  The adaptive immune system relies on the diversity of receptors expressed on
the surface of B and T-cells to protect the organism from a vast amount of
pathogenic threats. The proliferation and degradation dynamics of different
cell types (B cells, T cells, naive, memory) is governed by a variety of
antigenic and environmental signals, yet the observed clone sizes follow a
universal power law distribution. Guided by this reproducibility we propose
effective models of somatic evolution where cell fate depends on an effective
fitness. This fitness is determined by growth factors acting either on clones
of cells with the same receptor responding to specific antigens, or directly on
single cells with no regards for clones. We identify fluctuations in the
fitness acting specifically on clones as the essential ingredient leading to
the observed distributions. Combining our models with experiments we
characterize the scale of fluctuations in antigenic environments and we provide
tools to identify the relevant growth signals in different tissues and
organisms. Our results generalize to any evolving population in a fluctuating
environment.
