scholarly journals Longitudinal Pattern of Aerenchyma Formation Using the Ti-Gompertz Model in Rice Adventitious Roots

2021 ◽  
Vol 12 ◽  
Author(s):  
Yun Chen ◽  
Guoming Li ◽  
Buhong Zhao ◽  
Yajun Zhang ◽  
Kun Liu ◽  
...  
Keyword(s):  
Adventitious Roots ◽  
Goodness Of Fit ◽  
Gompertz Model ◽  
Root Apex ◽  
Information Criterion ◽  
Ordinary Least Squares ◽  
Parameter Estimates ◽  
Aerenchyma Formation ◽  
Root Aerenchyma ◽  
Longitudinal Pattern

The longitudinal pattern of root aerenchyma formation of its relationship with the function of adventitious roots in rice remains unclear. In this study, the percentage of the aerenchyma area to the cross-sectional area (i.e., aerenchyma percentage) was fit with four non-linear models, namely, W0-Gompertz, Ti-Gompertz, logistic, and von Bertalanffy. Goodness-of-fit criteria such as the R2, the Akaike information criterion (AIC), and the Bayesian information criterion (BIC) were used to select the model. The bias of the parameters was evaluated using the difference between the ordinary least squares-based parameter estimates and the mean of 1,000 bootstrap-based parameter estimates and the symmetry of the distributions of these parameters. The results showed that the Ti-Gompertz model, which had a high goodness-of-fit with an R2 close to 1, lower AIC and BIC values, parameter estimates close to being unbiased, and good linear approximation, provided the best fit for the longitude pattern of rice aerenchyma formation with different root lengths among the competing models. Using the second- and third-order derivatives according to the distance from the root apex, the critical points of Ti-Gompertz were calculated. The rapid stage for aerenchyma formation was from the maximum acceleration point (1.38–1.76 cm from the root apex) to the maximum deceleration point (3.13–4.19 cm from the root apex). In this stage, the aerenchyma percentage increased by 5.3–15.7% per cm, suggesting that the cortical cells tended to die rapidly for the aerenchyma formation rather than for the respiration cost during this stage. Meanwhile, the volume of the aerenchyma of the entire roots could be computed using the integral function of the Ti-Gompertz model. We proposed that the longitudinal pattern of root aerenchyma formation modeled by the Ti-Gompertz model helped to deeply understand the relationship between the anatomical traits and physiological function in rice adventitious roots.

scholarly journals Mathematical models describing disappearance of Lucerne hay in the rumen using the nylon bag technique

2021 ◽  
Vol 50 (5) ◽  
Author(s):  
V. Palangi ◽  
M. Macit ◽  
A.R. Bayat
Keyword(s):  
Mathematical Models ◽  
Crude Protein ◽  
Goodness Of Fit ◽  
Gompertz Model ◽  
Exponential Model ◽  
Parameter Estimates ◽  
Rumen Degradation ◽  
Degradation Data ◽  
Potential Use

It is essential to study the dynamics of rumen degradation of feeds before their potential use in formulating diets for ruminants. Various mathematical models have been developed to describe this degradation. The non-lagged exponential model (Model I), the lagged exponential model (Model II), the Gompertz model (Model III), and the generalized Mitscherlich model (Model IV) were examined using two alternative software (SAS and MATLAB) to determine their efficacy in accounting for variation in ruminal disappearance of dry matter (DM) and crude protein (CP) of lucerne hay from three cuttings. All models described DM degradability well (R2 >0.98). Only Models I and II converged when fitted to CP degradability data (R2 >0.98). It was concluded that any of these models could be used to describe the degradation of DM, whereas only Models I and II could be used to describe the degradation of CP from three cuttings of Lucerne hay. All the models that were fitted to the DM degradation data performed reasonably well, with only minor differences in goodness of fit. However, these models differed in values of the parameter estimates. Additionally, SAS failed to converge in the analyses of CP with Models III and IV, and MATLAB converged to nonsensical values with Model III. Model I might be recommended because it fitted the data well and required estimates of the fewest parameters Keywords: alfalfa hay, in situ digestion, model selection, nonlinear regression

scholarly journals Choice of non-linear models to determine the growth curve of meat-type quail

2021 ◽  
Vol 51 (2) ◽  
Author(s):  
Marta Jeidjane Borges Ribeiro ◽  
Fabyano Fonseca Silva ◽  
Maíse dos Santos Macário ◽  
José Aparecido Santos de Jesus ◽  
Claudson Oliveira Brito ◽  
...  
Keyword(s):  
Goodness Of Fit ◽  
Linear Models ◽  
Growth Curves ◽  
Information Criterion ◽  
Metabolizable Energy ◽  
Coefficient Of Determination ◽  
Parameter Estimates ◽  
Coturnix Coturnix ◽  
Non Linear ◽  
Meat Type

ABSTRACT: The objective of this study was to compare non-linear models fitted to the growth curves of quail to determine which model best describes their growth and check the similarity between models by analyzing parameter estimates.Weight and age data of meat-type European quail (Coturnix coturnix coturnix) of three lines were used, from an experiment in a 2 × 4 factorial arrangement in a completely randomized design, consisting of two metabolizable energy levels, four crude protein levels and six replicates. The non-linear Brody, Von Bertalanffy, Richards, Logistic and Gompertz models were used. To choose the best model, the Adjusted Coefficient of Determination, Convergence Rate, Residual Mean Square, Durbin-Watson Test, Akaike Information Criterion and Bayesian Information Criterion were applied as goodness-of-fit indicators. Cluster analysis was performed to check the similarity between models based on the mean parameter estimates. Among the studied models, Richards’ was the most suitable to describe the growth curves. The Logistic and Richards models were considered similar in the analysis with no distinction of lines as well as in the analyses of Lines 1, 2 and 3.

Diversity in root aeration traits associated with waterlogging tolerance in the genus Hordeum

2003 ◽  
Vol 30 (8) ◽  
pp. 875 ◽  
Author(s):  
Alaina J. Garthwaite ◽  
Roland von Bothmer ◽  
Timothy D. Colmer
Keyword(s):  
Adventitious Roots ◽  
Natural Habitat ◽  
Basal Region ◽  
Waterlogging Tolerance ◽  
Longitudinal Diffusion ◽  
Aerenchyma Formation ◽  
Root Aerenchyma ◽  
Important Trait ◽  
Hordeum Species ◽  
Wetland Habitats

Growth, root aerenchyma, and profiles of radial O2 loss (ROL) along adventitious roots were evaluated in 35 'wild' Hordeum accessions and cultivated barley (H. vulgare L. ssp. vulgare) when grown in stagnant nutrient solution (deoxygenated and containing 0.1% agar). When grown in stagnant solution, accessions from wetland and 'intermediate' habitats were superior, compared with accessions from non-wetland habitats, in maintaining relative growth rate, tillering, and adventitious root mass. Constitutive aerenchyma formation in adventitious roots was ≥�10% in 22 accessions (cf. H. vulgare at 2%). When grown in stagnant solution, aerenchyma was ≥� 20% in the adventitious roots of 14 accessions (cf. H. vulgare at 12%). Variation among the accessions in the volume of aerenchyma formed when grown in aerated or stagnant solution was not determined by the waterlogging regime of the species' natural habitat. However, the genus Hordeum comprises four genomes and when grown in stagnant solution accessions with the X genome formed, on average, 22% aerenchyma in adventitious roots (50 mm behind apex), whereas those with the H genome averaged 19%, and those with the Y or I genomes averaged 16 and 15%, respectively. Sixteen accessions formed a barrier to ROL in the basal region of adventitious roots when grown in stagnant solution. The formation of a barrier to radial O2 loss was predominant in accessions from wet habitats, and absent in accessions from non-wetland habitats. In addition, this trait was only present in accessions with the X or H genomes. The combination of aerenchyma and a barrier to ROL enhances the longitudinal diffusion of O2 within roots towards the apex. The possibility of a link between having a barrier to ROL and the X or H genomes in Hordeum species might, in future studies, enable a genetic analysis of this important trait.

scholarly journals Determination of the best non-linear function to describe the growth of Kajli sheep

2020 ◽  
Vol 50 (3) ◽  
pp. 452-459
Author(s):  
A. Ali ◽  
K. Javed ◽  
I. Zahoor ◽  
K.M. Anjum
Keyword(s):  
Linear Function ◽  
Goodness Of Fit ◽  
Linear Models ◽  
Information Criterion ◽  
Linear Functions ◽  
Coefficient Of Determination ◽  
Parameter Estimates ◽  
Early Maturity ◽  
Linear Pattern ◽  
Non Linear

The aim of the present study was to determine the best non-linear growth function to describe the growth of Kajli sheep. For this aim, the Brody, von Bertalanffy, Logistic, and Gompertz models were used to describe the sigmoidal relationship between bodyweight and age of the Kajli sheep. The records obtained from the Livestock Experiment Station, Khushab, were collected between 2007 and 2018. The records comprised 9864 age-weight observations (300 for male, 9564 for female, 7392 for single, 2388 for twin, and 84 for triplet lambs), which extended from birth to 12 months old. Candidate non-linear functions were fitted and the curve parameters were estimated by nlsfit (fit non-linear models) function in R statistical package, version 3.6.1. Goodness of fit criteria that were used to evaluate predictive performances of candidate models were adjusted coefficient of determination (R2adj), Akaike’s information criterion (AIC), Bayesian information criterion (BIC) and root means square error (RMSE). The Brody model was the best non-linear function that described the biological growth pattern of all, male, female, single, twin, and triplet lambs. Differences in curve parameter estimates between male and female suggested a definite pattern of sexual dimorphism. Moreover, a higher estimate of rate of maturity in female lambs reflects their early maturity compared with male Kajli lambs. Similarly, the single-born Kajli animals with highest maturity rate were maturing at an earlier age than twins and triplets. This is the first report on the non-linear pattern of visible changes in bodyweight of Kajli sheep from birth to 12 months old.Key words: age, bodyweight, growth curves, regression, sheep

scholarly journals Least Likely Observations in Regression Models for Categorical Outcomes

2002 ◽  
Vol 2 (3) ◽  
pp. 296-300 ◽  
Author(s):  
Jeremy Freese
Keyword(s):  
Logistic Regression ◽  
Regression Models ◽  
Binary Logistic Regression ◽  
Positive Outcome ◽  
Ordinary Least Squares ◽  
Parameter Estimates ◽  
Least Squares Regression ◽  
Binary Logistic Regression Model ◽  
Ordered Logistic Regression ◽  
Negative Outcome

This article presents a method and program for identifying poorly fitting observations for maximum-likelihood regression models for categorical dependent variables. After estimating a model, the program leastlikely will list the observations that have the lowest predicted probabilities of observing the value of the outcome category that was actually observed. For example, when run after estimating a binary logistic regression model, leastlikely will list the observations with a positive outcome that had the lowest predicted probabilities of a positive outcome and the observations with a negative outcome that had the lowest predicted probabilities of a negative outcome. These can be considered the observations in which the outcome is most surprising given the values of the independent variables and the parameter estimates and, like observations with large residuals in ordinary least squares regression, may warrant individual inspection. Use of the program is illustrated with examples using binary and ordered logistic regression.

scholarly journals Maximum Likelihood Analysis of Rare Binary Traits Under Different Modes of Inheritance

Genetics ◽  
1996 ◽  
Vol 143 (4) ◽  
pp. 1819-1829 ◽  
Author(s):  
G Thaller ◽  
L Dempfle ◽  
I Hoeschele
Keyword(s):  
Maximum Likelihood ◽  
Mixed Model ◽  
Major Gene ◽  
Likelihood Ratio Statistic ◽  
Information Criterion ◽  
Genetic Models ◽  
Parameter Estimates ◽  
Gene Effects ◽  
Binary Traits ◽  
Deterministic Algorithms

Abstract Maximum likelihood methodology was applied to determine the mode of inheritance of rare binary traits with data structures typical for swine populations. The genetic models considered included a monogenic, a digenic, a polygenic, and three mixed polygenic and major gene models. The main emphasis was on the detection of major genes acting on a polygenic background. Deterministic algorithms were employed to integrate and maximize likelihoods. A simulation study was conducted to evaluate model selection and parameter estimation. Three designs were simulated that differed in the number of sires/number of dams within sires (10/10, 30/30, 100/30). Major gene effects of at least one SD of the liability were detected with satisfactory power under the mixed model of inheritance, except for the smallest design. Parameter estimates were empirically unbiased with acceptable standard errors, except for the smallest design, and allowed to distinguish clearly between the genetic models. Distributions of the likelihood ratio statistic were evaluated empirically, because asymptotic theory did not hold. For each simulation model, the Average Information Criterion was computed for all models of analysis. The model with the smallest value was chosen as the best model and was equal to the true model in almost every case studied.

scholarly journals A generalized Gompertz growth model with applications and related birth-death processes

2020 ◽  
Author(s):  
Majid Asadi ◽  
Antonio Di Crescenzo ◽  
Farkhondeh A. Sajadi ◽  
Serena Spina
Keyword(s):  
Growth Model ◽  
Growth Curve ◽  
Goodness Of Fit ◽  
Gompertz Model ◽  
Death Process ◽  
Birth Process ◽  
Failure Data ◽  
First Case ◽  
Gompertz Growth Model ◽  
Birth Death

AbstractIn this paper, we propose a flexible growth model that constitutes a suitable generalization of the well-known Gompertz model. We perform an analysis of various features of interest, including a sensitivity analysis of the initial value and the three parameters of the model. We show that the considered model provides a good fit to some real datasets concerning the growth of the number of individuals infected during the COVID-19 outbreak, and software failure data. The goodness of fit is established on the ground of the ISRP metric and the $$d_2$$ d 2 -distance. We also analyze two time-inhomogeneous stochastic processes, namely a birth-death process and a birth process, whose means are equal to the proposed growth curve. In the first case we obtain the probability of ultimate extinction, being 0 an absorbing endpoint. We also deal with a threshold crossing problem both for the proposed growth curve and the corresponding birth process. A simulation procedure for the latter process is also exploited.

scholarly journals Comparison of growth models to describe growth from birth to 6 years in a Beninese cohort of children with repeated measurements

BMJ Open ◽  
2020 ◽  
Vol 10 (9) ◽  
pp. e035785
Author(s):  
Shukrullah Ahmadi ◽  
Florence Bodeau-Livinec ◽  
Roméo Zoumenou ◽  
André Garcia ◽  
David Courtin ◽  
...  
Keyword(s):  
Growth Model ◽  
Goodness Of Fit ◽  
Growth Models ◽  
Information Criterion ◽  
Height Growth ◽  
Sub Saharan Africa ◽  
Individual Growth ◽  
Secondary Outcome ◽  
Growth Trajectories ◽  
Best Fitting

ObjectiveTo select a growth model that best describes individual growth trajectories of children and to present some growth characteristics of this population.SettingsParticipants were selected from a prospective cohort conducted in three health centres (Allada, Sekou and Attogon) in a semirural region of Benin, sub-Saharan Africa.ParticipantsChildren aged 0 to 6 years were recruited in a cohort study with at least two valid height and weight measurements included (n=961).Primary and secondary outcome measuresThis study compared the goodness-of-fit of three structural growth models (Jenss-Bayley, Reed and a newly adapted version of the Gompertz growth model) on longitudinal weight and height growth data of boys and girls. The goodness-of-fit of the models was assessed using residual distribution over age and compared with the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). The best-fitting model allowed estimating mean weight and height growth trajectories, individual growth and growth velocities. Underweight, stunting and wasting were also estimated at age 6 years.ResultsThe three models were able to fit well both weight and height data. The Jenss-Bayley model presented the best fit for weight and height, both in boys and girls. Mean height growth trajectories were identical in shape and direction for boys and girls while the mean weight growth curve of girls fell slightly below the curve of boys after neonatal life. Finally, 35%, 27.7% and 8% of boys; and 34%, 38.4% and 4% of girls were estimated to be underweight, wasted and stunted at age 6 years, respectively.ConclusionThe growth parameters of the best-fitting Jenss-Bayley model can be used to describe growth trajectories and study their determinants.

scholarly journals A Method for Systemic Risk Estimation Based on CDS Indices

2015 ◽  
Vol 8 (1) ◽  
pp. 103-124
Author(s):  
Gabriel Gaiduchevici
Keyword(s):  
Goodness Of Fit ◽  
Risk Estimation ◽  
Multivariate Time Series ◽  
Tail Dependence ◽  
Dependence Structure ◽  
Parameter Estimates ◽  
Copula Models ◽  
Goodness Of Fit Tests ◽  
Multi Stage ◽  
Stage Estimation

AbstractThe copula-GARCH approach provides a flexible and versatile method for modeling multivariate time series. In this study we focus on describing the credit risk dependence pattern between real and financial sectors as it is described by two representative iTraxx indices. Multi-stage estimation is used for parametric ARMA-GARCH-copula models. We derive critical values for the parameter estimates using asymptotic, bootstrap and copula sampling methods. The results obtained indicate a positive symmetric dependence structure with statistically significant tail dependence coefficients. Goodness-of-Fit tests indicate which model provides the best fit to data.

scholarly journals Model Selection in Peptide-receptor Radionuclide Therapy for an Accurate Determination of Time Integrated Activity Coefficients

2021 ◽  
Vol 2019 (1) ◽  
pp. 012079
Author(s):  
N Atikah ◽  
A Riana ◽  
A Dwi ◽  
Z Anwari ◽  
Misrawati ◽  
...  
Keyword(s):  
Model Selection ◽  
Activity Coefficients ◽  
Radionuclide Therapy ◽  
Goodness Of Fit ◽  
Accurate Determination ◽  
Peptide Receptor Radionuclide Therapy ◽  
Information Criterion ◽  
Selection Function ◽  
Pharmacokinetic Data ◽  
Peptide Receptor

Abstract Calculation of accurate time-integrated activity coefficients (TIACs) is desirable in nuclear medicine dosimetry. The accuracy of the calculated TIACs is highly dependent on the fit function. However, systematic studies of determining a good function for peptide-receptor radionuclide therapy (PRRT) in different patients have not been reported in the literature. The aim of this study was to individually determine the best function for the calculation of TIACs in tumor and kidneys using a model selection based on the goodness of fit criteria and Corrected Akaike Information Criterion (AICc). The data used in this study was pharmacokinetic data of 111In-DOTATATE in tumor and kidneys obtained from 4 PRRT patients. Eleven functions with various parameterizations were formulated to describe the biokinetic data of 111In-DOTATATE in tumor and kidneys. The model selection was performed by choosing the best function from the function with sufficient goodness of fit based on the smallest AICc. Based on the results of model selection, function A 1 -(λ 1+λphys )t was selected as the best function for all tumor and kidneys in patients with meningioma tumors. By using this function, the calculated of TIACs could be more accurate for future patients with meningioma tumor.

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