  Context: The Hubble tuning fork diagram has always been the preferred scheme
for classification of galaxies. It is based on morphology only. At the
opposite, biologists have long taken into account the genealogical relatedness
of living entities for classification purposes. Aims: Assuming branching
evolution of galaxies as a 'descent with modification', we show here that the
concepts and tools of phylogenetic systematics widely used in biology can be
heuristically transposed to the case of galaxies. Methods: This approach that
we call "astrocladistics" is applied to Dwarf Galaxies of the Local Group and
provides the first evolutionary tree for real galaxies. Results: The trees that
we present here are sufficiently solid to support the existence of a
hierarchical organization in the diversity of dwarf galaxies of the Local
Group. This also shows that these galaxies all derive from a common ancestral
kind of objects. We find that some kinds of dIrrs are progenitors of both dSphs
and other kinds of dIrrs.We also identify three evolutionary groups, each one
having its own characteristics and own evolution. Conclusions: The present work
opens a new way to analyze galaxy evolution and a path towards a new
systematics of galaxies. Work on other galaxies in the Universe is in progress.
