Final answer:
To model energy flow through four trophic levels, assign 1,000 kilocalories as one energy unit and designate trophic levels from producers to tertiary consumers. Utilize the 10% rule for energy transfer, which results in a pyramid showing a decrease in energy and biomass at higher levels.
Step-by-step explanation:
To develop a mathematical model of energy flow through four trophic levels in an ecosystem, first, we need to define what will represent one energy unit. Let's say one energy unit is 1,000 kilocalories (kcal). Then, we will represent the trophic levels as follows: producers (level 1), primary consumers (level 2), secondary consumers (level 3), and tertiary consumers (level 4).
According to the ecological pyramid and the 10% rule, if producers have 1,000,000 kcal, then primary consumers will have 10% of that, which is 100,000 kcal. Secondary consumers will get 10% of the primary consumer's energy, making it 10,000 kcal, and tertiary consumers will receive 10% of that, resulting in 1,000 kcal. This model explains why energy decreases as one moves up the trophic levels due to metabolic processes and heat loss to the environment, leading to fewer organisms and less biomass at higher levels.
Ecological pyramids can demonstrate how biomass and the number of organisms decrease from lower to higher trophic levels. However, the size of organisms typically increases with higher trophic levels. While the number of organisms and total biomass decreases, the individual organisms tend to be larger.