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Maybe a better way to put this question is:

Given an isolated garden bed, that had no external inputs except light, water and air. If you were to grow plants in it, compost those plants and add them back to the garden. Over time (with no external inputs) would you end up with more nutrients over time or less?

To add context, I have a yard with soil, a few trees, lots of grass and a couple garden beds. I rake the leaves, cut the grass and compost them. Do the trees and grass only take nutrients from the soil, or do they create new nutrients that I can compost and add to garden. Meaning over time my yard as an enclosed system, does it lose or gain nutrients; assuming I also recycle all fruit and vegetable back through the compost.

Dan
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You are missing the fact that air is just as vital as an "external input" as light and water. Plants process carbon dioxide from the air directly, and specialist bacteria also convert nitrogen to forms useable by plants. (There is also a small amount of nitrogen converted by lightning strikes in the atmosphere, but that's probably not very important).

Almost all the increase in the mass of vegetation as it grows comes from the air, not from the soil.

Probably the most important elements (by quantity) that are "recycled" are phosphorous and calcium. Calcium is typically removed from the system by animals whose bones etc end up elsewhere when they die. \This is critical when feeding animals on grass - consider the weight of the bones in a herd of cows that are slaughtered for meat, for example.

These elements may be present in the soil in sufficient quantities to last a long time (decades or centuries) but there are many other essential trace elements which could be depleted.

alephzero
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Check out the Wikipedia plant nutrition article. Plants take carbon, oxygen and hydrogen from the atmosphere, the remainder from the soil. (There are exceptions - some plants can make use of atmospheric nitrogen; some plants derive some of their nutrients from trapping and consuming animals.) Plants cannot manufacture chemical elements, so all these will need to be taken in from their surroundings. If you recycle everything back into your garden as compost, over time your garden should be, more or less, a stable system. Of course, if an animal dies in your garden, the decaying body will increase the overall nutrient level.

Peter4075
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Over time a well balanced ecosystem will gain nutrients. Fertile top-soil is a natural occurrence. If it was a zero sum endeavor the entire planet would be a desert. Soil can be thought of as a living entity. It's filled with bacteria, fungi, insects and other living creatures. Also, legumes through their symbiotic relationship with soil-dwelling bacteria actually add nitrogen to the soil. Of course there are certain nutrients, especially minerals that must be already present in the soil.

Troy Turley
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An important thing that is relevant to your question but maybe not a nutrient per se is carbon. Growing plants and composting them into the soil will increase the soil's organic matter, which will make the soil more conducive to growing plants even though plants don't take up much carbon from the soil (most of their carbon comes from the air).

If you have nitrogen fixers among your plants, then growing them and composting them will increase soil nitrogen.

For all other nutrients (and for nitrogen, if you don't have nitrogen-fixing plants), no, growing and composting plants only recycles what's already there and doesn't add anything new.

Edit: over very long times, minerals in the soil and bedrock will break down to release additional nutrients. This is relevant to geologists but not gardeners.

Vulcan
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Not zero-sum. The garden would on average lose nutrients over time. An example? Australia. Nitrates can be somewhat replenished by rain, but phosphates decline.

Polypipe Wrangler
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