Immunoglobulin A is a class of antibodies produced by the adaptive immune system and secreted into the gut lumen to fight pathogenic bacteria. We recently demonstrated that the main physical effect of these antibodies is to enchain daughter bacteria, i.e. to cross-link bacteria into clusters as they divide, preventing them from interacting with epithelial cells, thus protecting the host. These links between bacteria may break over time. We study several models using analytical and numerical calculations. We obtain the resulting distribution of chain sizes, that we compare with experimental data. We study the rate of increase in the number of free bacteria as a function of the replication rate of bacteria. Our models show robustly that at higher replication rates, bacteria replicate before the link between daughter bacteria breaks, leading to growing cluster sizes. On the contrary at low growth rates two daughter bacteria have a high probability to break apart. Thus the gut could produce IgA against all the bacteria it has encountered, but the most affected bacteria would be the fast replicating ones, that are more likely to destabilize the microbiota. Linking the effect of the immune effectors (here the clustering) with a property directly relevant to the potential bacterial pathogeneicity (here the replication rate) could avoid to make complex decisions about which bacteria to produce effectors against.