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The Quantitative Relationships Between Plant Population And Crop Yield
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“The expected grain yield response to plant density in winter wheat (Triticum aestivum L.) follows a diminishing returns function.”
From A Bayesian framework to model variance of grain yield response to plant density (2025) · cites this paper as [48]
In the citing paper
“The mathematical equation of expected yield response to plant density can vary from quadratic [26, 30], quadratic-plateau [48], linear-plateau [4, 28] or exponential rise to maximum [27, 39, 48].”
From A Bayesian framework to model variance of grain yield response to plant density (2025) · cites this paper as [48]
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Intercropped Corn–Soyabean Density Studies. I. Yield Complementarity
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“Since competition between plants greatly affect yield [3,7] it is therefore possible to adjust size of the harvested crop to meet the requirements of the market by manipulating density [8].”
BackgroundRelationships between combined and individual field crops’ biomass and planting density
Friedman, S. P. (2023) · Field Crops Research · doi:10.1016/j.fcr.2023.109188 · Cited by 28
Traditional agrodiversity management: A case study of central himalayan village ecosystem
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Plant density and yield of shoot dry material in maize in England
Bunting, E. S. (1971) · The Journal of Agricultural Science · doi:10.1017/s002185960002428x · Cited by 24
Effects of Seeding Rate on Durum Crop Production and Physiological Responses
y Sánchez, J. I., Perry, B., Singh, A. K., Wang, H., DePauw, R. M., Pozniak, C. J., Beres, B. L., Johnson, E. N., & Cuthbert, R. D. (2017) · Agronomy Journal · doi:10.2134/agronj2016.09.0527 · Cited by 22
“In wheat, the SR for maximum grain yield was derived from the parabolic response curve which quickly reaches a maximum yield followed by a slow decline at high densities (Beres et al., 2011, 2010; Puckridge and Donald, 1967; Kirby, 1969; Willey and Heath, 1969).”
BackgroundSoeton, O., & Puckridge, D. (1982) · Australian Journal of Agricultural Research · doi:10.1071/ar9820171 · Cited by 23
Willey, R. W., & Rao, M. R. (1981) · Experimental Agriculture · doi:10.1017/s0014479700011248 · Cited by 23
Self-citationPlant density affects measures of biodiversity effects
Stachová, T., Fibich, P., & Lepš, J. (2012) · Journal of Plant Ecology · doi:10.1093/jpe/rts015 · Cited by 22
Vertical growth of mini watermelon according to the training height and plant density
Campagnol, R., Mello, S. D. C., & Barbosa, J. C. (2012) · Horticultura Brasileira · doi:10.1590/s0102-05362012000400027 · Cited by 22
“Increased plant density usually, for most species, raises biomass productivity to a certain limit, after which productivity remains equal or decreases (Willey & Heath, 1969).”
BackgroundYield-density equations and their application for agronomic research: a review.
Yahuza, I. (2011) · International Journal of Biosciences (IJB) · Cited by 22
Effects of Plant Density on Growth and Biomass Partitioning in Pickling Cucumbers
Widders, I. E., & Price, H. C. (1989) · Journal of the American Society for Horticultural Science · doi:10.21273/jashs.114.5.751 · Cited by 22
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Covariance of cropping systems and foxtail density as predictors of weed interference
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Weed reproduction model parameters may be estimated from crop yield loss data
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Evaluating the effects of competitive interference on plant performance
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Optimizing Seeding Rate for Late‐Seeded Winter Wheat in the Middle Atlantic Region
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Water use of maize in response to planting density and irrigation
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Les besoins en azote du blé d'hiver jusqu'au début de la montaison
Meynard, J.-M. (1985) · Agronomie · doi:10.1051/agro:19850703 · Cited by 17
“Nous nous sommes donc tourné vers un modèle beaucoup plus simple, celui de SI-IINOZAK & KIRA (cités par WILLEY & HEATH, 1969), qui exprime la réponse de la biomasse aérienne à la densité de plantes (NP), en utilisant un petit nombre de paramètres ayant une signification biologique : Ce modèle…”
BackgroundIV. Daylength, plant density and cultivar effects
Regel, P. A., & Sands, P. (1983) · Field Crops Research · doi:10.1016/0378-4290(83)90044-8 · Cited by 17
Nadali, B. J., Arvind, B., Kamaruzaman, M., & Keng, C. L. (2014) · Journal of Medicinal Plants Research · doi:10.5897/jmpr11.1053 · Cited by 18
“Plant population density and its components of interand intra-row spacing are important in determining yield and the practicability of both weed control and harvesting (Willey and Heath, 1969; Ratkowsky, 1983).”
BackgroundJones, M. J. (1987) · Experimental Agriculture · doi:10.1017/s0014479700017221 · Cited by 17
Salter, P. J., Andrews, D. J., & Akehurst, J. M. (1984) · Journal of Horticultural Science · doi:10.1080/00221589.1984.11515172 · Cited by 17
Planting date and row spacing effects on the agronomic potential of sesame in the southeastern USA
Gloaguen, R., Byrd, S. A., Rowland, D., Langham, D. R., & Couch, A. (2018) · Journal of Crop Improvement · doi:10.1080/15427528.2018.1434093 · Cited by 16
“In fact, the S26 CV in the 2014 Live Oak site was the only CV that had a parabolic relationship between density and yield, similar to that found by Willey and Heath (1969).”
MethodResultLiu, X. B., Herbert, S. J., Zhang, Q. Y., & Hashemi, A. M. (2006) · Journal of Agronomy and Crop Science · doi:10.1111/j.1439-037x.2006.00241.x · Cited by 16
Rees, D. J. (1986) · Experimental Agriculture · doi:10.1017/s001447970001423x · Cited by 16
Marker-Assisted Breeding in Sorghum
Madhusudhana, R. (2018) · Elsevier eBooks · doi:10.1016/b978-0-08-101879-8.00006-1 · Cited by 15
Wurr, D. C. E., Fellows, J. R., Sutherland, R. A., & Allen, E. J. (1990) · The Journal of Agricultural Science · doi:10.1017/s0021859600070945 · Cited by 15
Al‐Barzinjy, M., Stølen, O., Christiansen, J. L., & Jensen, J. E. (1999) · Acta Agriculturae Scandinavica Section B - Soil & Plant Science · doi:10.1080/09064719909362508 · Cited by 15
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Self-citationEcological Effects of Barnyardgrass on Soybeans in a Greenhouse
Maun, M. A. (1977) · Weed Science · doi:10.1017/s0043174500033099 · Cited by 15
Ellis, R. H., Salahi, M., & Jones, S. A. (1999) · Annals of Applied Biology · doi:10.1111/j.1744-7348.1999.tb05275.x · Cited by 14
Detection of Corn Plant Population and Row Spacing Using Computer Vision
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Seed quality and seedling emergence in onion(Allium cepaL.)
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Row cover and population density effects on yield of bell peppers in south coastal British Columbia
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Responses to precision planting in canola and grain legume crops
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Winter wheat response to plant density in yield contest fields
Lollato, R. P., Pradella, L. O., Giordano, N., Ryan, L. P., Soler, J. R., Simão, L. M., Jaenisch, B. R., & Horton, R. (2024) · Crop Science · doi:10.1002/csc2.21296 · Cited by 17
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Models for plant self‐thinning
Wade, R. K. (2018) · Ecosphere · doi:10.1002/ecs2.2219 · Cited by 13
Relationships of Plant Density and Harvest Index to Seed Yield and Quality in Carrot
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“The total dry matter produced per unit area (biological yield), on the other hand, approaches a maximum plateau at moderate to high densities (3, 17).”
BackgroundDensity effects and self-thinning in even-aged pure stands ofEucalyptus camaldulensis Dehn
Thoranisorn, S., Sahunalu, P., & Yoda, K. (1990) · Journal of Plant Research · doi:10.1007/bf02488640 · Cited by 13
Competition between cyanogenic and acyanogenic morphs of Trifolium repens
Noïtsakis, B., & JACQUARD, P. (1992) · Theoretical and Applied Genetics · doi:10.1007/bf00226532 · Cited by 13
The effect of spacing on the growth of two genotypes of perennial ryegrass
Simons, R. G., Davies, A., & Troughton, A. (1973) · The Journal of Agricultural Science · doi:10.1017/s0021859600058147 · Cited by 13
Plant Competition and its Implications for Cultural Methods in Calabrese
Thompson, R., & Taylor, H. (1976) · Journal of Horticultural Science · doi:10.1080/00221589.1976.11514674 · Cited by 13
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“Wiley and Heath [34] recognized that understanding the yield response curve to seeding rate was useful for making seeding rate decisions in different cropping systems and production settings.”
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Competitiveness of Herbicide-Resistant Waterhemp (Amaranthus tuberculatus) with Soybean
Butts, T. R., Vieira, B. C., Latorre, D. D. O., Werle, R., & Kruger, G. R. (2018) · Weed Science · doi:10.1017/wsc.2018.45 · Cited by 12
“The biological implications of the a and b constants have previously been discussed in the literature (Willey and Heath 1969).”
BackgroundInfluentialIshikawa, H., Batieno, B. J., Fatokun, C. A., & Boukar, O. (2022) · Agriculture · doi:10.3390/agriculture12020199 · Cited by 12
“Generally, yields do not increase linearly with an increase in plant density due to interplant competition [22,28,33].”
BackgroundLynch, D. R., Kozub, G. C., & Kawchuk, L. M. (2001) · American Journal of Potato Research · doi:10.1007/bf02874763 · Cited by 12
Cadmium accumulation in Agaricusblazei Murrill
Huang, J. C., Li, K. B., Yu, Y. R., Wu, H., & Liu, D. L. (2008) · Journal of the Science of Food and Agriculture · doi:10.1002/jsfa.3225 · Cited by 12
Stanhill, G. (1977) · Annals of Botany · doi:10.1093/oxfordjournals.aob.a085324 · Cited by 12
Population density studies with Russet Burbank I. Yield/stem density models
Lynch, D. R., & Rowberry, R. G. (1977) · American Journal of Potato Research · doi:10.1007/bf02851873 · Cited by 12
“A similar exception to the basic relationship has been reported for Red Globe beet by Willey and Heath (30).”
BackgroundInfluentialRendimento de híbridos de melão amarelo em diferentes densidades de plantio
Grangeiro, L. C., Pedrosa, J. F., Neto, F. B., & de Negreiros, M. Z. (1999) · Horticultura Brasileira · doi:10.1590/s0102-05361999000300005 · Cited by 12
Radiation-Use Efficiency Under Different Climatic Conditions
Bhattacharya, A. (2019) · Elsevier eBooks · doi:10.1016/b978-0-12-816209-5.00002-7 · Cited by 14
Han, Z., Liu, T., Sun, Q., Li, R., Xie, J., & Li, B.-L. (2014) · Ecological Modelling · doi:10.1016/j.ecolmodel.2014.01.024 · Cited by 11
Canner, S. R., Wiles, L. J., Erskine, R. H., McMaster, G. S., Dunn, G. H., & Ascough, J. C. (2009) · Weed Science · doi:10.1614/ws-08-036.1 · Cited by 11
“These three relationships have often been described by a class of equations called ‘‘rectangular hyperbolic equations’’ or ‘‘reciprocal yield equations’’ (Pacala 1986; Pacala and Silander 1990; Watkinson 1981; Weiner 1982; Willey and Heath 1969).”
BackgroundLi, L., Weiner, J., Wang, Y., Wang, S., & Zhou, D. (2016) · Plant Ecology · doi:10.1007/s11258-016-0616-7 · Cited by 11
“For example, unimodal density–productivity relationship has been documented for fruit or seed production (Willey and Heath 1969).”
BackgroundInfluentialSimulation of multiple cropping systems with CropSys
Caldwell, R. M., & Hansen, J. (1993) · Springer eBooks · doi:10.1007/978-94-011-2842-1_24 · Cited by 11
Chung, B. (1990) · The Journal of Agricultural Science · doi:10.1017/s0021859600075183 · Cited by 11
Cotton spacing experiments in Uganda
Hearn, A. B. (1972) · The Journal of Agricultural Science · doi:10.1017/s0021859600087633 · Cited by 11
Yield Components as Affected by Planting Dryland Maize in a Double-Skip Row Pattern
Pavlišta, A. D., Lyon, D. J., Baltensperger, D. D., & Hergert, G. W. (2010) · Journal of Crop Improvement · doi:10.1080/15427520903565307 · Cited by 10
“Reduction in prolificacy and development of second ear in P2S2 may be due to increased in-row crowding caused by halving the distance between plants in the row and is similar to PPD effects (Willey & Heath 1969; Motto & Moll 1983).”
ResultAdjustment for missing plants in cassava evaluation trials
Pérez, J. C., Ceballos, H., Ramírez, I. C., Lenis, J. I., Calle, F., Morante, N., Jaramillo, G., & Lentini, M. (2009) · Euphytica · doi:10.1007/s10681-009-0039-9 · Cited by 10
“The relationship between plant density and crop yield has received previous attention (Schmildt et al. 2001; Vencovsky and Cruz 1991; Verones et al. 1995; Willey and Heath 1969).”
BackgroundTHE EFFECT OF DIFFERENT ROW SPACINGS AND PLANT ARRANGEMENTS ON SOYBEANS
Safo-Kantanka, O., & Lawson, N. C. (1980) · Canadian Journal of Plant Science · doi:10.4141/cjps80-031 · Cited by 10
Leakey, C. L. A. (1972) · The Journal of Agricultural Science · doi:10.1017/s0021859600032238 · Cited by 10
Cultivar and management effects on industrial hemp yields in Wisconsin
Ortmeier‐Clarke, H. J., Laboski, C. A. M., de Oliveira, M. C., Arneson, N. J., Conley, S. P., & Werle, R. (2023) · Agronomy Journal · doi:10.1002/agj2.21297 · Cited by 9
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Plant–Plant Interactions in Tropical Agriculture
García‐Barrios, L. (2002) · Advances in agroecology · doi:10.1201/9781420039887.ch2 · Cited by 9
Modeling Plant Population and Rectangularity Effects on Broccoli Head Weights and Yield
Westcott, M. P., & Callan, N. W. (1990) · Journal of the American Society for Horticultural Science · doi:10.21273/jashs.115.6.893 · Cited by 9
“These attributes of the reciprocal form were cited as reasons for preference by Wiley and Heath (1969). for publication 5 Feb. 1990.”
BackgroundPlant Population and Irrigation Effects on Spanish Peanuts (Arachis hypogaea L.)1
Choy, E. W. C., Stone, J. F., Matlock, R. S., & McCauley, G. N. (1982) · Peanut Science · doi:10.3146/i0095-3679-9-2-7 · Cited by 9
Methods of analysing yield from trials in which the produce is graded according to diameter
Chapman, E. A. (1981) · The Journal of Agricultural Science · doi:10.1017/s002185960003584x · Cited by 9
Productivity and optimum plant density of pigeonpea in different environments in Tanzania
Mligo, J. K., & Craufurd, P. (2007) · The Journal of Agricultural Science · doi:10.1017/s0021859607006776 · Cited by 9
“All genotypersite responses to D were linear or asymptotic, except Kat 50/3 and QP 37 at Kibaha and QP 37 and Local at Ismani; they could therefore be quantified and compared using reciprocals of yield per plant (Eqn 1; Willey & Heath 1969).”
BackgroundInfluentialZhang, M., Xing, L., Ren, X., Zou, J., Song, F., Lei, W. A. N. G., & Miao-yun, X. U. (2022) · Journal of Integrative Agriculture · doi:10.1016/j.jia.2022.08.083 · Cited by 8
Predictions of non-linear responses to selection for forage yield under competition
Wright, A. J. (1977) · Theoretical and Applied Genetics · doi:10.1007/bf00274474 · Cited by 8
Fibich, P., & Lepš, J. (2011) · Ecological Modelling · doi:10.1016/j.ecolmodel.2011.04.013 · Cited by 8
Yields of upland and lowland taro at varying plant densities
Peña, R. (1978) · Field Crops Research · doi:10.1016/0378-4290(78)90021-7 · Cited by 8
EFFECTS OF PLANTING DENSITY AND DESIGN ON POD YIELD OF BUSH SNAP BEAN (Phaseolus vulgaris L.)
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MANAGING PLANT POPULATION AND COMPETITION IN FIELD CROPS
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Non-regular spatial patterns of plants and their effect on several agronomic traits per area
Hühn, M. (2000) · European Journal of Agronomy · doi:10.1016/s1161-0301(99)00041-6 · Cited by 8
“…constants k1, k2, k3, and k4 ( Kira et al., 1953; Shinozaki and Kira,the well-known agronomic fact that the yield increases with increasing uniformity of the spatial 1956, 1961; Bleasdale and Nelder, 1960; de Wit, 1960; Risser, 1969; Willey and Heath, 1969;distribution of the individual plants.”
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Modeling Plant Competition in Monocultures of Barley and Oilseed Rape
Fredshavn, J. R. (1993) · Acta Agriculturae Scandinavica Section B - Soil & Plant Science · doi:10.1080/09064719309410230 · Cited by 8
Interactions between genotype and density on the yield components of Zea mays:II. Grain production
Voldeng, H. D., & BLACKMAN, G. E. (1975) · The Journal of Agricultural Science · doi:10.1017/s0021859600071884 · Cited by 7
Selection of a Barley Yield Model Using Information–Theoretic Criteria
Jasieniuk, M., Taper, M. L., Wagner, N. C., Stougaard, R. N., Brelsford, M., & Maxwell, B. D. (2008) · Weed Science · doi:10.1614/ws-07-177.1 · Cited by 7
“Numerous functional specifications of the explanatory or predictor variables exist for each model type (reviewed in Willey and Heath 1969; Cousens 1985a,b; Cousens et al. 1987; Firbank and Watkinson 1990; Wagner et al. 2007).”
MethodGrowth and Vegetable Pod Yield of Edible Podded Pea as Influenced by Sowing Time and Plant Density
., M. S. I., Rahman, M. A., Salam, M. A., ., A. S. M. H. M., & Rahman, M. H. (2002) · Journal of Biological Sciences · doi:10.3923/jbs.2002.706.709 · Cited by 7
Craufurd, P. (1996) · The Journal of Agricultural Science · doi:10.1017/s0021859600077406 · Cited by 7
The effect of biofertilizer on soybean seed vigor and field emergence
Alahdadi, I., Tajik, M., Irannejad, H., & Armandpisheh, O. (2009) · Cited by 7
Metadata
- 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)
- 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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