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The species in question are Herbivores, bipedal in nature, around 50 to 80 pounds on average, and require around 2250 calories per day to stay healthy.

The ships these populations would live on are big, bulky floating towns, in an aproximate medieval period level of technology. Perhaps supporting dozens to even a thousand or so each and remaining out at sea for years, decades, or even indefinitely if possible.

If the upper limit of required calories per day per person were exactly 5000, how possible would it be to feed one thousand people off of underwater flora that can grow within 300 feet of the surface if the ocean were similar to one on Earth? If impossible, what would the upper limits be?

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    $\begingroup$ While this question isn't a duplicate (Being a different species, among other things), some of the answers and comments from this question might be relevant to other answerers. $\endgroup$ – Andon Jul 20 '18 at 3:16
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Building on the answer of @manassehkatz, I think we might be able to tweak things to work.

As previously mentioned, kelp (the highest calorie seaweed I've managed to find) only had 43 calories per 100g. Even spuds have 93 calories. However, let's try and solve a few of the problems.

Caloric Intake

The main issue highlighted in @manassehkatz answer was that with such a low-calorie food, your people would need to be eating a lot of seaweed to meet your 2250kcal daily intake to stay healthy. 5.2kg a day is a lot. About double what it would take in cooked potatoes (2.4kg).

However, is 2250kcal necessary?

Your humanoids weigh between 50-80lbs (~23-36kg). Baka pygmies in Africa weigh on average 53kg for men and 46kg for women. Not quite as light as your seafaring herbivores, but let's take that as an upper bound. Now, trying to find a recommended caloric intake for little people has proven to be depressingly difficult. Closest I've found is an offhand mention of 1000-1400kcal per day. Let's fudge some numbers a little and say that the upper bound for our heavier modern little people is roughly equivalent to what your lighter but more physically active mariners need.

So, 1400kcal/day. That's a little more manageable.

Assuming your people have been cultivating seaweed for a reasonable amount of time it's not too difficult to believe they'd cultivate a more nutritious variant. If we take wild rice (101kcal/100g) vs domestic rice (129kcal/100g) as an example, then we could conceivably bump the caloric content of domesticated kelp up to 50kcal/100g.

Running the numbers again, our leaner more efficient herbivores now only need to eat 2.8kg of kelp per day. Much more manageable :) even wild kelp at 43kcal/100g gives 3.3kg which isn't insurmountable.

Oh, and the 43kcal/100g for kelp is a figure for raw kelp. Cooking tends to increase the caloric density of food, so there's wiggle room there too despite not being able to find a figure for cooked kelp.

Area

Next, we need to find out how much area is required to grow enough food to support your population to see if kelp is viable as an agricultural staple.

Luckily, I've come across this article detailing the aquaculture of various different seaweed species including yield per hectare! Perfect :)

Let's take good old spuds as an example of typical agricultural efficiency. With modern agriculture, we can produce 17.4 tonnes of potatoes per hectare (17400kg per 10000 square metres, or 1.74kg per square metre). I'm not sure how far potato farming has come since the middle ages, but I'd be willing to bet that this yield is significantly higher than a medieval one. Still, it's a good upper bound.

Our kelp (wakame) produces about 10kg of wet weed from 1m of rope using rope aquaculture (and is less labour intensive than nori farming which is good). Let's say the density of rope aquaculture is one rope per square metre (might be able to squeeze two in based on pics of the plant from google), we're looking at over 5x the efficiency of wet weed compared to potatoes. From what I gather, wakame is eaten wet so there's no funny business with comparing dried calorie density vs wet.

This might just work...

Population density

From the above, we can hazard a guess at the population density your aquaculture can support.

If each mariner needs to eat 2.8kg of kelp per day, and each square metre of aquaculture produces 10kg then each mariner will need 102 square metres of aquaculture to survive for a year producing 1022kg of kelp. With wild kelp, the figure is 120 square metres.

Compare that to good old spuds and you'd need 314 square metres per mariner per year using modern techniques. Seaweed's looking pretty good now!

So like for like, your mariners can support roughly 3x the population of their land-based potato-eating cousins.

As a rule of thumb, there's a medieval source that claims 1 square mile supports 180 people all-inclusive (not only farmland but housing and roads and inefficient uncultivated land).

Now, including their smaller stature and more efficient aquaculture, we can support 4.96 mariners for every one person (based on 2250kcal/day people eating potatoes, which isn't exactly rigorous but hey ho). So, we end up with a figure of 4.96 mariners per square mile.

So using the medieval model of land usage we end up with our 1000-mariner settlement spread across 201 square miles. A little less than Lake Winnebago.

Further consideration

How herbivorous do you want them to be? In the wild, you'd be surprised at how blurred the line is between herbivores and carnivores. Many animals you'd assume to be wholly herbivorous eat a surprising amount of animal matter.

If you don't want them to actually eat meat, how about deep-frying your kelp in animal fat? Plenty of blubbery animals in the cold waters where kelp grows best, and from my cursory research deep-frying adds roughly 100-120kcal per 100g. Digesting oils and fats from animal sources is digestively little different from oils and fats from plant sources, and medieval people tend to have a lot less moral scruples when it comes to what they eat. Food's food after all...

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Seaweed Soup?

This would be trivial if they were omnivores - all the fish in the sea to eat. But they are herbivores. So the logical choice is seaweed. There is a problem though - at 43 calories per 100 grams, that works out to...around 12 pounds of seaweed a day to get 2,250 calories. I think that it would be too much. Actually, that might have more calories than 50 - 80 lb. herbivores need. Even 1/2 of that would be 6 lbs. a day. That's a lot. Seaweed and other plants that grow near the surface of the sea just aren't your high-calorie rice, potatoes, beans or wheat that you can grow so easily on land.

I don't think they can do it...

  • Medieval Technology

That rules out advanced hydroponic farms grown on the ship, diving with scuba gear to harvest from the bottom and a lot of other options

  • 300 feet?

The ways you normally harvest in the ocean more than a few feet down, without scuba equipment, is with fishing poles or nets. Fishing poles don't help if you don't eat fish. Nets can catch fish and other creatures, and also gather in seaweed and floating plants. But they won't eat the fish and other creatures, and it will be very hard to satisfy their caloric (and nutritional) needs with seaweed and floating plants.

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  • $\begingroup$ I'd like to add to this answer, you can farm seaweed by growing it on ropes. In a floating city for herbivores you would have a ton of rope dangling off the ship floating around in the water to provide you the seaweed you need. They would cycle through the ropes, pull them onboard, cut off some seaweed and throw it back into the water to let it regrow. I don't know how much rope and the growth rate of seaweed, but you could potentially support a population using this method. The biggest bonus would be if you could turn the seaweed into more ropes so you have more room to grow more seaweed. $\endgroup$ – Shadowzee Jul 20 '18 at 3:55
  • $\begingroup$ @Shadowzee If they depended on seaweed, I'm sure they would find ways to farm it - ropes as you suggest, or nets or something. The problem is that it just doesn't work with the caloric requirements. Compared to typical human staple crops, it is both less dense in calories per weight AND it less dense in weight per volume - you'd spend all day eating. $\endgroup$ – manassehkatz Jul 20 '18 at 4:02
  • $\begingroup$ What else are you doing to do all day besides, eating, sleeping and tending to seaweed when your on a floating platform with only ocean around you? $\endgroup$ – Shadowzee Jul 20 '18 at 4:08
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    $\begingroup$ @Shadowzee Specifically propelling the ship along, maintainance, diving, arts and crafts, processing saltwater, that sort of thing. Various exertions in general. $\endgroup$ – Higuera Jul 20 '18 at 4:13
  • $\begingroup$ Surely just building a floating island capable of housing a thousand people would not be possible with medieval technology. its only in the last 150 years or so we mastered over 1000 people on a boat, yes several tall ships strapped together could work but it wouldn't hold up well in a storm. $\endgroup$ – Blade Wraith Jul 20 '18 at 6:25
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Since they evolved to live this way, they didn't appear in the ocean one day out of nowhere, it's reasonable to think that they have breed the best plants as we did on the land, therefore we can assume that their food could be times more nutrient than the plants we currently see in the sea.

As manassehkatz wrote seaweed could be an option but with his assumptions the aliens will be more or less sea panda, busy eating seaweed all day long. IMHO they should have breeded more nutrient seaweeds, then they should eat for a lot of hours - and this is actaully really common for herbivores- but they won't be sea panda.

Moreover rain happen to happen also over the sea, and while it can't be considered a reasonable fresh water reserve for a wheat field, it could be used to farm some small yet really nourishing vegetable only by decreasing the salinity level of a special/confined pool.

They can also use bare solar power to harvest fresh water by distillation, it's not that difficult to do even with only medieval technology.

The main point is that the only need to have some water with low salinity (respect to the ocean), not pure fresh water. In fact there are some current vegetables that are salt tolerant (page 10, table 2):

  • asparagus
  • beetroot
  • barley
  • rye

Also Quinoa could be a good candidate since "Quinoa plants do best in sandy, well-drained soils with a low nutrient content, moderate salinity, and a soil pH of 6 to 8.5".

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Evolution might Interfere with your species, altering the feeding mechanism, and they might eat the ever present plant in the sea、Phytoplanktons.

This answer takes note that:

The ships' design is not specified.

The species' feature is not specified fully.

So your "Ship island" might be afloat, but somehow 2 feet deep in the water, just enough to make your species' feet to be drenched in water. The feet now has spores that could filter phytoplanktons and use it as food. They can also shut down their "Feet mouths" when they feel they are full already.

Not the most pleasing feature perhaps, but evolution does do things crazily just to make something survive a situation. I do think in this approach, there is a near infinite supply of food for all of your species.

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