The possible cycle of morphological mutations, i.e. from gas-rich objects to gas-poor systems by means of gas expulsion and back to a significant gas content by gas accretion, can be explored in the local environment, namely, in the galaxies around the Milky Way, their satellites. Except the Magellanic Clouds most of these can be characterized as gas-free spheroidal systems which manifest the faint end of dEs. Since these dSph are gathered around massive galaxies like our MWG and M31 orbiting them as satellites, go down to the lightest and most metal-poor end of galaxies, they have attracted increasing attention over the last years with the advent of more advanced observing facilities. Understanding their formation and evolution is of substantial relevance for our astrophysical picture of cosmological structure formation and of galaxy evolution. Four main questions are addressed:
The first three questions also concern the morphological transition from gas-rich satellites to dSphs. Nevertheless, dSphs follow a mass-metallicity relation [12, 26] and continue the total brightness vs. central surface-brightness relation from normal dEs to the faint end .
As the first models, Hensler et al.  performed chemo-dynamical simulations  of spherical low-mass galaxies in order to study galaxy survival, SF epochs and rates, gas loss, and (final) metallicity. They demonstrate that due to the SF self-regulation only short but vehement initial SF epochs occur and lead to mass-dependent gas loss. Nonetheless, the DGs remain gravitationally bound with the further issue that more cool gas survives than it is observed, but it forms a halo around the visual body. Although the stellar energetic feedback is the driving mechanism to expel the gas, its effect is not as dramatic as obtained in semi-analytic models  and the amount of unbound mass is considerably lower. To get lost, this gas has to be stripped off additionally  what probably happens by means of ram pressure of the galactic halo gas  or by tidal stripping . Otherwise it can return to the DG and produce subsequent events, from a second SF epoch to SF oscillations. The external gas reservoirs around some dSphs , in particular also the Hi that is kinematically coupled with the Scl dSph, might witness this effect.
The fascinating wealth of data and their precision on stellar ages and kinematics, on their chemical abundances, abundance gradients, and tidal tails of dSphs (for most recent reviews see e.g.  and ) have triggered numerous numerical models. Although they are advanced since  to 3D hydrodynamics (see e.g.  and ), they still lack of a self-consistent treatment of both, internal processes, as e.g. SF self-regulation (see sect. 1), and the environmental influences as e.g. tidal effects, external gas pressure, gas inflow, etc.
In a recent paper , e.g. a large set of DG models is constructed with the method of smooth-particle hydronamics (SPH), but considers all of them in isolation. In most of their models sufficient gas mass is retained and can fuel further SF epochs, if it would not be stripped of by ram pressure or tidal forces, as the authors mention. Those models that fit the presently best studied dSphs Fnx, Car, Scl, and Sex, are than chosen as test cases for further exploration. Although their results do not deviate too much from the further observational data, in addition to the already mentioned neglections, three further caveats exist: 1) If models are selected according to any agreement with one or two observed structural parameters, it is not surprising if also other values would not deviate significantly. 2) The numerical mass resolution of the SPH particles is too low to allow quantitative issues of galactic winds, heating and cooling, etc. 3) Because of the single gas-phase description released metals are too rapidly mixed with the cool gas and the metal-enrichment happens too efficiently. Despite these facts, with appropriate initial conditions always models in agreement to observations can be found.
Although the advancement to a two-phase ISM treatment in SPH is not trivial and implies various numerical problems, but is not impossible [3, 30, 88], such treatment would be absolutely necessary in order to approach reality and to achieve reliable results. In addition, the chemo-dynamical interaction processes must be applied .
From the CDM structure-formation paradigm and from numerical simulations with different computational tools, subhalos are expected to assemble around massive halos and to accumulate their masses. If they have already experienced SF, their stars should be merged into a spheroid and be identifiable by their kinematics and chemical abundances. Although these low-mass subhalos, their baryonic content as dSphs, and the accretion scenario , therefore, serve as the key to pinpoint this cosmological paradigm, observational detections of stellar streams within the Milky Way (MW) halo are rare . Furthermore, the stellar abundances in present-day dSphs deviate mostly from the halo, in particular /Fe with Fe/H, which characterizes the SF timescale ( and e.g. for the Car dSph ).
Yet evolutionary models of dSph with respect to SF, chemistry, and gas expulsion and their comparison with the Milky Way halo are still too simplistic. While their accretion epoch occurred continuously over the Hubble time some models  only considered it as a short early event; their gas is not only removed by tidal stripping and RPS  but also re-accreted on their orbits around the MW ; in general, consideration as isolated systems lacks reality .
To model instead of isolated subhalos the evolution of the system of dSphs in the gravitational field of the MWG for which the accretion by the host galaxy is probable over the Hubble time, the Via Lactea II  simulation was used. Since an acceptible computational time limits the number of gas particles to two million as also for the DM and in order to reach a high mass resolution of 103 M per SPH particle, only 250 subhaloes as DM progenitors of dSphs in the mass range of 106 < Msat / M < 6 × 108 from z = 4.56 could be followed. Unfortunately, this fact limits the radius of consideration to within a radius of 40 kpc around the MW's center of mass. In order to study the construction of the MWG halo by accretion of subhalos including baryonic matter, both gas and stars, as a first step, the chemo-dynamical evolution of the dSph system is followed for the first Gyr, i.e. until redshift z = 2.76  (see Fig. 5). For the simulations an advanced version of the single-gas chemo-dynamical SPH/N-body code is applied, treating the production and chemical evolution of 11 elements.
Figure 5. Cubes of 200 kpc length around the Milky Way (at their center). upper panel: Initial conditions of the Milky Way's satellite system: Distribution of Dark Matter (DM) subhalos within a sphere of 40 kpc radius around the Milky Way at redshift z = 4.56. lower panel: Snapshot of the satellites' dynamical evolution 1 Gyr after the numerical onset, i.e. at redshift z = 2.76. The DM subhalos are filled with baryonic gas of mass fraction of 17%, form stars, and lose mass of all constituents due to tidal interactions among the satellite system. For discussion see text.
Starting with a 104 K warm gas of 17% of the subhalo masses in virial equilibrium and under the assumption that re-ionization is improbable to have affected the Local Group dSphs , cooling allows the gas particles to achieve SF conditions in all satellites, but its efficiency directly depends on the mass of a satellite and its dynamical history (merging with other satellites or disruption by the MW gravitational potential). The stellar feedback by SNeII releases sufficient energy to expel hot gas from the main bodies of less massive dSphs, facilitated by tidal interactions. This gas accumulates in the MW halo while massive dSphs merge and continue SF. For the first 108 yr of the simulation there is a considerable variance of stellar oxygen abundance in the whole system (-5. [O/H] -0.5) reflecting the very inhomogeneous production and distribution of enriched gas. After 108 yrs the merging of satellites' ISM promotes the mixing of heavy elements. Finally, almost completely recycling of the gas erases the abundance inhomogeneities so that O in stars converges to -1. [O/H] 0. with a small dispersion.
Detailed analyses of the SF history, gas exchange, stellar abundance evolution of dSphs and the MW halo in the early universe are presented in a comprehensive paper  and will be discussed with their implications for our cosmological picture.
The author is grateful to Alessandro Boselli, Joachim Koeppen, Thorsten Lisker, Polis Papaderos, Mykola Petrov, Simone Recchi, and further more for their contributions and continuous discussions to this field and to the referee for valuable comments.