Abstract: Growth analysis is of significance in estimating the age of organisms, but in reality, the initial time for this estimation adopted by different authors is not always the same. For example, in the growth analysis of mammals, the age could be birth age or conceptional age. Such a discrepancy in time, the so-called time shift, may generate different results in parameter-simulating process. In this paper, the time-shift invariant properties of commonly used three-parameter growth models, i. e. , Spillman, Logistic, Gompertz and Bertalanffy models, were analyzed, and the results showed that these four models all had the invariant characters under any time shift, namely, no matter which initial time (age) of estimation was adopted, the same fitness was obtained. A case study was made with the growth data of Phodopus roborovskii and by adopting both birth age and conceptional age.

Key words: built-up areas, organic carbon storage, organic carbon density.