How to measure diversity

4 June 2018, by Lisa Wolf, CEN Universität Hamburg

Photo: UHH/CEN/L. Wolf

The number of different species living in an area is the usual measure of diversity. However, the number alone does not tell the whole story – it is the function they are performing for the ecosystem that truly matters, says Romain Frelat of the Institute for marine ecosystem and fishery science at Universität Hamburg. He and his colleagues have studied the shape diversity of the fish species in the North Sea with a new method comparing more objectively the diversity of shape in the fish community than ever before.

Mr Frelat, in your study you looked at the different shapes of all fish species in the North Sea. Why did you look at this special characteristic?

The shape of organisms is linked to their function. It is not just random; it is coming from evolution and is an adaption to their environment. For example, the shape of the tail fin is linked to the swimming performance – it makes the fish either a sprinter or a ‘marathon runner’, depending on its life strategy and its environment. Usually, scientist study shapes by measuring lengths and ratios that they choose subjectively. However, with my colleagues, we came up with a new idea: to use a mathematical method to describe rigorously and objectively the shapes.

How can mathematics describe the shape of fishes?

We used a mathematic method called elliptical Fourier transforms to describe the shape of fish. Therefore, we used about 200 images of different individuals of the fish species living in the North Sea. Then we transformed the images into black and white silhouettes to get only the outline. Then an algorithm transforms the x and y coordinates of the outline into a sum of sine and cosine functions. So we basically described mathematically the outline of a fish.

What is the advantage of this method?

Our method is very objective – we use the complete outline to describe the shape of fish without any subjective choice, so whoever will do the analysis, will find exactly the same results. Moreover, we get descriptors of shape which are unique to each shape, so we can go reconstruct the original shape from its descriptor. That’s an elegant property which really helps the interpretation of the results. It is the first time that such method has been used on fish communities.

Why is it important to learn more about the diversity of shapes or the morphology of species?

Usually, we always look at the number of species as an indicator of the diversity of an ecosystem. Though this number is informative, it actually does not mean so much – it would be too easy to say that if the number of species is increasing, the diversity is always increasing as well. If a new species is looking quite similar to the ones already there, it might not be so important for the ecosystem. If you instead loose a species which is very unique in its function in the ecosystem, that is far worse. Morphology is linking many different characteristics and functions of fishes for their ecosystem – the shape tells you something about what they are eating, how fast they are able to swim, how good they can maneuver. That is why it is interesting to look at shapes.

Which different shapes did you find? Are there key factors for diversity in shapes?

The average shape of the fish species living in the North Sea looks a bit like Atlantic cod. From this, the main variation is elongation. So for example, it goes from herring, which is a pelagic fish with an elongated body, to normal shaped cod to flounder, which is a flat fish with rounded body shape. Elongation is the main factor of diversity in shapes. The second one is the shape of the ventral fin, i.e. the pair of fins towards the rear end of a fish. It reveals how much a fish can maneuver around e.g. in order to look for prey or to escape a predator. Third, you have the shape of the tail, which is linked to the swimming performance. Some are better long-distance swimmers, some are more fast sprinters.

What where the results for the North Sea?

The North Sea is interesting because it has a strong environmental gradient. The south has very shallow waters, and a strong seasonality, because the water is warming very high in the summer. There is a high primary production – so many things to eat. Whereas in the north, the water is deeper, and it is a more stable environment at least for the fish living at the bottom. This leads to different communities of fish in the north and in the south. Interestingly, we found that these communities have a different range of shapes. In the South, the shapes of fish species are more different than expected, and in the North, most of the fish species have similar shapes. There seems to be a strong environmental pressure that restrains the diversity of shapes of fish species in the north.

After studying the fish of the North Sea - What are your plans for the future?

Right now, we are looking at the shape diversity in a tropical reef. The diversity of fish in a coral reef is incredible, so it is a very interesting case study. The goal is to compare the traditional methods used to study the shape of fish with our novel method. The long-term perspective would be to characterize the shape of all the fish species on Earth.

Scientific Paper: Caillon, F., V. Bonhomme, C. Mollmann, and R. Frelat. 2018. A morphometric dive into fish diversity. Ecosphere 00(00):e02220. 10.1002/ecs2.2220

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