  Quantitative assessment of the growth of biological organisms has produced
many mathematical equations. Many efforts have been given on statistical
identification of the correct growth model from experimental data. Every growth
equation is unique in terms of mathematical structures; however, one model may
serve as a close approximation of the other by appropriate choice of the
parameter(s). It is still a challenging problem to select the best estimating
model from a set of model equations whose shapes are similar in nature. Our aim
in this manuscript is to develop methodology that will reduce the efforts in
model selection. This is achieved by utilizing an existing model selection
criterion in an innovative way that reduces the number of model fitting
exercises substantially. In this manuscript, we have shown that one model can
be obtained from the other by choosing a suitable continuous transformation of
the parameters. This idea builds an interconnection between many equations
which are scattered in the literature. We also get several new growth
equations; out of them large number of equations can be obtained from a few key
models. Given a set of training data points and the key models, we utilize the
idea of interval specific rate parameter (ISRP) proposed by Bhowmick et al
(2014) to obtain a suitable mathematical model for the data. The ISRP profile
of the parameters of simpler models indicates the nature of variation in
parameters with time, thus, enable the experimenter to extrapolate the
inference to more complex models. Our proposed methodology significantly
reduces the efforts involved in model fitting exercises. The proposed idea is
verified by using simulated and real data sets. In addition, theoretical
justifications have been provided by investigating the statistical properties
of the estimators.
