Maths Skills: Calculating Productivity and Efficiency within Ecosystems
- Given the appropriate data, it is possible to calculate the net productivity of producers or consumers and the efficiency of energy transfers within ecosystems
Net productivity of producers
- The net productivity of producers (also known as net primary productivity or NPP) can be calculated using the following equation:
NPP = GPP - R
- Where:
- GPP = gross primary productivity
- R = respiratory losses
Worked example
The wheat crop growing in a farmer’s field has a gross primary production of 10,000 kJ m-2 yr-1. The wheat crop loses 5,500 kJ m-2 yr-1 as heat from respiration. Calculate the net primary productivity of the wheat crop.
Step 1: Write out the equation and substitute in the known values
NPP = GPP - R
NPP = 10,000 - 5,500
Step 2: Calculate the net primary productivity and give appropriate units
NPP = 4,500 kJ m-2 yr-1
Net productivity of consumers
- The net productivity of consumers can be calculated using the following equation:
N = I - (F + R)
- Where:
- I = the chemical energy store in ingested food
- F = the chemical energy lost to the environment in faeces and urine
- R = the respiratory losses to the environment
Worked example
In a grassland ecosystem, the net production of rabbits is 2,400 kJ m-2 yr-1. These rabbits ingest 18,900 kJ m-2 yr-1 of grass. Calculate the total energy loss of the rabbits.
Step 1: Rearrange the equation to find the total energy loss (F + R)
N = I - (F + R)
(F + R) = I - N
Step 2: Substitute in the known values
(F + R) = I - N
(F + R) = 18,900 - 2,400
Step 3: Calculate the total energy loss and give appropriate units
Total energy loss = 16,500 kJ m-2 yr-1
The efficiency of energy transfers within ecosystems
- In some cases, the efficiency of energy transfer refers to the percentage of energy that is transferred from the sun to producers
- This can be calculated using the following equation:
% Efficiency = (gross primary productivity ÷ light energy falling on the producer) × 100
- In other cases, the efficiency of energy transfer refers to the percentage of energy that is transferred from one trophic level to a higher trophic level (e.g. from producers to primary consumers or from primary consumers to secondary consumers)
- This can be calculated using the following equation:
% Efficiency = (chemical energy in consumer ÷ chemical energy in ingested food) × 100
- If it is a producer that is being ingested (e.g. by a primary consumer), the chemical energy in the ingested food is the same as the net primary productivity of the producer and the chemical energy in the consumer is the same as the net productivity of the consumer, so that:
% Efficiency = (net productivity of consumer ÷ net primary productivity ) × 100
- If it is a consumer being ingested (e.g. a primary consumer being ingested by a secondary consumer), the chemical energy in the ingested food is the same as the net productivity of the consumer being ingested and the chemical energy in the consumer is the same as the net productivity of the consumer (that is doing the ingesting), so that:
% Efficiency = (net productivity of secondary consumer ÷ net productivity of primary consumer) × 100
Worked example
The total solar energy received by an area of heather is 6 × 105 kJ m-2 yr-1. The gross primary productivity of the heather is 4.25 × 103 kJ m-2 yr-1. Calculate the percentage of solar energy converted into chemical energy by photosynthesis.
Step 1: Write out the equation and substitute in the known values
% Efficiency = (gross primary productivity ÷ light energy falling on the producer) × 100
% Efficiency = (4.25 × 103 ÷ 6 × 105) × 100
Step 2: Calculate the efficiency
% Efficiency = (0.0071) × 100
% Efficiency = 0.71 %
Worked example
A wheat farmer’s crops are being damaged by insect pests. The net primary productivity of the wheat is 112,500 kJ m-2 yr-1. The net production of the insect pests is 10,000 kJ m-2 yr-1. Calculate the percentage efficiency of energy transfer from the wheat to the insects.
Step 1: Write out the equation for % efficiency and substitute in the known values
% Efficiency = (chemical energy in consumer ÷ chemical energy in ingested food) × 100
or
% Efficiency = (net productivity of consumer ÷ net primary productivity ) × 100
% Efficiency = (10,000 ÷ 112,500) × 100
Step 2: Calculate the efficiency
% Efficiency = (0.089) × 100
% Efficiency = 8.9%
Worked example
The wheat farmer decides to use biological control against insect pests that are eating the wheat. The farmer introduces a species of toad. By eating the insect pests, the toads ingest 10,000 kJ m-2 yr-1 of energy but lose 2,000 kJ m-2 yr-1 of this energy in faeces and urine. They lose a further 7,000 kJ m-2 yr-1 using energy for respiration. Calculate the percentage efficiency of energy transfer from the insects to the toads.
Step 1: Calculate the net production of the toads
N = I - (F + R)
N = 10,000 - (2,000 + 7,000)
N = 10,000 - 9,000
N = 1,000 kJ m-2 yr-1
Step 2: Write out the equation for % efficiency and substitute in the known values
% Efficiency = (chemical energy in consumer ÷ chemical energy in ingested food) × 100
or
% Efficiency = (net productivity of secondary consumer ÷ net productivity of primary consumer) × 100
% Efficiency = (1,000 ÷ 10,000) × 100
Step 3: Calculate the efficiency
% Efficiency = (0.1) × 100
% Efficiency = 10%
Exam Tip
Based on the data you are given in an exam question, you may occasionally need to rearrange the equations above to calculate the right answer, so make sure you practice rearranging these! As always, keep a careful eye on the units being used and don't forget the final step of multiplying by 100 if you are calculating % efficiency.
