Fig. 4

Four exemplary jump diffusion models of microbial migration vs. mutation across a 3D lattice. The two leftmost panels show the polyphasic distributions resulting from allowing longer distance jumps (d _jump  > 1, here d _jump  = 2), while the two right panels show Poisson distributions that emerge from restricting jumps to adjacent lattice cells (d _jump  = 1). d _physical and d _genetic correspond, respectively, to lattice and genetic Euclidean distances, plotted here as histogram heat maps for all pairs of cells in each population after 100 time steps (2¹⁰⁰ cells). Panels 1 vs. 2 and 3 vs. 4 illustrate the (linear) effect of halving the jump probability, which effectively cuts the average physical distance between populations in half. A clocklike assumption of mutation rates and identical number of time steps for each simulation results in essentially identical d_genetic (x axis) distributions. The combined graph at right shows the d _physical sum for each of the four panels.