Recent outbreaks of infectious diseases have been monitored closely from an epidemiological and microbiological perspective. Extracting from this wealth of data the information that is relevant for the evolution of the pathogen and predict the further dynamic of the epidemic is a difficult task. We therefore consider clusterings of these data to condense this information. We interpret the relative abundance of (genetic) variants of the pathogen as a time-dependent probability distribution and consider clusterings that keep the Fisher information (approximately) invariant, in order to ensure that they capture the dynamics of the pandemic. By first studying analytic models, we show that this condition groups variants together that interact in a similar fashion with the population and show comparable adaptation to the epidemiological situation. Moreover, we demonstrate that the same clustering can be achieved by grouping variants together according to the time-derivative of their information, which is defined as a function of the probabilities alone. A computationally simple clustering based on the probability distribution therefore allows us to probe interactions of different variants of the pathogen with its environment. To validate these findings, we consider data of 551.459 amino acid sequences of the spike protein of SARS-CoV-2 in France over the course of almost 4 years. We demonstrate that our proposed clustering enables us to identify and track point mutations that allow variants to become dominant and identify temporal correlations among such mutations. We identify indicators which point out dangerous variants, with a potential to grow to large probabilities. We show that we can accurately predict the temporal dynamics of such variants by using a universal model discussed in previous work.