Rugulopteryx okamurae is a brown alga native to the northwestern Pacific and invasive elsewhere. It was first sighted in the southern Strait of Gibraltar in 2015, expanded to the northern Strait of Gibraltar in 2016, and had covered most of the northern Alboran Sea by 2021. Understanding the factors that may explain its different phases of colonisation is crucial for developing mitigation and control measures. We modelled the yearly distribution of R. okamurae in the northern Alboran Sea from 2016 to 2021 using the favourability function, which produces commensurable biogeographic models despite variations in species prevalence across years. This function also allows the use of fuzzy logic operations to combine previous environmental models based on different explanatory factors, namely biotope, biocoenosis, coastal influence, accessibility through dispersion, and oceanographic characteristics. Significant environmental models were assembled, and their fuzzy intersection and union applied. This resulted in two final biogeographic models for each year, which were used to predict the distribution of the species in following years. The biogeographic models exhibited a high predictive capacity, as most years accurately predicted colonisation in the following year or even multiple years ahead. Accessibility through dispersion and oceanographic characteristics were critical during the initial years of establishment, while complete establishment depended on all five factors together. Expansion to the whole northern Alboran coast was explained by favourable conditions for any of the explanatory factors, while all factors except coastal influence explained the saturation of the invasion. We conclude that the biogeographic models prove valuable in understanding the factors that contributed to the spread of R. okamurae in the northern Alboran Sea. This approach could help prevent further colonisation and mitigate the ecosystem and commercial consequences of R. okamurae's invasion.