This series of papers is intended to present astrocladistics in some detail
and evaluate this methodology in reconstructing phylogenies of galaxies. Being
based on the evolution of all the characters describing galaxies, it is an
objective way of understanding galaxy diversity through evolutionary
relationships. In this first paper, we present the basic steps of a cladistic
analysis and show both theoretically and practically that it can be applied to
galaxies. For illustration, we use a sample of 50 simulated galaxies taken from
the GALICS database, which are described by 91 observables (dynamics, masses
and luminosities). These 50 simulated galaxies are indeed 10 different galaxies
taken at 5 cosmological epochs, and they are free of merger events. The
astrocladistic analysis easily reconstructs the true chronology of evolution
relationships within this sample. It also demonstrates that burst characters
are not relevant for galaxy evolution as a whole. A companion paper is devoted
to the formalization of the concepts of formation and diversification in galaxy
evolution.Comment: 16 pages, 6 figure