The distinction: there's a frequent understanding or expression that a single common ancestor means that that was the only individual <i>alive</i> at a time, or that its ultimate dominance was evident immediately or very shortly afterwards.<p>Neither of these is the case.<p>Nor, strictly, is the notion that the individual (or its descendants) were necessarily evolutionarily fitter than others.<p>In the first instance, a common ancestor may have come long before some evolutionary chokepoint or contest in which their gene line ultimately survived whilst others died out. And in some cases (mitochondria), the alternative gene lines <i>didnt'</i> die out. Non-mitochondrial organisms are the prokaryotes, and they have continued (for many hundreds of millions of years) to live alongside their mitochondrial-bearing eukaryotic cousins. Bacteria are AFAIU largely prokaryotic. <i>Even some eukaryotes have lost their mitochondria</i>, though it seems that <i>all</i> eukaryotes <i>had</i> mitochondria at some point in their evolution. But where it comes to complex organisms, <i>overwhelmingly</i> mitochndria-bearing cell forms out-compete those which lack same.<p>As for evolution, that which is expressed in genomes requires a threefold process: variation, selection, <i>and inheritance</i>. That is, whatever leads to the eventual <i>survival</i> of a particular line of descendants must be based on an <i>inheritable</i> characteristic: stronger muscles, lower metabolism, superior coordination, robustness to environmental variance, faster development within a given niche, mate-selection advantage, etc., etc. (And note that what works in one selective environment may well <i>not</i> be suited to another.)<p>Other selection events are not directly heritable, or are far <i>less</i> heritable. Getting smacked by an asteroid is an example, though there are features (e.g., being an aquatic life-form, small body size) which may increase survival odds after a major impact. Other natural disasters (earthquakes, tsunamis, volcanoes, wildfires) etc., are to an extent random and arbitrary in what they kill, though there may be specific adaptations which increase survival odds after such events. Even given this, <i>many species will see a fairly arbitrary selection of extinction and survival</i>, often with little prediction for a future repeat of such an event. Which individuals survive, or don't, is pretty much a wash. Those are still <i>selection</i> events, but don't convey any <i>heritable advantage</i>.<p>The possibility that some common ancestor or LUCA is at least in part arbitrarily determined seems high to me.