Insertion sequences (IS) are the simplest and most abundant form of transposable DNA found in bacterial genomes. When present in multiple copies, it is thought that they can promote genomic plasticity and genetic exchange, thus being a major force of evolutionary change. The main processes that determine IS content in genomes are, though, a matter of debate. In this work, we take advantage of the large amount of genomic data currently available and study the abundance distributions of 33 IS families in 1811 bacterial chromosomes. This allows us to test simple models of IS dynamics and estimate their key parameters by means of a maximum likelihood approach. We evaluate the roles played by duplication, lateral gene transfer, deletion and purifying selection. We find that the observed IS abundances are compatible with a neutral scenario where IS proliferation is controlled by deletions instead of purifying selection. Even if there may be some cases driven by selection, neutral behavior dominates over large evolutionary scales. According to this view, IS and hosts tend to coexist in a dynamic equilibrium state for most of the time. Our approach also allows for a detection of recent IS expansions, and supports the hypothesis that rapid expansions constitute transient events-punctuations-during which the state of coexistence of IS and host becomes perturbated. 