One problem is that plants and algae would be quite happy in an atmosphere containing uncomfortably high levels of carbon dioxide, so we can’t rely on biological regulation of the atmosphere to work favourably for humans. Although some animals might thrive in a closed terrarium, I wouldn’t want to live there myself unless there were some other ways to regulate the atmosphere.
I recall an interview with the guy who funded Biosphere 2 before the experiments started that they expected failures and to learn from them. I don’t think they expected quite the clusterf**k the first round of experimenting to be, but a lot was learned from it. The second round was more successful - they were maintaining food self-sufficiency and adequate oxygen levels - when the company running/funding it fell apart and that’s what fell through. Funding had always been a problem, running such an experiment is not cheap and Biosphere 2 was privately funded rather than having access to government deep pockets.
There’s been a lot of focus on what a failure Biosphere 2 was while ignoring that it was successful in what was learned. Just taking the concrete issue alone - imagine if there had been plans to build, say, a Moon or Mars colony with extensive use of concrete and no one had known what we now know about concrete and curing in a closed environment. In Biosphere 2 we could inject enough oxygen to keep the inhabitants healthy and alive. Colony on the Moon? Not so much. In reality, a lot was learned about what NOT to do in a closed environment, which in many ways is just as important as learning what to do.
As usual, one of the biggest problems of Biosphere 2 were the humans - humans in tight quarters with other humans can lead to problems. I don’t think the people running Biosphere 2 did the same sort of psychological screening that organizations like NASA do. Interpersonal relations between the “Biospherans” get pretty ugly although they were able to continue working together to maintain the environment.
Interpersonal friction is always a problem in human societies and in micro-sized societies it’s intensified. It’s been an issue with space travel, and with small research stations in places like Antarctica. It would definitely be a problem in a generation ship. It would probably be a worse problem with the second generation onwards because those people would be born on the ship and not pre-screened for compatibility.
I suspect that the whole idea of having a closed society like those postulated, even if it is several thousand strong, simply would not work.
Policing would be a major problem. At first, everyone will be a highly motivated volunteer, but a generation or two along, social unrest seems inevitable to me. Then you have a post-apocalyptic scenario with the strongest and least inhibited taking charge. This would probably be followed by a decline in just about every metric and the ship might well arrive at its destination (assuming it wasn’t sabotaged) full of human remains.
Cryogenics seems to be a better solution, assuming that it has been perfected by then. AI will get the ship to its destination and progressively wake people up in a pre-determined sequence.

One problem is that plants and algae would be quite happy in an atmosphere containing uncomfortably high levels of carbon dioxide, so we can’t rely on biological regulation of the atmosphere to work favourably for humans.
I’m confused. Your second clause doesn’t follow from the first. In fact, the fact that plants thrive in a high level of carbon dioxide isn’t a problem; it’s an essential part of how the regulation works.

Policing would be a major problem. At first, everyone will be a highly motivated volunteer, but a generation or two along, social unrest seems inevitable to me. Then you have a post-apocalyptic scenario with the strongest and least inhibited taking charge. This would probably be followed by a decline in just about every metric and the ship might well arrive at its destination (assuming it wasn’t sabotaged) full of human remains.
Is this not a problem with societies on Earth?
All biomass must be converted back into food using the most energy-efficient means possible.
The most direct means of converting a human body back into food is eating it. I wouldn’t want to do that, and most people won’t, but any such project would involve large investments in socially engineering the population to gladly perform all tasks, duties, and lifeways required to further the success of the project, and cannibalism could be one of those practices. It would be in essence be joining a cannibal cult, and voluntarily submitting to the necessary brainwashing to reinforce the right behaviors in yourself (and eventually in others).
If the cannibalism approach turns out to be too much to ask, then a slower, lower-energy approach could be used such as fungal decomposition for the soft tissues, generating biomass that could be converted back to food. Special processing would be needed for the remaining bone and teeth, probably an acid digestion system to convert it back to calcium for nutritional supplements, setting aside phosphorous for plant fertilizer.

Space is big.
"You just won’t believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it’s a long way down the road to the chemist’s, but that’s just peanuts to space.”

Flower gardens seem to be a popular idea in this thread. Would flower plants draw calcium from the corpse fast enough to recycle it?

All I saying is might be better to use new tech and science than trying to re-create earth in a spaceship. Still it’s an interesting read.
Yes, Earlier I referred to “purely ornamental plants”, but in reality, there’d be no such thing on the ship. I’d assume that every plant we send would be genetically engineered to maximize its usefulness. They’d produce oxygen and scavenge other materials much more efficiently than the plants we currently grow.
So even the memorial flower garden would be an important part of maintaining life support, and recycling other materials for use.

Are you saying yuck because you’ve tasted it and dislike it? Or does the idea of it disgust you?
The way it was written out was just sounded very unappealing. Artificial meat from a vat just sounds… yuck. But if packaged nicely I might be tempted try it.
Nothing against it, in fact as I get older I eat less and less animal products out of ethical reasons.

Humans do have a psychological need for space, but I expect there will be ways to simulate wide open spaces and combat claustrophobia long before we can build generation ships.
It’s not just space. The presence of plants is beneficial for humans, or at least for many humans. There have been quite a lot of studies done; I’ll hunt up some for you if you want.

There is a ways to go on that front (yes, the whole generation ship as well, but), remember Biosphere 2
We’re certainly not ready to build generation ships yet. I think that’s part of the reason.
As others have said, a good deal was learned from Biosphere. To the extent that we haven’t learned enough about closed environments to make one work – and we haven’t – we haven’t learned enough to make a generation ship work. Yes, one of the things we have to learn is what items we may need to try to bring in sufficient quantities to make the trip, including by recycling them enroute by either natural or mechanical processes; and what things may best be dealt with by mechanical processes instead of trying to keep natural systems functioning on the ship. Maybe algae tanks will be an important part of such environments; but that’s one of the things we have to learn. And do we even know how to keep algae tanks functioning for hundreds or thousands of years?

As others have said, a good deal was learned from Biosphere. To the extent that we haven’t learned enough about closed environments to make one work – and we haven’t – we haven’t learned enough to make a generation ship work.
And of course, any generation ship will be built in space. By the time we have the infrastructure for such a project, we’ll already have lots of experience with smaller self-contained environments on the Moon and in space stations.
The space station’s not self-contained. It relies on the availability of shipments from Earth; both of rotating human crews, and of supplies for them.
I agree that we can learn useful things from even such situations that could help us learn how to build truly self-contained environments.
ETA: are you suggesting that we’d try building self-contained space stations before we tried building a generation ship? That would make a good deal of sense. I expect there’d have to be a number of emergency re-supply trips before we got it figured out; but it would be a useful way to learn how to.

The space station’s not self-contained. It relies on the availability of shipments from Earth; both of rotating human crews, and of supplies for them.
Yes, but mass is always going to be expensive in space, so there’s economic pressure to make it as efficient as possible. We keep a few astronauts going at the ISS via shipments, but if there’s thousands of people (and there would have to be, in this scenario), keeping them fed via shipments becomes untenable.

ETA: are you suggesting that we’d try building self-contained space stations before we tried building a generation ship? That would make a good deal of sense. I expect there’d have to be a number of emergency re-supply trips before we got it figured out; but it would be a useful way to learn how to.
I’m more suggesting that we would have to build such stations. Sure, having emergency supplies available is great, because it’s a safe bet we’ll have a few near-disasters along the way, but we’d want them to be self-contained as much as is possible.

Yes, but mass is always going to be expensive in space, so there’s economic pressure to make it as efficient as possible. We keep a few astronauts going at the ISS via shipments, but if there’s thousands of people (and there would have to be, in this scenario), keeping them fed via shipments becomes untenable
True. But that doesn’t mean that running an efficient operation that relies on as few shipments as possible means that we know how to do without the shipments.
Accelerated composting?
Can it be done?

Accelerated composting?
Can it be done
Some composting techniques are faster than others; and we might be able to develop even faster ones.
But we’re talking about a trip taking hundreds or thousands of years. Why would the speed of the composting process be a critical issue?
You would want it to keep pace with replacement crew to maintain a balance.
Why not use bugs to eat the fleash and then eat the bugs as protien? Then grind the bones down into dust and use as fertilizer or building material.

You would want it to keep pace with replacement crew to maintain a balance.
You’re going to need to control birth rate levels to maintain a balance. But I doubt you’re going to also control precise death rates by killing somebody every time someone’s born; though you might, I suppose, only give out a pregnancy license after somebody dies. Humans being as we are, I’d strongly recommend planning for some leeway due to failure to follow the rules.
I still don’t see how the exact speed of decomposition is an issue. There are multiple reasons not to let your nutrient balance get so tight that you’ve only got enough to feed everybody for the next few days; plus which, once you’ve got multiple bodies composting, there are always going to be some finishing the process as others are starting it.

As others have said, a good deal was learned from Biosphere. To the extent that we haven’t learned enough about closed environments to make one work – and we haven’t – we haven’t learned enough to make a generation ship work. Yes, one of the things we have to learn is what items we may need to try to bring in sufficient quantities to make the trip, including by recycling them enroute by either natural or mechanical processes; and what things may best be dealt with by mechanical processes instead of trying to keep natural systems functioning on the ship. Maybe algae tanks will be an important part of such environments; but that’s one of the things we have to learn. And do we even know how to keep algae tanks functioning for hundreds or thousands of years?
It’s not just algae tanks we’ll need to keep functioning for thousands of years; every single component of the ship is going to need replacing multiple times over the course of the journey. To pick a simple example, you might use LED light bulbs because they have a long life and are efficient, but last only few years. What infrastructure is needed to make new ones? Perhaps the ship should use incandescent lighting, because they’re simpler to manufacture?
Any generation ship would obviously need to have the manufacturing ability to produce any and all of its parts, from lightbulbs to circuit boards to rockety engines. It’ll also have to be able to break broken parts down to their component elements, and recycle them.