The utility of species distribution models for applications in invasion and global change biology is critically dependent on their transferability between regions or points in time, respectively. We introduce two methods that aim to improve the transferability of presence-only models: density-based occurrence thinning and performance-based predictor selection. We evaluate the effect of these methods along with the impact of the choice of model complexity and geographic background on the transferability of a species distribution model between geographic regions. Our multifactorial experiment focuses on the notorious invasive seaweed Caulerpa cylindracea (previously Caulerpa racemosa var. cylindracea) and uses Maxent, a commonly used presence-only modeling technique. We show that model transferability is markedly improved by appropriate predictor selection, with occurrence thinning, model complexity and background choice having relatively minor effects. The data shows that, if available, occurrence records from the native and invaded regions should be combined as this leads to models with high predictive power while reducing the sensitivity to choices made in the modeling process. The inferred distribution model of Caulerpa cylindracea shows the potential for this species to further spread along the coasts of Western Europe, western Africa and the south coast of Australia.