Earth and Environmental Science 11–12 · Year 12

Overharvesting a renewable resource: a fishing model and maximum sustainable yield

Module 8: Resource Management

Practical, model not builtLow risk

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The idea

A renewable population replaces itself fastest at half its carrying capacity, so a harvest above that maximum sustainable yield drives it to collapse, however large the stock looks at the start.

What you need

a bowl with 100 dried beans (the fish stock; the bowl holds at most 100, the carrying capacity), a spare supply of beans
record sheet or spreadsheet with the growth rule, calculator

How to do it

At the start of each round count the stock N and add new beans by the growth rule: new = 0.5 × N × (1 − N/100), rounded to a whole bean.
Then remove the agreed harvest H from the bowl.
Play 20 rounds at H = 10, then repeat from 100 beans at H = 12, 13 and 15; continue the H = 13 run on the spreadsheet beyond 20 rounds.
Plot the stock against round for each harvest and find the largest harvest that the stock can sustain.
Relate the result to a real Australian fishery or other renewable resource and to Aboriginal and Torres Strait Islander resource management.

What you should see

For the logistic rule with growth rate r = 0.5 per round and carrying capacity K = 100, the maximum sustainable yield is rK/4 = 12.5 per round, taken when the stock is 50. A harvest of 12 settles the stock at 60 (the stable root of 0.5N(1 − N/100) = 12). A harvest of 13 exceeds the yield the stock can replace: after the 20 rounds played the model stock is 53.0 and still falling, and it reaches zero after 55 rounds; 15 leaves 4.6 after 20 rounds and is gone at round 21; 20 empties it after 10 rounds. With whole beans (growth rounded to the nearest bean) the H = 12 stock levels off at 64 rather than 60 and the H = 15 bowl is empty at round 20, so the bean thresholds fall close to the model’s.

What changes

What you change: harvest per round
What you measure: stock after each round
What you keep the same: starting stock
growth rule
carrying capacity
number of rounds

Common misconceptions

Each of these ideas is wrong, and the activity is a chance to test it.

A renewable resource cannot run out.
The biggest stock gives the biggest sustainable catch.
A slow decline means the harvest is safe.

Safety card

Low riskLearners carry it out

Hazards

dried beans are a choking hazard for young children

Controls

count beans back into their container

Note

No hazardous chemicals or heat sources: record the activity in the school's RiskAssess risk assessment, following the NSW Department of Education Science safety and compliance page; the Chemical Safety in Schools package is not triggered.

Curriculum references

The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.

Earth and Environmental Science Stage 6 Syllabus (2017), NESA; current, replaced by the 11–12 Syllabus (2025) from 2028EES12-15 EES11/12-5 EES11/12-6 EES11/12-7
Earth and Environmental Science 11–12 Syllabus (2025), NESA; to be implemented from 2028, not yet taughtEES-12-04
Australian Curriculum v9No Australian Curriculum v9 code is listed.

Sources

The pages the author read to write this activity.

All Concept Studio activities