A generalized Michaelis-Menten equation for the analysis of growth

Abstract

The functional form W (W0 K c Wf t c) /(K c t c), whereWis body size at age t,W0 andWf are the zero- and infinite time values ofW, respectively,and K and c are constants, is derived. This new generalizedMichaelis-Menten-type equation provides a flexiblemodel for animal growth capable of describing sigmoidaland diminishing returns behavior. The parametersof the nonlinear model are open to biologicalinterpretation and can be used to calculate reliable estimatesof growth traits, such as maximum or averagepostnatal growth rates. To evaluate the new model, thederived equation and standard growth functions suchas the Gompertz and Richards were used to fit 83growth data sets of different animal species (fish, mice,hamsters, rats, guinea pigs, rabbits, cats, dogs, broilers,turkeys, sheep, goats, pigs, horses, and cattle) with alarge range in body size. A comparative study was car- ried out based on mathematical, statistical, and biologicalcharacteristics of the models. The statistical goodness-of-fit achieved with the new model was similar tothat of Richards, and both were slightly superior to theGompertz. The new model differed from the others withrespect to some of the estimated growth traits, but therewere highly significant correlation coefficients betweenestimates obtained with the different models, and theranking of animals based on growth parameters computedwith the new function agreed with the rankingscomputed by the other models. Therefore, the newmodel, with its variable inflection point, was able toadequately describe growth in a wide variety of animals,to fit a range of data showing sigmoidal growthpatterns, and to provide satisfactory estimates of traitsfor quantifying the growth characteristics of each typeof animal.