 There is a further complication with respect to the nature of the genic selection models put forward by genic pluralists. These models function under the presupposition that they are at least mathematically equivalent to hierarchical models. This claim has largely depended on the work of Dugatkin and Reeve in establishing this equivalence (Dugatkin &amp; Reeve 1994, Sterelny 1996b, Sober &amp; Wilson 1998, Sterelny &amp; Griffiths 1999, Kerr &amp; Godfrey-Smith 2002a, Waters 2005). However, foundational work has indicated that this equivalence does not in fact hold. In Dugatkin and Reeve and the rest of this literature, comparison of population genetic models was largely based on predictions of allele frequency changes; in other words, if two models made the same predictions as to the changes of allelic frequencies in a given situation, then the models are equivalent. However, this is an overly simplistic method for testing model equivalence which pays little mind to the details of the models themselves. When the notion of representational adequacy of the models is taken into account, specifically through the inclusion of parametric and dynamical sufficiency as important points of comparison, this equivalence between genic and hierarchical models disappears (Lloyd, Lewontin, &amp; Feldman 2008; Lewontin 1974; see also  group selection  for more on formal equivalence).