Exploring The Role of Cooperative Motility in Range Expansion

Range expansion is a key feature of many populations, from bacteria colonizing a surface to entire forests shifting with climate change. These expanding populations exhibit rich emergent phenomena such as sectoring and allele surfing, which can impact their expansion rate and genetic diversity. Many bacteria, including Proteus mirabilis, use cooperative motility strategies to traverse hard surfaces. While the role of cooperative growth in expanding populations is frequently explored, the role of cooperative motility remains understudied. We modify the Fisher-KPP diffusion model by introducing a cooperative, density-dependent diffusion rate. Our model produces finite, travelling wave solutions that capture the dynamics of experimental P. mirabilis colonies. We then expand our model to compare range expansion dynamics with cooperative versus non-cooperative motility. Additionally, we investigate how cooperative motility influences the advantages of specific swarming strategies, such as a lag time before initiating swarming. This research not only helps us to understand the expansion dynamics of a particular pathogen, but sheds light on the broader dynamics of cooperative motility in range expansion.