Arbuscular mycorrhizal fungi (AMF) are ancient asexually reproducing organisms that form symbioses with the majority of plant species, improving plant nutrition and promoting plant diversity. Little is known about the evolution or organization of the genomes of any eukaryotic symbiont or ancient asexual organism. Direct evidence shows that one AMF species is heterokaryotic; that is, containing populations of genetically different nuclei. It has been suggested, however, that the genetic variation passed from generation to generation in AMF is simply due to multiple chromosome sets (that is, high ploidy). Here we show that previously documented genetic variation in Pol-like sequences, which are passed from generation to generation, cannot be due to either high ploidy or repeated gene duplications. Our results provide the clearest evidence so far for substantial genetic differences among nuclei in AMF. We also show that even AMF with a very large nuclear DNA content are haploid. An underlying principle of evolutionary theory is that an individual passes on one or half of its genome to each of its progeny. The coexistence of a population of many genomes in AMF and their transfer to subsequent generations, therefore, has far-reaching consequences for understanding genome evolution.