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Islands were key to the development of allopatric speciation theory because they are a natural laboratory of repeated barriers to gene flow caused by open water gaps. Despite their proclivity for promoting divergence, little empirical work has quantified the extent of gene flow among island populations. Following classic island biogeographic theory, two metrics of interest are relative island size and distance. Fiji presents an ideal system for studying these dynamics, with four main islands that form two large‐small pairs. We sequenced thousands of ultraconserved elements (UCEs) of the Fiji bush‐warbler Horornis ruficapilla, a passerine distributed on these four Fijian islands, and performed a demographic analysis to test hypotheses of the effects of island size and distance on rates of gene flow. Our demographic analysis inferred low levels of gene flow from each large island to its small counterpart and little or none …