Why does Yosemite want to throw away all my backups? Huh? “To improve reliability, ... will remove your existing backup history”
Doesn't that kind of miss the point of having backups??

Time Machine is set to use a network share dedicated to that purpose.  It claims to have 7T free, which would be true only if the volume in the sparse bundle automatically expands (does it?).  The bands files total 118G which sounds like the size I created the volume for initially.  I think the initial full backup consumed about 25G.

Thinking the volume might have been corrupted, I restored it from a snapshot of the host storage's volume that was made just before Yosemite was installed.

What's going on?  I can't imagine that Apple is serious about casually throwing away all backups.
When I posted, I suspected that this was specifically related to the Yosemite update, as I'd seen a few hits in Google with similar things (but no fixes), especially since I had already restored the meta-backup meant to address exactly the issue discussed in the older Q's of generic network disk corruption.  

After reading the Troubleshooting post referenced by the older Q, I learn that this message is produced by a verification (fsck) that's run once a month.  This means that whatever anomaly it found was not something that occurred in the previous backup, but could have occurred any time in the last month!  Now, I think the correlation with this “happening” right after the Yosemite upgrade may be that the last-check-date gets lost or it intentionally performs a check right away after installing.  So, any problem that occurred in the last few weeks suddenly is brought to your attention.

If this is checked on purpose, I think it would be better to check before installing the update, to give people a chance to get a working backup of their system before the update.

I rolled back the NAS volume another week, and all was well.  Just let it finish “finding” and then checking the disk.