  We are interested in the genealogical structure of alleles for a
Bienaym\'e-Galton-Watson branching process with neutral mutations (infinite
alleles model), in the situation where the initial population is large and the
mutation rate small. We shall establish that for an appropriate regime, the
process of the sizes of the allelic sub-families converges in distribution to a
certain continuous state branching process (i.e. a Jirina process) in discrete
time. It\^o's excursion theory and the L\'eevy-It\^o decomposition of
subordinators provide fundamental insights for the results.
