How probable is common ancestry according to different evolutionary processes?

Darwin and contemporary biologists argue that all present-day life traces back to one or a few common ancestors. Here we investigate the relationship of different evolutionary processes to this hypothesis of common ancestry. We identify the property of an evolutionary process that determines what its probabilistic impact on the common ancestry thesis will be. The point of this exercise is to understand how the parts of Darwin׳s powerful theory fit together, not to call into question common ancestry or natural selection, since these two pillars of Darwin׳s theory enjoy strong support.