We extend the ecological laws of species-time relationship (STR) and species-time-area relationship(STAR) to general diversity time-period relationship (DTR) and diversity-time-area relationship (DTAR),and test the extensions with the human vaginal microbiome datasets by building 1460 DTR/DTARmodels. Our extensions were inspired by the observation that Hill numbers, well regarded as the mostappropriate measure of alpha-diversity and also particularly suitable for multiplicative beta-diversitypartitioning, are actually in the units of effective species, and therefore, should be able to substitute forspecies in the STR and STAR. We found that the traditional power law (PL) model is only applicable forDTR at diversity order zero (i.e., species richness); at higher diversity orders (q = 1–4), the power lawwith exponent cutoff (PLEC) and power law with inverse exponent cutoff (PLIEC) are more appropriate.In particular, PLEC has an advantage over PLIEC in predicting maximal accumulation diversity (MAD)over time. In fact, with the DTR extensions, we can construct DTR and MAD profiles. To the best ofour knowledge, this is the first comprehensive investigation of the DTR/DTAR in human microbiome.Methodologically, our DTR/DTAR profiles can characterize general diversity scaling beyond speciesrichness, covering both alpha- and beta-diversity regimes across different diversity orders.