Just three kinds of birds?

Nazca Booby, Chinstrap Penguin, Little auk.

Those were just the studies I could find offhand of monogamous species with no EPCs. If you include EPCs, about 90% of birds are socially monogamous[1]. According to [2] ~25% of those species are genetically monogamous (i.e. no EPCs). Though I should mention that genetic monogamy is a pretty high bar, which humans do not pass by a long shot. Is this sufficient evidence for you?

[1]Lack, D. 1968. Ecological Adaptations for Breeding in Birds. Methuen and Company, London.

[2]Griffith, S. C. , I. P F. Owens , and K. A. Thuman . 2002. Extra-pair paternity in birds: A review of interspecific variation and adaptive function. Molecular Ecology 11:2195–2212.

> Is this sufficient evidence for you?

Sufficient if we just consider birds, of course. But what do we discuss here? It started with the

"There are plenty of species which are well documented to have monogamous relationships"

claim and all I see is birds and birds.

Edit: thanks for finally answering below my question "how much in percents is that "plenty of species"?" Your answer is "90% of birds." The rest of discussion would have been unnecessary, especially quoting some three specific birds as the answer. I also agree with yours "the average sexual behaviors across all species doesn't give you much insight."

I chose birds because it's a taxa I know well and I knew to be largely monogamous. I've shown 90% of birds are socially monogamous, and 1/6 of vertebrate species are birds, so at least 15% of all vertebrates are monogamous, and that's plenty enough for me. If you want more exact numbers feel free to look for them yourselves, but I think I've given you a pretty good starting place. For the record, I doubt you'll find anything in the existing literature which attempts to give exact percentages, mostly because it's a rather useless figure. Taking averages over species assigns equal weight to some obscure insect species on one particular island with only a couple hundred individuals to a species with a global distribution and billions of individuals. And even once you get that number, the average sexual behaviors across all species doesn't give you much insight.