Modification of a photosynthetic light-response (PLR) model for modeling the vertical gradient in the response of crown PLR curves

2019 ◽  
Vol 49 (8) ◽  
pp. 949-959
Author(s):  
Qiang Liu ◽  
Lihu Dong ◽  
Fengri Li
Keyword(s):  
Goodness Of Fit ◽  
Light Response ◽  
Information Criterion ◽  
Vertical Gradient ◽  
Leaf Nitrogen ◽  
Coefficient Of Determination ◽  
Relative Depth ◽  
Tree Crown ◽  
Modified Model ◽  
Mathematical Techniques

The photosynthetic light-response (PLR) curve is a mathematical description of a single biochemical process that has been widely applied in many ecophysiological models. For trees, the heterogeneity of PLR curves within the crown is significant but rarely modeled by mathematical techniques. This paper establishes a modified model for estimating crown PLR curves based on PLR functions by linking the parameters of the PLR functions to leaf nitrogen (N), specific leaf area (SLA), and relative depth into the crown (RDINC). The modified models were assessed by considering the goodness of fit (adjusted coefficient of determination, [Formula: see text]; root mean square error, RMSE; and Akaike information criterion, AIC) and model structure. Significant correlations were observed between the parameters of PLR functions and N, SLA, and RDINC. The optimal modified PLR model, by linking RDINC into a modified Mitscherlich function, fit well due to its simple and easily understood structure. Therefore, it is feasible to simultaneously estimate the multilayered and varied PLR curves of the tree crown.

scholarly journals Modeling net CO2 assimilation (AN) within the crown of young planted Larix olgensis trees

2018 ◽  
Vol 48 (9) ◽  
pp. 1085-1098 ◽  
Author(s):  
Q. Liu ◽  
L.H. Dong ◽  
F.R. Li
Keyword(s):  
Goodness Of Fit ◽  
Light Response ◽  
Information Criterion ◽  
Growing Season ◽  
Absolute Error ◽  
Co2 Assimilation ◽  
Coefficient Of Determination ◽  
Leaf Mass Per Area ◽  
Relative Depth ◽  
Larix Olgensis

Net CO2 assimilation (AN) is an important physiological indicator that reflects the photosynthetic capacity. The seasonal and spatial variations of AN play an important role in carbon uptake simulations, especially for trees. To gain a clearer understanding of the state of the branch carbon balance, it is necessary to more carefully evaluate the dynamic variation of AN over different gradients in the crown during the growing season. Gas exchange, leaf temperature (Tleaf), vapor pressure deficit (VPD), leaf mass per area (LMA), and relative depth into crown (RDINC) were measured throughout the growing season of planted Larix olgensis A. Henry trees. A semi-empirical model for predicting multilayered crown AN was established by incorporating Tleaf, VPD, LMA, RDINC, and their combinations into a photosynthetic light response (PLR) curve model using re-parameterization. The model was assessed based on goodness of fit (adjusted coefficient of determination ([Formula: see text]), root mean square error (RMSE), and Akaike’s information criterion (AIC)) and on the validation results (mean error (ME), mean absolute error (MAE), precision estimation (P)) and performed well. The multilayered predicted model of crown AN lays the foundation for calculating the multilayered photosynthetic production within the crown and determining the range of the functional crown for individual trees.

Introducing a sinusoidal equation to describe lactation curves for cumulative milk yield and composition in Holstein cows

2020 ◽  
Vol 87 (2) ◽  
pp. 220-225
Author(s):  
Navid Ghavi Hossein-Zadeh ◽  
Hassan Darmani Kuhi ◽  
James France ◽  
Secundino López
Keyword(s):  
Linear Model ◽  
Milk Yield ◽  
Milk Fat ◽  
Goodness Of Fit ◽  
Growth Models ◽  
Information Criterion ◽  
Holstein Cows ◽  
Coefficient Of Determination ◽  
Production Traits ◽  
Lactation Curve

AbstractThe aim of the work reported here was to investigate the appropriateness of a sinusoidal function by applying it to model the cumulative lactation curves for milk yield and composition in primiparous Holstein cows, and to compare it with three conventional growth models (linear, Richards and Morgan). Data used in this study were 911 144 test-day records for milk, fat and protein yields, which were recorded on 834 dairy herds from 2000 to 2011 by the Animal Breeding Centre and Promotion of Animal Products of Iran. Each function was fitted to the test-day production records using appropriate procedures in SAS (PROC REG for the linear model and PROC NLIN for the Richards, Morgan and sinusoidal equations) and the parameters were estimated. The models were tested for goodness of fit using adjusted coefficient of determination $\lpar {R_{{\rm adj}}^2 } \rpar $, root mean square error (RMSE), Akaike's information criterion (AIC) and the Bayesian information criterion (BIC). $R_{{\rm adj}}^2 $ values were generally high (>0.999), implying suitable fits to the data, and showed little differences among the models for cumulative yields. The sinusoidal equation provided the lowest values of RMSE, AIC and BIC, and therefore the best fit to the lactation curve for cumulative milk, fat and protein yields. The linear model gave the poorest fit to the cumulative lactation curve for all production traits. The current results show that classical growth functions can be fitted accurately to cumulative lactation curves for production traits, but the new sinusoidal equation introduced herein, by providing best goodness of fit, can be considered a useful alternative to conventional models in dairy research.

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

2018 ◽  
Vol 39 (6) ◽  
pp. 2659 ◽  
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.

scholarly journals Modeling and Model Comparison for Industrial Production Index of Turkey, Brazil and G7 Countries

2018 ◽  
Vol 6 (04) ◽  
Author(s):  
Nihan Öksüz Narinç
Keyword(s):  
Industrial Production ◽  
Goodness Of Fit ◽  
Model Comparison ◽  
Information Criterion ◽  
Estimation Methods ◽  
Coefficient Of Determination ◽  
G7 Countries ◽  
Production Index ◽  
Industrial Production Index ◽  
Expected Values

In this study, it was aimed to modeling and model comparison for the industrial production index values of Turkey, Brazil and G7 countries among the years 1990-2017. The curve estimation methods (linear, quadratic, qubic, and hyperbolastic) and some non-linear time series models (Weibull, Negative Exponential, Brody, Gompertz, Logistic, Von Bertalanffy, Richards) were used for modeling the longitudinal data of monthly industrial production index values. The most fitted Gompertz model for all three data sets was determined according to the criteria of goodness of fit (coefficient of determination, mean square error, Akaike's information criterion, Bayesian information criterion), using the process between 1990-2008 (up to the 2008 crisis). After the 2008-2009 crisis, Brazil and G7 countries' industrial production index values were well below their expected values. In contrast, Turkey's expected values and the actual values for the industrial production index have been fairly close. Considering these results, it can be said that Turkey was less affected in terms of the effects of the 2008-2009 economic crisis than other countries. Industrial production index values of Turkey at 100th anniversary of the founding of the Republic of Turkey in 2023, and other important dates in 2041 and 2050 were estimated to be 177.62, 353.49 and 485.63, respectively.

Predicting the incidence of hand, foot and mouth disease in Sichuan province, China using the ARIMA model

2015 ◽  
Vol 144 (1) ◽  
pp. 144-151 ◽  
Author(s):  
L. LIU ◽  
R. S. LUAN ◽  
F. YIN ◽  
X. P. ZHU ◽  
Q. LÜ
Keyword(s):  
Goodness Of Fit ◽  
Arima Model ◽  
Foot And Mouth Disease ◽  
Information Criterion ◽  
Sichuan Province ◽  
Mouth Disease ◽  
Control Measures ◽  
Coefficient Of Determination ◽  
Goodness Of Fit Test ◽  
Foot And Mouth

SUMMARYHand, foot and mouth disease (HFMD) is an infectious disease caused by enteroviruses, which usually occurs in children aged <5 years. In China, the HFMD situation is worsening, with increasing number of cases nationwide. Therefore, monitoring and predicting HFMD incidence are urgently needed to make control measures more effective. In this study, we applied an autoregressive integrated moving average (ARIMA) model to forecast HFMD incidence in Sichuan province, China. HFMD infection data from January 2010 to June 2014 were used to fit the ARIMA model. The coefficient of determination (R2), normalized Bayesian Information Criterion (BIC) and mean absolute percentage of error (MAPE) were used to evaluate the goodness-of-fit of the constructed models. The fitted ARIMA model was applied to forecast the incidence of HMFD from April to June 2014. The goodness-of-fit test generated the optimum general multiplicative seasonal ARIMA (1,0,1) × (0,1,0)12 model (R2 = 0·692, MAPE = 15·982, BIC = 5·265), which also showed non-significant autocorrelations in the residuals of the model (P = 0·893). The forecast incidence values of the ARIMA (1,0,1) × (0,1,0)12 model from July to December 2014 were 4103–9987, which were proximate forecasts. The ARIMA model could be applied to forecast HMFD incidence trend and provide support for HMFD prevention and control. Further observations should be carried out continually into the time sequence, and the parameters of the models could be adjusted because HMFD incidence will not be absolutely stationary in the future.

scholarly journals Evaluation of non-linear models to describe development and fertility of codling moth at constant temperatures

2017 ◽  
Vol 20 (1) ◽  
pp. 3 ◽  
Author(s):  
H. Ranjbar Aghdam ◽  
Y. Fathipour ◽  
D. C. Kontodimas
Keyword(s):  
Goodness Of Fit ◽  
Linear Models ◽  
Information Criterion ◽  
Developmental Rate ◽  
Codling Moth ◽  
Coefficient Of Determination ◽  
Temperature Threshold ◽  
Optimum Temperature ◽  
Non Linear ◽  
Lower Temperature

Developmental rate of immature stages and age-specific fertility of females of codling moth at constant temperatures was modeled using non-linear models. The equations of Enkegaard, Analytis, and Bieri 1 and 2 were evaluated based on the value of adjusted R2 (R2adj) and Akaike information criterion (AIC) besides coefficient of determination (R2) and residual sum of squares (RSS). All models have goodness of fit to data especially for development [R2, R2adj, RSS and AIC ranged 0.9673-0.9917, 0.8601-0.9861, 0.08-6.7x10-4 and (-75.29) – (-46.26) respectively]. Optimum temperature (Topt) and upper threshold (Tmax) were calculated accurately (Topt and Tmax ranged 29.9-31.2oC and 35.9-36.7oC) by all models. Lower temperature threshold (Tmin) was calculated accurately by Bieri-1 model (9,9-10,8oC) whereas Analytis model (7,0-8,4oC) underestimated it. As far as fertility is concerned the respective values were better fitted near the optimum temperature (in 30oC) [R2 ,R2adj, RSS and AIC ranged 0,6966-0,7744, 0,5756-0,6455, 2,44-3,33 x10-4 and (-9,15)-7,15 respectively].

scholarly journals Comparison of the parameters of the lactation curve between normal and difficult calvings in Iranian Holstein cows

2019 ◽  
Vol 17 (1) ◽  
pp. e0401
Author(s):  
Navid Ghavi Hossein-Zadeh
Keyword(s):  
Dairy Cows ◽  
Milk Yield ◽  
Goodness Of Fit ◽  
Linear Models ◽  
Information Criterion ◽  
Holstein Cows ◽  
Coefficient Of Determination ◽  
Lactation Curve ◽  
Non Linear ◽  
Best Fit

To evaluate effect of dystocia on the lactation curve characteristics for milk yield and composition in Holstein cows, six non-linear models (Brody, Wood, Sikka, Nelder, Dijkstra and Rook) were fitted on 5,917,677 test day records for milk yield (MY), fat (FP) and protein (PP) percentages, fat to protein ratio (FPR) and somatic cell score (SCS) of 643,625 first lactation Holstein cows with normal calving or dystocia from 3146 herds which were collected by the Animal Breeding Center of Iran. The models were tested for goodness of fit using adjusted coefficient of determination, root means square error, Akaike’s information criterion and Bayesian information criterion. Rook model provided the best fit of the lactation curve for MY and SCS in normal and difficult calvers and dairy cows with dystocia for FP. Dijkstra model provided the best fit of the lactation curve for PP and FPR in normal and difficult calvers and dairy cows with normal calving for FP. Dairy cows with dystocia had generally lower 100-d, 200-d and 305-d cumulative milk yield compared with normal calvers. Time to the peak milk yield was observed later for difficult calvers (89 days in milk vs. 79 days in milk) with lower peak milk yield (31.45 kg vs. 31.88 kg) compared with normal calvers. Evaluation of the different non-linear models indicated that dystocia had important negative effects on milk yield and lactation curve characteristics in dairy cows and it should be reduced as much as possible in dairy herds.

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.

scholarly journals Selection of models of lactation curves to use in milk production simulation systems

2010 ◽  
Vol 39 (4) ◽  
pp. 891-902 ◽  
Author(s):  
Daniel de Noronha Figueiredo Vieira da Cunha ◽  
José Carlos Pereira ◽  
Fabyano Fonseca e Silva ◽  
Oriel Fajardo de Campos ◽  
José Luis Braga ◽  
...  
Keyword(s):  
Milk Production ◽  
Goodness Of Fit ◽  
Information Criterion ◽  
Coefficient Of Determination ◽  
Mean Square ◽  
Good Convergence ◽  
Lactation Curve ◽  
Production Group ◽  
Daily Milk Production ◽  
Simulation Systems

The objective of this study was to select models of lactation curves with a better adjustment to the observed data in models of milk production simulation systems. A data base on 6,459 recordings of daily milk production was used. These data were obtained from monthly and fortnightly controls of milk between 2004 and 2007, from 472 lactations of animals from ten different milking cow herd farms. Based on rolling averages of milk production (MP-L/day) per cow, the ten herd farms were divided into low (L < 15), medium (15 <M < 20) and high (H > 20). Data were also divided according to the lactation numbers in first, second, third or greater. Eight lactation curve models commonly used in literature were compared. The models were individually adjusted for each lactation. The goodness of fit used for comparison of those models was the coefficient of determination, mean square error, mean square prediction error and the Bayesian information criterion. The values for the goodness of fit obtained in each model were compared by using 95% probability confidence interval. Wilmink (1987) model showed a better adjustment for cows of the first lactation numbers, whereas the Wood (1967) model showed a better adjustment for cows of the third or greater lactations numbers for the low milk production groups. Wood model showed a better adjustment for all the lactation numbers for the medium milk production group. Dijkstra (1997) model showed a better adjustment for all lactation numbers for the high milk production group. Despite of being more recent, the model by Pollott (2000), mechanist based and with a higher number of parameters, showed a good convergence for the used data.

scholarly journals NONLINEAR MODELS FOR INFRARED DRYING OF MINT

2019 ◽  
Vol 49 (1) ◽  
pp. 19-24
Author(s):  
E. K. BASAR ◽  
N. HEYBELI ◽  
M. Z. FIRAT ◽  
C. ERTEKIN*
Keyword(s):  
Goodness Of Fit ◽  
Nonlinear Models ◽  
Information Criterion ◽  
Coefficient Of Determination ◽  
Drying Process ◽  
Infrared Drying ◽  
Thin Layer Drying ◽  
Drying Models ◽  
Thin Layer Drying Models ◽  
Logistic Functions

In this paper, 105 different semitheoretical and empirical thin layer drying models were used for describing the drying process of the mint leaves. Comparisons of the overall goodness of fit were based on Coefficient of Determination (R2), Root Mean Square Error (RMSE), Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). It was concluded that five parameter Cedergreen-Ritz-Streibig modified log-logistic functions with alpha equal to 0.25 (CRS5C) model describe the infrared drying process of the mint leaves. Furthermore, temperature effect was investigated by using reduction test. Finally, it was found that the effect is statistically significant and the model with separate trends fits these data better.

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