Sexual maturity at nine years, 12 month gestation period, and one calve every two to five years. Animal is believed to have a low metabolism
Tough. My impression is that gestation periods are very hard to manipulate. With effective selective breeding, you might get the maturation rate down to 6 years, with a faster growing, smaller animal. That's still very long, almost intolerably so. And you might get the reproduction rate up to one every two years.
So what would this look like.
Let's assume a starting population of 10,000 'fast' breeding Manatee. Let's say that males are intensively harvested, leaving one male for every four females. That keeps the Manatee reproductive quotient high. So 8000 breeding females. These 8000 females will each produce a calve every 2nd year. So 4000 calves in any given year. Not too bad, eh?
So we can harvest 4000 Manatee a year, and still leave a starting population of 10,000?
Not quite. The 4000 Manatee we harvest will be the breeding adults, not the calves. So in 2.5 years, we will have harvested all of the adult manatees and eliminated the breeding population, leaving a replacement population of 10,000 immature Manatee, the oldest generation of which is 3.5 years from sexual maturity, and a 4.5 years from producing the third generation. But they won't make it, because in another 2.5 years, the 10,000 immature Manatee will be harvested. Ouch!
How about 1000 Manatee a year? In six years, you will have harvested the majority of adult Manatee = 6000, there will be a first generation of 4000 entering the population, so your mature Manatee population is now 8000. Take 1000 of that, and you're down to 7000 Manatee, who will breed 2800 new Manatee. On the other hand another 3600 will be entering the adult populations. Which takes us back up to 10,600, in year eight. Take a thousand of those, down to 9,600. But the new cohort is 3200, which takes us up to 12,800 in
Well, what if we only take Manatee calves at 4000 a year? Okay, but then you're cancelling any future generation. But this may be viable. Continually harvesting calves might well start selecting for twin births, and shorten the period between pregnancies. You might get a newborn manatee every 16 to 18 months. But at that harvesting rate, there's no selection, because you are taking the entire crop.
This isn't actually too bad. You're harvesting about 10% of the population a year, sustainably, and perhaps can go higher than that. It's nowhere near the rate of meat production you'd get with cattle or chickens, but its nothing to sneeze at. Particularly since the manatee are harvesting and processing completely inaccessible biomass. You're not going to use this waterway terrain to produce anything else that humans can eat.
Of course, this is an extremely arbitrary illustrative example. You are not going to start from zero with a population of 10,000 manatee and no juveniles and newborns. Any Manatee population is going to be a mixture of newborns, juveniles, adolescents, and mature animals. So let's assume 5000 harvestable adults, and 5000 juveniles divided up among 5 cohorts from newborn to pre-adult. Every year, a thousand pre-adults join the adult population. But the five thousand adults (assuming 4000 females and 1000 males), will produce 2000 newborns a year. So for a sustainable harvest, you could take 1000 adults and 1000 juveniles a year and maintain a stable population.
Conceivably you could embrace a harvesting strategy aimed at taking only juveniles, biasing strongly towards males, which would produce a fair amount of useful protein, and leave a strong enough surviving cohort that they could leave the manatee population going strong.
There's all sorts of scenarios in terms of trying to create sustainable harvest strategies.
But you know what? It's not bad. Particularly when you've got an environment which is highly inaccessible for agriculture. This strategy is probably a lot closer to herding and shepherding, but these often take place in resource poor areas, so their yields are reduced from optimum. Manatees are in a resource rich but inaccessible environment, so they might well produce returns that compare favourable to dryland or scrubland shepherding. Of course, the Manatee will be storing a lot more protein in the bank, so to speak. But its not bad at all.
The big risk of course will be excess harvesting, particularly poaching from invasive cultures.
But (and my models are using a comparatively fast breeding, fast maturing version of Manatee - rather than the current ones) (achievable through selective breeding/harvesting) it seems viable, at least in terms of production.
So, its at least theoretically possible that some culture might have domesticated the Manatee.