Forests are complex ecosystems where all the necessary elements have been taken up into the biomass. When something dies, falls to the ground, gets decomposed by decomposers, the soil micro and macro organisms get fed the decomposed organic matter and plants are able to uptake a bit more of the chemicals necessary with which to do photosynthesis and make their own food.
In other words, Sanjihan, the soil is deplete of the 'nutrients' you are imagining. When we cut forests down we are actually 'mining' that forest of all the elements that we humans are responsible to put back into the soil so that we can grow crops. That is why I giggle when people think that fertilizer is a bad thing, that 'robs' the soil of 'nutrients'...plants make their own food. I hate using the word nutrients because that implies food.
The forest soil will be full of life, bacteria, nematodes, fungus as well as millipedes, ants, earthworms etc. But when leaves fall, or a branch is broken by the wind and falls to the ground, the first organisms to go to work are the decomposers. They jump into action when there is material that was once alive and now dead. Decomposers need nitrogen to do their work. Little nitrogen, slower decomposition. While this is happening all the other soil organisms go dormant or die until the decomposers do their work. When the decomposers have decomposed the organic matter only then the soil comes alive with organisms because there is now food for both micro and macro organisms in the soil.
The micro organisms, now alive, are critical for the uptake of chemicals by plant roots that the plant's leaves need to do the incredible job of photosynthesis. With the proper elements, CO2 and water, chloroplasts are able to change the light of the sun into food and living tissue, giving off O2 and H2O to the atmosphere.
I know you know this but you have fallen for what the media has done to us oh so smart people by calling these elements 'food'. This is one of my missions. To undo the notion that fertilizer is 'food' for plants as it most certainly is not. The other mission is to dispel this completely erroneous notion that adding fertilizer (synthetic) is bad for the soil. Chemicals are chemicals no matter their origin. Synthetics are made with the use of petroleum, organic fertilizers are also made with petroleum products for packaging and consistency and usability.
We humans are pretty funny in a way. We think man made or synthetics are bad while organics are the only way to go. Yet we eat soft serve ice cream, use makeup on our faces, take pills, skin lotions, drive cars, on and on that are made with or using petroleum. Then we get on this soap box being 'organic' gardeners to the point of ridiculous.
We strip away the biomass of stable ecosystems and that makes us responsible to replace what we took away or forget growing healthy plants, fruitful crops. The forest soil is great for little pieces of rock (soil) and organic matter but the chemicals are already up in the trees and plants. In a way this part of the system controls the population of a stable ecosystem. But make no mistake, there will not be much in the way of nutrients. They've already been used and won't be put back until something dies and goes through the process of decomposition and then it is immediately taken back up into the biomass.