  Selection, the tendency of some traits to become more frequent than others in
a population under the influence of some (natural or artificial) agency, is a
key component of Darwinian evolution and countless other natural and social
phenomena. Yet a general theory of selection, analogous to the
Fisher-Tippett-Gnedenko theory of extreme events, is lacking. Here we introduce
a probabilistic definition of selection and show that selected values are
attracted to a universal family of limiting distributions. The universality
classes and scaling exponents are determined by the tail thickness of the
random variable under selection. Our results are supported by data from
molecular biology, agriculture and sport.
