He was most respected among his colleagues and students for his genius in discerning and articulating the differences in form between plant species in the context of their variation with environmental factors.
This work was honored by James Farris and Arnold Kluge in their later appellation of related algorithms as "Wagner parsimony."
Having served in the U.S. Military in the Pacific Theater in World War II, he maintained a lifelong interest in the diversity and origin of the ferns of Hawaii.
Working with his wife Florence Signaigo Wagner, an accomplished cytologist, he resolved the relationships of an array of polyploid complexes in North American ferns, first the Appalachian trio of Asplenium species, then in Dryopteris and Polystichum.
Apparently among modern phylogenetic systematists, Wagner is alone in having been mentioned in a Hollywood film − A New Leaf, starring Elaine May and Walter Matthau.