"(i) Brood parasites might selectively target cooperative breeders to maximize the care of their offspring (7); (ii) cooperative
breeders may be more obvious targets as a result of the increased activity of helpers near the nest (6, 7); and (iii) cooperative breeders may be better able to defend their nests against brood parasitism (7), selecting for cooperative breeding hosts."
They then tested these predictions by investigating with superb fairy-wrens and Horsefiled's bronze cuckoos. They found that cuckoo chicks grew faster when reared in larger groups, and they had a better chance of surviving to fledge. Cuckoos thus gain a potential fitness advantage from parasitizing large groups, but large groups had a lower parasitism rate. Therefore, the authors conclude that their results support hypothesis iii) cooperative breeders are better able to defend against brood parasites. They then tested mobbing behaviour of fairy wren groups and found that large groups were more vigilant around the nest and mobbed cuckoos for longer.
The results are interesting and provide a new perspective on the evolution of cooperation. The results show that cooperative breeding is of great benefit to reducing the costs of brood parasitism but it may not be the initial driver to cause cooperation to evolve.
As a side note and a perspective from me, cooperation does seem to provide benefits against interspecific brood parasitism, but it may also increases the risk of intraspecific brood parasitism: many studies have found that subordinate females will lay eggs in nests (for example Nelson-Flower et al 2013).
For more details and perspectives on this paper you can read Claire Spottiswoode's comments: https://www.sciencemag.org/content/342/6165/1452.summary