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Algorithm Reveals Secrets of Leaf Shape

Plant biologist have long puzzled over the huge variety of leaf shapes that appear in nature. Now a simple algorithm could explain all

“Leaves have evolved over millions of years to optimize light collection, transport of nutrients to and from the plant body, and mechanical stability against natural stresses,” says David Young a physicist at the Lawrence Livermore National Laboratories near San Francisco.

The puzzle is how leaves grow into such a wide variety of similar shapes. What process can control this growth? Clearly, there is a genetic component to leaf growth but that cannot be the whole story because leaves on the same plant sometimes grow into different shapes, a phenomenon known as heteroblasty. That’s because environmental factors such as nutrition, sunlight also influence growth and shape.

Various theories attempt to explain leaf shape using ideas such as fractals and the Turing reaction-diffusion process. But none provide a convincing explanation for the variety of leaf shapes that occur in nature.

Today, Young attempts to change that by putting forward a simple model of leaf growth that reproduces much of the spectrum of leaf shapes that appear in nature. “My objective is to explain not only the range of leaf shapes found in the higher plants, but also the large variations in shape seen in leaves on closely related plants,” he says.

In his model, the growth of leaf lobes is governed by the position of leaf veins. The leaf then simply grows in 2 dimensions in a way that is governed by a simple algorithm. It is this growth pattern that determines the ultimate shape of the leaf. In Young’s model, the final leaf shape is really an accidental by product of this growth process.

That’s an interesting and powerful approach. By varying just a handful of parameters, Young can produce a surprisingly rich variety of shapes. For example, his model produces various oak, acer, poplar and willow-like leaves and many more.

It also produces one or two shapes not found in nature, which begs the question why natural selection appears to have avoided them.

Perhaps most importantly, Young’s algorithm is biologically plausible: it’s not hard to see how genetic and environmental process might combine to behave in this way.

What he needs now is somebody to map the algorithm’s parameters onto the real genetic/chemical processes that go on in leaves as they grow. That might take some doing but it’s by no means beyond plant biologists. Any volunteers?

Ref: arxiv.org/abs/1004.4388: Growth-Algorithm Model of Leaf Shape

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