Each year, large volumes of crop are harvested from fields.
- Where does this biomass get replenished from?
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There are biogeochemical cycles for the building stones of the biomass (e.g. hydrogen, carbon, nitrogen, oxygen, etc...), so all of these atoms are recycled. To recycle them the organisms need energy, which they get from sunlight, from chemical materials, etc... (check microbial metabolism for further details).
Plants use sunlight as energy source, CO2 from air as carbon source, water and O2 from air as oxygen source, and so on... You can find more info about plant metabolism on wikipedia.
The matter in plants is mostly carbon, hydrogen, oxygen, and nitrogen, with various metal ions and some sulfur and phosphorus. The carbon, hydrogen, and oxygen are taken from carbon dioxide in the air and water from the soil through photosynthesis. Nitrogen is taken up from the soil as ammonia or nitrates, or fixed from nitrogen gas, but this only happens in legumes. Phosphorus is also part of a nutrient cycle. Metal ions such as sodium, potassium, magnesium, and calcium are taken up through the roots with water.
If you're asking about how this material is replenished, fertilizer is an important answer. For centuries, nitrogen was a limiting nutrient in farms because it would get removed faster than it was replaced, especially if crop rotation was not used or legumes weren't grown. Thanks to the Haber Process we can produce humongous amounts of ammonia from nitrogen gas, this has greatly increased the amount of nitrogen available for plants, but has also resulted in nitrate pollution in waterways and algal blooms and eutrophication. Phosphate and potassium are also used in fertilizer and are usually mined, however phosphorus reserves are limited.
The biomass of crops is definitely mostly carbon (from the air in the form of CO2) and water. However, in terms of how it affects the environment: Crops use up trace elements that make up a tiny fraction of the biomass, but it is these trace elements that are not ubiquitously available. Most notably phosphorus and to a lesser extent nitrogen. The impact on the environment is that farming, and especially monocultures, deplete the environment of these essential trace elements. It is often these elements that restrict growth due to competition. Therefore, it may inhibit growth of native species. However, a far more devastating effect is that farmers will re-supply these trace elements in excessive amounts through artificial fertilizers, leading to surplus and run-off phosphates (phosphates are the main form in which phosphorus is applied in fertilizers) (Hart et al, 2004). This in turn dramatically shifts the natural competition for this normally restricting element, in turn promoting growth of non-native plants and promoting the growth of P and N-tolerant plants while suppressing the growth of plants that are intolerant. As most plants are actually intolerant it will eventually lead to species loss and imbalance in the ecosystem (popular link).