In this example, we explore the concepts of net production efficiency (MPE) and trophic efficiency (TE) through a two-part problem involving energy transfer in an ecosystem.

To calculate the net production efficiency (MPE), we use the formula:

MPE = \(\frac{\text{Net Productivity}}{\text{Assimilated Energy}} \times 100\%\)

In the first part, we analyze a grasshopper that has a total energy of 600 joules after assimilating 4,000 joules of plant matter. The MPE for the grasshopper is calculated as follows:

MPE (Grasshopper) = \(\frac{600 \text{ joules}}{4000 \text{ joules}} \times 100\% = 15\%\)

This indicates that 15% of the grasshopper's assimilated energy is converted into biomass, while the remaining 85% is used for cellular respiration.

Next, we calculate the MPE for a praying mantis that consumes the grasshopper. The mantis assimilates 475 joules of energy and gains 220 joules of biomass:

MPE (Praying Mantis) = \(\frac{220 \text{ joules}}{475 \text{ joules}} \times 100\% \approx 46.32\%\)

This means that approximately 46.32% of the mantis's assimilated energy is converted into its biomass, with the rest used for respiration.

In the second part, we calculate trophic efficiency (TE) using the formula:

TE = \(\frac{\text{Net Productivity of Current Trophic Level}}{\text{Net Productivity of Previous Trophic Level}} \times 100\%\)

We first assess the trophic efficiency between primary producers (the tree) and primary consumers (the grasshoppers). The tree provides 100,000 joules of energy, and with 10 grasshoppers each having 600 joules of biomass, the total net productivity for the grasshoppers is:

Net Productivity (Grasshoppers) = \(10 \times 600 \text{ joules} = 6000 \text{ joules}\)

Thus, the trophic efficiency from the tree to the grasshoppers is:

TE (Producers to Consumers) = \(\frac{6000 \text{ joules}}{100000 \text{ joules}} \times 100\% = 6\%\)

This indicates that only 6% of the energy from the tree is converted into grasshopper biomass.

Next, we calculate the trophic efficiency between primary consumers (grasshoppers) and secondary consumers (the praying mantis). The mantis has a biomass of 1,000 joules:

TE (Consumers to Secondary Consumers) = \(\frac{1000 \text{ joules}}{6000 \text{ joules}} \times 100\% \approx 16.67\%\)

This shows that about 16.67% of the energy from the grasshoppers is converted into mantis biomass. Overall, these calculations illustrate the efficiency of energy transfer across different trophic levels in an ecosystem.

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