Sinusoidal function to describe the growth curve of dairy heifers

Abstract

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.

Modeling the growth curve in ducks: a sinusoidal model as an alternative to classical nonlinear models

“…Overall, the statistical criteria used for evaluating the growth models revealed some significant variations in the functions that represent the future growth of ducks. The estimated goodness of fit criteria showed that the sinusoidal growth function was found to be the most suitable for explaining the age-related changes in bodyweight in ducks when growth functions were compared, although the suitability of the models may depend on the data and gender ( Darmani Kuhi et al, 2019a ). However, choosing the optimal function necessitates paying close attention to how animals grow in various environmental settings ( Dogan et al, 2010 ).…”

“…In general, alternative equations are still required for several reasons: 1) It is possible that different breeds of chickens have unique growth patterns that are not well represented by traditional models, 2) Growth rates and patterns can vary significantly depending on the production systems and management techniques used, and 3) Due to the impact that environmental factors such as temperature, humidity and feed quality can have on growth, differentiated modeling approaches are required. Previous studies have reported on the suitability of a sinusoidal function (as an alternative) to model the growth curve of turkeys, broilers, quails, and dairy heifers ( Darmani Kuhi et al, 2018 , 2019a , b , c ). The production of ducks has developed into extremely specialized, well-coordinated systems.…”

Modelling growth in dairy heifers based on linear body measurements (withers height) using non-linear functions

“…Growth curves of BW against age are typically sigmoidal, thus functions representing such a pattern (e.g. Gompertz, von Bertalanffy, Schumacher, Richards, López) are highly suitable for describing these curves in most farm animal species (López et al, 2000), including dairy heifers (Darmani Kuhi et al, 2019). However, curves based on linear body measurements do not show a clear sigmoidal pattern, explaining the best fits obtained in the current study were with the Michaelis-Menten and monomolecular equations, both representing diminishing returns (nonsigmoidal) behaviour.…”

“…The pattern of growth can be related to the nutrient requirements, efficiency of the production system and the longevity of the cow. Growth curve studies in cattle have mainly focused on non-linear models that relate body weight (BW) to age (López et al, 2015;Darmani Kuhi et al, 2019). Non-linear models such as growth functions provide an effective means of summarizing information contained in a data series into a few parameters and indicators with biological meaning.…”

Comparison of nonlinear functions to describe lactation curves for cumulative milk production in buffalo

“…These handicaps can be surmounted by using cumulative lactation curves (López et al, 2015). Currently, the suitability of sinusoidal functions, as newly applied equations, is confirmed for describing growth curves in broiler chicks, quail, dairy heifers and turkeys (Darmani Kuhi et al, 2018Kuhi et al, , 2019aKuhi et al, , 2019bKuhi et al, , 2019c. Therefore, the objective of this study was to investigate the suitability of sinusoidal and conventional growth functions (viz.…”