A generalized Michaelis-Menten equation for the analysis of growth

The functional form W = (W0Kc + W(f)t(c))/(K-c + t(c)), where W body size a t age t, W-0 and W-f are the zero- and infinite-time values of W, respectiv ely, 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 t he 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 f it 83 growth data sets of different animal species (fish, mice, hamsters? r ats, guinea pigs, rabbits, cats, dogs, broilers, turkeys, sheep, goats, pig s, horses, and cattle) with a large range in body size. A comparative study was carried out based on mathematical, statistical, and biological charact eristics of the models. The statistical goodness-of-fit achieved with the n ew model was similar to that of Richards, and both were slightly superior t o the Gompertz. The new model differed from the others with respect to some of the estimated growth traits, but there were highly significant correlat ion coefficients between estimates obtained with the different models, and the ranking of animals based on growth parameters computed with the new fun ction agreed with the rankings computed by the other models. Therefore, the new model, with its variable inflection point, was able to adequately desc ribe growth in a wide variety of animals, to fit a range of data showing si gmoidal growth patterns, and to provide satisfactory estimates of traits fo r quantifying the growth characteristics of each type of animal.