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.

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 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 Evaluation of lactation models in pasture-based dairy ewes in Bosnia and Herzegovina

2020 ◽  
Vol 70 (4) ◽  
pp. 275-283
Author(s):  
Dragica Šalamon ◽  
Alen Džidić ◽  
Neven Antunac ◽  
Stanko Ivanković ◽  
Vinko Batinić
Keyword(s):  
Root Mean Square Error ◽  
Milk Production ◽  
Bosnia And Herzegovina ◽  
Milk Fat ◽  
Milk Composition ◽  
Coefficient Of Determination ◽  
Mean Square ◽  
Dairy Ewes ◽  
Lactation Curve ◽  
Curve Model

Milk of Kupres, Privor and Stolac dairy ewe breeds is used for the production of the fine cheese varieties. To the best of our knowledge there are no information about milk production and milk composition of these pasture-based dairy ewes. The aim was to determine the best lactation curve model in autochthonous pasture-based dairy ewes in Bosnia and Herzegovina. Milk production was recorded and milk composition sampled (milk fat and protein) during early, mid and late lactation in 129 Kupres, 141 Privor and 129 Stolac pramenka ewes. Four lactation models (Wilmink, Cubic, Ali-Shaeffer and Guo-Swalve) were compared and selected based on the lowest coefficient of determination and root mean square error. The Guo-Swalve model described all of the measured variables most successfully. Kupres pramenka dairy ewe was the highest producing breed with 139 kg of milk during 175 days of lactation (0.79 kg/d; between lactation day 50 to 225) and showed the standard lactation curve. Privor pramenka produced 118 kg of milk during 175 days of lactation (0.67 kg/d) and Stolac pramenka 101 kg of milk during 175 days of lactation (0.58 kg/d). Both showed atypical constantly decreasing shape of the lactation curve common in low producing dairy ewes. The prediction of milk yield and milk composition from the Guo-Swalve model could be used by the national breeding program for the Kupres, Privor and Stolac pramenka sheep breeds. Additional research during a more stable management conditions is recommended for Privor and Stolac pramenka.

scholarly journals Estimating Maximum Daily Precipitation in the Upper Vistula Basin, Poland

Atmosphere ◽  
2019 ◽  
Vol 10 (2) ◽  
pp. 43 ◽  
Author(s):  
Dariusz Młyński ◽  
Andrzej Wałęga ◽  
Andrea Petroselli ◽  
Flavia Tauro ◽  
Marta Cebulska
Keyword(s):  
Root Mean Square Error ◽  
Mean Square Error ◽  
Root Mean Square ◽  
Goodness Of Fit ◽  
Daily Precipitation ◽  
Probability Distributions ◽  
Random Variables ◽  
Coefficient Of Determination ◽  
Mean Square ◽  
Probability Of Exceedance

The aim of this study was to determine the best probability distributions for calculating the maximum annual daily precipitation with the specific probability of exceedance (Pmaxp%). The novelty of this study lies in using the peak-weighted root mean square error (PWRMSE), the root mean square error (RMSE), and the coefficient of determination (R2) for assessing the fit of empirical and theoretical distributions. The input data included maximum daily precipitation records collected in the years 1971–2014 at 51 rainfall stations from the Upper Vistula Basin, Southern Poland. The value of Pmaxp% was determined based on the following probability distributions of random variables: Pearson’s type III (PIII), Weibull’s (W), log-normal, generalized extreme value (GEV), and Gumbel’s (G). Our outcomes showed a lack of significant trends in the observation series of the investigated random variables for a majority of the rainfall stations in the Upper Vistula Basin. We found that the peak-weighted root mean square error (PWRMSE) method, a commonly used metric for quality assessment of rainfall-runoff models, is useful for identifying the statistical distributions of the best fit. In fact, our findings demonstrated the consistency of this approach with the RMSE goodness-of-fit metrics. We also identified the GEV distribution as recommended for calculating the maximum daily precipitation with the specific probability of exceedance in the catchments of the Upper Vistula Basin.

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.

Application of the Wood model to analyse lactation curves of organic dairy sheep farming

2014 ◽  
Vol 54 (10) ◽  
pp. 1609 ◽  
Author(s):  
Juan Carlos Ángeles Hernández ◽  
Octavio Castelán Ortega ◽  
Benito Albarrán Portillo ◽  
Hugo H. Montaldo ◽  
Manuel González Ronquillo
Keyword(s):  
Milk Yield ◽  
Goodness Of Fit ◽  
Evaluation Criteria ◽  
Coefficient Of Determination ◽  
Dairy Sheep ◽  
Organic System ◽  
Dairy Ewes ◽  
Lactation Curve ◽  
Total Milk ◽  
Wood Model

The aim of the present study was to evaluate the performance of the Wood model to describe the characteristics of lactation curves of dairy ewes under organic management in Mexico. In total, 4861 weekly test-day milk yield records from 194 lactations of crossbred dairy ewes were analysed to assess the performance of an empirical model to fit their lactation curve. We used the mathematical model proposed by Wood. The evaluation criteria were the correlation coefficient (r) between the values of total milk yield observed and estimated, the coefficient of determination (R2), and the mean square prediction error (MSPE). In addition, the peak yield (PYest) and time at peak yield (PTest) were calculated. The Wood model showed adequate goodness of fit (r = 0.95, R2 = 0.92 and MSPE = 0.024). The Wood model detected that 52.06% of lactation curves had a continuously decreasing shape (atypical curve), probably as a consequence of the characteristic management of the organic system, mainly due to the genotype used and the nutritional management. Residuals were greater for atypical curves than for typical ones, indicating differences in the ability of the Wood model to fit the two types of shapes. In typical curves, the Wood model showed adequate estimates of total milk yield and time at peak yield. The peak yield was underestimated both in typical and atypical curves. The Wood model in atypical curves underestimated the time at peak yield and milk yields in late lactation. The Wood model showed a reasonable fit of lactation curve in dairy sheep in organic systems but presented deficiencies of fit in atypical curves; therefore, estimates should be interpreted carefully.

DRYING KINETICS AND MOISTURE DIFFUSIVITY OF FOUR VARIETIES OF BAMBARA BEANS

2021 ◽  
Vol 6 (1) ◽  
pp. 30-33
Author(s):  
E.O. Awotona ◽  
A.O. Alade ◽  
S.A. Adebanjo ◽  
O. Duduyemi ◽  
T.J. Afolabi
Keyword(s):  
Root Mean Square Error ◽  
Mean Square Error ◽  
Root Mean Square ◽  
Goodness Of Fit ◽  
Moisture Diffusivity ◽  
Coefficient Of Determination ◽  
Mean Square ◽  
Fit Statistics ◽  
Drying Behavior ◽  
Maximum Coefficient

Drying of bambara beans was studied at 40oC at every 30 minutes in a Laboratory oven. Effective moisture diffusivity ranges between 5.886 x 10-10 m2/s – 4.354 x 10-10 m2/s respectively. The statistical criteria used in evaluation of the model were maximum coefficient of determination R2 and minimum root mean square error [RMSE]. Determination for goodness of fit statistics for drying of the beans was carried out. Midilli model was used to predict the drying curve. The Midili model was found to produce accurate predictions for all the four varieties of bambara beans and the model was shown to be an excellent model for predicting drying behavior of TVSU-47 and the R2 value was 0.9971 and the value of root mean square error was 0.0149 respectively.

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 Sinusoidal function to describe the growth curve of dairy heifers

2019 ◽  
Vol 59 (6) ◽  
pp. 1039
Author(s):  
H. Darmani Kuhi ◽  
N. Ghavi Hossein-Zadeh ◽  
S. López ◽  
S. Falahi ◽  
J. France
Keyword(s):  
Root Mean Square Error ◽  
Mean Square Error ◽  
Bayesian Information Criterion ◽  
Information Criterion ◽  
Coefficient Of Determination ◽  
Mean Square ◽  
Dairy Heifers ◽  
Growth Functions ◽  
Best Fit ◽  
Sinusoidal Function

The objective of the present study is to introduce a sinusoidal function into dairy research and production by applying it to bodyweight records (from 1 to 24 months) from six dairy cow breeds reported by the Dairy Heifer Evaluation Project of Penn State Extension (USA) from 1991 to 1992. The function was evaluated with regard to its ability to describe the relationship between bodyweight and age in dairy heifers, and then compared with seven standard growth functions, namely monomolecular, logistic, Gompertz, von Bertalanffy, Richards, Schumacher and Morgan. The models were fitted to monthly bodyweight records of dairy heifers using non-linear regression to derive estimates of the parameters of each function. The models were tested for goodness of fit by using adjusted coefficient of determination, root mean square error, Akaike’s information criterion and Bayesian information criterion. Values of adjusted coefficient of determination were generally high for all models, suggesting the generally appropriate fit of the models to the data. The sinusoidal function provided the best fit of the growth curves for Brown Swiss, Guernsey and Milking Shorthorn breeds due to the lowest values of root mean square error, Akaike’s information criterion and Bayesian information criterion. According to the chosen statistical criteria, the Richards function provided the best fit for Ayrshire heifers, and the monomolecular the best for Holstein and Jersey. The least accurate estimates were obtained with the logistic. In conclusion, the sinusoidal function introduced here can be considered as an appropriate alternative to standard growth functions when modelling growth patterns in dairy heifers.

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