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The role of geometry in catching prey

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Science & Technology, UK (Commonwealth Union) – Researchers from the University of Oxford’s Botanic Garden and the Mathematical Institute have shed light on how the shape, size, and geometry of carnivorous pitcher plants dictate the type of prey they ensnare. Their findings, featured in the Proceedings of the National Academy of Sciences (PNAS) recently, illuminate the intriguing world of pitcher plants.

Pitcher plants, belonging to the Nepenthes genus, are carnivorous flora predominantly found in tropical regions, particularly Southeast Asia. They derive their name from the hollow, cup-like structures they create to ensnare animal prey, typically insects. These plants exhibit a staggering diversity in their shapes and sizes, ranging from tubular forms to goblets, some even adorned with spine-like “teeth.” However, the reasons behind these significant variations have long puzzled botanists.

Dr. Chris Thorogood, a botanist and Deputy Director of Oxford Botanic Garden, reflects on his first encounter with these remarkable plants in the wild nearly two decades ago, indicating that he remembers wondering: how and why do they vary so much? To have helped solve this mystery he found truly exciting.

The mechanism by which pitcher plants capture prey is well-established: each pitcher possesses a slippery rim at the top, known as a peristome, covered in ridges that create a water film. This causes the prey to slip and descend into a pool of digestive enzymes at the base of the pitcher, akin to a car hydroplaning on water. Although this process is common to all pitcher plants, the shapes of the rims range from simple cylinders to highly ornate, fluted, or toothed structures. The more intricate the rim, the higher the cost of its production. There was a question as to why do some pitcher plants opt for elaborate designs while others maintain simplicity?

To explore this question, the research team employed mathematical models on pitcher plants cultivated at the Botanic Garden. They investigated how the shape of the rim influences prey capture efficiency. Shapes were categorized into four groups that exist in nature and could be readily compared using mathematical simulations. The team assessed hypothetical capture efficiencies for each shape by employing a “point mass” equivalent to an insect entering the trap. They also calculated the energy cost of producing the rim by examining the relative surface area and steepness of the various structures.

Derek Moulton, Professor of Applied Mathematics from the University of Oxford, Mathematical Institute, says “Mathematical reconstructions enable us to explore the trade-offs that exist in these plants in nature. Large, flared rims are costly for a plant to produce. By simulating both realistic peristomes and extreme versions – geometries that don’t exist in nature – we were able to show that in an optimal structure, the cost of production might be offset by the extra prey that can be caught.”

Dr. Hadrien Oliveri, a Postdoctoral Researcher at the University of Oxford’s Mathematical Institute, highlighted another aspect of this complex phenomenon, indicating that a similar scenario pertains to trap size.

In order to delve into the influence of trap size, the research team devised a mathematical model that connected the 3D geometries of pitcher plant rims with the physical mechanics of capturing prey. This model took into account various characteristics of the rims, including their width, degree of flaring, and orientation, as well as the stability and sliding direction of prey at different locations within the trap.

The findings indicated that the diversity in peristome geometries significantly affected the plant’s ability to ensnare specific types of prey. Notably, highly flared peristomes appeared to be exceptionally effective at capturing walking insects like ants.

Pitcher plants naturally thrive in nitrogen-poor environments, such as mountain slopes, swamps, and tropical forests. Consequently, their capacity to extract nitrogen from trapped insects offers them a competitive advantage over non-carnivorous plants. Each of these habitats presents a unique array of potential prey, suggesting that pitcher plants may have evolved an array of traps tailored to exploit the various insect species available in specific locations.

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