These flightless birds are traditionally known as ratites. The ratites are simply the flightless members of the infraclass Palaeognathae. Palaeognathae includes the ratites: the African ostriches, the South American rheas, the Australian emu and cassowaries, the New Zealand kiwis and extinct moas, and the extinct elephant birds of Madagascar. Also in Palaeognathae are the various South American species of tinamous that do fly, but usually only for very short distances.
Previously it had been believed that all these birds but the various species of tinamous had evolved from a flightless bird on the southern continent of Gondwana, also called Gondwanaland. When Gondwana broke up forming Africa, South America, Australia, Madagascar, New Zealand, and other land masses the different flightless birds evolved into their present species and the recently extinct moas and elephant birds. Both the moas and elephant birds were driven into extinction by humans in the past few thousand years.
Not everyone will be able to read more than the abstract on the Science site. I believe unpaid access is limited to members of the AAAS, American Association for the Advancement of Science. For the intelligent layman you can read an article posted by NPR, National Public Radio here.
All other birds are in Neognathae. So all the other birds are more closely related to each other than they are to the species in the infraclass Palaeognathae. For example, the hummingbird, robin, chicken, hawk, parrot, and penguin are all more closely related to one another than they are to the ostrich.
Similarly, the closest relatives of the white-tailed deer in North America, the larger deer, for example, the elk and moose, find it difficult or impossible to survive in the white-tailed deer's range because it carries diseases that kill those larger deer, but not the white-tailed deer. (Note to Europeans, what Americans call a moose, you call an elk, and what Americans call an elk is closely related to the red deer.)
But the large population has more individuals, any one of which might through mutation gain an immunity that allowed the animal to live with the pathogen. This animal will have more descendants and eventually the whole population will enjoy the immunity. The closely related species with a smaller population suffers from an increasing variety of pathogens but does not have the advantage of more individuals to evolve an immunity. This species will frequently be driven into extinction within the range of their more numerous relative. As mentioned above elk and moose have difficulty surviving in the range of the smaller and more numerous white-tailed deer.
So the Palaeognathae independently took over and largely monopolized the large flightless bird niche in Africa, South America, Australia, Madagascar, and New Zealand, because their competition the Neognathae were constantly flying in with new plagues that had evolved around the world. Some of those plagues infected and killed both Palaeognathae and Neognathae, giving little advantage to either group, but others only infected and killed the Neognathae. This was because the birds that carried the diseases were Neognathae. No species of Palaeognathae was capable of flying into the isolated land masses.
For example, the largest trees Sequoias and coastal redwoods until recently had no relatives in their natural range with a common ancestor more recent than the Mesozoic. Like the ratites, they are part of an ancient lineage that had largely died out. In the ocean, the largest fish are the sharks, which are living fossils. In South America, the largest exclusively freshwater fish is another living fossil, the arapaima. In North America, the largest exclusively freshwater fish is still another living fossil, the alligator gar. Jumping from fish to spiders, the tarantulas, the largest spiders, are the second earliest branch off the spider family tree. This is but a small sampling of the examples that can be drawn from our present flora and fauna and natural history.
Similarly, the largest birds, the ratites, have relatively few close relatives in their environment compared to the Neognathae. So it is not surprising that they are the largest.
Those who are familar with biological literature will note that I committed the faux pas of calling sharks, arapaima, and the aligator gar living fossils. What I really mean is that they are part of an early branch off the phylogenetic tree of a larger clad. For example, sharks are part of the earliest existant branch of the clad of jawed fish. But the term living fossil while not quite correct is more widely known.
This essay does provide an explination. We can see that the independent loss of flight was perfectly natural and to be expected.
Why was quetzalcoatlus so big?
Why cold-blooded crocodiles so big?
Why tuatara bigger than New Zealand Lizards.
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