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 t, 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 th erefore should be considered as a generalized version of the classical logi stic equation. With its additional fourth parameter b, the new equation yie lds an unfixed value of inflexion point which enables it to possess good fl exibility for depicting diverse growth patterns. In order to evaluate the f itness of the new growth equation, some commonly encountered models are com pared to the new one using 12 sets of somatic growth data of mammalian spec ies including hamster, rat, vole, pika, mouse, rabbit, cattle, and bear. Th e new equation possesses excellent fitness to each data set, suggesting tha t it is worth being considered by growth data analysts.