How far away is the other side of a hill? If you’re looking at a map, it might be a few kilometers. If you’re looking to know, the straight line distance doesn’t mean very much.

What matters is the distance along creeks and rivers. Two streams on opposite sides of a ridge might not connect for hundreds of kilometers, or in some cases, they never meet at all!

The animals determine distance by visual or non-visual cues. Many scientists work hard to model the environment and protect native plants and animals. If you’re trying to protect freshwater environments, then it’s important to know the secrets how they measure distances.

A team of scientists from NOAA and CSIRO wanted to predict how river ecosystems might react to future conditions. They constructed a computer model with two different ways of measuring distances. They used straight line distance like on maps but they also added stream distance – the distance a fish would have to swim. Using a fish finder you can see the location of fish when they swim under water.

Some environmental conditions that affect fish, such as air temperature and vegetation coverage, used straight line distances. Other important information, including stream water temperatures, used stream distances. Having the two in the same model allowed these different types of information to interact.

This new system is timely because fish are increasingly under threat from rising water temperatures. Temperature has a strong effect on fish, as most cannot easily control their own body temperatures. In most cases, the best they can do is swim to a cooler patch of water, perhaps shaded by a tree.

The system is already used to model stream temperatures in over 350 000 kilometers of rivers across several states in the United States. But there are still millions of kilometers of rivers all around the world that could use this maths.