This reported just this year. This report suggests that there has never been a study about the transport of fish eggs by water birds.
https://www.sciencedaily.com/releases/2018/02/180219103258.htmThe report also claims that fish egg dispersal is a commonly held opinion of researchers stating that :
"For their study, the Basel researchers also reviewed online forums and surveyed around 40 experts from research, private institutions, and enviromental NGOs. Their aim was to determine the prevalence of the theory of fish dispersal by water birds both inside and outside the research community. The majority of experts that took part in the survey found the theory so plausible that they deemed the mystery to have been solved. However, none of them could draw on any empirical evidence."
The hypothesis is certainly not well tested nor well examined employing science.
A couple of fairly recent links where researchers discuss the hypothesis:
https://www.researchgate.net/post/Does_a...o_pond_by_birdshttps://www.researchgate.net/post/Is_the...ody_to_an_otherEvidently the first reference missed this paper?
http://faunaofindia.nic.in/PDFVolumes/records/107/01/0019-0031.pdfIf you read through the researcher's forum, you will find other references where research has attempted to invalidate the waterbird transport of fish eggs hypothesis. The research doesn't provide evidence of transport but rather tests whether evidence may contradict the plausibility of hypothesis. Research found that the eggs of some species of fish are resistant to dessication while another found that the eggs of some species of fish can be ingested by ducks and remain viable after being deposited in the faeces.