Could a farm remain productive indefinitely without external inputs?

Is it possible to have a farm sustain itself without the addition of external nutrients? If so, how does the soil regain nutrients taken by the crops and eaten by the humans?

Do you mean infinite or indefinite? Indefinite, sure. Infinite, no.

Well nitrogen is found in the air and enters the soil via electrical storms and the activities of various organisms. Nitrogen can never become truly depleted. The other elements will eventually become depleted, but it takes a hell of along time for most of them. Most crop plants only feed ion the top few metres of soil at most, and those nutrients are found throughout the soil profile, so it’s quite possible to rejuvenate the soil by taking material from deep rooted vegetation such as trees growing on one part of the farm and using it to mulch the cultivated areas. In that way nutrients get brought up from much deeper soil levels and made available to crops.
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However none of this is infinite of course. Given enough time the soil will still become depleted. In fact using this method productivity will decline significantly on most soils within a century, then stabilise for the next couple of centuries as the rate of loss is counter balanced by the input from mulches.

Crop rotation.

Legumes, in particular, are good at replenishing nitrogen levels.

Farmers rotate crops in the fields to reduce depleting the soil. They also skip planting anything in a field to allow the soil time to recover.

There’s a whole schedule they follow. The farmers I knew growing up leased a lot of land. They didn’t own enough to rotate crops like they needed.

Well, ideally farmers rotate their crops and manage their land to use minimal external inputs.

Many farmers, though, just alternate growing corn and soybeans, and dump huge quantities of fertilizer on the fields so they don’t have to worry about managing soil nutrients. Theoretically soybeans are legumes that put nitrogen back in the soil, but the soybeans get all of the nitrate they need from fertilizer so they don’t bother spending energy on nitrogen fixation.

Current agricultural practices require huge fertilizer inputs, which is present only transiently in the soil, so there are huge outputs of polluted runoff.

To answer the OP a bit more directly: Yes, agriculture can work in a mostly closed system. Most farmers for most of human history managed to produce enough food without major external inputs. Though of this doesn’t always happen through perfectly harmonious crop rotation – there are plenty of examples of land that was overused, abandoned, and then farmed again many years later after its fertility was restored. And a lot of the most productive lands like flood plains rely on humongous external inputs of nutrients and organic matter. Still, for most of human history farmers got by just with resources they could trade with neighbors (manure for hay, etc.)

Of course, with cheap synthetic fertilizers are modern industrial methods, our farmland is far more productive. But that productivity is entirely dependent on all of the external inputs. A piece of land used like that won’t grow anything if you stop pouring fertilizer on it.

Depends on the definition of “external”, since, technically, the nitrogen in the air doesn’t come from the farm.

Neither does the sunlight that makes the plants grow.

What are waste products on the farm treated as? Internal or external? Because if you compost human waste and run cattle, goats and chickens on the fallow land, you can restock the soil nutrients without buying any fertilizers.

Only if they are tilled back into soil or allowed to decompose back into the ground. If the plant (or majority of the mass of plant) is removed from the field/soil, then there is no real ‘input’ if I am understanding the OP’s intent of question. I’d also presume that it would depend on which crop(s) were grown as (iirc) some crops really do not use/require much of ‘trace chemicals’ while others won’t grow (or produce good output, per se) well unless there is an ample amount of those traces. I forget which ones feed heavily upon trace minerals, but I’ve been told that most leafy crops tend to require less than ones that are dependent upon putting nutrients into post-pollinated flowers (tomatoes, corns, peppers, etc…)

Of course, not all are like that and I mean it as a wide example. Rate of growth/production slows way down if nutrients are removed faster than Nature replaces it (wind, flood, rot of organics, etc).

you would both need the amount of land for the rotations and multiple cropping, room for animals and their feed.

you would also need to start with a good and fertile location. location would need generally favorable weather.

though [thread=576558]discussion[/thread] has been on simpler situations

There are a few sources of minerals other than those mentioned above. Fallout from volcanoes and weathering of rocks are two. These are the sources of all the soil, AFAIK. But it is good to try to return all residues to the soil, including, obviously, human waste.

The Amish in Pennsylvania and elsewhere have farmed the same land for several hundreds of years without depleting it.

Not really, no. The nutrients in animal wastes aren’t created by the animals, they are taken from the soil by plants. So they don’t restock soil nutrients, they just put back a little of the nutrient that was taken out already. IOW it might slow the rate of nutrient depletion, but it won’t i any sense restock the soil nutrients.

If you actually want to restock soil nutrients, those nutrients have to come from somewhere. IOW you need to buy fertilisers.

Fields used for growing soybeans and alfalfa are given nitrogen credits when figuring your fertilizer needs for the following year. We’ve been known to skip putting fertilizer on at all in a field that used to be in beans during years when money is tight and gotten along okay. After a couple of years of doing that, however, corn yields will drop off drastically (30-40 bushel an acre sometimes). Corn needs fertilizer to yield well.