400-million-year-old fossil changes thinking about Fibonacci spiral

Plant fossils from more than 400 million years ago have irregular structures, unlike most plants today which follow the Fibonacci spiral.

The arrangement of leaves on a tree branch, the structure of a pineapple, the petals of a sunflower or the scales of a pinecone are all wonderful examples of mathematical patterns in nature. A common feature of most plants today is that they have a spiral structure, which follows the Fibonacci sequence.

These spirals — simply known as Fibonacci spirals — are common in plants and have fascinated famous scientists, from Leonardo da Vinci to Charles Darwin.

The prevalence of the Fibonacci spiral in plants today is considered to represent an ancient and highly conserved trait, occurring from the earliest stages of plant evolution to the modern period.

However, a new discovery by biologist Sandy Hetherington from the University of Edinburgh and paleobotanist and PhD student Holly-Anne Turner at University College Cork could overturn that perception.

Scientists examined the spirals in the leaves and reproductive structures of a 407-million-year-old fossil plant. They were surprised to find that all the spirals observed in this particular species did not follow the same pattern . Today, there are very few plants that do not follow the Fibonacci spiral.

What is Fibonacci Spiral?

Spirals are ubiquitous in nature, found in leaves, animal shells, and even the double helix of human DNA. In most cases, spirals are related to the Fibonacci sequence - a series of numbers in which each number is the sum of the two preceding it (1, 1, 2, 3, 5, 8, 13, 21…).

These patterns are common in plants, and can even be seen with the naked eye. If you pick up a pine cone and look at the base, you can see the scales forming a spiral that converges toward the point where it attaches to the branch.

A digitized, color-coded image of a pinecone identifies eight clockwise and 13 counterclockwise Fibonacci spirals. (Photo: Sandy Hetherington).

At first glance, you will see spirals in one direction. But if you look closely, you can see both clockwise and counterclockwise spirals. If you count the number of clockwise and counterclockwise spirals, most of the time the number of spirals will be an integer in the Fibonacci sequence.

This is no exception. According to a study that analyzed 6,000 pine cones, 97% had the Fibonacci spiral. This structure is also common in other plant organs such as leaves and flowers.

If you look at the top of a tree, such as the shoots of the Araucaria araucana, you can see the leaves arranged in a spiral pattern that starts at the top and gradually winds around the trunk. A study of 12,000 spirals from over 650 plant species found that Fibonacci spirals were present in over 90% of cases.

Based on its frequency of occurrence in living plants, it has long been assumed that the Fibonacci spiral is an ancient and highly conserved feature in all plants.

Non-Fibonacci spirals in primitive plants

To test this hypothesis, scientists studied the leaf arrangement and reproductive structures in an ancient group of plants related to today's mosses in the family Lycopodiopsida.

Specifically, Sandy Hetherington and Holly-Anne Turner studied fossils of the extinct plant species Asteroxylon mackiei . The fossils are held in museum collections in the UK and Germany. They were originally collected from Rhynie chert – an ancient sedimentary deposit located in northern Scotland.

Holly-Anne Turner, lead author of the study, creates digital 3D models of Asteroxylon mackiei at the University of Edinburgh. (Photo: Luisa-Marie Dickenmann).

Scientists photographed thin slices of the fossil, then used digital reconstruction techniques to visualize the arrangement of Asteroxylon mackiei leaves in 3D and identify the whorl.

Based on this analysis, the authors found that leaf arrangements in Asteroxylon mackiei are highly variable. In fact, non-Fibonacci spirals are the most common arrangement.

The discovery of non-Fibonacci spirals in such an ancient fossil is surprising because they are rare in most plants living today.

Different evolutionary history

These findings change our understanding of Fibonacci spirals in land plants. They show that non-Fibonacci spirals were present in the ancient ground pines, overturning the view that all leafy plants began growing leaves in a Fibonacci pattern.

A reconstructed image of a fossil of Asteroxylon mackiei. (Photo: Hetherington).

Furthermore, the new findings suggest that the evolution of leaves and the Fibonacci spiral structure in ground pines has a different history than other groups of plants alive today, such as ferns, conifers, and flowering plants. It suggests that Fibonacci spirals emerged multiple, separate times throughout plant evolution.

This work also adds another piece to an important evolutionary puzzle: Why are Fibonacci spiral structures so common in plants today?

This question continues to generate debate among scientists. Various hypotheses have been proposed, including maximizing the amount of light each leaf receives or efficiently packaging seeds.

The discovery by Sandy Hetherington and Holly-Anne Turner opens up new insights into fossils, and shows that plants like mosses can provide important clues in finding answers.