For Biospheres, Size Matters

Quantity has a quality all its own.
-- Attributed to several Soviet leaders, including Stalin

One crucial quality that can be possessed by quantity is given by the Central Limit Theorem, which basically states that if you have N independent random samples taken from a sufficiently well-behaved probability distribution (which is the usual assumption), the average from the N sampled values will follow a bell curve, and the width of the bell curve is inversely proportional to the square root of N.  This is used, for example, in polling; if a poll of 1,000 people produces a margin of error of 4%, to produce a margin of error of 0.4% would require a poll of 100,000 people, which is too expensive for most purposes.

The Biosphere 2 structure has a footprint of 1.27 hectares, compared with the surface area of earth, which is 51.01 billion hectares, making the earth about 40 billion times as large as Biosphere 2.  Of course, the conditions at any location are affected by conditions like droughts, fires, hurricanes, insect hordes, etc., that affect fairly broad areas, so there are not 40 billion times as many independent samples on the earth as there are in Biosphere 2.  It is hard to say by how much that number should be reduced, but let's reduce it by a factor of 10,000, which seems reasonable enough.  That means that fluctuations in the average amount of carbon dioxide taken up by the plants or oxygen produced by them should be expected to be 2,000 times larger than similar fluctuations on earth, even if there were no mistakes with how Biosphere 2 was set up.  Such a large fluctuation is likely to "break" the system; some organisms may flourish and others will probably die, preventing the mixture of gases from being returned to near its desired stable point.  I suspect this was an important contribution to why the Biosphere 2 experiment failed.

As a result, I have little confidence in any human-scaled terrarium being a working solution for colonizing Mars.  The same would apply to greenhouses in space to which the human race retreats in the movie "Interstellar", or even to the ground-based greenhouses that would have been a more sensible solution.  I'll have to add this to my list of problems with that very disappointing movie.