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The antiquity of human dispersal into Mediterranean islands and ensuing coastal adaptation have remained largely unexplored due to the prevailing assumption that the sea was a barrier to movement and that islands were hostile environments to early hunter-gatherers [J. F. Cherry, T. P. Leppard, J. Isl. Coast. Archaeol. 13, 191-205 (2018), 10.1080/15564894.2016.1276489]. Using the latest archaeological data, hindcasted climate projections, and age-structured demographic models, we demonstrate evidence for early arrival (14,257 to 13,182 calendar years ago) to Cyprus and predicted that large groups of people (~1,000 to 1,375) arrived in 2 to 3 main events occurring within <100 y to ensure low extinction risk. These results indicate that the postglacial settlement of Cyprus involved only a few large-scale, organized events requiring advanced watercraft technology. Our spatially debiased and Signor-Lipps-corrected estimates indicate rapid settlement of the island within <200 y, and expansion to a median of 4,000 to 5,000 people (0.36 to 0.46 km-2) in <11 human generations (<300 y). Our results do not support the hypothesis of inaccessible and inhospitable islands in the Mediterranean for pre-agropastoralists, agreeing with analogous conclusions for other parts of the world [M. I. Bird et al., Sci. Rep. 9, 8220 (2019), 10.1038/s41598-019-42946-9]. Our results also highlight the need to revisit these questions in the Mediterranean and test their validity with new technologies, field methods, and data. By applying stochastic models to the Mediterranean region, we can place Cyprus and large islands in general as attractive and favorable destinations for paleolithic peoples. [ABSTRACT FROM AUTHOR]