(Mis)interpreting Mathematical Models: Drift as a Physical Process

Philosophy and Theory in Biology 1 (20130604):e002 (2009)
Abstract
Recently, a number of philosophers of biology (e.g., Matthen and Ariew 2002; Walsh, Lewens, and Ariew 2002; Pigliucci and Kaplan 2006; Walsh 2007) have endorsed views about random drift that, we will argue, rest on an implicit assumption that the meaning of concepts such as drift can be understood through an examination of the mathematical models in which drift appears. They also seem to implicitly assume that ontological questions about the causality (or lack thereof) of terms appearing in the models can be gleaned from the models alone. We will question these general assumptions by showing how the same equation — the simple (p + q)2 = p2 + 2pq + q2 — can be given radically different interpretations, one of which is a physical, causal process and one of which is not. This shows that mathematical models on their own yield neither interpretations nor ontological conclusions. Instead, we argue that these issues can only be resolved by considering the phenomena that the models were originally designed to represent and the phenomena to which the models are currently applied. When one does take those factors into account, starting with the motivation for Sewall Wright’s and R.A. Fisher’s early drift models and ending with contemporary applications, a very different picture of the concept of drift emerges. On this view, drift is a term for a set of physical processes, namely, indiscriminate sampling processes (Beatty 1984; Hodge 1987; Millstein 2002, 2005).
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