The history of life is often represented by a tree, with each existing species evolving directly from a single progenitor species. The newer species arises after some population of the original species adapts to different conditions and diverges genetically so much from the original group that the two can no longer mate. That's the standard story, but biology eschews absolutes. Many studies suggest that although individuals from different species normally do not interbreed, they may interbreed. What is more, such interbreeding, or hybridization, occasionally yields new species.

Suppose you are trying to trace the origins of a collection of species, some of which are known to be source, or founder, species and others of which are known to be derived. For this puzzle, we want each derived species to have as few direct evolutionary progenitors as possible. The direct evolutionary progenitors of species X are those species in the collection that combine to supply X's traits without the involvement of any other species. Note that three species may combine to form a new species, Y, by first producing unseen intermediate species. Species Y would then be considered to have three direct progenitors, though, because we count only the species we see. One more constraint: no species can arise before its progenitors appear.

This article was originally published with the title The Graph of Life.

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