I am struggling with a statistical method to assess whether two populations have “changed” over time.
In my case I have a clonal bacteria species, some strains with a mutation conferring resistance to drugs and others without this mutation (e.g. susceptible). Under drug therapy, one would expect a small clonal subpopulation with resistance to eventually dominate the population (because everything else is eventually killed off).
In my case, I will first attempt some test tube experiments. Obviously one can set up a highly controlled experiment where the starting conditions is 1% resistance of a single mutation and 99% the susceptible clonal strain, adding drugs, and watching over time. In this case I was going to try a non-parametric test for trend such as Mann-Kendall and then using Sen-Slope estimation.
However, I want to also look at this situation in ‘nature’ where there are multiple mutations and I am struggling to conceptualize how to analyze my data. Also, to make things worse, I will instead of being able to count population size, unfortunately my genetic tests will only give me the proportion of the sample (0-100%) for each mutation.
The closest analogous situation I can find is Clonal Interference (see bottom image below which comes from https://en.wikipedia.org/wiki/Clonal_interference).