A couple examples:
"Required ratio" based on percentage of "snatched" (i.e. downloaded) torrents you are seeded. For example, if you're seeding all torrents you have ever downloaded, your required can be 0 (instead of initially common values of 1 or 0.9).
Ratioless: no ratio requirements, but you must instead seed all torrents for a specified time.
Among people involved in private torrent communities it's fairly well-known that a purely ratio-based system does not provide the best incitements (which would be a library of content that is as diverse and well-seeded as possible).
Anyway, the main reason many prefer private trackers to public is not only because of enforcement of contributing back, but because of rules that ensure that the available content has high quality (i.e. curation).
1. You get one point for seeding a torrent per hour, up to 10 total. You can exchange 1,000 pts for 10GB of upload credit (e.g. improves your ratio). The torrents don't need to actually be downloaded by anyone to count. This seems to work well as torrents that are weeks and weeks old still have seeds.
2. Popular torrents are listed as 'FREE', which means that downloads don't count against your ratio, but upload is still counted. So anything that gets swarmed gets lots of activity.
But this isn't actually the most usrful result! In this model distributing 100MB of GoT is as valuable as distributing 100MB of some file with only 2 or 3 seeders. But those Megs are not equivalent if the objective is to maximize availability of files.
Being the seeder of last resort on a rarely (but still downloaded!) file is way more valuable than being the 100k'th seeder on some new TV show.
This isn't necessarily what the GP was getting at but is a good example of seed ratios not having the best incentives.