# 400 million-year-old fossil reveals the evolution of Fibonacci spirals in plants

Scientists have long believed that Fibonacci spirals are an ancient and highly conserved feature in plants. But, a new study challenges this belief.
Fibonacci spiral in an aloe vera plant

Plants date back some 470 million years. Plants come in various patterns, such as leaf arrangement, branching patterns, and floral symmetry, but one has baffled scientists the most.

Fibonacci spirals are a specific type of spiral pattern that occurs in nature, especially in plants. They are named after the Italian mathematician Leonardo Fibonacci, who introduced the Fibonacci sequence in the 13th century.

Scientists have long believed that Fibonacci spirals are an ancient and highly conserved feature in plants. But, a new study challenges this belief by examining the spirals in the leaves and reproductive structures of a 407-million-year-old fossilized plant.

The team of researchers was led by first author Holly-Anne Turner, a Paleontology Ph.D. student at University College Cork (UCC), who started this research when she was an undergraduate student at the University of Edinburgh.

## Fibonacci spirals

The Fibonacci sequence is a series in which each number is the sum of the two numbers preceding it. The Fibonacci series goes 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on.

Fibonacci spirals are visuals created by drawing arcs starting from a center and drawing outward circles increasing in size. The radii of the circles follow the Fibonacci sequence, and these spirals are seen commonly in nature.

The arrangement of sunflower seeds is one of the most common examples of Fibonacci spirals. If you examine the head of a sunflower, you'll notice a pattern of spirals formed by the seeds. Typically, there are two sets of spirals in opposite directions—one clockwise and one counterclockwise.

Pine cones also exhibit Fibonacci spirals. When you see a pine cone up close, you'll notice that the scales wrap around the cone in a spiral formation. By counting the number of clockwise and counterclockwise spirals, you'll often find consecutive Fibonacci numbers, such as 5 and 8 or 8 and 13.

Due to their prevalence, scientists believe that Fibonacci spirals were present in the earliest plants on Earth, that is, until now.

## Reconstructing an ancient plant fossil

The research team began their study in a Scottish sedimentary near Aberdeen called the Rhynie Chert. Here, they focused on a 407 million-year-old fossilized plant known as Asteroxylon mackiei, belonging to the earliest group of leafy plants.

The team analyzed the reproductive structure and leaf arrangements of the ancient plant. The team worked with digital artist Matt Humpage to recreate 3D models of the Asteroxylon mackiei using 3D printing and digital rendering.

They used 3D reconstruction techniques to visualize and measure the arrangement of the lateral organs, such as leaves or reproductive structures, along the stem or axis of a plant, known as phyllotaxis. The phyllotaxis determines the spatial positioning and distribution of these organs.

The team found that the leaf arrangement of the Asteroxylon mackiei showed distinct non-Fibonacci spirals. This observation contradicted our earlier assumptions about Fibonacci spirals being present in the most ancient plant species.

Their findings suggest that non-Fibonacci spirals were prevalent in early clubmosses, indicating separate evolutionary paths for leaf spirals in different plant groups.

Now that we understand that Fibonacci spirals are more prevalent today, the next question is why. Some scientists believe that the Fibonacci spirals allow maximum packing efficiency and optimal exposure to sunlight for the seeds.

This study highlights the need for more research about early plants and their growth patterns which will lead to a better understanding of plant life on Earth today.

The findings of the study are published in the journal Science.

Study abstract:

Lateral plant organs, including leaves and reproductive structures, are arranged on stems in distinct patterns termed phyllotaxis. Most extant plants exhibit phyllotactic patterns that are mathematically described by the Fibonacci series. However, it remains unclear what lateral organ arrangements were present in early leafy plants. To investigate this, we quantified phyllotaxis in fossils of the Early Devonian lycopod Asteroxylon mackiei. We report diverse phyllotaxis in leaves, including whorls and spirals. Spirals were all n:(n+1) non-Fibonacci types. We also show that leaves and reproductive structures occurred in the same phyllotactic series, indicating developmental similarities between the organs. Our findings shed light on the long-standing debate about leaf origins and demonstrate the antiquity of non-Fibonacci spirals in plants.