In a surprising discovery, researchers at the University of Oxford have found a connection between the digit sum function of number theory and a key aspect of evolutionary genetics, phenotypic mutation robustness. The study, published in the Journal of The Royal Society Interface, sheds new light on the relationship between mathematics and the natural world. The digit sum function, which deals with positive integers and number sequences, has previously been applied to encryption techniques and the Fibonacci sequence. However, this new research shows that it also has implications for understanding the maximum level of mutation that can occur without affecting an organism’s phenotype.
The study found that the maximum phenotypic mutation robustness is proportional to the logarithm of the fraction of all possible sequences of a phenotype, with a correction given by the digit sum function. The research team, made up of mathematicians, engineers, physicists, and medical professionals, believes that this discovery could have a significant impact on evolutionary genetics. Understanding the rate of neutral mutations can help determine when two organisms’ last common ancestors lived, and knowing the maximum level of mutation that can occur without affecting the phenotype is crucial for understanding the evolution of biological systems.
The study also found a connection between the maximum mutation robustness and the Tagaki function, a function that is continuous but nowhere differentiable. The researchers believe that this discovery highlights the beauty of number theory and its ability to reveal deep mathematical structures in the natural world. They hope that this research will lead to further connections between number theory and genetics in the future.
