Counting krill

Krill (Euphausia superba). Photo: Steve Nicol

Antarctic krill are probably the most abundant species of multi-celled animals on earth. Krill occur in vast swarms, often containing tens of thousands of tonnes of krill. There are estimated to be some between 300 billion and 1 million billion (1,000,000,000,000,000) individual krill in the Southern Ocean at any one time with a total weight, or biomass, of between 150 million and 500 million tonnes. (The total weight of humans on the planet at the moment is around 160 million tonnes.) (These figures can be used to create some interesting problem solving and number work.)

To manage the krill fishery, we need to assess krill populations accurately. The abundance of krill is currently estimated using scientific echo-sounders that measure the reflection of sound from objects below a ship. The distribution of krill occurs over an area of 30 million square kilometres (compared with the area of Australia - 8 million square kilometres). In a summer survey a single ship can only survey less than 1 million square kilometre - it's impossible to survey the whole area. And krill swarms are patchy in their distribution.

• To help students understand the principle of surveying, including its 'hit and miss' nature, divide them into pairs and have them play a variant on the game 'Battleships'. Provide them with two sheets of paper each marked with a grid 10 cm by 10 cm, numbered horizontally 1 to 10 and vertically A to J or use a printable grid.
  
  Student A places at random eight swarms of krill of varying sizes as follows: two x four squares, two x three squares, two x two squares and two x one square. Student B then tells Student A the grid route to be followed by the ship, seeking maximum coverage with minimum passes (it might be row B, then back via row D, two rows down, then row F and so on, then vertical passes at similar intervals). Each time there is a 'hit', Student B will have to work out location and size of the swarm by deviating from the track, and then must return to their agreed tracking route. The students then change places and repeat the exercise. The object is to find the krill swarms with the smallest number of passes.
  
  - What effect does it have if the swarms are all heavily biased in one direction?
  - What effect does swarm size have?
  - What are the possible real-life implications?
  - How likely are you to estimate the numbers correctly if you use only one pass of the ship? Two? Ten?

Emperor huddle from above at Taylor Rookery Photo: Andrew Plumridge

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• Give the students a similar situation (such as the numbers of spectators at a football match) and have them come up with various counting methods.