Immune repertoire dynamics out of steady state*

Over the last ten years high-throughput sequencing has enabled increasingly quantitative measurements of the diversity of lymphocyte receptor repertoires. A striking finding of these sequencing efforts has been that the clone sizes of cells sharing the same receptor are heavy-tail distributed. Here, we show how such long tails can emerge out of steady state from a simple neutral model for immune repertoire formation. In our theory homeostatic proliferation leads to a founder effect, which produces transient but long-lived power-law scaling of clone sizes. In a human cohort study we find evidence for the prediction that early founded clones are overrepresented among the largest clones. We show how the slow multidecadal decay of this overrepresentation suggests a dynamical model of immune aging in which peripheral selection only slowly reshapes the initially established repertoire. Overall, our work suggests a mechanism through which dynamical processes early in life can have a strong and long-lasting influence on the adaptive immune system with potential implications for pathogen defense and autoimmunity.