Infinite Population Models and Random Drift - Marshall Abrams (Philosophy, Theory, and Practice in Biology)
Philosophers of science sometimes seem to imply that there are evolutionary models in which a counterfactual infinite population of organisms plays a crucial role. As is sometimes noted, this idea is incoherent if “infinite population” is understood literally. This paper uses case studies of modeling in evolutionary biology to examine roles that “infinite population”, and assumptions about random drift, play in modeling practices. Sometimes various effects of the absence of drift are understood as having to do with limits as population size goes toward infinity; in other cases these effects are conceptualized as having to do with large population sizes. Some models make assumptions about population size and effects of drift that might seem inconsistent: in some cases drift is included in part of a model, but excluded in another, or excluded even though population size is treated as finite. Because of such facts, I argue that there is no fixed set of assumptions associated with drift or its absence, and that there is no clear meaning for “infinite population” and similar terms. Rather “infinite population” is figurative language that is merely associated with various assumptions about the absence of drift.