Proposals of non-linear models to adjust in vitro gas production at different incubation times in cassava genotypes

The present study aimed to propose new two-compartment models from the combination of the Gompertz, Logistic and Von Bertalanffy models and to identify between Gompertz and Logistic models, in their uni and two-compartiment versions, the one that presents the highest quality of fit to cumulative gas production curves of five cassava genotypes: Brasília, Engana Ladrão, Dourada, Gema de Ovo e Amansa Burro. The gas production readings were 2, 4, 6, 8, 10, 12, 14, 17, 20, 24, 28, 32, 48, 72, and 96 hours after the start of the in vitro fermentation process. The estimation of the parameters for the models was made by the least squares method through the Gauss-Newton iterative process. The selection of the best model to describe the gas accumulation was based on the adjusted coefficient of determination, residual mean squares, mean absolute deviation, Akaike information criterion and Bayesian information criterion. Among the adjusted models, the proposed models were the best to describe the accumulation of gases over time according to the methodology and conditions under which this study was developed.

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Method to generate growth and degrowth models obtained from combinations of existing models applied to agrarian sciences

10.1101/585224 ◽

2019 ◽

Author(s):

André Luiz Pinto dos Santos ◽

Guilherme Rocha Moreira ◽

Frank Gomes-Silva ◽

Cícero Carlos Ramos de Brito ◽

Maria Lindomárcia Leonardo da Costa ◽

...

Keyword(s):

Least Squares Method ◽

Kinetic Curve ◽

Information Criterion ◽

Compartment Model ◽

Gas Production ◽

Coefficient Of Determination ◽

Von Bertalanffy ◽

Absolute Deviation ◽

Two Compartment Model

AbstractMathematical models that describe gas production are widely used to estimate the rumen degradation digestibility and kinetics. The present study presents a method to generate models by combining existing models and to propose the von Bertalanffy-Gompertz two-compartment model based on this method. The proposed model was compared with the logistic two-compartment one to indicate which best describes the kinetic curve of gas production through the semi-automatedin vitrotechnique from different pinto peanut cultivars. The data came from an experiment grown and harvested at the Far South Animal Sciences station (Essul) in Itabela, BA, Brazil and gas production was read at 2, 4, 6, 8, 10, 12, 14, 17, 20, 24, 28, 32, 48, 72, and 96 h after the start of thein vitrofermentation process. The parameters were estimated by the least squares method using the iterative Gauss-Newton process in the software R version 3.4.1. The best model to describe gas accumulation was based on the adjusted coefficient of determination, residual mean squares, mean absolute deviation, Akaike information criterion, and Bayesian information criterion. The von Bertalanffy-Gompertz two-compartment model had the best fit to describe the cumulative gas production over time according to the methodology and conditions of the present study.

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New model of evaluation of sunflower and corn silages by the in vitro gas production technique

Semina Ciências Agrárias ◽

10.5433/1679-0359.2020v41n4p1373 ◽

2020 ◽

Vol 41 (4) ◽

pp. 1373

Author(s):

André Luiz Pinto dos Santos ◽

Cícero Carlos Ramos de Brito ◽

Guilherme Rocha Moreira ◽

Frank Gomes-Silva ◽

Moacyr Cunha Filho ◽

...

Keyword(s):

Goodness Of Fit ◽

Least Squares Method ◽

Kinetic Curve ◽

Information Criterion ◽

Gas Production ◽

Corn Silage ◽

Coefficient Of Determination ◽

Von Bertalanffy ◽

Production Technique

This study aimed to propose a model called Two-compartment Logistic-von Bertalanffy (LVB) and to identify among the proposed and Two-compartment Logistic (TL) models the one that has the best goodness of fit to the kinetic curve of cumulative gas production (CGP) of sunflower and corn silages alone and combined using the in vitro semi-automated gas production technique. A random block split-plot experimental design was employed in which the inoculums were the blocks, the incubation times were the split-plots, and the experimental diets were: CS - corn silage, SS - sunflower silage (as single roughage), and their mixtures, i.e., 340SS (660 g kg-1 corn silage and 340 g kg-1 sunflower silage) and 660SS (340 g kg-1 corn silage and 660 g kg-1 sunflower silage). The parameters were estimated by the least squares method using the iterative Gauss-Newton process in the software R version 3.4.1. The criteria adopted were: adjusted coefficient of determination (R2adj.), residual mean squares (RMS), mean absolute deviation (MAD), Akaike information criterion (AIC), Bayesian information criterion (BIC), and relative efficiency (RE). The TL model had higher R2adj. values compared to LVB, however, such difference may be considered negligible. The LVB model had RE above one, which indicates it is superior to the TL model, in addition to the lowest RMS, MAD, AIC, and BIC values, The Two-compartment Logistic-von Bertalanffy model had the best fit to describe the CGP over time according to the methodology and conditions of the present study.

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The use of the nonlinear models in the growth of pears of ‘Shinseiki’ cultivar

Ciência Rural ◽

10.1590/0103-8478cr20161097 ◽

2017 ◽

Vol 48 (1) ◽

Cited By ~ 4

Author(s):

Thais Destefani Ribeiro ◽

Taciana Villela Savian ◽

Tales Jesus Fernandes ◽

Joel Augusto Muniz

Keyword(s):

Logistic Model ◽

Least Squares Method ◽

Nonlinear Models ◽

Logistic Models ◽

Information Criterion ◽

Fruit Weight ◽

Coefficient Of Determination ◽

Pear Fruit ◽

Asian Pear ◽

Residual Correlations

ABSTRACT: The goal of this study was to elucidate the growth and development of the Asian pear fruit, on the grounds of length, diameter and fresh weight determined over time, using the non-linear Gompertz and Logistic models. The specifications of the models were assessed utilizing the R statistical software, via the least squares method and iterative Gauss-Newton process (DRAPER & SMITH, 2014). The residual standard deviation, adjusted coefficient of determination and the Akaike information criterion were used to compare the models. The residual correlations, observed in the data for length and diameter, were modeled using the second-order regression process to render the residuals independent. The logistic model was highly suitable in demonstrating the data, revealing the Asian pear fruit growth to be sigmoid in shape, showing remarkable development for three variables. It showed an average of up to 125 days for length and diameter and 140 days for fresh fruit weight, with values of 72mm length, 80mm diameter and 224g heavy fat.

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Method to generate growth and degrowth models obtained from differential equations applied to agrarian sciences

Semina Ciências Agrárias ◽

10.5433/1679-0359.2018v39n6p2659 ◽

2018 ◽

Vol 39 (6) ◽

pp. 2659 ◽

Cited By ~ 3

Author(s):

André Luiz Pinto dos Santos ◽

Guilherme Rocha Moreira ◽

Cicero Carlos Ramos de Brito ◽

Frank Gomes-Silva ◽

Maria Lindomárcia Leonardo da Costa ◽

...

Keyword(s):

Differential Equations ◽

Goodness Of Fit ◽

Least Squares Method ◽

Growth Curves ◽

Information Criterion ◽

Coefficient Of Determination ◽

Absolute Deviation ◽

Marquardt Algorithm ◽

Maturation Rate ◽

Biological Interpretation

This study aims to propose a method to generate growth and degrowth models using differential equations as well as to present a model based on the method proposed, compare it with the classic linear mathematical models Logistic, Von Bertalanffy, Brody, Gompertz, and Richards, and identify the one that best represents the mean growth curve. To that end, data on Undefined Breed (UB) goats and Santa Inês sheep from the works of Cavalcante et al. (2013) and Sarmento et al. (2006a), respectively, were used. Goodness-of-fit was measured using residual mean squares (RMS), Akaike information criterion (AIC), Bayesian information criterion (BIC), mean absolute deviation (MAD), and adjusted coefficient of determination . The models’ parameters (?, weight at adulthood; ?, an integration constant; ?, shape parameter with no biological interpretation; k, maturation rate; and m, inflection point) were estimated by the least squares method using Levenberg-Marquardt algorithm on the software IBM SPSS Statistics 1.0. It was observed that the proposed model was superior to the others to study the growth curves of goats and sheep according to the methodology and conditions under which the present study was carried out.

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Kinetics of In Vitro Gas Production and Fitting Mathematical Models of Corn Silage

Fermentation ◽

10.3390/fermentation7040298 ◽

2021 ◽

Vol 7 (4) ◽

pp. 298

Author(s):

Camila da Silva Zornitta ◽

Luis Carlos Vinhas Ítavo ◽

Camila Celeste Brandão Ferreira Ítavo ◽

Geraldo Tadeu dos Santos ◽

Alexandre Menezes Dias ◽

...

Keyword(s):

Mathematical Models ◽

Gas Production ◽

Feed Additives ◽

Corn Silage ◽

Feed Additive ◽

Coefficient Of Determination ◽

Production Data ◽

In Vitro Gas Production ◽

Kinetics Of

This study aimed at examining the effects of rumen inoculum of steers receiving different combinations of ionophore and probiotics in their diets on in vitro gas production of corn silage. The fitting of gas production was performed with five mathematical models and its kinetics was evaluated. Four crossbred steers (403.0 ± 75.5 kg body weight) with ruminal cannula were assigned to a 4 × 4 Latin square design. The additives used were Monensin sodium (Rumensin® 100, 3 g/day), Bacillus toyonensis (Micro-Cell Platinum® 109, 1 g/day) and Saccharomyces cerevisiae boulardii (ProTernative®20, 0.5 g/day). Additives were arranged into the following treatments, supplied daily into total mixed diet: (1) Monensin; (2) Monensin + B. toyonensis; (3) Monensin + S. boulardii; and (4) B. toyonensis + S. boulardii. The gas production data were fitted into the models of Gompertz, Groot, Ørskov, Brody, Richards, and Dual-pool Logistic. A perfect agreement between observed and predicted values in curves of accumulated in vitro gas production was observed in the Groot and Richards models, with higher coefficient of determination (R2 = 0.770 and 0.771, respectively), concordance correlation coefficient (CCC = 0.871 and 0.870, respectively), and root mean square error of prediction (RMSEP = 1.14 and 1.15, respectively). Evaluating the feed additives throughout the Groot model, the B. toyonensis + S. boulardii treatment presented higher VF (12.08 mL/100 mg of DM; p = 0.0022) than Monensin and Monensin + S. boulardii (9.16 and 9.22 mL/100 mg of DM, respectively). In addition, the fractional rate of gas production (k) was higher (p = 0.0193) in B. toyonensis + S. boulardii than in Monensin, not presenting a statistical difference (p > 0.05) from the other two treatments. Additionally, with the time of beginning to gas production, the lag time (λ), was greater (p < 0.001) with Monensin and Monensin + B. toyonensis than with Monensin + S. boulardii and B. toyonensis + S. boulardii. The combination of Monensin and probiotics (B. toyonensis + S. boulardii) resulted in better kinetics of degradation of corn silage, being that the Groot and Richards models had the best fit for estimates of the in vitro gas production data of corn silage tested with different feed additive combinations.

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Growth models for morphological traits of sunn hemp

Semina Ciências Agrárias ◽

10.5433/1679-0359.2017v38n5p2933 ◽

2017 ◽

Vol 38 (5) ◽

pp. 2933

Author(s):

Cláudia Marques de Bem ◽

Alberto Cargnelutti Filho ◽

Giovani Facco ◽

Denison Esequiel Schabarum ◽

Daniela Lixinski Silveira ◽

...

Keyword(s):

Morphological Traits ◽

Logistic Models ◽

Information Criterion ◽

Coefficient Of Determination ◽

Percentage Error ◽

Mean Absolute Deviation ◽

Absolute Deviation ◽

Sunn Hemp ◽

Number Of Leaves ◽

Second Period

The objective of the present study was to fit Gompertz and Logistic nonlinear to descriptions of morphological traits of sunn hemp. Two uniformity trials were conducted and the crops received identical treatment in all experimental area. Sunn hemp seeds were sown in rows 0.5 m apart with a plant density of 20 plants per row meter in a usable area of 52 m × 50 m. The following morphological traits were evaluated: plant height (PH), number of leaves (NL), stem diameter (SD), and root length (RL). These traits were assessed daily during two sowing periods—seeds were sown on October 22, 2014 (first period) and December 3, 2014 (second period). Four plants were randomly collected daily, beginning 7 days after first period and 13 days after for second period, totaling 94 and 76 evaluation days, respectively. For Gompertz models the equation was used y=a*e^((?-e?^((b-c*xi))and Logistic models the equation was used yi= a/(1+e^((-b-c*xi)). The inflection points of the Gompertz and Logistic models were calculated and the goodness of fit was quantified using the adjusted coefficient of determination, Akaike information criterion, standard deviation of residuals, mean absolute deviation, mean absolute percentage error, and mean prediction error. Differences were observed between the Gompertz and Logistic models and between the experimental periods in the parameter estimate for all morphological traits measured. Satisfactory growth curve fittings were achieved for plant height, number of leaves, and stem diameter in both models using the evaluation criteria: coefficient of determination (R²), Akaike information criterion (AIC), standard deviation of residuals (SDR), mean absolute deviation (MAD), mean absolute percentage error (MAPE), and mean prediction error (MPE).

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Romanov Kuzularının Vücut Özelliklerinin Tanımlanmasında Doğrusal ve Doğrusal Olmayan Modellerin Karşılaştırılması

Turkish Journal of Agriculture - Food Science and Technology ◽

10.24925/turjaf.v8i2.499-503.3342 ◽

2020 ◽

Vol 8 (2) ◽

pp. 499

Author(s):

Yalçın Tahtalı ◽

Ahmet Tahsin Yaldızbaş

Keyword(s):

Body Length ◽

Growth Curve ◽

Linear Models ◽

Logistic Models ◽

Live Weight ◽

Growth Period ◽

Coefficient Of Determination ◽

Linear Quadratic ◽

Absolute Deviation ◽

Cubic Model

In this study, the purpose of defining the development of body characteristics of 50 Romanov lambs 180. During the growth period up to the age of day, records of body characteristics such as body weight, body length, height of cidago were taken every 15 days and the parameters of the growth curves were calculated from the Linear models with the obtained data and the Linear, Quadratic and Cubic model, Non-Linear models with Gompertz, and Logistic models. The coefficient of determination (R2), mean square error (MSE) and mean absolute deviation (MAD) values were used in determining the model that best fit the growth curve. As a result of the study, the highest R2 value and the lowest HKO values were 0.992-0.591 in live weight, 0.993-0.441 in cidago height, and 0.986-1.164 in body length, respectively. The highest R2 value in all body characteristics was obtained from the cubic model. SPSS statistics program was used to determine the parameters of the growth curve model. According to the obtained data, it was determined that the most compatible model to explain the development of all body characteristics of the Romanov lambs is the Cubic model.

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Comparative study of some non-linear models for predicting the yield of Gmelina arborea plantation

Journal of Applied and Natural Science ◽

10.31018/jans.v6i2.528 ◽

2014 ◽

Vol 6 (2) ◽

pp. 738-743

Author(s):

F. O. Oboite ◽

V. D. Ade-Oni

Keyword(s):

Linear Models ◽

Logistic Models ◽

Basal Area ◽

Weibull Model ◽

Volume Estimation ◽

Coefficient Of Determination ◽

Gmelina Arborea ◽

Non Linear ◽

The One ◽

Log Normal

Yield models are important for effective forest management and as such were developed for the University of Benin Gmelina arborea plantation, Nigeria. The objectives of the study were to develop, evaluate and compare predictions from some non-linear models for timber volume estimation. A total of nine non-linear models comprising of three models each for weibull, logistic and log-normal models were developed using the three independent variables combinations (Basal area and merchantable height, diameter at base and merchantable height, diameter at middle and merchantable height). The assessment criteria (correlation coefficient (R), coefficient of determination (R2), standard error of estimate (SE)) with the validation results (using percentage bias and probability plots of residuals) showed that all categories of weibull and logistic models generated in this study discovered to be very adequate for tree volume estimation. The highest R2 (93.80), lowest SE (0.25) and lowest bias% (1.29) in the study were achieved from Weibull model 1a. The log-normal models were the least adequate for tree volume estimation with the highest bias%. The one way analysis of variance revealed that there were no significant differences in the performance of the non-linear models when varying predictor variables were used. The weibull, logistic models were therefore recommended for further use in this ecosystem and in any other forest ecosystem with similar site condition.

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Nonlinear Models for Plant Height of Rye Cultivars at Sowing Times

Journal of Agricultural Science ◽

10.5539/jas.v10n12p157 ◽

2018 ◽

Vol 10 (12) ◽

pp. 157 ◽

Cited By ~ 1

Author(s):

Jéssica Andiara Kleinpaul ◽

Alberto Cargnelutti Filho ◽

Daniela Lixinski Silveira ◽

Ismael Mario Marcio Neu ◽

Cirineu Tolfo Bandeira ◽

...

Keyword(s):

Plant Height ◽

Nonlinear Models ◽

Logistic Models ◽

Information Criterion ◽

Coefficient Of Determination ◽

Maximum Acceleration ◽

Inflection Points ◽

Thermal Sum ◽

Average Plant ◽

The One

Adjusting nonlinear Gompertz and Logistic models will help in the understanding of the growth pattern of the rye crop and also in the height response of the plant, when planted in different environmental conditions. The the aims of this study were to adjust the nonlinear Gompertz and Logistic models for plant height and indicate the one that best describes growth of two rye cultivars in five sowing times. Ten uniformity trials were conducted with the rye crop in the 2016 harvest. In each trial, ten randomly selected plants were evaluated from the first expanded leaf weekly. In each plant height was measured. The adjustment of the Gompertz and Logistic models as a function of the accumulated thermal sum was performed with the average plant height at each evaluation. The parameters a, b, and c were estimated for each model. The confidence interval for each parameter and the inflection points, maximum acceleration, maximum deceleration and asymptotic deceleration were calculated. The quality of fit of the models was verified by the coefficient of determination, Akaike's information criterion and residual standard deviation. Intrinsic non-linearity and non-linearity of the parameter effect were quantified. Both models describe satisfactorily the plant height. The model that best describes the growth of rye cultivars is Logistic.

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