Dexiothetism refers to a reorganisation of a clade

Clade

A clade is a group consisting of a species and all its descendants. In the terms of biological systematics, a clade is a single "branch" on the "tree of life". The idea that such a "natural group" of organisms should be grouped together and given a taxonomic name is central to biological...

's bauplan, with right becoming ventral and left becoming dorsal. The organism would then recruit a new left hand side.

Details

If a bilaterially symmetrical ancestor were to become affixed by its right hand side, it would occlude all features on that side. When that organism wanted to become secondarily bilaterally symmetrical again, it would be forced to resculpt its new left and right hand sides from the old left hand side. The end result is a bilaterially symmetrical animal, but with its dorsoventral axis rotated a quarter of a turn.

Implications

Dexiothetism has been implicated in the origin of the unusual embryology of the cephalochordate amphioxus, whereby its gill slits originate on the left hand side and the migrate to the right hand side.

In Jefferies

Dick Jefferies

Richard P.S. Jefferies was a paleontologist famous for developing the Calcichordate Theory of the origin of chordates, now widely discredited. Jefferies joined the British Museum in 1960, and was largely based there for the remainder of his career....

' Calcichordate Theory

Calcichordate Theory

The Calcichordate Theory holds that each separate lineage of chordate evolved from its own lineage of mitrate, and thus the echinoderms and the chordates are sister groups, with the hemichordates as an out-group....

, he supposes that all chordate

Chordate

Chordates are animals which are either vertebrates or one of several closely related invertebrates. They are united by having, for at least some period of their life cycle, a notochord, a hollow dorsal nerve cord, pharyngeal slits, an endostyle, and a post-anal tail...

s and their mitrate

Mitrate

Mitrates are a group of stem group Echinoderms, which may be closely related to the hemichordates.-Morphology:The organisms were a few millimetres long. Like the echinoderms, they are covered in armour plates, each of which comprises a single crystal of calcite...

ancestors are dexiothetic.