One major morphological difference between chordates and annelids or arthropods is the opposite orientation of the nerve cord and heart. A long-standing proposal is that the chordate axis evolved by inverting the body of an ancestor with the annelid/arthropod orientation. However, the data can also be explained by a common ancestor with diffuse dorsoventral organization, followed by oppositely directed condensation of the nerve cord and relocation of the heart in the two lines.
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John C. Gerhart (2000) studied this question.
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