Fruits fly like their wings

All in the service of science, naturally. Biologists were trying to understand how ants found their way home from distant food sources. These experiments showed that they remembered the number of steps it took to reach the food.

Amusing stuff, and of course I’m a sucker for anything to do with ants, those wonderful perennial creatures. But now I have made a research effort that is equally wince-inducing, though not this time with ants, nor was it just biologists at work. This time mathematicians were involved.

They pulled wings from fruit flies (Drosophila melanogaster). All in the service of science, naturally.

Now fruit flies are tiny insects, so their wings are tiny bits of tissue. Grow them, and they are exquisite creations. Shaped like elongated teardrops and outlined with short bristles, they have a sparse network of veins running across their surface, like your palm, and are transparent, even iridescent. But even to get such a great view of a feather, you have to be really careful after breaking it off—as it gets bent and damaged easily. The scientists placed each wing between two glass plates. Then they could be photographed and examined closely.

What were they looking for? Well, when you start studying evolution, at one point you run into a seemingly insurmountable conflict. Take us humans. Even though we lived and thrived in a completely different environment, it didn’t lead us to evolve into separate species. On the contrary, we all bear a certain similarity to each other in form and ability. Call it “strength,” and it’s why wherever we find ourselves and under any circumstances, we can all truly function as human beings.

And yet there is a rigorous argument for evolution as well. For a species to develop at all, individual humans must show distinct characteristics from others. They are the differences upon which the process of natural selection is built. To understand this, let’s say there’s a particular disease that’s running wild, killing people left and right. But there are some individuals who have something inside that is able to resist the disease, so they survive. They were naturally chosen to survive. When they breed, they pass on that special ability to resist to their descendants. So that a different trait would drive the evolution of a new generation of humans – but still humans – that are resistant to the dreaded disease. Call it “development”, and it’s the reason we can evolve.

This tension between robustness and evolution—similarities and differences—has long haunted evolutionary biologists. And that’s exactly what Madhav Mani, who teaches applied mathematics at Northwestern University, and a team of colleagues interested in biology set out to find out. According to their paper, they “put forth a general mathematical strategy for the direct quantification of the degree and nature of the developmental robustness of a fully integrated body organ” (bit.ly/3oH5fYy).

The “fully integrated body part” they chose was the wing of Drosophila, partly because it has been extensively studied and many Drosophila genes are known to influence its development. The strategy involved a direct comparison of 2,000 wings which he dismantled and preserved. Given their uniquely identifiable shape and size, they found a mathematical way to standardize the feathers so that they could be compared. Each was “computationally mapped to the interior of a disk of a fixed size… [relying] On efficient numerical implementations of the Riemann mapping theorem.”

Never mind computations that call for Riemann mapping. What is relevant here is that it distorts the boundary of the wing – from the teardrop to the circle – and thus the wing veins mark different regions. The authors comment that they apply this technique to “any 2D surface with no holes, with or without borders… a simple 2D shape like a feather or a complex 3D shape closed surface such as a tooth, brain, or Can. Another part of the body.” You can say, any shape whose range is less important to study than the inside of the range. Because the mapping doesn’t distort what’s inside – in the case of these Drosophila wings, it preserves the angles between the intersecting veins.

The scientists say this approach is “both a strength and a limitation”—as it underlines variation in vein patterns, but it emphasizes any changes in the overall shape of the wing. But because the wings are now represented by discs of equal size, we can stack them on top of each other. This makes possible detailed comparisons between and between feathers. In fact, they effectively had 30,000 points of comparison—each pixel in the stacked disc image.

And what story did this repository of data tell? The wings were much more alike than they were apart. There were only a few characteristics in which they differed, such as the shape and configuration of the vein where the wing attaches to the body of the fly. Not only this. When one of these characteristics differs significantly from the norm, the others differ as well. Remember that development depends on differences, and these were just some of the differences at work here. But since the feathers are very similar, these particular characteristics did not greatly affect the evolution of the feather. Nevertheless, these observed variations suggest that wing instability has not completely decreased in importance. It is possible that in the future Drosophila will have wings that have evolved a different form and may even function.

As for robustness, however: Overall, these findings give mathematical support to the theory of robustness – that it is based on limited variations between individuals. Fruit flies all look remarkably alike, and of course their wings look even more alike – you’ve seen one, you’ve seen (almost) all of them – and this suggests that robustness has driven their evolution. has been interrupted. Thus, wing development is strong. In a real sense, mathematics shows us the workings of the principle of robustness and what is the nature of robustness.

As one of the authors commented, as flies grow into adulthood, they have a “magical ability to mend differences and create a very strong final look.” And this whole exercise—breaking the wings of the flies, preserving them between glass plates, photographing them, applying Riemann mapping to them, and then virtually stacking them—gives us a remarkable insight into the variations we see. , or do not see in a given species.

Is that insight worth permanently disabling several hundred flies? Well, do the lessons learned about their tricks justify biting off Tunisian ants’ legs? Your answers may say something about your attitude towards science.

Postscript: Speaking of fruit flies. In my computer science days, they appeared in a famous example to show the difficulty of getting a computer to understand English. How would you write software to differentiate between these apparently similar sentences?

* Time flies like an arrow.

The fruit flies like a banana.

Dilip D’Souza, once a computer scientist, now lives in Mumbai and writes for his dinner. His Twitter handle is @DeathEndsFun