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We derive the stellar population parameters of 11 quiescent ultra-diffusegalaxies (UDGs) from Keck/KCWI data. We supplement these with 14 literatureUDGs, creating the largest spectroscopic sample of UDGs to date (25). We find astrong relationship between their $\alpha$-enhancement and their star formationhistories: UDGs that formed on very short timescales have elevated [Mg/Fe]abundance ratios, whereas those forming over extended periods present lowervalues. Those forming earlier and faster are overall found in high-densityenvironments, being mostly early infalls into the cluster. No other strongtrends are found with infall times. We analyze the stellar mass-metallicity,age-metallicity and [Mg/Fe]-metallicity relations of the UDGs, comparing themto other types of low mass galaxies. Overall, UDGs scatter around theestablished stellar mass--metallicity relations of classical dwarfs. We findthat GC-rich UDGs have intermediate-to-old ages, but previously reported trendsof galaxy metallicity and GC richness are not reproduced with thisspectroscopic sample due to the existence of GC-rich UDGs with elevatedmetallicities. In addition, we also find that a small fraction of UDGs could be'failed-galaxies', supported by their GC richness, high $\alpha$-abundances,fast formation timescales and that they follow the mass-metallicity relation ofz~2 galaxies. Finally, we also compare our observations to simulated UDGs. Wecaution that there is not a single simulation that can produce the diverse UDGproperties simultaneously, in particular the low metallicity failed-galaxy likeUDGs.

The star formation histories of quiescent ultra-diffuse galaxies and their dependence on environment and globular cluster richness