Successive range expansion promotes diversity and accelerates evolution in spatially structured microbial populations
Colonies of bacteria, Bacillus subtilis, that grow on the surface of thin agar plates show various morphological patterns in response to environmental conditions, such as the nutrient concentration, the solidity of an agar medium and temperature. For instance, the colony pattern shows a dense-branching morphology with a smooth circular envelope (DBM-like) in a nutrient-poor semi-solid agar medium, and it turns to a simple disk-like colony as both the nutrient concentration and the agar's softness increase. These patterns have been shown to involve cell movement inside colonies. In a DBM-like colony, individual cells actively move, particularly in the expanding periphery of the colony, while they become immotile at the inner region of the colony where nutrient is very low. In a disk-like colony, cells are highly active in the whole region of the colony. Based on such experimental observations, we develop a diffusion-reaction model, in which density dependent cell movements are incorporated by the level of nutrient concentration available for the cell. Numerical simulations of the model under different environmental conditions closely reproduce various colony patterns ranging from DBM-like pattern to the homogeneous disk-like one in a unifying manner. The analysis also predicts the growth velocity of a colony as a function of the nutrient concentration.