EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 19 (2024) Math. Model. Nat. Phenom., 19 (2024) 21 References
Open Access
Issue
Math. Model. Nat. Phenom.
Volume 19, 2024
Article Number 21
Number of page(s) 18
Section Population dynamics and epidemiology
DOI https://doi.org/10.1051/mmnp/2024018
Published online 02 December 2024
  1. R.J. Hanks and V.P. Rasmussen, Predicting crop production as related to plant water stress. Adv. Agron. 35 (1982) 193–215. [CrossRef] [Google Scholar]
  2. J.E. Newman, Symposium: responses of field crops to environmental factors summary statements. Agron. J. 55 (1963) 31–31. [CrossRef] [Google Scholar]
  3. J.F. Farrar and M.L. Williams, The effects of increased atmospheric carbon dioxide and temperature on carbon partitioning, source-sink relations and respiration. Plant Cell Environ. 14 (1991) 819–830. [CrossRef] [Google Scholar]
  4. P. Stiling and T. Cornelissen, How does elevated carbon dioxide (co2) affect plant–herbivore interactions? A field experiment and meta-analysis of co2-mediated changes on plant chemistry and herbivore performance. Global Change Biol. 13 (2007) 1823–1842. [CrossRef] [Google Scholar]
  5. N.M. Crawford, Nitrate: nutrient and signal for plant growth. Plant Cell 7 (1995) 859. [PubMed] [Google Scholar]
  6. Z. Wang and S. Li, Effects of nitrogen and phosphorus fertilization on plant growth and nitrate accumulation in vegetables. J. Plant Nutr. 27 (2004) 539–556. [CrossRef] [MathSciNet] [Google Scholar]
  7. D.P. Aikman and L.R. Benjamin, A model for plant and crop growth, allowing for competition for light by the use of potential and restricted projected crown zone areas. Ann. Bot. 73 (1994) 185–194. [CrossRef] [Google Scholar]
  8. A. Barnes, The influence of the length of the growth period and planting density on total crop yield. Ann. Bot. 41 (1977) 883–895. [CrossRef] [Google Scholar]
  9. L.R. Benjamin and D.P. Aikman, Predicting growth in stands of mixed species from that in individual species. Ann. Bot. 76 (1995) 31–42. [CrossRef] [Google Scholar]
  10. J. Goudriaan and J.L. Monteith, A mathematical function for crop growth based on light interception and leaf area expansion. Ann. Bot. 66 (1990) 695–701. [CrossRef] [Google Scholar]
  11. H.J.W. Mutsaers, A dynamic equation for plant interaction and application to yield-density-time relations. Ann. Bot. 64 (1989) 521–531. [CrossRef] [Google Scholar]
  12. M.A. Scaife and D. Jones, The relationship between crop yield (or mean plant weight) of lettuce and plant density, length of growing period, and initial plant weight. J. Agric. Sci. 86 (1976) 83–91. [CrossRef] [Google Scholar]
  13. D.P. Aikman and A. Scaife, Modelling plant growth under varying environment conditions in a uniform canopy. Ann. Bot. 72 (1993) 485–492. [CrossRef] [Google Scholar]
  14. A. Scaife, E.F. Cox and G.E.L. Morris, The relationship between shoot weight, plant density and time during the propagation of four vegetable species. Ann. Bot. 59 (1987) 325–334. [CrossRef] [Google Scholar]
  15. F. Tei, D.P. Aikman and A. Scaife, Growth of lettuce, onion and red beet. 2. growth modelling. Ann. Bot. 78 (1996) 645–652. [CrossRef] [Google Scholar]
  16. F. Tei, A. Scaife and D.P. Aikman, Growth of lettuce, onion, and red beet. 1. Growth analysis, light interception, and radiation use efficiency. Ann. Bot. 78 (1996) 633–643. [CrossRef] [Google Scholar]
  17. S.A. Barber, Soil Nutrient Bioavailability: A Mechanistic Approach. John Wiley & Sons (1995). [Google Scholar]
  18. F.J. Molz, Models of water transport in the soil-plant system: A review. Water Resources Res. 17 (1981) 1245–1260. [CrossRef] [Google Scholar]
  19. T. Roose and A. Schnepf, Mathematical models of plant–soil interaction. Philos. Trans. Roy. Soc. A: Math. Phys. Eng. Sci. 366 (2008) 4597–4611. [CrossRef] [PubMed] [Google Scholar]
  20. N. Bessonov and V. Volpert, Dynamical models of plant growth. Mathematics Subject Classification (2000). [Google Scholar]
  21. N. Bessonov, F. Crauste and V. Volpert, Modelling of plant growth with apical or basal meristem. Math. Model. Natural Phenomena 6 (2011) 107–132. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  22. J.P. Baldwin, P.B. Tinker and P.H. Nye, Uptake of solutes by multiple root systems from soil: II. The theoretical effects of rooting density and pattern on uptake of nutrients from soil. Plant Soil 36 (1972) 693–708. [CrossRef] [Google Scholar]
  23. L. Dupuy, P.J. Gregory and A.G. Bengough, Root growth models: towards a new generation of continuous approaches. J. Exp. Bot. 61 (2010) 2131–2143. [CrossRef] [PubMed] [Google Scholar]
  24. R. Pearl and L.J. Reed, Skew-growth curves. Proc. Natl. Acad. Sci. U.S.A. 11 (1925) 16–22. [CrossRef] [PubMed] [Google Scholar]
  25. P.-F. Verhulst, Notice sur la loi que la population suit dans son accroissement. Correspondence Math. Phys. 10 (1838) 113–129. [Google Scholar]
  26. B. Gompertz, On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. in a letter to francis baily, esq. frs &c. by benjamin gompertz, esq. fr s, In Abstracts of the Papers Printed in the Philosophical Transactions of the Royal Society of London. The Royal Society London (1833) 252–253. [Google Scholar]
  27. D.P. Aikman, Tuning and validation illustrated by a model of plant competition. In: The art and craft of modelling in applied biology. Asp. Appl. Biol. 26 (1991) 122–134. [Google Scholar]
  28. A.G. Bengough, Modelling rooting depth and soil strength in a drying soil profile. J. Theor. Biol. 186 (1997) 327–338. [CrossRef] [Google Scholar]
  29. D.J. Greenwood, T.J. Cleaver, S.M.H. Loquens and K.B. Niendorf, Relationship between plant weight and growing period for vegetable crops in the United Kingdom. Ann. Bot. 41 (1977) 987–997. [CrossRef] [Google Scholar]
  30. M.A.P. de León and B.N. Bailey, Evaluating the use of Beer’s law for estimating light interception in canopy architectures with varying heterogeneity and anisotropy. Ecol. Model. 406 (2019) 133–143. [CrossRef] [Google Scholar]
  31. M. Monsi, The light factor in plant communities and its significance for dry matter production. Jap. J. Bot. 14 (1953) 22. [Google Scholar]
  32. J.S. Huxley, Problems of Relative Growth. Dial Press, New York (1932). [Google Scholar]
  33. H. Nagashima and I. Terashima, Relationships between height, diameter and weight distributions of chenopodium album plants in stands: effects of dimension and allometry. Ann. Bot. 75 (1995) 181–188. [CrossRef] [Google Scholar]
  34. A. Scaife, R.A. Sutherland et al., A new photothermal growth unit: the ‘ffective day-degree’, in First Congress of the European Society of Agronomy. European Society of Agronomy (1990). [Google Scholar]
  35. K. Shinozaki, Intraspecific competition among higher plants. VII. Logistic theory of the cd effect. J. Biol. Osaka City Univ. 7 (1956) 35–72. [Google Scholar]
  36. H. Chini, Python code for “Multi-Scale Hybrid Modeling of Plant Growth in Response to Environmental Conditions and Soil Nutrients Availability” (2024). https://github.com/HassanChini/MultiScaleHybridModeling [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.