The Modified Brière Equation and Its Applications
The Brière equation (BE) is widely used to describe the effect of temperature on the development rate of insects, and it can produce both symmetrical and asymmetrical bell-shaped curves. Because of its elasticity in curve fitting, the integrated form of BE has been recommended for use as a sigmoid g...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-07-01
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| Series: | Plants |
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| Online Access: | https://www.mdpi.com/2223-7747/11/13/1769 |
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| author | Jun Jin Brady K. Quinn Peijian Shi |
| author_facet | Jun Jin Brady K. Quinn Peijian Shi |
| author_sort | Jun Jin |
| collection | DOAJ |
| description | The Brière equation (BE) is widely used to describe the effect of temperature on the development rate of insects, and it can produce both symmetrical and asymmetrical bell-shaped curves. Because of its elasticity in curve fitting, the integrated form of BE has been recommended for use as a sigmoid growth equation to describe the increase in plant biomass with time. However, the start time of growth predicted by the sigmoid growth equation based on the BE is not completely comparable to empirical crop growth data. In the present study, we modified the BE by adding an additional parameter to further increase its elasticity for data fitting. We termed this new equation the modified Brière equation (MBE). Data for the actual height and biomass of 15 species of plants (with two cultivars for one species) were fit with the sigmoid growth equations based on both the BE and MBE assuming that the growth start time was zero for both. The goodness of fit of the BE and MBE sigmoid growth equations were compared based on their root-mean-square errors and the corresponding absolute percentage error between them when fit to these data. For most species, we found that the MBE sigmoid growth equation achieved a better goodness of fit than the BE sigmoid growth equation. This work provides a useful tool for quantifying the ontogenetic or population growth of plants. |
| first_indexed | 2024-03-09T12:40:08Z |
| format | Article |
| id | doaj.art-b744c96837a94c858a902d056aca1dae |
| institution | Directory Open Access Journal |
| issn | 2223-7747 |
| language | English |
| last_indexed | 2024-03-09T12:40:08Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Plants |
| spelling | doaj.art-b744c96837a94c858a902d056aca1dae2023-11-30T22:19:59ZengMDPI AGPlants2223-77472022-07-011113176910.3390/plants11131769The Modified Brière Equation and Its ApplicationsJun Jin0Brady K. Quinn1Peijian Shi2Research Institute of Architecture, Southeast University, Nanjing 210096, ChinaBiological Effects Section, St. Andrews Biological Station, Fisheries and Oceans Canada, St. Andrews, NB E5B 0E4, CanadaBamboo Research Institute, College of Science, Nanjing Forestry University, Nanjing 210037, ChinaThe Brière equation (BE) is widely used to describe the effect of temperature on the development rate of insects, and it can produce both symmetrical and asymmetrical bell-shaped curves. Because of its elasticity in curve fitting, the integrated form of BE has been recommended for use as a sigmoid growth equation to describe the increase in plant biomass with time. However, the start time of growth predicted by the sigmoid growth equation based on the BE is not completely comparable to empirical crop growth data. In the present study, we modified the BE by adding an additional parameter to further increase its elasticity for data fitting. We termed this new equation the modified Brière equation (MBE). Data for the actual height and biomass of 15 species of plants (with two cultivars for one species) were fit with the sigmoid growth equations based on both the BE and MBE assuming that the growth start time was zero for both. The goodness of fit of the BE and MBE sigmoid growth equations were compared based on their root-mean-square errors and the corresponding absolute percentage error between them when fit to these data. For most species, we found that the MBE sigmoid growth equation achieved a better goodness of fit than the BE sigmoid growth equation. This work provides a useful tool for quantifying the ontogenetic or population growth of plants.https://www.mdpi.com/2223-7747/11/13/1769axial symmetrycurve fittingontogenetic growthsigmoid curvesymmetry |
| spellingShingle | Jun Jin Brady K. Quinn Peijian Shi The Modified Brière Equation and Its Applications Plants axial symmetry curve fitting ontogenetic growth sigmoid curve symmetry |
| title | The Modified Brière Equation and Its Applications |
| title_full | The Modified Brière Equation and Its Applications |
| title_fullStr | The Modified Brière Equation and Its Applications |
| title_full_unstemmed | The Modified Brière Equation and Its Applications |
| title_short | The Modified Brière Equation and Its Applications |
| title_sort | modified briere equation and its applications |
| topic | axial symmetry curve fitting ontogenetic growth sigmoid curve symmetry |
| url | https://www.mdpi.com/2223-7747/11/13/1769 |
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