Food Chains
When a habitat changes, what happens to the food chain?
Age
11 to 14
Challenge level
Problem
Here is a food chain:
Image
A wildcat will eat 3 birds every day. These three birds will eat 10 caterpillars each, every day, totaling 30 caterpillars. The 30 caterpillars will eat one small bush together every day.
a. In the area that these animals live in, the ecosystem can support 500 small bushes being eaten every day. Calculate the numbers of each animal in the food chain.
b. As you go up the food chain, the amount of energy available to the following predator decreases. For this food chain, the amount of energy available decreases by 25% for every level in the chain. Calculate how much more energy the wildcat could obtain from becoming a
vegetarian and eating the bush rather than from eating birds.
c. One year, a bacteria kills 5000 caterpillars. What effect will this have on the food chain?
d. Suppose that the wildcats decide to become vegetarians and eat bushes instead of other animals. How many wildcats could 500 bushes support (ignoring the other animals)?
e. If the wildcats became omnivorous (with some of them eating animals and some eating bushes), how many animals would there be if half of the bushes were eaten by caterpillars and the other half were eaten by wildcats?
e. If the wildcats became omnivorous (with some of them eating animals and some eating bushes), how many animals would there be if half of the bushes were eaten by caterpillars and the other half were eaten by wildcats?
Student Solutions
Well done to Amina from Greenacre Public School, Australia and Carl who sent us their solutions to this problem.
Amina found the ratio between the different organisms in the food chain and used it to find the answer to the first part or the problem:
a. The ratio is:
$$ \begin{align}
\begin{array}{ccccccc}
\text{Bushes} &:& \text{Caterpillars}&:& \text{Birds}&:& \text{Wildcats}\\
1 & :& 30 & :& 3 & :& 1 \\
500 & :& 15000 & :& 1500 & :& 500
\end{array}
\end{align}
$$Therefore, if there are $500$ bushes, there will be $15000$ caterpillars, $1500$ birds and $500$ wildcats.
$$ \begin{align}
\begin{array}{ccccccc}
\text{Bushes} &:& \text{Caterpillars}&:& \text{Birds}&:& \text{Wildcats}\\
1 & :& 30 & :& 3 & :& 1 \\
500 & :& 15000 & :& 1500 & :& 500
\end{array}
\end{align}
$$Therefore, if there are $500$ bushes, there will be $15000$ caterpillars, $1500$ birds and $500$ wildcats.
Carl sent us the following solutions to the other parts of the problem:
b. Each predator gets $100-0.25=0.75=75\%$ of the energy from the previous level of the food chain. So the caterpillars eat the bushes, and get $75\%$ of the energy. The birds eat the caterpillars and get $75\%$ of the caterpillars' energy, which is only $0.75^2=0.5625=56.25\%$ of the energy from the bush. So the wildcats get $75\%$ of the birds' energy, which is
$0.75^3=0.421875=42.1875\%$ of the energy from the bush.
If the wildcats became vegetarian and ate the bush, they would get $75\%$ of the energy instead. So the wildcats could get $\frac{0.75-0.421875}{0.421875}=\frac{7}{9}=77.\dot{7}\%$ more energy by eating the bushes if they were vegetarian.
If the wildcats became vegetarian and ate the bush, they would get $75\%$ of the energy instead. So the wildcats could get $\frac{0.75-0.421875}{0.421875}=\frac{7}{9}=77.\dot{7}\%$ more energy by eating the bushes if they were vegetarian.
c. We still have $500$ bushes but now we only have $10000$ caterpillars, so we would then have:
$$ \frac{10000}{10} = 1000 \text{ birds}\\
\frac{1000}{3} = 333 \text{ wildcats} $$This means that $500-333=167$ wildcats would starve due to a lack of food.
$$ \frac{10000}{10} = 1000 \text{ birds}\\
\frac{1000}{3} = 333 \text{ wildcats} $$This means that $500-333=167$ wildcats would starve due to a lack of food.
d. The wildcats only need to eat $56.25\%$ of a bush, so there is more food for the wildcats because a bush can feed $\frac{1}{0.5625} = \frac{16}{9} = 1.\dot{7}$ wildcats. So $500$ bushes would feed $500 \times \frac{16}{7} = 888$ wildcats.
e. In this (arguably fairer) situation $500$ bushes would feed $7500$ caterpillars and $444$ wildcats. This would allow for $750$ birds, which would then feed another $250$ wildcats. So in total there would be $500$ bushes, $7500$ caterpillars, $750$ birds and $694$ wildcats.
Teachers' Resources
It is not envisaged that this problem would be used as a class problem. It is more appropriate for an enthusiastic student or small group of students looking for a challenge to work on independently.