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...
Main Authors: | , , , |
---|---|
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 |
id |
doaj-bc32abad12324fbcbde62b58f01713f9 |
---|---|
record_format |
Article |
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 |
work_keys_str_mv |
AT joseraimundodesouzapassos criticalpointsinlogisticgrowthcurvesandtreatmentcomparisons AT sheilazambellodepinho criticalpointsinlogisticgrowthcurvesandtreatmentcomparisons AT lidiaraqueldecarvalho criticalpointsinlogisticgrowthcurvesandtreatmentcomparisons AT marthamariamischan criticalpointsinlogisticgrowthcurvesandtreatmentcomparisons |
_version_ |
1725349755329970176 |