Competition for space is ubiquitous in the ecology of both microorganisms and macro-organisms. We introduce a bacterial model system in which the factors influencing competition for space during colonization of an initially empty habitat can be tracked directly. Using fluorescence microscopy, we follow the fate of individual Escherichia coli bacterial cell lineages as they undergo expansion competition (the race to be the first to colonize a previously empty territory), and as they later compete at boundaries between clonal territories. Our experiments are complemented by computer simulations of a lattice-based model. We find that both expansion competition, manifested as differences in individual cell lag times, and boundary competition, manifested as effects of neighbour cell geometry, can play a role in colonization success, particularly when lineages expand exponentially. This work provides a baseline for investigating how ecological interactions affect colonization of space by bacterial populations, and highlights the potential of bacterial model systems for the testing and development of ecological theory.