Math in plant pathology: is the early blight of tomato one more example of the golden ratio?

Abstract

The spiral is a common pattern in nature, with Nautilus pompilius often cited as a prime example of the mathematical principles behind spiral growth, such as the “logarithmic spiral.” In plant biology, sunflower seeds are arranged in spirals that follow the Fibonacci sequence, optimizing space and minimizing shadowing among the seeds. The Fibonacci spiral and numbers are also prevalent in nature, appearing in the arrangement of leaves, the structure of pinecones, and the scales of pineapples. This pattern reflects how plants grow efficiently, maximizing space for each leaf and the amount of light they receive. Our study on microorganisms causing early blight disease in tomatoes, such as Alternaria solani, reveals that Fibonacci numbers frequently appear in the lesion patterns of the fungus. Moreover, our data show that these Fibonacci numbers approach the “golden ratio” (approximately 1.618), suggesting that this pattern optimizes resource allocation for fungal mycelial growth within plant tissue and enhances reproductive success of the fungus.