What's in a name? How organelles of endosymbiotic origin can be distinguished from endosymbionts

Mitochondria and plastids evolved from free-living bacteria, but are now considered integral parts of the eukaryotic species in which they live. Therefore, they are implicitly called by the same eukaryotic species name. Historically, mitochondria and plastids were known as "organelles", even before their bacterial origin became fully established. However, since organelle evolution by endosymbiosis has become an established theory in biology, more and more endosymbiotic systems have been discovered that show various levels of host/symbiont integration. In this context, the distinction between "host/symbiont" and "eukaryote/organelle" systems is currently unclear. The criteria that are commonly considered are genetic integration (via gene transfer from the endosymbiont to the nucleus), cellular integration (synchronization of the cell cycles), and metabolic integration (the mutual dependency of the metabolisms). Here, I suggest that these criteria should be evaluated according to the resulting coupling of genetic recombination between individuals and congruence of effective population sizes, which determines if independent speciation is possible for either of the partners. I would like to call this aspect of integration "sexual symbiont integration". If the partners lose their independence in speciation, I think that they should be considered one species. The partner who maintains its genetic recombination mechanisms and life cycle should then be the name giving "host"; the other one would be the organelle. Distinguishing between organelles and symbionts according to their sexual symbiont integration is independent of any particular mechanism or structural property of the endosymbiont/host system under investigation.