Growth curve: an intelligent life history described by a mathematical model! - Garcia-Neto, Manoel; Kebreab, Ermias (My University, 2020)
A mystery! This is a classic answer to define what growth is (von Bertalanffy, 1952 p. 136). The growth process is probably the most common occurrence and observed in several systems, biological or not (Burkhart & Tomé, 2012; Dadson et al., 2017; Parker, 2012). And how does it occur? It is easily observable with the naked eye. So, it is feasible to certify that growth generally follows a sigmoid curve (S-shaped), this being a universal characteristic. Still, visually it is allowed to contemplate different phases in its path (Bertin, 2014; Pommerening & Grabarnik, 2019). Thus, growth is characterized and clearly subdivided into different phases (e.g. lag, exponential, stationary, etc.) (Levert & Xia, 2001; Bukhman et al., 2015). In order to verify these different moments, measurements of size or proportions are recorded on several occasions along this route (von Bertalanffy, 1957; Paine, 2012). In this way, through growth curves it is possible to describe changes in mass, size, volume, area, population and other units to represent the information of the wise behavior of growth over time with only a few parameters (Jørgensen et al., 2000; Pommerening & Grabarnik, 2019). There are many candidate curves to represent the growth period, but they always adequately demonstrate the moments in which the transition between phases occurs (Bukhman et al., 2015; Paine, 2012; Zeide, 2004). Therefore, in order to delve deeper into the essence of this mystery and contribute to answering other questions, it is essential to understand why several stages in the growth process are necessary, this question actually represents the essence of the mystery (Grimm et al., 2011). This mystery presents strategies and optimizations (Karkach, 2006). In view of this, mathematical models are very appropriate to represent the route geometry in two dimensions (e.g. position × time) (Curran et al., 2010; Kebreab et al., 2010; Koya, & Goshu, 2013).
Keywords: Mathematical Modeling; Derivatives of position; Derivatives of force; Growth stages; Kinematics and Kinetics; Ontogenetic growth force curve; Principle of action