I'm trying to analyze the microbial difference between each radiation therapy time point(collection column in metadata) for each patient. From previous suggestions, I performed similar analysis as the Parkinson's Mouse Tutorial. I tried out the PCoA-based analyses(volatility plot) and distance-based analysis. However, I'm having trouble interpreting the y-axis of the output plots and also some of the timepoints are missing.

For the PCoA-based analyses output, it seems like COH004 is weirdly missing the first collection point somehow. And I'm also having trouble understanding what is y-aixs or metric column. My guess is that each axis represents a PCoA, but what is each principal component.

Sorry for my complicated question but I think I'm having a general misunderstanding of what exactly is each plot plotting. Thanks for any clarifications and suggestions of what other type of analyses are suitable for my project.

In case you have not found it already, here's the section on Volatility analysis, which explains those plots.

As is convention, the y-axis is the 'output variable' or 'dependent variable', while the x-axis is the input variable. You can plot multiple different dependent variables and see if any have a clear response, and also break up your samples into cohorts to see if one cohorts responds more strongly than another. (I think you may know this already, I'm just including this for future readers.)

That's correct. If you used PCoA, Axis 1 is Principle Coordinate 1. Because principle coordinates are calculated without knowledge of the metadata (a.k.a unsupervised learning, like blinding in statistics), any changes based on metadata category should be due by that category.

In your metadata, how did you calculate the 'Distance' column? Is that the output from qiime longitudinal first-distances or something else?