A new four-parameter, generalized logistic equation and its applications to mammalian somatic growth

A new mathematical equation is introduced in this paper: w = f - 1/(b/f +(1/(f-s)-b-f)exp(kt)) where W is the size at any convenient unit of time /, s is the initial size, f is the upper asympotic size, k is the growth coefficient (k > 0), and b is the constant. The new equation encompasses the logistic equation and therefore should be considered as a generalized version of the classical logistic equation. With its additional fourth para­meter 6, the new equation yields an unfixed value of inflexion point which enables it to possess good flexibility for depicting diverse growth patterns. In order to evaluate the fitness of the new growth equation, some commonly encountered models are compared to the new one using 12 sets of somatic growth data of mammalian species including hamster, rat, vole, pika, mouse, rabbit, cattle, and bear, The new equation possesses excellent fitness to each data set, suggesting that it is worth being considered by growth data analysts.