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It basically says it all in the title. I assume the human will eventually succumb to malnutrition, but I wonder what the minimum number of trees are necessary to provide the human with enough energy to survive the longest.

Assuming the human:

  1. has ample shelter
  2. has a way to open coconuts
  3. is in a climate that can support year-round coconut production
  4. is on an island big enough to contain the minimum number of trees
  5. has no other form of food on the island / surrounding waters

Bonus : How long until they succumb to malnutrition and die?

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  • $\begingroup$ Just make sure you never eat a coconut that's under- or over-ripe... In either of those states, they can be a fairly powerful purgative, and... well, let's just say that on a deserted island, the effects would likely lead to severe dehydration, which would either kill you, or render you unable to keep up the coconut-harvesting efforts for long enough that the malnutrition would finish you off. $\endgroup$ – anaximander Sep 7 '16 at 10:40
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    $\begingroup$ @n_b are you assuming there is a freshwater source or does the single human need to get his water requirements from coconut water $\endgroup$ – Foon Sep 7 '16 at 19:12
  • $\begingroup$ @Foon Yeah, there is fresh water. But you could assume there isn't if it's more interesting that way. $\endgroup$ – n_b Sep 7 '16 at 22:56
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    $\begingroup$ Can they drink sea water for sodium ? $\endgroup$ – Babika Babaka Sep 8 '16 at 8:29
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    $\begingroup$ @chepner I wanted to ask if they could drink sea water for sodium, as a complement of their coconut diet, not as a replacement for drinkable water. (Sorry, I'm not fluent in English, is there a better way to ask it ?) $\endgroup$ – Babika Babaka Sep 8 '16 at 13:15
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Well, start with the Wikipedia page.

On fertile soil, a tall coconut palm tree can yield up to 75 fruits per year, but more often yields less than 30, mainly due to poor cultural practices

The same page lists the nutritional value as 354 kcalories per 100 gram serving.

And finding the weight of the edible fruit part alone, the USDA says that one medium coconut has 397 grams of meat.

So one tree gives 354 × 3.97 × 30 ≈ 42,000 kcal/year.

Of all the nutrients needed, I expect lack of calories will kill someone the fastest. You can repeat the analysis with other requirements and timescales for the deficiency to become debilitating, with the information “food label” on that page.

If each adult male needs 1,500 kcal per day, that comes to 13 trees. But that’s for a sedentary white-collar worker; it’s suggested that harvesting will take some effort and the castaway may need to be more active in general. With a ration of 2,000 kcal per day, 18 trees will be enough. That assumes production is continuous or food can be stored, and that the wild coconut is similar to a “medium” cultivated coconut. Add a few extra to be sure. You can adjust that based on the activity level you need for the story.

We assume the low value indicated for yield at least for the first year. If he knows what he’s doing and “farms” them then yield can go up. But if there is nothing else to eat there’s nothing to use as fertilizer either, so it might be slim pickings.

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    $\begingroup$ Why the downvote? It’s an exact answer to the question! Please leave a comment to explain how it is «egregiously sloppy, no-effort-expended post, or an answer that is clearly and perhaps dangerously incorrect.» so I may improve it. Because I just don’t see any of that applying here. $\endgroup$ – JDługosz Sep 6 '16 at 18:23
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    $\begingroup$ Does a coconut even provide the nutrients to sustain life? I have no idea. I would've guessed there'd be some serious problems like rickets or some other missing critical piece to make surviving on just coconuts a short-lived option, regardless of the coconut count. Anyone know enough nutrition info to answer? $\endgroup$ – SRM Sep 6 '16 at 18:47
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    $\begingroup$ @SRM Coconuts almost certainly don't provide all required nutrients, but that's not a problem that can be solved by growing more coconuts, which seems to be the only option granted in the OP $\endgroup$ – Deolater Sep 6 '16 at 18:56
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    $\begingroup$ Agreed - you will not get all essential vitamins from a coconut. There is no B12, for example, in a coconut. You will not survive without b12 from some other source, or if you do, you will be suffering some major hallucinations - like talking volley balls... $\endgroup$ – Jim Sep 6 '16 at 20:56
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    $\begingroup$ It should be noted that coconuts are not the only edible part of a coconut palm tree. $\endgroup$ – rek Sep 6 '16 at 21:02
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In addition to JDługosz's answer on the number of trees required to provide calories, I would suggest growing further trees to ferment into coconut milk kefir and alcoholic beverages. Although best made with starter cultures, there are wild yeast almost everywhere on earth that can start fermentation. Because these cultures contain yeast and bacteria they contain nutrients not found in the original coconut. The yeast (trub) can be collected after fermentation and processed into yeast extract for a nutritious and tasty supplement. In particular, yeast is rich in B vitamins that are otherwise hard to obtain.

And booze helps pass the long years of subsisting on your own on an island...

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    $\begingroup$ Now if only a pineapple would float ashore now and again... $\endgroup$ – iamnotmaynard Sep 7 '16 at 14:05
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BONUS QUESTION: This page http://www.npr.org/sections/thesalt/2015/12/03/457124796/death-by-coconut-a-story-of-food-obsession-gone-too-far says a man lived on coconuts from 1902 (and Wiki says he adopted a monodiet around 1905 or 1906) until imprisonment during WWI in Sept 1914, at which time he weighed 86 pounds. So, a while.

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    $\begingroup$ The article says "from 1902 to 1919." 17 years?!!? That's quite a lot. Things are looking up for the protagonist. $\endgroup$ – n_b Sep 6 '16 at 21:44
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    $\begingroup$ No, read again. He wasn't there the whole period, there were hospitalisations and return to Germany. Other people joining the colony died within months. $\endgroup$ – congusbongus Sep 7 '16 at 6:22
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    $\begingroup$ If you can edit the answer to when he left germany to when he returned that would give you a good idea of the answer... otherwise this answer is wrong with it implying that he lasted as 17 years. $\endgroup$ – Durakken Sep 7 '16 at 11:07
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    $\begingroup$ Sorry guys, I did edit with a bit more detail. Best I can tell, he was on the island from 1902 but was also eating other fruit until true monodiet in 1905 or 1906. Other people on the colony did die, though I can't tell if that was from malaria or monodiet. I bet this guy did not stick to his monodiet because he seems like a real piece of sh*t nutjob. $\endgroup$ – Xplodotron Sep 7 '16 at 16:28
  • $\begingroup$ " At the end of his life, der Kokovore was reduced to a mentally ill, rheumatic, severely malnourished sack of bones with ulcers on his legs. He was only 44" $\endgroup$ – Deolater Sep 8 '16 at 15:46
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It seems body stores quite a lot of B12, thus can survive very long without it. The guy could obviously drink sea water, but, if he does not, he will soon die of sodium deficiency. It seems humans should take at least 500mg of sodium per day [1]. I experienced sodium deficiency first hand, its no fun.

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    $\begingroup$ Not a lot of calcium in coconut meat, either. Maybe he could munch on some sea shells or something... mmmmm. $\endgroup$ – Jason C Sep 7 '16 at 1:30
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    $\begingroup$ If there are enough coconut trees to support a human, there are probably enough ancillary food sources (insects, fish, birds) to make up any vitamin or protein deficiencies. $\endgroup$ – user151841 Sep 7 '16 at 1:39
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    $\begingroup$ I would think so but Rule #5 states nothing else. $\endgroup$ – Cem Kalyoncu Sep 7 '16 at 7:15
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    $\begingroup$ I mentioned that, but then he could eat fish. $\endgroup$ – Cem Kalyoncu Sep 7 '16 at 15:48

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