In a recent conversation with a colleague, these quotes arose:
The Vermin only teaze and pinch
Their Foes superior by an Inch.
So Nat'ralists observe, a Flea
Hath smaller Fleas that on him prey,
And these have smaller Fleas to bite 'em,
And so proceed ad infinitum.
[1733, Jonathan Swift, Poems II. 651]
Great fleas have little fleas upon their backs to bite 'em,
And little fleas have lesser fleas, and so ad infinitum.
And the great fleas themselves, in turn, have greater fleas to go on;
While these again have greater still, and greater still, and so on.
[1872, Augustus De Morgan, A Budget of Paradoxes 377]
I recalled reading, at least twice (but can't recall which books or journals), that every species has at least one parasitic species, and in one of those places, the term was "one obligate species", meaning a host-specific parasite.
Now, let's think about that a moment. The latter statement would really proceed ad infinitum! I just had to look into it a bit. A quick search in Google Books yielded the following:
The average number of host species per parasite species (14.0) was considerably higher than the average number of prey species per predator species (6.7)…The authors are discussing a food web compiled from observations in a salt marsh. Among 134 species in the parasite-host subweb, 87 hosted 47 parasites. I can't tell if they considered parasites of parasites, though with 615 parasite-host links, it seems likely. [From those numbers I get 13 not 14.]
[2006 Sharon K. Collinge and Chris Ray, Disease ecology: community structure and pathogen dynamics, p127]
The singular feature here is that obligate host-species relationships are very rare. The average parasite has fourteen hosts, and some have many more (think of mosquitos, which bite any mammal; even if certain ones have a preference, they are not specific).
A couple of other snippets confirm the point. There are lots of ways for "every species to have at least one species of parasite" without requiring an infinite variety of parasites. From Swift's or De Morgan's point of view, the regression proceeded to the invisible, and we now know that the ultimate parasites of all species are bacterial and viral pathogens. These last might well outnumber (in diversity) all the rest.
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