Critical points in logistic growth curves and treatment comparisons

Several biological phenomena have a behavior over time mathematically characterized by a strong increasing function in the early stages of development, then by a less pronounced growth, sometimes showing stability. The separation between these phases is very important to the researcher, since the ma...

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Main Authors: José Raimundo de Souza Passos, Sheila Zambello de Pinho, Lídia Raquel de Carvalho, Martha Maria Mischan
Format: Article
Language:English
Published: Universidade de São Paulo 2012-10-01
Series:Scientia Agricola
Subjects:
Online Access:http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0103-90162012000500004
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spelling doaj-bc32abad12324fbcbde62b58f01713f92020-11-25T00:25:10ZengUniversidade de São PauloScientia Agricola0103-90161678-992X2012-10-0169530831210.1590/S0103-90162012000500004Critical points in logistic growth curves and treatment comparisonsJosé Raimundo de Souza PassosSheila Zambello de PinhoLídia Raquel de CarvalhoMartha Maria MischanSeveral biological phenomena have a behavior over time mathematically characterized by a strong increasing function in the early stages of development, then by a less pronounced growth, sometimes showing stability. The separation between these phases is very important to the researcher, since the maintenance of a less productive phase results in uneconomical activity. In this report we present methods of determining critical points in logistic functions that separate the early stages of growth from the asymptotic phase, with the aim of establishing a stopping critical point in the growth and on this basis determine differences in treatments. The logistic growth model is fitted to experimental data of imbibition of araribá seeds (Centrolobium tomentosum). To determine stopping critical points the following methods were used: i) accelerating growth function, ii) tangent at the inflection point, iii) segmented regression; iv) modified segmented regression; v) non-significant difference; and vi) non-significant difference by simulation. The analysis of variance of the abscissas and ordinates of the breakpoints was performed with the objective of comparing treatments and methods used to determine the critical points. The methods of segmented regression and of the tangent at the inflection point lead to early stopping points, in comparison with other methods, with proportions ordinate/asymptote lower than 0.90. The non-significant difference method by simulation had higher values of abscissas for stopping point, with an average proportion ordinate/asymptote equal to 0.986. An intermediate proportion of 0.908 was observed for the acceleration function method.http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0103-90162012000500004nonlinear regressionasymptotic regressionstopping critical levelseeds imbibition
collection DOAJ
language English
format Article
sources DOAJ
author José Raimundo de Souza Passos
Sheila Zambello de Pinho
Lídia Raquel de Carvalho
Martha Maria Mischan
spellingShingle José Raimundo de Souza Passos
Sheila Zambello de Pinho
Lídia Raquel de Carvalho
Martha Maria Mischan
Critical points in logistic growth curves and treatment comparisons
Scientia Agricola
nonlinear regression
asymptotic regression
stopping critical level
seeds imbibition
author_facet José Raimundo de Souza Passos
Sheila Zambello de Pinho
Lídia Raquel de Carvalho
Martha Maria Mischan
author_sort José Raimundo de Souza Passos
title Critical points in logistic growth curves and treatment comparisons
title_short Critical points in logistic growth curves and treatment comparisons
title_full Critical points in logistic growth curves and treatment comparisons
title_fullStr Critical points in logistic growth curves and treatment comparisons
title_full_unstemmed Critical points in logistic growth curves and treatment comparisons
title_sort critical points in logistic growth curves and treatment comparisons
publisher Universidade de São Paulo
series Scientia Agricola
issn 0103-9016
1678-992X
publishDate 2012-10-01
description Several biological phenomena have a behavior over time mathematically characterized by a strong increasing function in the early stages of development, then by a less pronounced growth, sometimes showing stability. The separation between these phases is very important to the researcher, since the maintenance of a less productive phase results in uneconomical activity. In this report we present methods of determining critical points in logistic functions that separate the early stages of growth from the asymptotic phase, with the aim of establishing a stopping critical point in the growth and on this basis determine differences in treatments. The logistic growth model is fitted to experimental data of imbibition of araribá seeds (Centrolobium tomentosum). To determine stopping critical points the following methods were used: i) accelerating growth function, ii) tangent at the inflection point, iii) segmented regression; iv) modified segmented regression; v) non-significant difference; and vi) non-significant difference by simulation. The analysis of variance of the abscissas and ordinates of the breakpoints was performed with the objective of comparing treatments and methods used to determine the critical points. The methods of segmented regression and of the tangent at the inflection point lead to early stopping points, in comparison with other methods, with proportions ordinate/asymptote lower than 0.90. The non-significant difference method by simulation had higher values of abscissas for stopping point, with an average proportion ordinate/asymptote equal to 0.986. An intermediate proportion of 0.908 was observed for the acceleration function method.
topic nonlinear regression
asymptotic regression
stopping critical level
seeds imbibition
url http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0103-90162012000500004
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