Fibonacci spirals: An unexpected twist in plant evolution •
Fibonacci spirals

Fibonacci spirals: An unexpected twist in plant evolution

In a groundbreaking study, researchers have challenged long-standing theories about the origins of Fibonacci spirals, one of nature’s most ubiquitous mathematical patterns.

Contrary to the traditional belief that these spirals are a conserved trait originating from Earth’s first land-dwelling plants, the new research indicates that the earliest plants developed an entirely different type of spiral.

Spirals can be found in many forms in nature, ranging from the twist of a DNA helix to the vortex of a hurricane. The most prolific of these are Fibonacci spirals, which are named after Leonardo Fibonacci, the Italian mathematician who made the sequence famous. 

The Fibonacci sequence is particularly prevalent in plants, comprising more than 90 percent of all spirals found among them. Sunflower heads, pinecones, pineapples, and succulent houseplants all display Fibonacci spirals on their petals, leaves, and seeds.

Origins of the Fibonacci spiral

The omnipresence of these spirals in plants, often referred to as nature’s secret code, has intrigued scientists for centuries. Despite the depth of study into the patterns, the evolutionary origins of these spirals were, until recently, largely overlooked. Given their extensive distribution, it was generally accepted that Fibonacci spirals date back to when land plants first appeared and remained highly preserved across species and time.

Challenging this idea, a team of researchers led by the University of Edinburgh has unearthed evidence of non-Fibonacci spirals in a fossilized plant that lived approximately 407 million years ago. The team utilized digital reconstruction techniques to generate the first-ever 3D models of the leafy shoots of the fossilized clubmoss Asteroxylon mackiei, a species that belongs to the earliest group of leafy plants.

The fossil was sourced from the Rhynie chert, a world-renowned fossil site in a sedimentary deposit near Rhynie, a village in Aberdeenshire, Scotland. This site holds valuable insight into some of the planet’s earliest ecosystems – the era when land plants first evolved, gradually enveloping the earth’s rocky surface, and eventually rendering it habitable.

What the researchers discovered 

The analysis revealed that the leaves and reproductive structures of Asteroxylon mackiei primarily followed non-Fibonacci spirals, a pattern that’s quite rare in present-day plants. This transformative finding forces a reevaluation of the prevalent understanding of Fibonacci spirals in land plants, suggesting that non-Fibonacci spirals were common in ancient clubmosses. 

The research implies that the evolutionary path of leaf spirals took two separate routes, with the leaves of ancient clubmosses carving out a distinct evolutionary history from other major groups of plants today, such as ferns, conifers, and flowering plants.

In order to create the 3D model of the extinct Asteroxylon mackiei, the team collaborated with digital artist Matt Humpage, employing digital rendering and 3D printing techniques. The research, funded by UK Research and Innovation (UKRI), The Royal Society, and the German Research Foundation, has been published in the journal Science.

Dr. Sandy Hetherington, an evolutionary palaeobiologist at the University of Edinburgh and the project’s lead, expressed excitement about the technological advancements that made the research possible. 

“Our model of Asteroxylon mackiei lets us examine leaf arrangement in 3D for the first time. The technology to 3D print a 407-million-year-old plant fossils and hold it in your hand is really incredible,” said Dr. Hetherington. “Our findings give a new perspective on the evolution of Fibonacci spirals in plants.”

More about Fibonacci spirals

The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones, usually starting with 0 and 1. The sequence goes 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so forth.

In nature, the Fibonacci sequence manifests itself in numerous ways. When we talk about Fibonacci spirals, they are logarithmic spirals that grow outward by a factor of the golden ratio for every quarter turn they make. The golden ratio, approximately 1.618, is itself intimately connected to the Fibonacci sequence. In fact, the ratio of successive Fibonacci numbers converges to this value.

A Fibonacci spiral can be drawn by placing squares with sides of length equal to each consecutive Fibonacci number, and drawing a quarter-circle that connects the far corners of these squares. The resulting spiral approximates the golden spiral, which is a logarithmic spiral whose growth factor is φ, the golden ratio.

In plants, Fibonacci spirals are commonly seen in the arrangement of leaves, seeds, petals, and more. They appear because of an efficient packing strategy that allows plants to maximize their exposure to sunlight and other resources. 

For example, the seeds in a sunflower are arranged in two sets of spirals, one winding clockwise and the other counterclockwise, and the numbers of spirals are usually adjacent Fibonacci numbers. In pinecones and pineapples, the number of spirals also aligns with the Fibonacci sequence.

These spirals are so commonplace in the plant kingdom that scientists have long assumed they must have evolved as an ancient feature, highly conserved due to some kind of evolutionary advantage. This is what makes the new research finding non-Fibonacci spirals in ancient plants so striking: it suggests a more complicated evolutionary history of spiral patterns in plants than previously assumed.


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