Reproduction rate is certainly a BIG part of it. The main factors that influence evolution when we remove environmental influence are production rate as you mentioned or fecundity (how often you reproduce, how many you reproduce at a time and how many of your offspring survive to reproduce themselves), and fidelity (how well your genome is reproduced and how often mutations occur).

Now, a species that has greater fecundity, all other things being equal, will be more adaptable than another species (they don't evolve faster per se, they are more evolvable, selective pressure is still required). This is exactly why viruses, bacteria and insects are so successful. This species are more responsive and accomodating of changes in selective pressures. One need only look at the evolution of antibiotic resistant bacteria and pesticide resistant insects in the last few decades. The only reason we need to keep inventing new antibiotics, is because these diseases quickly adapt to the poisons we invent for them.

Hope that answers your question, I'm happy to elaborate if need be.

If you don't mind I'd like to crosspost this on my "Ask the Evolutionist" thread over at infidelguy.com.