dIrrs are characterized by large gas fractions, ongoing SF, and low metallicities. That dIrrs contain the same or slightly higher gas fractions than giant spiral galaxies and mostly suffer the same SF efficiency, but appear with lower metallicity Z than spirals, cannot be explained by simple evolutionary models. When gas is consumed by astration but replenished partly by metal-enhanced stellar mass loss, the general analytical derivation relates the element enrichment Z(t) with the logarithm of decreasing remaining gas fraction = Mg(t) / Mg(0) as Z(t) = y [-ln(µ)], where y as the slope is determined by the stellar yield (see e.g. textbooks like  or reviews as e.g. by [76, 35]). As demonstrated by  and , however, the effective yields of gas-rich galaxies decrease to smaller galaxy masses. This means that their element abundances, particularly O measured in Hii regions, are smaller than those released by a stellar population and confined in a "closed box".
Two processes can reduce the metal abundances in the presence of old stellar populations: loss of metal-enriched gas by galactic outflows or infall of metal-poor (even pristine) intergalactic gas (IGM). It is widely believed, that a fundamental role in the chemical evolution of dIrrs is played by galactic winds, because freshly produced metals in energetic events are carried out from a shallow potential well of DGs through a wind (which will be therefore metal-enhanced). Some SBDGs are in fact characterized by galactic winds  or by large expanding supernova type II (SNeII)-driven X-ray plumes (e.g. [32, 59]). Studies have raised doubts to whether the expanding H loops, arcs, and shells mostly engulfing X-ray plumes, really imply gas expulsion from the galaxies because their velocities are mostly close to escape, but adiabatic expansion against external gas tends to hamper this.
As an extreme,  speculated that galactic winds are able to empty DGs from its fuel for subsequent SF and, by this, transform a gas-rich dIrr to a fading gas-poor system. In order to manifest this scenario and to study mass and abundance losses through galactic winds numerous numerical models are performed under various, but mostly uncertain conditions and with several simplifications (e.g. [55, 93]). The frequently cited set of models by MacLow & Ferrara  (rotationally supported, isothermal Hi disks of dIrrs with fixed structural relations for four different gas masses between Mg = 106 - 109 M and three different SNII luminosities in the center corresponding to SN rates of one per 3 × 104 yrs to 3 Myrs) is mostly misinterpreted: The hot gas is extremely collimated from the center along the polar axis, but cannot sweep-up sufficient surrounding ISM to produce significant galactic mass loss. On the other hand, the loss of freshly released elements from massive stars is extremely high. Moreover, these models lack of realistic physical conditions, as e.g. the existence of an external pressure, self-consistent SFRs, a multi-phase inhomogeneous ISM, and further more.
Also more detailed numerical simulations [15, 79], show that galactic winds are not very effective in removing gas from a galaxy. Although galactic winds develop vertically, while the horizontal transport along the disk is very limited, their efficiency depends very sensitively on the galaxy structure and ISM properties, as e.g. on the Hi disk shape . Fig. 1 reveals clearly that the more eccentric the disk is, the more pronounced does the superbubble expand. On the one hand, the hot SN gas has to act against the galactic ISM, exciting turbulence and mixing between the metal-rich hot gas with the surrounding Hi. Not taken into account in present-day models is the porosity of the ISM, consisting of clouds and diffuse less dense gas. In particular, the presence of clouds can hamper the development of galactic winds through their evaporation. This so-called mass loading reduces the wind momentum and internal energy. Since the metallicity in those clouds are presumably lower than the hot SNII gas, also the abundances in the outflow are diminished as e.g. observed in the galactic X-ray outflow of NGC 1569  for which a mass-loading factor of 10 is derived to reduce the metallicity to 1-2 times solar. In recent simulations  demonstrate that turbulent mixing can effectively drive a galactic wind. Although they stated that their models lead to a complex, chaotic distribution of bubbles, loops and filaments as observed in NGC 1569, other observational facts have not been compared.
Figure 1. Density contours after 200 Myr of evolution for models differing on the semi-minor axis b of their initial configurations (semi-minor axis indicated on top of each panel), while the semi-major axis is set to a = 1 kpc: left: b = a = 1 kpc (spherical); right: b = 400 pc, (eccentricity of (a - b) / a = 0.6). The density scale ranges from 10-27 (black) to 10-24 g/cm3 (brightest). (for details see .)
Detailed numerical simulations of the chemical evolution of these SBDG by  could simultaneously reproduce both, the oxygen abundance in the warm gas as well as the metallicity in the hot outflow. Surprisingly,  demonstrated that the leakage of metals from a SBDG is not prevented by the presence of clouds because the clouds pierce holes into the wind shells. This leads to a final metallicity a few tenths of dex lower than in models without clouds.
Consequently, the crucial question must be answered which physical processes trigger such enormous SFRs as observed in SBDGs and consume all the gas content within much less than the Hubble time. One possibility which has been favoured until almost two decades ago was that at least some of these objects are forming stars nowadays for the very first time. Today it is evident that the most all metal-poor ones (like I Zw 18) contain stars at least 1 Gyr old , and most SBDGs have several Gyrs old stellar populations. This means that SF in the past should have proceeded in dIrrs, albeit at a low intensity and long lasting, what can at best explain their chemical characteristics, like for instance the low [/Fe] ratio . The [/Fe] vs. [Fe/H] behaviour is representative of the different production phases, -elements from the short-living massive stars and 2/3 of iron from type Ia SNe of longer-living binary systems. If the SF duration in a galaxy is very short, type Ia SNe do not have sufficient time to enhance the ISM with Fe and most of the stars will be overabundant in [/Fe].
In most SBDGs large Hi reservoirs enveloping the luminous galactic body have been detected (NGC 1569 , NGC 1705 , NGC 4449 , NGC 5253 , I Zw 18 , II Zw 40 ) with clearly disturbed gas kinematics and disjunct from the galactic body. Nevertheless, in not more than two objects, NGC 1569  and NGC 5253  gas infall is proven, while for the other cases the gas kinematics obtrudes that the gas reservoir feeds the engulfed DGs. In another object, He 2-10, the direct collision with an intergalactic gas cloud  is obviously triggering a huge SB. Reasonably, for their measurable Hi surface density the SFRs of most of these objects exceed those of "normal" gas disks (Fig. 2).
Figure 2. Comparison of the surface star-formation rate vs. Hi column density of a few prototypical starburst dwarf galaxies (SBDGs) denoted by crosses and names with the well-known Kennicutt-Schmidt relation derived by  with an exponent of 1.4 (long full-drawn line). The SBDGs' Hi surface density is averaged over the optical galactic body (from ).
Yet it is not clear, what happens to dIrrs if they move into a region with increasing external pressure as e.g. by means of a denser IGM and of ram pressure when they fall into galaxy clusters. In sect. 3 we will discuss the effect of ram pressure on the structure of the ISM for which numerical models for spiral galaxies (e.g. ) as well as for gas-rich DGs (e.g. ) exist, but only hints from observations (as e.g. for the Magellanic stream). The effect on the SFR due to compression of the ISM is observed, but not yet fully understood and convincingly studied by models.  e.g. observed a coherent enhancement of SF in group galaxies falling into a cluster.
Although the mass-metallicity relation also holds for dIrrs and even steepens its slope , what can be interpreted by galactic mass loss and the corresponding lower effective yield , the abundance ratios are unusual. As mentioned above, O/Fe reaches already solar values for subsolar oxygen or iron abundances. While this can be explained by a long SF timescale, another characteristic signature is that the ratio log(N/O) stays at about -1.6 to -1.5 with O abundances below 1/10 solar and with an increasing scatter with O (see Fig. 3). Their regime of N/O-O/H values overlaps with those of Hii regions in the outermost disk parts of spirals at about 12 + log(O/H) = 8.0 ... 8.5 .
Figure 3. The abundance ratio N/O as a function of oxygen abundance observed in spiral and irregular galaxies (shaded area, after ) overlayed with evolutionary loops due to infall of primordial intergalactic gas clouds. These have different mass fractions Mcl / MSF with respect to the mass involved in the SF region The crosses represent evolutionary timesteps of models, the arrows depict the direction of the evolutionary paths. The dashed straight line represents a simple model relation for purely secondary nitrogen production. For discussion see .
In the 90th several authors have tried to model these observations by SF variations with gas loss through galactic winds under the assumptions that these dIrrs and blue compact DGs (BCDs) are young and experience their first epochs of SF (for a detailed review see ). Stellar population studies contradict this youth hypothesis, so that another process must be invoked. Since these objects are embedded into Hi envelops and are suggested to suffer gas infall as manifested e.g. in NGC 1569 (see above, [91, 67]), the influence of metal-poor gas infall into an old galaxy with continuous SF on particular abundance patterns were exploited by Koeppen & Hensler . With the reasonable assumption that the fraction of infalling-to-existing gas mass increases with decreasing galaxy mass, their results could match not only the observational regime of BCDs in the [12 + log(O/H)] - log(N/O) space but also explain the shark-fin shape of observational data distribution .
Fig. 3 demonstrates how self-enriched galaxies which have reached the secondary nitrogen-track already within 2-3 Gyrs of their evolution are thrown back in O abundance by gas infall while N/O stays the same. After a time delay depending on the mass fraction of infalling gas to that existing already within the SF site, along a loop-like evolutionary paths in the [12 + log(O/H)] - log(N/O) diagram the ISM abundances reach again the starting point. In summary, one can state that old dIrrs mutate temporarily to youngly appearing examples with respect to their gas abundances.