New approaches in choosing a suitable growth model: Mean Curvature and Arc Length Values

Abstract

Logistic, Gompertz and Bertalanffy sigmoid growth models are widely used to study the growth dynamics of populations such as living plants, animals and bacteria. Appropriate model selection and parameter estimation are very important as these models will be used to make practical inferences. Because different growth models are modeled biologically, regardless of whether the parameters are definable or not. Applications that do not take into account parameter identifiability can lead to unreliable parameter estimates and misleading interpretations. Therefore, first the most suitable model should be determined and then the parameters should be defined. In this study, two new suitable model determination criteria such as mean curvature and arc length are proposed. For this, firstly, the definition of curvature was given. Then, the mean curvature and arc length values of the data belonging to two different species (kangal dog growth and eucalyptus plant growth) were calculated. For this purpose, a comparison was made with model selection criteria available in the literature such as coefficient of determination, error sum of squares and Akaike information criterion (AIC). It has been determined that the results obtained from the mean curvature and arc length values are in accordance with the existing criteria. In the two datasets, it was seen that the fit model ranking for both the existing criteria and the criteria we proposed was the same. For this reason, it is thought that the mean curvature and arc length values can be accepted as suitable model selection criteria.