They are referring specifically to East Mediterranean-related ancestry, from the study :
“Ancestry analysis of the Roman Period individuals reveals the significant presence of East Mediterranean-related ancestry (Figure 2B) that we modeled with Roman and Byzantine groups from West Anatolia. This signal can be detected as soon as the 3rd century CE at Tarraco (Barranc de Sales archaeological site) or at Empuries, and it is attested as well at the Y-chromosome level,with lineages like J-L210, J-L26, and J-Z2177 (Table S1) that are absent during the Iron Age in Iberia to the limits of our resolution, but typical in the Eastern Mediterranean. These patterns are consistent with those observed in other parts of the Roman Empire, such as the Imperial core in
Rome and central Italy (Antonio et al., 2019; Posth et al., 2021) and the Balkans (Olalde et al.,2023). The Iberian Peninsula also received this demographic input, which could have its proximal source in the Italian Peninsula, where this ancestry was already widespread, or in more eastern provinces where this ancestry has its distal origin. Unlike the Italian Peninsula or the Balkans, where individuals fully deriving from Eastern Mediterranean populations are documented, in Iberia, this ancestry tends to be always in admixed form.”
WestAnatolia_Roman_Byzantine: This population is composed by a group of individuals who inhabited the Aegean cost of Anatolia during the Roman-Byzantine period (Lazaridis et al., 2022). We use this source as a proxy for the Eastern Mediterranean signal present in the Italian Peninsula and the Balkans during the Imperial Period (Antonio et al., 2019; Olalde et al., 2023; Posth et al., 2021).