A Dynamical Model Based on the Chapman–Richards Growth Equation for Fitting Growth Curves for Four Pine Species in Northern Mexico
Tree growth models describe the growth and development of forest ecosystems by considering how the dimensions of each simulated tree change within a certain time. These models have commonly used three growth parameters that describe various biological processes and behaviours, considering a sigmoid...
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| Format: | Article |
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MDPI AG
2022-11-01
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| Series: | Forests |
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| Online Access: | https://www.mdpi.com/1999-4907/13/11/1866 |
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| author | Joao Marcelo Brazao Protazio Marcos Almeida Souza Jose Ciro Hernández-Díaz Jonathan G. Escobar-Flores Carlos Antonio López-Sánchez Artemio Carrillo-Parra Christian Wehenkel |
| author_facet | Joao Marcelo Brazao Protazio Marcos Almeida Souza Jose Ciro Hernández-Díaz Jonathan G. Escobar-Flores Carlos Antonio López-Sánchez Artemio Carrillo-Parra Christian Wehenkel |
| author_sort | Joao Marcelo Brazao Protazio |
| collection | DOAJ |
| description | Tree growth models describe the growth and development of forest ecosystems by considering how the dimensions of each simulated tree change within a certain time. These models have commonly used three growth parameters that describe various biological processes and behaviours, considering a sigmoid growth function: (i) the upper asymptote (<i>θ</i><sub>1</sub>), which is the maximal yield indicated by a final dimension (such as the maximal stem diameter); (ii) the maximum specific growth rate (<i>θ</i><sub>2</sub>), defined as the slope of the tangent at the inflexion point; and (iii) the time elapsed (<i>θ</i><sub>3</sub>), defined by the intercept of this tangent with the abscissas. To the best of our knowledge, however, associations between the three parameters have not been documented for tree species. Using diameter growth data from pine trees located in typical mixed and uneven-aged pine-oak forests in the Sierra Madre Occidental, Mexico, our study aims were: (i) to quantify the putative associations between the three growth parameters and (ii) to test the accuracy of a proposed Hybrid Chapman-Richards growth model based on associations between the three growth parameters, but including only one single parameter, relative to the widely used Generalized Algebraic Difference Approach (GADA) based on the Chapman-Richards, Lundqvist and Hossfeld models and the Hybrid Weibull Model. For statistical comparison of the quality of the models, we used the mean relative percentage error, root mean square error, coefficient of determination and Akaike information criterion to assess the quality of the fit. Although the quality of the five growth models studied was similar, from a practical point of view, the proposed Hybrid Chapman-Richards Model (CR-H) is easier to apply than the other models and has a lower data collection and computational cost. The parameter of CR-H can be easily obtained, by measuring just the dominant trees, especially in coniferous forests with irregular ages. Moreover, in contrast to the Chapman-Richards-GADA factor <i>χ</i><sub>0</sub>, when <i>θ</i><sub>2</sub> is assumed to be site-specific, the CR-H has always a closed-form solution. |
| first_indexed | 2024-03-09T19:04:39Z |
| format | Article |
| id | doaj.art-8c49cc6942d44bb3a94748ef8ed15af8 |
| institution | Directory Open Access Journal |
| issn | 1999-4907 |
| language | English |
| last_indexed | 2024-03-09T19:04:39Z |
| publishDate | 2022-11-01 |
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| series | Forests |
| spelling | doaj.art-8c49cc6942d44bb3a94748ef8ed15af82023-11-24T04:44:31ZengMDPI AGForests1999-49072022-11-011311186610.3390/f13111866A Dynamical Model Based on the Chapman–Richards Growth Equation for Fitting Growth Curves for Four Pine Species in Northern MexicoJoao Marcelo Brazao Protazio0Marcos Almeida Souza1Jose Ciro Hernández-Díaz2Jonathan G. Escobar-Flores3Carlos Antonio López-Sánchez4Artemio Carrillo-Parra5Christian Wehenkel6Postgraduate Program in Mathematics and Statistics (PPGME), Universidade Federal do Pará (UFPA), Belém 66075-110, BrazilMaestría Institucional en Ciencias Agropecuárias y Forestales (MICAF), Universidad Juárez del Estado de Durango (UJED), Durango 34120, MexicoInstituto de Silvicultura e Industria de la Madera, Universidad Juárez del Estado de Durango (UJED), Durango 34120, MexicoCentro Interdisciplinario de Investigación para el Desarrollo Integral Regional, Unidad Durango, Instituto Politécnico Nacional, Durango 34220, MexicoSmart Forest Group, Department of Biology of Organisms and Systems, Mieres Polytechnic School, University of Oviedo, 33600 Oviedo, SpainInstituto de Silvicultura e Industria de la Madera, Universidad Juárez del Estado de Durango (UJED), Durango 34120, MexicoInstituto de Silvicultura e Industria de la Madera, Universidad Juárez del Estado de Durango (UJED), Durango 34120, MexicoTree growth models describe the growth and development of forest ecosystems by considering how the dimensions of each simulated tree change within a certain time. These models have commonly used three growth parameters that describe various biological processes and behaviours, considering a sigmoid growth function: (i) the upper asymptote (<i>θ</i><sub>1</sub>), which is the maximal yield indicated by a final dimension (such as the maximal stem diameter); (ii) the maximum specific growth rate (<i>θ</i><sub>2</sub>), defined as the slope of the tangent at the inflexion point; and (iii) the time elapsed (<i>θ</i><sub>3</sub>), defined by the intercept of this tangent with the abscissas. To the best of our knowledge, however, associations between the three parameters have not been documented for tree species. Using diameter growth data from pine trees located in typical mixed and uneven-aged pine-oak forests in the Sierra Madre Occidental, Mexico, our study aims were: (i) to quantify the putative associations between the three growth parameters and (ii) to test the accuracy of a proposed Hybrid Chapman-Richards growth model based on associations between the three growth parameters, but including only one single parameter, relative to the widely used Generalized Algebraic Difference Approach (GADA) based on the Chapman-Richards, Lundqvist and Hossfeld models and the Hybrid Weibull Model. For statistical comparison of the quality of the models, we used the mean relative percentage error, root mean square error, coefficient of determination and Akaike information criterion to assess the quality of the fit. Although the quality of the five growth models studied was similar, from a practical point of view, the proposed Hybrid Chapman-Richards Model (CR-H) is easier to apply than the other models and has a lower data collection and computational cost. The parameter of CR-H can be easily obtained, by measuring just the dominant trees, especially in coniferous forests with irregular ages. Moreover, in contrast to the Chapman-Richards-GADA factor <i>χ</i><sub>0</sub>, when <i>θ</i><sub>2</sub> is assumed to be site-specific, the CR-H has always a closed-form solution.https://www.mdpi.com/1999-4907/13/11/1866forest simulationgrowth modelsADA modelsGADA models |
| spellingShingle | Joao Marcelo Brazao Protazio Marcos Almeida Souza Jose Ciro Hernández-Díaz Jonathan G. Escobar-Flores Carlos Antonio López-Sánchez Artemio Carrillo-Parra Christian Wehenkel A Dynamical Model Based on the Chapman–Richards Growth Equation for Fitting Growth Curves for Four Pine Species in Northern Mexico Forests forest simulation growth models ADA models GADA models |
| title | A Dynamical Model Based on the Chapman–Richards Growth Equation for Fitting Growth Curves for Four Pine Species in Northern Mexico |
| title_full | A Dynamical Model Based on the Chapman–Richards Growth Equation for Fitting Growth Curves for Four Pine Species in Northern Mexico |
| title_fullStr | A Dynamical Model Based on the Chapman–Richards Growth Equation for Fitting Growth Curves for Four Pine Species in Northern Mexico |
| title_full_unstemmed | A Dynamical Model Based on the Chapman–Richards Growth Equation for Fitting Growth Curves for Four Pine Species in Northern Mexico |
| title_short | A Dynamical Model Based on the Chapman–Richards Growth Equation for Fitting Growth Curves for Four Pine Species in Northern Mexico |
| title_sort | dynamical model based on the chapman richards growth equation for fitting growth curves for four pine species in northern mexico |
| topic | forest simulation growth models ADA models GADA models |
| url | https://www.mdpi.com/1999-4907/13/11/1866 |
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