Infinite populations and counterfactual frequencies in evolutionary theory

One finds intertwined with ideas at the core of evolutionary theory claims about frequencies in counterfactual and infinitely large populations of organisms, as well as in sets of populations of organisms. One also finds claims about frequencies in counterfactual and infinitely large populations-of events-at the core of an answer to a question concerning the foundations of evolutionary theory. The question is this: to what do the numerical probabilities found throughout evolutionary theory correspond? The answer in question says that evolutionary probabilities are 'hypothetical frequencies' (including what are sometimes called 'long-run frequencies' and 'long-run propensities'). In this paper, I review two arguments against hypothetical frequencies. The arguments have implications for the interpretation of evolutionary probabilities, but more importantly, they seem to raise problems for biologists' claims about frequencies in counterfactual or infinite populations of organisms and sets of populations of organisms. I argue that when properly understood, claims about frequencies in large and infinite populations of organisms and sets of populations are not threatened by the arguments. Seeing why gives us a clearer understanding of the nature of counterfactual and infinite population claims and probability in evolutionary theory. (C) 2006 Elsevier Ltd. All rights reserved.