Contrary to common wisdom, small fluctuations can under certain circumstances control macroscopic systems. The history of fluctuation dominated fronts started with attempts [1] to explain aspects of viscous fingering experiments seen in [2]. This idea, namely that macroscopic propagating fronts in reaction-diffusion systems can sometimes be controlled by vanishingly small numbers of individuals at the leading edge, has since made a significant impact on our understanding of Darwinian evolution [3,4]. It has most recently re-appeared in models of the coevolution of viruses and the immune system [5]. This talk will survey the history of this idea, sketch our present work [6] following up on that of [5], and speculate about the future of this interesting part of statistical biological physics.
1. Brener, Efim, Herbert Levine, and Yuhai Tu. "Mean-field theory for diffusion-limited aggregation in low dimensions." Physical review letters 66, no. 15 (1991): 1978.
2. Arneodo, A., Y. Couder, G. Grasseau, V. Hakim, and M. Rabaud. "Uncovering the analytical Saffman-Taylor finger in unstable viscous fingering and diffusion-limited aggregation." Physical review letters 63, no. 9 (1989): 984.
3. Tsimring, Lev S., Herbert Levine, and David A. Kessler. "RNA virus evolution via a fitness-space model." Physical Review Letters 76, no. 23 (1996): 4440.
4. Rouzine, Igor M., John Wakeley, and John M. Coffin. "The solitary wave of asexual evolution." Proceedings of the National Academy of Sciences 100, no. 2 (2003): 587-592.
5. Marchi, Jacopo, Michael Lässig, Aleksandra M. Walczak, and Thierry Mora. "Antigenic waves of virus–immune coevolution." Proceedings of the National Academy of Sciences 118, no. 27 (2021): e2103398118.
6. Kessler, David A., and Herbert Levine. "Multiple possible patterns can emerge from virus-immune coevolution." Physical Review Research6.3 (2024): 033300..