A variant of the 3-hydroxypropionate cycle was found to operate in the aerobic extreme thermoacidophile archaeon Metallosphaera sedula. This pathway is called the 3-hydroxypropionate/4-hydroxybutyrate cycle.
Yet another variant of the 3-hydroxypropionate cycle is the dicarboxylate/4-hydroxybutyrate cycle.  It was discovered in anaerobic archaea.
It was proposed in 2008 for the hyperthermophile archeon Ignicoccus hospitalis.