Armchair note:
I think that "resources" implies use and use value. The economically
efficient way to control resources is through property rights and
markets. I don't think there have been many users missing the use
value of the extinct species; though the potential in lost information
is certainly there.
The use value of the Dodo, was as a big, dumb, tasty
bird -- dogs apparently liked it. Chicken seems such a fine
substitute for this use that, while Dodos are gone, there are still
lots, in fact even more, dumb tasty birds.

I don't believe we'll be able to fully reconstruct all lost bio-species,
so their loss may well be a real, finite, lost information source.
The keys to "infinity of resources", such as oil, for instance, are
property rights, markets, and substitutability.
Once oil/a resource is owned, as it is used "up", the price will rise.
At some price point, other substitutes will become preferred
choice for use. Tech progress helps in the
substitution possibilities.

Large species extinctions are becoming rarer as the need for property rights
becomes more accepted (though also heavy gov't development restrictions
to protect some animals). Arabian Leopards, for instance, have been owned
in zoos and are starting to be bred, although the BBC interviewed expert
thought he wouldn't see them reintroduced into the wild in his lifetime.

In a similar way, there is no infinite supply of "Mona Lisa"(s), so if the
one original is lost, burned up, say, then it's gone. But it moves more
into the category of "treasure" than of resource. I think species are
more like a finite treasure than like a resource.

Tom Grey