Invasive alien species often have reduced genetic diversity and must adapt to new environments. Given the success of many invasions, this is sometimes called the genetic paradox of invasion. Phytophthora ramorum is invasive, limited to asexual reproduction within four lineages, and presumed clonal. NA1 is responsible for sudden oak death in the USA, NA1, NA2 and EU1 are responsible for ramorum blight in the USA and Canada and EU1 and EU2 are responsible for sudden larch death and blight in Europe. We sequenced 107 genomes to determine how this pathogen can overcome the invasion paradox. Mitotic recombination (MR) associated with transposons and low gene density has generated runs of homozygosity (ROH) affecting 2698 genes, resulting in novel genotypic diversity within the lineages. One ROH enriched in putative pathogenicity genes was fixed in NA1. An independent ROH affected the same scaffold in EU1 suggesting an MR hotspot and selection target. EU1 individuals with and without the ROH may differ in aggressiveness. Non-core regions (not shared by all lineages) had signatures of accelerated evolution and were enriched in putative pathogenicity genes and transposons. There was a striking pattern of gene loss, including all effectors, in the non-core EU2 genome. Positive selection was observed in 8.0% of RxLR and 18.8% of Crinkler effector genes compared with 0.9% of the core eukaryotic gene set. We conclude that the P. ramorum lineages are diverging via a rapidly evolving non-core genome and the invasive asexual lineages are not clonal, but display genotypic diversity caused by MR.