Nonlinear modeling of the growth of ornamental pepper accessions under high-temperature stress conditions

The aim ofthe present study is to determine the time-dependent changes in the live weights of the geese, for which environmental enrichment was applied (Turkish local goose genotype), between the days 7 and 98. For this purpose, nonlinear Brody, Gompertz, Logistic, von Bertalanffy, and Richards growth models, which are used commonly, were used to determine the growth and development of poultry. Geese were divided into 3 groups (control group (C), broom group (B), mirror group (M)) based on their enrichment characteristics. The success status of the models applied in the present study was assessed based on error mean square (EMS) and coefficient of determination (R2) values. It was found thatR2 value was be 96.86 in the Logistic model, 96.82 in Brody model, 96.16 in vonBertalanffy model,95.04 in Gompertz model and 93.85 in Richards model, respectively, and EMS value was 0.2368 in Logistic model, 0.2004in Brody model, 0.1992 in von Bertalanffy model, 0.3567 in Gompertz model and 0.3711 in Richards model, respectively. As a result, it was concluded that the most suitable models with high coefficient of determination but low error mean square were Brody,Gompertz, and von Bertalanffy models, respectively, in determining the time-dependent live weight change in the geese (Turkish local goose genotype), for which environmental enrichment was applied, and it was suitable to use these three models in determining the effect of environmental enrichment on live weight.

The objective of this study was to select the best non-linear model that fits the growth curve of turkeys managed under the tropical conditions of Southern Mexico. Data from 481 Hybrid converter turkeys (236 females and 245 males) reared under commercial conditions typical of that region were used. Turkeys were given ad libitum access to feed and water. Body weight was weekly recorded from 1 day to 23 weeks of age. Five non-linear mathematical models (Brody, Gompertz, Logistic, von Bertalanffy and Richards) were chosen to describe the age-weight relationship. The Brody and Richards' models fail to converge. The best fitting model was chosen based on the average prediction error (APE); the multiple determination coefficient R2 and the Akaike information criterion (AIC). In both sexes, von Bertalanffy and Gompertz were the best models. The highest estimates of parameter A (mature weight) for both females and males were obtained with the von Bertalanffy model followed by the Gompertz and Logistic. The estimates of A were higher for males than for females. The highest estimates of parameter k (rate of maturity) for both females and males were, in decreasing order for the Logistic, Gompertz, and von Bertalanffy models. k values for female turkeys was higher than for males. The age at the point of inflection and body weight at the age of point of inflection varied with the model used. The largest values of TI and WI corresponded to the Logistic model. Between sexes, the largest TI and WI values corresponded to males. The best models to describe turkey growth were the von Bertalanffy and Gompertz models, because it presented the highest APE, R2 and AIC values.

Objetivo. Determinar el modelo no lineal que mejor ajuste la curva de crecimiento de pavos locales criados en confinamiento. Material y métodos. Veinticuatro y 43 pavos hembras y machos, respectivamente, criados en confinamiento fueron alimentados con dietas comerciales. Cada animal se pesó desde el nacimiento hasta la semana 29 de edad. Los modelos de Gompertz, Brody, Richards, von Bertalanffy y Logístico fueron elegidos para describir la relación edad-peso. El mejor modelo se seleccionó con base en el coeficiente de determinación (R2), el criterio de información de Akaike (AIC) y el análisis visual de las curvas observadas y predichas. Resultados. El mejor ajuste (machos y hembras) correspondió al modelo von Bertalanffy. El más alto valor del parámetro A (edad a la madurez), para hembras y machos correspondió al modelo von Bertalanffy, seguido de Gompertz y Logístico. El estimador A fue mayor para machos que hembras. El mayor valor del parámetro k (tasa de madurez), para hembras y machos, variaron según el modelo utilizado. Los valores de k fueron más altos para hembras que para machos. La edad al punto de inflexión (TI) y peso vivo al punto de inflexión (WI) también variaron de un modelo a otro. Los valores más altos de TI y WI correspondieron al modelo Logístico. Entre sexos, los valores mayores de TI y WI correspondieron a los machos. Conclusiones. El mejor modelo que describió la curva de crecimiento de los pavos locales fue el de von Bertalanffy.

This study was developed with longitudinal data measurements of Norfolk rabbits from birth to 119 days of age to estimate the average growth curve, with the primary objective of proposing a non-linear model. It also selected the most appropriate sigmoidal model to describe the growth of Norfolk rabbits. The adjustments provided by the logistic, von Bertalanffy, Gompertz, Brody, Richards, and proposed models were compared. The parameters were estimated using the “nls” function of the “stats” package in R software, the least-squares method, and the Gauss-Newton convergence algorithm. The goodness-of-fit comparison was based on the following criteria: adjusted coefficient of determination (), mean square error (MSE), mean absolute deviation (MAD), Akaike information criterion (AIC), and Bayesian information criterion (BIC). Cluster analysis helped select and classify the non-linear growth models, considering the other goodness-of-fit criteria results. The proposed non-linear, von Bertalanffy, Gompertz, and Richards models described the growth curve of Norfolk rabbits satisfactorily, providing parameters with practical interpretations. The goodness-of-fit criteria showed that the proposed and von Bertalanffy models best represented the growth of rabbits.

In this study, the Von Bertalanffy, Richards, Gompertz, Brody, and Logistics non-linear mixed regression models were compared for their ability to estimate the growth curve in commercial laying hens. Data were obtained from 100 Lohmann LSL layers. The animals were identified and then weighed weekly from day 20 after hatch until they were 553 days of age. All the nonlinear models used were transformed into mixed models by the inclusion of random parameters. Accuracy of the models was determined by the Akaike and Bayesian information criteria (AIC and BIC, respectively), and the correlation values. According to AIC, BIC, and correlation values, the best fit for modeling the growth curve of the birds was obtained with Gompertz, followed by Richards, and then by Von Bertalanffy models. The Brody and Logistic models did not fit the data. The Gompertz nonlinear mixed model showed the best goodness of fit for the data set, and is considered the model of choice to describe and predict the growth curve of Lohmann LSL commercial layers at the production system of University of Antioquia.

ObjectiveThe identification of nonlinear mixed models that describe the growth trajectory of New Zealand rabbits was performed based on weight records and carcass measures obtained using ultrasonography.MethodsPhenotypic records of body weight (BW) and loin eye area (LEA) were collected from 66 animals raised in a didactic-productive module of cuniculture located in the southern Piauí state, Brazil. The following nonlinear models were tested considering fixed parameters: Brody, Gompertz, Logistic, Richards, Meloun 1, modified Michaelis-Menten, Santana, and von Bertalanffy. The coefficient of determination (R2), mean squared error, percentage of convergence of each model (%C), mean absolute deviation of residuals, Akaike information criterion (AIC), and Bayesian information criterion (BIC) were used to determine the best model. The model that best described the growth trajectory for each trait was also used under the context of mixed models, considering two parameters that admit biological interpretation (A and k) with random effects.ResultsThe von Bertalanffy model was the best fitting model for BW according to the highest value of R2 (0.98) and lowest values of AIC (6,675.30) and BIC (6,691.90). For LEA, the Logistic model was the most appropriate due to the results of R2 (0.52), AIC (783.90), and BIC (798.40) obtained using this model. The absolute growth rates estimated using the von Bertalanffy and Logistic models for BW and LEA were 21.51g/d and 3.16 cm2, respectively. The relative growth rates at the inflection point were 0.028 for BW (von Bertalanffy) and 0.014 for LEA (Logistic).ConclusionThe von Bertalanffy and Logistic models with random effect at the asymptotic weight are recommended for analysis of ponderal and carcass growth trajectories in New Zealand rabbits. The inclusion of random effects in the asymptotic weight and maturity rate improves the quality of fit in comparison to fixed models.

Simple SummaryAshidan yak is a new breed of hornless yak developed by Chinese scientists, which has an important economic value. However, little is known about the growth of Ashidan yaks. This study analyzed the body weight and body size measurements of 260 female Ashdan yaks and compared the performance of five nonlinear models (Logistic model, Gompertz model, Brody model, von Bertalanffy model and Richards model). Our results showed that the early growth and development of Ashidan yak change with the seasons, and the Richards model performs better among the five models.Understanding animal growth plays an important role in improving animal genetics and breeding. In order to explore the early growth and development law of Ashidan yak, the body weight (BW), wither height (WH), body oblique length (BL) and chest girth (CG) of 260 female Ashidan yaks were measured. These individuals grew under grazing conditions, and growth traits were measured at 6, 12, 18 and 30 months of age. Then the absolute growth and relative growth of Ashidan yak were calculated, and five nonlinear models (Logistic model, Gompertz model, Brody model, von Bertalanffy model and Richards model) were used to fit the growth curve of Ashidan yak. The fitting effect of the model was evaluated according to MSE, AIC and BIC. The results showed that the growth rate of Ashidan yak was the fastest from 12 to 18 months old, and the growth was slow or even stagnant from 6 to 12 months old. The AIC and BIC values of the Richards model were the lowest among the five models, with an AIC value of 4543.98 and a BIC value of 4563.19. The Richards model estimated body weight at 155.642 kg. In summary, the growth rate of female Ashidan yak changes with the seasons, growing faster in warm seasons and slower in cold seasons. Richards model is the best model to describe the growth curve of female Ashidan yak in five nonlinear models.

Growth curves models provide a visual assessment of growth as a function of time, and prediction body weight at a specific age. This study aimed at estimating tinamous growth curve using different models, and at verifying their goodness of fit. A total number 11,639 weight records from 411 birds, being 6,671 from females and 3,095 from males, was analyzed. The highest estimates of a parameter were obtained using Brody (BD), von Bertalanffy (VB), Gompertz (GP,) and Logistic function (LG). Adult females were 5.7% heavier than males. The highest estimates of b parameter were obtained in the LG, GP, BD, and VB models. The estimated k parameter values in decreasing order were obtained in LG, GP, VB, and BD models. The correlation between the parameters a and k showed heavier birds are less precocious than the lighter. The estimates of intercept, linear regression coefficient, quadratic regression coefficient, and differences between quadratic coefficient of functions and estimated ties of quadratic-quadratic-quadratic segmented polynomials (QQQSP) were: 31.1732±2.41339; 3.07898± 0.13287; 0.02689±0.00152; -0.05566±0.00193; 0.02349±0.00107, and 57 and 145 days, respectively. The estimated predicted mean error values (PME) of VB, GP, BD, LG, and QQQSP models were, respectively, 0.8353; 0.01715; -0.6939; -2.2453; and -0.7544%. The coefficient of determination (R²) and least square error values (MS) showed similar results. In conclusion, the VB and the QQQSP models adequately described tinamous growth. The best model to describe tinamous growth was the Gompertz model, because it presented the highest R² values, easiness of convergence, lower PME, and the easiness of parameter biological interpretation.

Aim:This study aimed to identify the effect of the insulin-like growth factor 1 (IGF1) gene on growth, to uncover the genetic marker at the IGF1 gene, and to predict growth performance by analyzing growth models of Kejobong goats based on their genotype.Materials and Methods:DNA and records of body weight (BW) and body measurements (BM) of Kejobong goats were collected, the IGF1 gene was amplified from the DNA template by polymerase chain reaction (PCR); the PCR products were then sequenced to determine single nucleotide polymorphisms (SNP). Linear mixed model (LMM) was used to analyze the association between SNP and growth traits. Four non-linear growth models were analyzed using non-LMM to describe the growth model and to compare the growth within genotypes.Results:An SNP at intron 4 (g5752G→C) genotyped into GG and CC was significantly associated with BW and BM. Goats of genotype GG had a significantly higher BW and BM (p<0.05) than those of genotype CC. Growth analysis showed that the von Bertalanffy model was the most fit for describing BW, the Brody model for chest width and hip height, the Gompertz and Logistic models for heart girth, and the von Bertalanffy and Gompertz models for hip width.Conclusion:An SNP at intron 4 of the IGF1 gene was associated with the growth trait and was usable as a genetic marker candidate for improvement of growth traits of Kejobong goats while von Bertalanffy model provides proper and accurate estimates of parameters to describe the growth performance of Kejobong goats.

Seven non-linear growth models were compared in the Andalusian turkey, an endangered native breed. To this aim, turkeys were weekly weighted until they reached 35 weeks. The goodness-of-fit and flexibility criteria of Brody, Von Bertalanffy, Verhulst, Logistic, Gompertz, Richards, and Sinusoidal growth models were evaluated to quantify their ability to describe the biological growth curve. Goodness-of-fit criteria were assessed comparing the mean squared error (MSE) and adjusted determination coefficient (Pseudo-R2), while the flexibility criteria of Akaike (AIC) and Bayesian information criteria (BIC) were evaluated to quantify the explanatory and predictive ability of the models tested. Afterward, all criteria were considered in a combined index to determine the most efficient model to describe and predict growth patterns. The best-fitting model for males growth was Logistic (MSE: 250,349.87; Pseudo-R2: 0.97) which also reported the best explanatory and predictive properties (AIC: 18,949.25; BIC: 18,963.24), while best goodness-of-fit criteria, explanatory and predictive capacity in females were reported for the Richards model (MSE: 144,432.45; Pseudo-R2: 0.95; AIC: 17,529.83; BIC: 17,549.02, respectively). Von Bertalanffy and Richards models underestimated the weight at early age stages, contrary to Logistic and Verhulst models. The asymptotic weight was higher in males than in females at all evaluated models, being 11,085.37 g for Logistic and 5,706.38 g for Richards, respectively. In conclusion, a marked sexual dimorphism is evident, with females reaching maturity earlier than males. The higher inflection point in males may enable their relatively easier commercial standardisation than in turkey hens. Highlights Logistic was the best fitting model for males' growth and Richards for females. Females reach maturity earlier than males with higher rates of maturity. Andalusian turkey breed shows an intense sexual dimorphism.

Prediction of growth patterns of commercial chicken strains is important. It can provide visual assessment of growth as function of time and prediction body weight (BW) at a specific age. The aim of current study is to compare the three nonlinear functions (i.e., Logistic, Gompertz, and von Betalanffy) for modeling the growth of twenty five commercial Korean native chicken (KNC) strains reared under a battery cage system until 32 weeks of age and to evaluate the three models with regard to their ability to describe the relationship between BW and age. A clear difference in growth pattern among 25 strains were observed and classified in to the groups according to their growth patterns. The highest and lowest estimated values for asymptotic body weight (C) for 3H and 5W were given by von Bertalanffy and Logistic model 4629.7 g for 2197.8 g respectively. The highest estimated parameter for maturating rate (b) was given by Logistic model 0.249 corresponds to the 2F and lowest in von Bertalanffy model 0.094 for 4Y. According to the coefficient of determination (<TEX>$R^2$</TEX>) and mean square of error (MSE), Gompertz and von Bertalanffy models were suitable to describe the growth of Korean native chicken. Moreover, von Bertalannfy model was well described the most of KNC growth with biologically meaningful parameter compared to Gompertz model.

The present study was conducted to estimate and compare the three types of growth models in Hanwoo steer (Bos aurus coreanae). The Gompertz, Von Bertalanffy, and Logistic nonlinear models were used. A total of 2,239 Hanwoo steers (Bos taurus coreanae) from 6 months to 24 months old (2003 to 2014) and 8,916 growth data from the Hanwoo improvement Center were used to estimate the growth model which included three parameters. These parameters were A, mature body weight; b, growth ratio; and k, intrinsic growth rate. Regression equations using the Gompertz, Von Bertalanffy, and Logistic models were calculated as respectively. The mean square errors (MSEs) for each model were 1945.9, 1958.7, and 1935.0, respectively. The equation using the Logistic model showed the lowest value among three models. The estimated birth weights from the Gompertz, Von Bertalanffy, and Logistic models were 50.35 kg, 36.94 kg, and 74.13 kg, respectively. Furthermore, the estimated mature weights from the Gompertz, Von Bertalanffy, and Logistic models were 919.0 kg, 1043.3 kg, and 770.0 kg, respectively. In addition, the estimated age and body weight at inflection from the Gompertz, Von Bertalanffy, and Logistic models were 349.0 days and 338.1 kg, 317.9 days and 308.2 kg, and 397.8 days and 385.0 kg, respectively. Based on the results, we concluded that the regression equation using the Logistic model was the most appropriate among the growth models for measuring data. However, further studies would be needed in order to obtain more accurate parameters using a much wider period of data from birth to shipping age.

This study aimed to estimate growth curve parameters in Hanwoo cattle using nonlinear models. Body weight records were collected from the Hanwoo Research Center, the Nonghyup Hanwoo Improvement Center, and commercial farms. Animals were categorized by sex and feeding system, and growth was modeled using Gompertz, Richards, and von Bertalanffy equations.For breeding cows, estimated mature weights were 416.4±1.4 kg (1980s), 451.5±1.5 kg (1990s), and 442.7±1.4 kg (2000s) with the Gompertz model; 488.0±4.2 kg, 497.7±3.0 kg, and 484.6±2.2 kg with the Richards model; and 426.5±1.5 kg, 462.3±1.6 kg, and 451.3±1.4 kg with the von Bertalanffy model. For fattening heifers, mature weights were 756.5±9.0 kg (Gompertz), 782.3±20.0 kg (Richards), and 816.5±12.3 kg (von Bertalanffy). In bulls, mature weights at the Hanwoo Research Center were 801.2±7.3 kg (Gompertz), 892.6±19.7 kg (Richards), and 905.5±10.7 kg (von Bertalanffy); at the Improvement Center, they were 563.0±7.4 kg and 612.5±10.1 kg using Gompertz and von Bertalanffy, respectively. For steers, estimates from Gompertz and von Bertalanffy were 893.2±10.4 kg and 1065.0±17.3 kg (Research Center), 1046.2±11.2 kg and 1285.5±20.8 kg (Improvement Center), and 903.3±13.6 kg and 1037.2±21.4 kg (farm). Richards model parameters were often not estimable in certain subgroups. Overall, the von Bertalanffy model showed the best overall fit and stability, making it the most suitable model for describing Hanwoo growth and supporting breeding and management strategies.

Comparison of growth models for sequential hermaphrodites by considering multi-phasic growth

본 연구는 1970년대 이후 축산기술연구소 대관령지소에서 출생한 한우 암소로부터 한우암소의 성장곡선 모수에 영향하는 환경요인의 효과를 추정함으로써 한우의 개량을 위한 정보를 얻고자 실시하였다. Gompertz 모형, von Bertalanffy 모형 및 Logistic 모형에 의해 추정된 성장곡선 모수들의 분산분석 결과는 모두 같은 경향을 나타냈는데, 출생년도-계절의 효과는 성숙체중, 성장비 및 성숙률 모두에게 영향을 미치며, 어미소 연령의 효과는 성장비에서만 영향을 미쳤고, 공변이로 선형 모형에 포함된 최종 체중 측정시 일령의 효과는 성장비를 제외한 성숙체중과 성숙률에 영향을 미치는 것으로 나타났다. Gompertz 모형, von Bertalanffy 모형 및 Logistic 모형에 의해 개체별로 추정한 모수 A는 가을에 출생한 개체들이 봄에 출생한 개체들에 비해 10.47<TEX>${\pm}$</TEX>7.9, 19.01<TEX>${\pm}$</TEX>9.79 및 13.43<TEX>${\pm}$</TEX>5.94kg 더 무거웠으며 Logistic 모형에서 통계적 유의성(P〈.05)이 있었으며, 성숙률은 봄에 출생한 개체들이 가을에 출생한 개체들에 비해 0.00021<TEX>${\pm}$</TEX>0.00009, 0.00022<TEX>${\pm}$</TEX>0.00009 및 0.00041<TEX>${\pm}$</TEX>0.00013으로 높았고 통계적인 유의성(P〈.05)이 있었다. 어미소 연령 그룹별 성장모수들의 최소자승평균치를 보면 연령이 2세나 3세인 어미소로부터 태어난 암소들은 다른 연령그룹의 어미소로부터 태어난 암소들에 비해 성숙체중은 크지 않으면서 성장비가 크고 성숙률은 작은 경향을 보이고 있는데 성숙체중은 크지 않으면서 성장비가 크다는 것은 생시체중이 작다는 것을 시사한다. 따라서 한우 암소를 1산이나 2산까지만 번식에 이용한 후 비육 출하하는 생산체계를 유지하는 집단에서는 축군의 생시체중이 작아지고 성숙체중도 작아지는 현상이 나타날 우려가 있다. 본 연구에서는 성장곡선 모수에 영향을 미치는 환경요인으로서 출생년도-계절과 어미소 연령을 고정효과로 하고 여기에 최종 체중 측정시 일령의 1차식 효과를 공변이로 추가시켰는데, 분산분석 결과 최종 체중 측정시 일령이 세 가지 성장 모형으로 추정한 성숙체중과 성숙률에 영향을 미치는 것으로 나타났다. 이러한 결과들은 최종 체중 측정시 일령에 따라서 성장특성이 달라질 수 있음을 의미하므로 성장곡선 모형의 연구를 위해서는 최종 체중 측정 시점을 변이요인으로 고려하여야 한다. 그리고 한우의 성장 패턴을 좀더 잘 규명하기 위해서는 2차 이상의 다항회귀식 효과에 대한 검토가 필요하다. Some growth curve models were used to fit individual growth of 1,083 Hanwoo cows born from 1970 to 2001 in Daekwanryeong branch, National Livestock Research Institute(NLRI). The effects of year-season of birth and age of dam were analyzed. In analysis of variance for growth curve parameters, the effects of birth year-season were significant for mature weight(A), growth ratio(b) and maturing rate(k)(P〈.01). The effects of age of dam were significant for growth ratio(b) but not significant for mature weight(A) and maturing rate(k). The linear term of the covariate of age at the final weights was significant for the A(P〈.01) and k(P〈.01) of Gompertz model, von Bertalanffy model and Logistic model. For the growth curve parameters fitted on individual data using Gompertz model, von Bertalanffy model and Logistic model, resulting the linear contrasts(fall-spring), Least square means of A in three nonlinear models were higher cows born at fall and A of Logistic model was significant(P〈.05) between the seasons. According to the results of the least square means of growth curve parameters by age of dam, least square means of mature weight(A) in Gompertz model was largest in 6 year and smallest estimating for 3 and 8 years of age of dam. The growth ratio(b) was largest in 2 year of age of dam and smallest estimating in 8 year. The A and k were not different by age of dam(p〉.05), On the other hand, the b was different by age of dam(p〈.01). The estimate of A in von Bertalanffy model was largest in 6 year and smallest in 8 and 9 years of age of dam. The b was largest in 2 year and tend to decline as age of dam increased. The A and k were not different by age of dam(p〉.05), On the other hand, the b was highly significant by age of dam(p〈.01).