influence of Population and Nitrogen Levels on Yield and Protein and Oil Contents of Nine Corn Hybrids1
Lang, A. L., Pendleton, J. W., & Dungan, G. H. (1956) · Agronomy Journal · doi:10.2134/agronj1956.00021962004800070002x · Cited by 88
A Mathematical Model for the Estimation of Inter-Plant Competition
Mead, R. (1967) · Biometrics · doi:10.2307/2528155 · Cited by 85

Show all 35 references

Research works printed but not linked: 23

Bruinsma, 1966, Neth. J. Agr. Sci., 14, 198
Crawford, 1964, New Zealand J. Agr., 108, 455
de Wit, 1959, Jaarb. Inst. Biol. Scheik. Onders. LandbGewass. Meded., 83, 129
de Wit, 1960, Verslag. Landbouwk. Onderzoek., 66.8, 1
de Wit, 1958, Jaarb. Inst. Biol. Scheik. Onderz. LandbGewass. Meded., 50, 59
Dumanovic, 1962, Savremera Polio Priverda, 4, 240
Farazdaghi, H. 1968. Ph.D. Thesis, Reading University, England.
Goodall, 1960, Bull. Res. Council Israel, D8, 181
Harvey, 1958, Exptl. Husbandry, 3, 31
Holliday, 1960, Field Crop Abstr., 13, 159
Hozumi, 1956, J. Inst. Polytech., Osaka City Univ., D7, 15
Jones, 1968, Agr. Prog., 42, 32
Kira, 1953, J. Inst. Polytech., Osaka City Univ., D4, 1
Kira, 1954, J. Inst. Polytech., Osaka City Univ., D5, 1
Kira, 1956, J. Inst. Polytech., Osaka City Univ., D7, 1
Koyama, 1956, J. Inst. Polytech., Osaka City Univ., D7, 73
Mitscherlich, 1919, Landwirtsch. Jahrb., 53, 341
Montgomery, 1912, Nebraska Univ., Agr. Expt. Sta., Bull., 24
Reestman, 1959, Neth. J. Agri. Sci., 7, 257
Reynolds, 1950, Agriculture (London), 56, 527
Saunt, J. 1960. M.Sc. Thesis, University of Leeds, England.
Shinozaki, 1956, J. Inst. Polytech., Osaka City Univ., D7, 35
Willey, R. W. 1965. Ph.D. Thesis, Leeds University, England.

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Shrestha, A., Rajčan, I., Chandler, K., & Swanton, C. J. (2001) · Weed Technology · doi:10.1614/0890-037x(2001)015[0517:aiwmsf]2.0.co;2 · Cited by 36
“Willey and Heath (1969) suggested that in the absence of weeds, the response of crop yield to increased crop density was quite variable.”
Background
Broccoli (Brassica oleraceavar.botrytis) Yield Loss from Italian Ryegrass (Lolium perenne) Interference
Bell, C. E. (1995) · Weed Science · doi:10.1017/s0043174500080917 · Cited by 36
“Italian ryegrass density was compared to Italian ryegrass biomass using a reciprocal linear regression model (13).”
Method
Agriculture, Statistics In
Freeman, G. H. (2004) · Encyclopedia of Statistical Sciences · doi:10.1002/0471667196.ess0025 · Cited by 36
The effect of plant population on peanuts (Arachis hypogaea) in a monsoonal tropical environment
Bell, M. J., Muchow, R. C., & Wilson, G. L. (1987) · Field Crops Research · doi:10.1016/0378-4290(87)90085-2 · Cited by 35
SELF-THINNING IN EARLY POSTFIRE CHAPARRAL SUCCESSION: MECHANISMS, IMPLICATIONS, AND A COMBINED APPROACH
Guo, Q., & Rundel, P. W. (1998) · Ecology · doi:10.1890/0012-9658(1998)079[0579:stiepc]2.0.co;2 · Cited by 35
Evaluation of the groundnut model PNUTGRO for crop response to plant population and row spacing
Singh, P., Boote, K. J., & Virmani, S. M. (1994) · Field Crops Research · doi:10.1016/0378-4290(94)90018-3 · Cited by 32
Effect of plant density on grain yield and yield stability of sorghum hybrids differing in maturity
Wade, L. J., & Douglas, A. (1990) · Australian Journal of Experimental Agriculture · doi:10.1071/ea9900257 · Cited by 32
“Variation in hybrid yield response to density was further examined using the reciprocal relationship between grain weight per plant and density (Willey and Heath 1969).”
Growth and Yield of White Lupin Under Mediterranean Conditions
López‐Bellido, L., Fuentes, M., & Castillo, J. E. (2000) · Agronomy Journal · doi:10.2134/agronj2000.922200x · Cited by 32
Plant–Plant Interactions in Tropical Agriculture
Vandermeer, J. H. (2002) · CRC Press eBooks · doi:10.1201/9781420039887-5 · Cited by 31
Plant density and yield of grain maize in England
Bunting, E. S. (1973) · The Journal of Agricultural Science · doi:10.1017/s0021859600086512 · Cited by 31
Crop–Weed Competition
Gallandt, E. R., & Weiner, J. (2015) · Encyclopedia of Life Sciences · doi:10.1002/9780470015902.a0020477.pub2 · Cited by 31
EFFECT OF PLANT DENSITY ON THE YIELD OF SORGHUM–COWPEA AND PEARL MILLET–COWPEA INTERCROPS IN NORTHERN NIGERIA
Craufurd, P. (2000) · Experimental Agriculture · doi:10.1017/s0014479700003124 · Cited by 29
“Relations between dry matter yields, both biomass (BY) and seed (SY), and plant density (D) can be analysed by regressing the reciprocal of BY and SY per plant on plant density (Willey and Heath, 1969; Craufurd, 1996) 1/BY or 1/SY= a+ b*D (1) where a and b are constants.”
Background
Nuisibilité et seuils de nuisibilité des mauvaises herbes dans une culture annuelle : situation de concurrence bispécifique
Caussanel, J. P. (1989) · Agronomie · doi:10.1051/agro:19890301 · Cited by 29
The relationship between crop yield (or mean plant weight) of lettuce and plant density, length of growing period, and initial plant weight
Scaife, M. A., & Jones, D. A. C. (1976) · The Journal of Agricultural Science · doi:10.1017/s002185960006500x · Cited by 29
Simulation of multiple cropping systems with CropSys
Caldwell, R. M., & Hansen, J. (1993) · Systems approaches for sustainable agricultural development · doi:10.1007/978-94-011-2840-7_24 · Cited by 28

Authors: Willey, R. W., & Heath, S. B.
Affiliations: University of Reading (GB)
Venue: Advances in Agronomy
Publisher: Elsevier
Published: 1969
Pages: 281-321
ISSN: 0065-2113 (ISSN-L)
DOI: 10.1016/s0065-2113(08)60100-5
OpenAlex: W1432766941
Cited by: 310
References: 35
Citations by year: 2026: 2 · 2025: 5 · 2024: 8 · 2023: 8 · 2022: 3 · 2021: 5 · 2020: 5 · 2019: 3 · 2018: 8 · 2017: 5 · 2016: 6 · 2015: 3 · 2014: 7 · 2013: 4 · 2012: 9
FWCI: 6.25
Type: book chapter
Language: en
Open access: closed
Locations: Advances in agronomy (publishedVersion)
Topics: Life Sciences › Agricultural and Biological Sciences › Agronomy and Crop Science › Crop Yield and Soil Fertility
Life Sciences › Agricultural and Biological Sciences › Agronomy and Crop Science › Agriculture, Soil, Plant Science
Life Sciences › Agricultural and Biological Sciences › Agronomy and Crop Science › Agronomic Practices and Intercropping Systems
Keywords: plant population, crop yield, plant density, yield-density relationship, competition (biology), mathematical model, reciprocal equations, yield prediction, crop density

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