Biologists like to divide life forms into Kingdoms (plants vs animals) then subdivide those Kingdoms into Phylums and then subdivide those Phylums into Classes (reptiles vs mammals) etc.  The taxonomic hierarchy (ranked from broadest to most specific)traditionally looked something like this:

Kingdom > Phylum > Class > Order > Family > Genus > Species > Race

What I always found odd was that the only one of these ranks to be clearly defined was species and species is commonly defined as a group of organisms that can produce fertile offspring.  However I think that definition is probably too inclusive.  After all Neanderthals could interbreed with modern humans yet were not considered part of our species morphologically.

Thus I would use that definition for genus and use a more exclusive definition (a group that can produce fertile offspring regardless of the subgroup of father or sex of offspring).  This should exclude Neanderthals from our species yet still keep them in our genus since there’s evidence that male Neanderthal hybrids fathered by Neanderthals were infertile.

This got me thinking: why not use the concept reproductive compatibility to easily define all the taxonomic categories (at least for sexually reproducing life)?  Thus the taxonomic hierarchy could go from the most inclusive to most exclusive levels of reproductive compatibility.  For example:
Kingdom: A group that does or does not reproduce sexually
Phylum: A group that could use each other as sex dolls
Class: A group that could technically have sex, but would not enjoy it
Order: A group that could enjoy having sex, even though no offspring are possible
Family: A group that can produce any offspring at all, fertile or not
Genus: A group that can produce fertile offspring
Species: A group that can produce fertile offspring regardless of offspring’s sex and what subgroup the father is
Race: A group that can produce fertile offspring of both sexes without increased risk of infant prematurity or low birth weight

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