The genetic connections among organisms within a species that reproduces sexually form a tangled web, through the generations of interbreeding. However, these genetic connections do not extend much between species, and so, through time, each species is descends like a bundle of genetic connections isolated from other such bundles.
Each species is therefore a reproductive community. Occasionally, by various causes, a species might be broken into two isolated reproductive communities. The two isolated reproductive communities become separate species, and each becomes its own isolated bundle of genetic connections.
One species makes two, those two each make more, and so on. This process gives rise of a tree of species lineages descending and splitting. At the same time, some of the species go extinct, thus pruning the growing tree. In the end, this process has produced the many species of organisms we see around us today.
The notion that all of life is genetically connected via a vast phylogenetic tree is one of the most romantic notions to come out of science. How wonderful to think of the common ancestor of humans and beetles. An ancestral worm species was divided in two. Little did they know those hundreds of million years ago that some of their number would end up evolving into beetles, while their brothers and sisters would end up as humans.
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