This river of DNA originally flowed as one river (one species) which eventually branched into two, three, four, and eventually millions of rivers. Each river is distinct from the others and no longer exchanges water with the others, just as species are isolated reproductively from other species. This metaphor allows Dawkins to explain both the common ancestry of all life, along with the necessity of gradualism in the evolutionary process.
The commitment to gradual evolution is no surprise coming from Dawkins, but he forces himself to do some rather grotesque hand-waving when he chooses to discuss the Cambrian explosion. He notes that some in the past have suggested that the Cambrian creatures may have evolved by some unknown mechanism, since gradual Darwinism simply can’t achieve the level of diversity in the Cambrian in only 5–10 million years. Dawkins exclaims:
The fallacy is glaring! Even creatures as radically different from one another as mollusks and crustaceans were originally just geographically separated populations of the same species. For a while, they could have interbred if they had met, but they did not. After millions of years of separate evolution, they acquired the characteristics which we, with the hindsight of modern zoologists, now recognize as those of mollusks and crustaceans respectively.