Simultaneous identification of growth law and estimation of its rate parameter for biological growth data: a new approach

• Published in: Journal of biological physics Vol. 40; no. 1; pp. 71 - 95
• Main Authors: Bhowmick, Amiya Ranjan, Chattopadhyay, Gaurangadeb, Bhattacharya, Sabyasachi
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 2014; Springer Nature B.V
• Subjects: Algorithms; Animals; Biochemistry; Biological and Medical Physics; Biophysics; Complex Fluids and Microfluidics; Complex Systems; Growth models; Human growth; Humans; Least-Squares Analysis; Models, Theoretical; Neurosciences; Original Paper; Physics; Physics and Astronomy; Population Dynamics; Population Growth; Regression Analysis; Soft and Granular Matter; Growth curve models; Interval specific rate parameter; Overall rate parameter; Average relative growth rate; Model selection
• ISSN: 0092-0606; 1573-0689
• DOI: 10.1007/s10867-013-9336-6

Scientific formalizations of the notion of growth and measurement of the rate of growth in living organisms are age-old problems. The most frequently used metric, “Average Relative Growth Rate” is invariant under the choice of the underlying growth model. Theoretically, the estimated rate parameter and relative growth rate remain constant for all mutually exclusive and exhaustive time intervals if the underlying law is exponential but not for other common growth laws (e.g., logistic, Gompertz, power, general logistic). We propose a new growth metric specific to a particular growth law and show that it is capable of identifying the underlying growth model. The metric remains constant over different time intervals if the underlying law is true, while the extent of its variation reflects the departure of the assumed model from the true one. We propose a new estimator of the relative growth rate, which is more sensitive to the true underlying model than the existing one. The advantage of using this is that it can detect crucial intervals where the growth process is erratic and unusual. It may help experimental scientists to study more closely the effect of the parameters responsible for the growth of the organism/population under study.