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.