The diagram below depicts energy flow within a single trophic level, where I=amount ingested, NA = amount not assimilated, R = respiration, and Pn = biomass production at trophic level.

Which one of the following options represents correct values for Pn, NA, R and I in kcal respectively, if Pn - 1 = 1000 kcal, I/Pn - 1 = 20%, A/I = 35% and Pn/A = 20%?

The correct answer is Option 2 i.e. 14 130 56 200

Key Points

• The efficiency with which energy is transferred from one trophic level to the next is called ecological efficiency. 
• Energy transfer in the ecosystem is not efficient, as only almost 10% of energy is transferred to the next trophic level, while 90% of the energy is lost to the environment. 
• Due to non-predation death, egestion, and cellular respiration, a  notable amount (almost 80 -90 %)  of energy is lost to the environment.
• Ecological efficiency included various related efficiency, which is as follow: 

1. Exploitation efficiency/ consumption efficiency(CE)
   • It is defined as the percentage of food available at one trophic level that is consumed (ingested) by the consumers. at one trophic level. 
   • \(CE = \frac {I_n}{p_{n-1}} \times 100\)
2. Assimilation efficiency (AE)
   • It is defined as the percentage of food assimilated across the gut wall and becomes incorporated into growth.
   • \(AE = \frac {A_n}{I_n} \times 100\)
3. Net production efficiency (PE)
   • It is defined as the percentage of assimilated energy \((A_n)\) that is converted into new biomass. 
   • \(PE = \frac{P_n}{A_n} \times 100\)

Explanation:

• Given : Pn - 1 = 1000 kcal, I/Pn - 1 = 20%, A/I = 35% and Pn/A = 20%
• First we will find the amount ingested i.e., I.
• \(\begin{equation} \begin{split} \frac{I}{Pn-1} & = 20\% \\ \frac{I}{1000kcal} & = \frac{20}{100} \\ I & = \frac{20}{100} \times 1000 \\ I& = 200 \space kcal \end{split} \end{equation} \)
• Now, we will find the amount assimilated
•  \(\begin{equation} \begin{split} \frac{A}{I} & = 35\% \\ \frac{A}{200\space kcal} & = \frac{35}{100} \\ A & = \frac{35}{100} \times 200 \\ A& = 70 \space kcal \end{split} \end{equation} \)
• Ingestion =  Assimilated + Non-assimilated 
• \(\begin {equation} \begin {split} NA &= I-A \\ NA &= 200 -70\\ NA &= 130 \space kcal \end {split} \end {equation} \)
• Now, we will find the amount of biomass produced at the trophic level. 
• \(\begin{equation} \begin{split} \frac{Pn}{A} & = 20\% \\ \frac{Pn}{70\space kcal} & = \frac{20}{100} \\ Pn & = \frac{20}{100} \times 70 \\ Pn& = 14 \space kcal \end{split} \end{equation}\)
• Lastly, we will find the amount of biomass lost in the respiration 
• The amount of biomass assimilated is used for carrying out respiration and also passed on to the next trophic level. 
• \(\begin{equation} \begin{split} A& = R + Pn \\ R & = A-Pn \\ R & = 70-14 \\ R& = 56 \space kcal \end{split} \end{equation}\)
• So, Pn = 14, NA = 130, R = 56 and I = 200

Hence, the correct answer is Option 2.