The Lotka-Volterra equation may do a wonderful job of explaining simple predator-prey relationships, but it assumes exponential growth of the prey population, which is exactly what I'm disputing.

I've got a book somewhere (small trade paperback, dull silver cover[1], title might be Life) which claims that no one has ever gotten those pretty predator-prey equations to cycle nicely in the real world, not even with two species of micro-organisms in a test tube.

The Wiki page for the equation didn't seem to mention real-world examples.

I'll update with more detail if I find the book.

[1] It's a shame amazon doesn't have searches based on the way people really remember books.