We combine observations from ALMA, ATCA, MUSE, andHerschel to study gas-to-dust ratios in 15 Fornax cluster galaxies detected in the FIR/sub-mm by Herschel and observed by ALMA as part of the ALMA Fornax Cluster Survey (AlFoCS). The sample spans a stellar mass range of 8.3 $leq$ log (M$_*$ / M$_odot$) $leq$ 11.16, and a variety of morphological types. We use gas-phase metallicities derived from MUSE observations (from the Fornax3D survey) to study these ratios as a function of metallicity, and to study dust-to-metal ratios, in a sub-sample of nine galaxies. We find that gas-to-dust ratios in Fornax galaxies are systematically lower than those in field galaxies at fixed stellar mass/metallicity. This implies that a relatively large fraction of the metals in these Fornax systems is locked up in dust, which is possibly due to altered chemical evolution as a result of the dense environment. The low ratios are not only driven by HI deficiencies, but H$_2$-to-dust ratios are also significantly decreased. This is different in the Virgo cluster, where low gas-to-dust ratios inside the virial radius are driven by low HI-to-dust ratios, while H$_2$-to-dust ratios are increased. Resolved observations of NGC1436 show a radial increase in H$_2$-to-dust ratio, and show that low ratios are present throughout the disc. We propose various explanations for the low H$_2$-to-dust ratios in the Fornax cluster, including the more efficient stripping of H$_2$ compared to dust, more efficient enrichment of dust in the star formation process, and altered ISM physics in the cluster environment.
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