What happens to the popularity of Open source packages, measured in monthly downloads, once they cease to be updated or attract new users?
If the software does not have any competition within its domain, there is no reason why its popularity should decline. In practice, there are usually alternative packages offering the same or similar functionality. Even when alternatives are available, existing practice and sunk costs can slow migration. A year or so after I started using Asciidoc to write by Software Engineering book, the author announced that he was no longer going to update the software; initially there was no alternative, but the software did what I wanted, and I have been happily using it over the last 12 years.
The paper: Do All Software Projects Die When Not Maintained? Analyzing Developer Maintenance to Predict OSS Usage by Emily Nguyen measured the monthly downloads, commits and other characteristics of 38K GitHub packages having at least 10K downloads during any month between January 2015 and December 2020. The data made available (more here) is a subset, i.e., downloads for 1,583 projects starting in May 2015.
The author investigated the connection between various project characteristics (focusing on commits or lack thereof in particular) and downloads by fitting a Cox proportional hazards model.
The plot below shows the 67 monthly downloads for a selection of packages; the red line is a fitted local regression used to smooth the data (code and data):
Reasons for a decline from a peak number of downloads include: competition from alternative packages, change of fashion, and market saturation, or perhaps the peak was caused by a one-off event. Whatever the reason for a peak+decline, my interest is learning about patterns in the rate of decline.
Some of the monthly package downloads in the above plot have an obvious peak and decline, with others continually increasing, and others having multiple peaks. The following algorithm was used to select packages having a peak followed by a decline, based on the predicted values from a fitted loess model:
- find the month with the most downloads, this is the primary peak,
- if this month is within 10 months of the end of the measurement period, this is not a peak/decline package,
- does a secondary peak exist? A secondary peak is a month containing the most downloads from 10 months after the end of the primary peak, where the number of downloads is within 66% of the primary peak downloads,
- the secondary peak becomes the primary peak, provided it is not within 10 months of the end of the measurement period.
The final fraction of the primary peak is the average monthly download during the last three months divided by the peak month downloads.
The plot below shows the 693 packages whose final fraction of peak was below 0.6 against months from peak to the last month (at the end of 2020), with the red line showing a fitted regression of the form 
(code and data):
As the above plot shows, there don’t appear to be any patterns in the decline of package downloads, and 
is a poor predictor of fraction of peak.
Perhaps a more sophisticated peak+decline selection algorithm will uncover some patterns. Both ChatGPT (its generated python script failed) and Grok (very wrong answers) failed miserably at classifying the plots. Deepseek will only process images to extract text.