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The Wikipedia article for "Symmetry in Biology" claims: "Animals with bilateral symmetry are classified into a large group called the Bilateria which contains 99% of all animals (comprising over 32 phyla and 1 million described species)." This claim that almost all animals are Bilateria can be found in other sources too, e.g. in "A new paradigm for animal symmetry" by Gábor Holló. In both cases, however, no source is provided. I'm no biologist so I don't no exactly how self-evident this claim is.

Does someone know a source corroborating these claims?

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Well, you could count yourself.

Kingdom Animalia encompasses about 1.3 million known species. There is one large phylum where most species lack symmetry - Porifera (5,500 species). Cnidaria (10,000 species) have radial symmetry.

All the other broad phyla, from flatworms to chordates, have bilateral symmetry during embryonic development. Echinoderms (7,000 species) are pentaradially symmetrical as adults but bilateral as larvae and considered part of Bilateria.

Source:

Campbell biology (specifically, chapters 32 and 33)/ Lisa A. Urry, Michael L. Cain, Steven A. Wasserman, Peter V. Minorsky, Rebecca B. Orr, Neil A. Campbell. -- Twelfth edition. | New York, NY : Pearson, 2020.

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    $\begingroup$ Strictly speaking, the Bilateria classification refers to animals with bilateral symmetry during embryonic development. Despite the lack of obvious bilateral symmetry in more developed specimens, Echinoderms are part of the Bilateria group. $\endgroup$
    – MikeyC
    Commented Oct 27, 2021 at 19:15

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