The mitochondrial genetic diversity, distribution and invasive potential of multiple cryptic operational taxonomic units (OTUs) of the red invasive seaweed Asparagopsis were assessed by studying introduced Mediterranean and Hawaiian populations. Invasive behavior of each Asparagopsis OTU was inferred from phylogeographic reconstructions, past historical demographic dynamics, recent range expansion assessments and future distributional predictions obtained from demographic models. Genealogical networks resolved Asparagopsis gametophytes and tetrasporophytes into four A. taxiformis and one A. armata cryptic OTUs. Falkenbergia isolates of A. taxiformis L3 were recovered for the first time in the western Mediterranean Sea and represent a new introduction for this area. Neutrality statistics supported past range expansion for A. taxiformis L1 and L2 in Hawaii. On the other hand, extreme geographic expansion and an increase in effective population size were found only for A. taxiformis L2 in the western Mediterranean Sea. Distribution models predicted shifts of the climatically suitable areas and population expansion for A. armata L1 and A. taxiformis L1 and L2. Our integrated study confirms a high invasive risk for A. taxiformis L1 and L2 in temperate and tropical areas. Despite the differences in predictions among modelling approaches, a number of regions were identified as zones with high invasion risk for A. taxiformis L2. Since range shifts are likely climate-driven phenomena, future invasive behavior cannot be excluded for the rest of the lineages
