Plants, Roots, Spirals and Palaeobotany — Sandy Hetherington

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Plants have transformed the surface of the earth and the contents of our atmosphere. To do this they’ve developed elaborate systems of roots and branches which (sometimes) follow uncanny mathematical patterns such as the Fibonacci sequence.

Sandy Hetherington leads Edinburgh’s Molecular Palaeobotany and Evolution Group, they take a no-holds-barred approach to understanding plant development by combining genomics, fossil records, herbaria, and 3D modeling.

Recently Sandy’s lab has created three-dimensional models from ancient fossils that challenge our understanding of patterns in nature.

Look carefully at the scales of pinecones, or the way that leaves are positioned corkscrewing around a stem and you will start to notice spirals. One way of quantifying these spirals is to count the number of arms (or “parastiches”) in one direction and those in another. Note in the image below how the parastiches move in two directions.

Counting the numbers of parastiches in either direction we (almost always) get adjacent numbers in the Fibonacci sequence (or doubles of these), for example 8, 13 (or 16, 26). Recall that the Fibonacci sequence adds together the two previous terms to generate each subsequent one 1, 1, 2, 3, 5, 8, 13, 21.

Such Fibonacci spirals have been widely accepted to be a common thread in plant evolution — a so-called conserved feature — occurring naturally due to a variety of possible reasons such as optimizing light absorption or efficient seed packing. However, Hetherington’s recent research challenges the status quo. Studying fossils of ancient clubmosses, Hetherington discovered that spirals in these species defied the Fibonacci rule. Today, such non-Fibonacci occurrences are very rare in most plant species. It was assumed that modern clubmosses — which fail to follow this rule — were a recent evolutionary accident.

If clubmosses have failed to follow the Fibonacci rule for four hundred million years we must either rethink assumptions that Fibonacci rules are optimal, or else we need to explain why this pathway seems to have been closed off to clubmosses. Concepts from morphogenesis — introduced by Darcy Thompson in On Growth and Form — could play a role here. Thompson’s insight was that evolution may not be the best, or only, explanation for the forms of natural structures. Chemical gradients or reaction-diffusion processes (a field pioneered by Alan Turing) are simple mechanisms that can account for complex or uncannily mathematical forms.

In a field, a few hundred miles from me in the northeast corner of Scotland is a field that preserves a record of some of the earliest plants on land. Encased in the silica of the Rhynie chert the fossils are so exquisitely preserved that individual cells can be discerned. It’s from these that Sandy’s team made their discoveries.

It is inspiring to think how the distant past can continue to surprise us and how the rules and pathways explored by natural life can bind structure so tightly that even as every plant is unique, the mold may be as old as the hills.

Notes

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