Biodiversity is multifaceted and has been measured in various indices. Thus, each indicator would respond differently to shared environmental changes, and ecosystem conservation and management must select appropriate ones for its needs. In this study, we analyzed how the ten representative indicators reflect biodiversity dynamics based on nonlinear time series forecasting. Specifically, using the underwater visual census data of a fish community under anthropogenic water temperature changes, we estimated temporal changes in dynamical similarity from predictions with a certain period as supervised data and compared the patterns between the diversity indicators. As a result, they were classified into three super-groups, which may reflect the similar aspects of biodiversity dynamics: Group I (species richness and community mean of the center of distribution (COD)) with the most invariable dynamics; Group II (total abundance and species diversity) with rapid dynamical changes when water temperature increased; Group III (species evenness) with the most sensitive dynamics to environmental changes. Further analyses suggested that immigration from the open sea might be a major driver of species richness dynamics, causing this classification. These findings indicate that indices need to be selected from the different super-groups to evaluate the response of biodiversity to environmental changes correctly.