A tree log contains both bark and wood. The bark contains 2.5 times higher concentration of potassium than the wood. 62% of the potassium in the bark is available for uptake. 92% of the potassium in the wood is available for uptake. The potassium that is not available is in an insoluble form. One mushroom was found growing on the log. The density of mycelium in the log is 3.5 times higher in the bark than in the wood. I would like to know what percentage of potassium found in a mushroom is theoretically sourced from the bark and wood. It is not possible to empirically answer this question, so I would like to answer it mathematically. Researchers always assume that mushroom source their nutrients primarily from the wood and not from the bark of a log, even though the bark is known to nutritionally richer than the wood.
I would be grateful if someone could confirm if I did the calculation correct.
How I did the calculation: Concentration of potassium in the bark: 250 ppm. Concentration of potassium in the wood: 100 ppm.
Percentage potassium in mushroom sourced from bark = (250 * 0.62 * 3.5) / (100 * 0.92 * (1 / (3.5)) + 250 * 0.62 * 3.5) * 100.
The first part of the formula, (250 * 0.62 * 3.5), calculates the amount of potassium in the bark that is available for uptake. The expression is then divided by the sum of both the potassium from the wood and the bark, which is calculated by adding (100 * 0.92 * (1 / (3.5))) to (250 * 0.62 * 3.5). This gives the percentage of potassium in the mushroom that came from the bark.
Answer: 95.4% of the potassium in the mushroom was sourced from the bark.
Percentage potassium in mushroom sourced from wood = (100 * 0.92 * (1 / (3.5))) / (100 * 0.92 * (1 / (3.5)) + 250 * 0.62 * 3.5) * 100.
The first part of the formula, (100 * 0.92), calculates the amount of potassium in the wood that is available for uptake. The next part, (1 / (3.5)), normalizes the amount of mycelium in the wood to account for the difference in mycelium growth between the wood and bark. The entire expression is then divided by the sum of both the potassium from the wood and the bark, which is calculated by adding (100 * 0.92 * (1 / (3.5))) to (250 * 0.62 * 3.5). This gives the fraction of the total amount of potassium in the mushroom that came from the wood.
Answer: 4.6% of the potassium in the mushroom was sourced from the wood.
Assumptions:
- If bark and wood were to contain equal amounts of potassium and if this potassium was 100% available to the mushroom for uptake, the mushroom would likely source equal amounts of potassium from the bark and wood.
- Because there are 3.5 times more mycelium in the bark than in the wood, 3.5 times more potassium would be absorbed from the bark by the mushroom (compared to being absorb from the wood).
Notes for non-biologists: Mycelium are like the roots of a tree. Like how roots penetrate the soil, mycelium can penetrate bark and wood to scavage for nutrients. The nutrients are taken up through the mycelium into the mushroom.