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Cal Academy of Sciences display

Did a 1990s Cal Academy of Sciences display on Cambrian phyla showed the phyla connected without common ancestors?

…A fossil exhibit on display at the California Academy of Sciences in the 1990s. It showed fossils arranged in the familiar branching-tree pattern… the phyla lines are parallel, illustrating that each phylum remains distinct--separate from the other phyla--during the entire time it appears in the fossil record.
Explore Evolution, p. 34

Summary of problems with claim: If description of exhibit is accurate, this display does not undermine evolution. Even if a hypothetical exhibit were inaccurate, one mistaken exhibit is not evidence against evolution any more than a misspelling on a picture caption changes the spelling of the word.

Full discussion:

Attempts by NCSE to verify this with the California Academy of Sciences have proven fruitless; this was so long ago that the information is unverifiable.

But if we accept their premise and assume that the diagram is a faithful representation of the CAS exhibit, then several things are wrong with Explore Evolution's claims:

1. Explore Evolution Misunderstands the Definition of Phyla

Phyla are ways of classifying body plans of animals. We are part of Phylum Chordata, for example, meaning that we have a spinal cord. So are birds, fish, snakes, and so on. Phylum Cnidaria is the home of animals without a spinal cord and with stinging cells; jellies and corals and anemones are all cnidarians.

2. Phyla Remain Distinct

Phyla are not expected to change within the fossil record; they are expected to evolve in parallel, separate branches. While Phylum Chordata plays many variations on the theme of spinal cords, no one would expect a chordate to evolve into Phylum Cnidaria. A jelly might evolve into another type of jelly, but not into a bird. Nor will the chordate bird evolve into a cnidarian.

Explore Evolution assumes that such transformations should occur, yet this evolutionary route has never been claimed by scientists.