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Identifying and analysing isolated populations is critical for conservation. Isolation can make populations vulnerable to local extinction due to increased genetic drift and inbreeding, both of which should leave imprints of decreased genome-wide heterozygosity. While decreases in heterozygosity among populations are frequently investigated, fewer studies have analysed how heterozygosity varies among individuals, including whether heterozygosity varies geographically along lines of discrete population structure or with continuous patterns analogous to isolation by distance. Here we explore geographical patterns of differentiation and individual heterozygosity in the threatened eastern barred bandicoot (Perameles gunnii) in Tasmania, Australia, using genomic data from 85 samples collected between 2008 and 2011. Our analyses identified two isolated demes undergoing significant genetic drift, and several areas of fine-scale differentiation across Tasmania. We observed discrete genetic structures across geographical barriers and continuous patterns of isolation by distance, with little evidence of recent or historical migration. Using a recently developed analytical pipeline for estimating autosomal heterozygosity, we found individual heterozygosities varied within demes by up to a factor of two, and demes with low-heterozygosity individuals also still contained those with high heterozygosity. Spatial interpolation of heterozygosity scores clarified these patterns and identified the isolated Tasman Peninsula as a location where low-heterozygosity individuals were more common than elsewhere. Our results provide novel insights into the relationship between isolation-driven genetic structure and local heterozygosity patterns. These may help improve translocation efforts, by identifying populations in need of assistance, and by providing an individualised metric for identifying source animals for translocation.