In spite of the importance of plasmids in bacterial adaptation we have a poor understanding of their dynamics. It is not known if or how plasmids persist in and spread through (invade) a bacterial population when there is no selection for plasmid-encoded traits. Moreover, the differences in dynamics between spatially structured and mixed populations are poorly understood. Through a joint experimental/theoretical approach we tested the hypothesis that self-transmissible IncP-1 plasmids can invade a bacterial population in the absence of selection when initially very rare, but only in spatially structured habitats and when nutrients are regularly replenished. Using protocols that differed in degree of spatial structure and nutrient levels, the invasiveness of plasmid pB10 in E. coli was monitored during at least 15 days, with an initial fraction of plasmid-bearing (p+) cells as low as 1E-7. To further explore the mechanisms underlying plasmid dynamics we developed a spatially explicit mathematical model. When cells were grown on filters and transferred to fresh medium daily, the p+ fraction increased to 13%, while almost complete invasion occurred when the population structure was disturbed daily. The plasmid was unable to invade in liquid. When carbon source levels were lower or not replenished, plasmid invasion was hampered. Simulations of the mathematical model closely matched the experimental results, and produced estimates of the effects of alternative experimental parameters. This allowed us to isolate the likely mechanisms most responsible for the observations. In conclusion, spatial structure and nutrient availability can be key determinants in the invasiveness of plasmids.