Abrupt ecosystem changes have been reported in oceans, grasslands, and lakes. The previous studies classified them to the following three kinds of change on the relationships between driver and response (Anderson et al. 2008): 1) Linear tracking, 2) Threshold, 3) Hysterisis. In the first case, abrupt baseline changes in driver parameters should be accompanied by those in response parameters, while large changes are not always required in other two cases. Meanwhile, instead of the baseline change, event such as climate extremes have been generating abrupt changes in various ecosystems (Turner et al. 2020). However, in general, there is a time lag between diver and response change (TLDR), making their relationship obscure on the field chronological data.
TLDR, reported to be within a year to decades, should be associated with the physical distance, chemical response rate, and biological interactions between driver and response parameters. Once the combination of driver and response parameters and the kind of the field are fixed, TLDR should be roughly determined, such as in the case of forest recovery after eruption, and fish recovery after runoff. When the response parameter significantly changes solely by the driver parameter, the temporal difference of the abrupt change between driver and response should be stable and close to TLDR. Thus, it is valuable to examine whether the stable TLDR could be found on the chronological dataset only in the combination of real driver and response parameter. We selected two lakes with the water retention time of ca. 0.25 and 0.65 yr, that would be ideal for the evaluation of TLDR stability as factor analysis in the abrupt algal transition. We verified that the combination with the highest stability in TLDR was a reliable shortcut to find the real factor causing algal community composition.