What happens after TM deletes full backup & only incrementals are left?

Question

If I understand this correctly, Time Machine does 1 complete backup & then incremental backups after that. If that's correct, what happens when the full backup is about to be erased because the backup drive is full? Does TM alert you to this & ask if you want to create a new full backup instead of another incremental one? Also, is there any way to get TM to create a log so you can see at a glance what's in the incremental backups without having to click through all the folders in each one?
TIA,
Elllen

Answer 1

Answering this dives into how files are represented on a disk. Basically, a disk is a huge expanse of storage space and an index/catalogue/"table of contents". When you copy data to a disk you physically copy the data into the storage space and then make a reference in the index as to where it resides on the disk. The operating system sees the reference, and doesnt go scouring the disk for files whenever you open a folder. This makes finding files and tracking their locations in the directory tree much easier. A single index-link to a storage chunk is called a "hard link". When the operating system "deletes" a file, it doesnt erase it from storage, but instead just removes the "hard link" index entry.
Since files are referenced through an index instead of reading the actual storage space of the disk itself, you can have multiple references in the index to the same chunk of storage space. Hence, you can have multiple hard links which are essentially the same file.
Keeping that in mind, read on...
Every "incremental" backup is a representation of the full backup, including the first "full" backup. Its no different than any other backup (the only difference is that it was the first one so it took longer to copy everything over). Once a file is copied over to the backup disk, it is referred to by a "hard link" in the disk's index. This is essentially how a disk points to a file on any drive. It copies the data over and then creates a hard link to the file's physical location on the disk, which is how the file is accessed by the operating system (or rather, howe the operating system knows the file exists on the disk). You can have multiple hard links to a file, where the same allocation of disk space is pointed to by two different hard links in the index. As such, you can have two representations of the same file (and therefore two links to it) represented on the same disk. If you delete one of the hard links, it will behave as if it's deleted the file, but in fact the file will still remain on disk and will be accessible through the second hard link.
Note that this is different from an Alias (which is also called a "soft link"), which is a file in itself that points to a single hard link. An alias can be removed without the original file being touched.
When TM does the initial backup it copies all the contents over to the backup disk, and then creates hard links to those files which it represents in the first backup folder. When the next backup occurs, any changed files are copied over with new hard links created. The unchanged files, however, are not copied again but instead are just referred to again with new hard links in the new backup folder. As such, new files have one hard link to them (until the next backup), and the old files have two (one in the current backup folder and one in the previous folder). This creates a situation where if the first backup folder is deleted, the original files that were copied are not lost, as they are still represented by hard links in the newer backup folder, and can be accessed that way.
So, why is this different than creating aliases to the original files in the initial backup? Since aliases are just files that point to hard links, if Aliases to the original backups were used instead of hard links, when the original hard links in the initial backup folder are removed the aliases would no longer point to anything anymore and the files would be gone. This defeats the purpose of a backup.
When a file changes from the initial backup, on the next backup the newer version will be copied over and a new hard link to it will be created. If you delete all hard links to the initial backup (by deleting the initial backup folder) the newer file will still be there in the new folder but all references to the old file will be gone and you'll be left with only the new file (along with everything else that was unchanged).
Now to answer your question: Basically, when the old backups are deleted by Time Machine, its not the full/initial backup that's deleted, but only the old versions of files that have been changed. All the original files that were not changed are still there, represented in every backup (new and old) by hard links.