Heilmann published an English revision of his series of Danish papers in 1926 as The Origin of Birds. Like Thomas Huxley, Heilmann compared Archaeopteryx and other birds to an exhaustive list of prehistoric reptiles, and also came to the conclusion that theropod dinosaurs like Compsognathus were the most similar. However, Heilmann noted that birds possessed clavicles fused to form a bone called the furcula ('wishbone'), and while clavicles were known in more primitive reptiles, they had not yet been recognized in theropod dinosaurs. A firm believer in Dollo's Law, which states that evolution is not reversible, Heilmann could not accept that clavicles were lost in dinosaurs and re-evolved in birds, so he was forced to rule out dinosaurs as bird ancestors and ascribe all of their similarities to convergence. Heilmann stated that bird ancestors would instead be found among the more primitive 'thecodont' grade of reptiles. Heilmann's extremely thorough approach ensured that his book became a classic in the field and its conclusions on bird origins, as with most other topics, were accepted by nearly all evolutionary biologists for the next four decades, despite the discovery of clavicles in the primitive theropod Segisaurus in 1936. Clavicles and even fully developed furculae have since been identified in numerous other non-avian dinosaurs.
In 1912 he contaced Adolf Herluf Winge at the Zoological Museum in Copenhagen. Winge had initially shown some interest in his work but was not particularly helpful. Winge's short responses to an eight page letter of queries and ideas caused much irritation and Heilmann decided to stop writing to him. Heilmann later noted that Winge was a Lamarckist, and from that point he worked alone without communication with Danish academics. He sent a short paper in Danish in 1912 and this was accepted by the editor Otto Helms. Helms was attacked by numerous Danish academics for allowing it to be published. A letter from the Danish zoologist R. H. Stamm to Helms read: May I offer my condolences as to the latest issue? It must have been rough on you – who must know birds well, and as a medical doctor must possess some general sense of natural history – to include in the journal the dilettantish mess which occupies most of the issue. His first paper published in the Danish ornithology journal was however discovered by American paleontologist R. W. Shufeldt, who was able to make sense of it thanks to help from his Norwegian wife. This opened up Heilmann to connections outside Denmark. His work was introduced to D'Arcy Thompson by R. W. Shufeldt and this led to the two exchanging ideas on morphological evolution. His past bitter encounters with Danish academics led to Heilmann initially writing "I wonder why Dr. R.W. Shufeldt has written to you about my work; he ought to have told you, that I am an artist and only an incipient amateur in science. This is my ﬁrst work in this line." In the course of his interactions with Thompson, he also contributed some illustrations for use in "On Growth and Form".
In 1940, Heilmann published a second book on Darwinian evolution, the Univers og traditionen (Universe and Tradition, in Danish). He also expressed his sentiments against religious beliefs in this book. The bird-like dinosaur species Scansoriopteryx heilmanni was named in honour of Gerhard Heilmann in 2002.
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