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

Abstract

) 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 = p 2 + 2pq + q 2 -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 2002Millstein , 2005.

A critical review of the statisticalist debate

“…In this regard Millstein et al (2009) may concede too much by accepting or at least not questioning the statisticalists' premise that evolutionary principles used in population genetics are of purely mathematical nature. The second line of response challenges this premise.…”

“…The first line of response is to assert that statisticalists are looking for a wrong place to read off a causal implication of the theory. Millstein et al (2009) criticize statisticalists for concluding selection to be non-causal just because it is expressed by some mathematical formula. That something can be represented with an a priori equation does not prove its non-causal nature, for it is not an equation itself but its interpretation that gives a causal content.…”

“…Rather evolutionary concepts -selection and drift -are introduced post hoc as representing these two processes, and by this fact, Millstein et al (2009) argue, they acquire definite and distinct causal meanings.…”

“…An interpretation maps a theory -a set of linguistic entities such as mathematical equations like a binomial equation -to a particular domain like a set of squares or sexually reproducing populations. The premise of Millstein et al (2009) is that this connection "infuses" a theory with the empirical or causal contents of the target domain. This reflects a pragmatic stance toward scientific theories (e.g.…”

The Nature of Evolutionary Biology: At the Borderlands Between Historical and Experimental Science

“…The status of shifting balance in evolutionary theory is itself under perennial discussion (Wade 1992 ;Coyne et al 1997 ), though there seems to be an emerging sense that the mechanism, while theoretically feasible, is unlikely to play a major role in the evolution of actual biological lineages. Still, the concept of drift has become incorporated into standard population genetic theory, and has even been the focus of detailed, and still unsettled, philosophical analyses (e.g., Pigliucci and Kaplan 2006 ;Millstein et al 2009 ).…”