An organism never returns exactly to a former state, even if it finds itself placed in conditions of existence identical to those in which it has previously lived.
Louis Dollo (1893)
Often termed “Dollo's law,” the proposition that organisms never revert to a former evolutionary state was controversial since its inception (see Gould 1970 for a detailed review). The original formulation of Dollo's law is so broad as to be of limited use (Simpson 1953; Hennig 1966; Bull 2000), and a narrower version—the irreversible loss of single complex characters—is almost exclusively the concept considered in the literature (Muller 1939; Simpson 1953; Kohlsdorf and Wagner 2006). Much of the debate about Dollo's law centered on the criteria for sufficient complexity, the metrics for identifying whether mutations are true reversals or merely analogs (e.g., homologous reversion vs. analogous novelty, exact nucleotide substitution reversal vs. compensatory mutation), speculative estimates of the general probabilities of reversal, and the status of biological laws. These are important issues, and they are reviewed elsewhere (Gould 1970; Wagner 1982; Marshall et al. 1994; McIntyre 1997). We instead focus on phylogenetic methods for testing Dollo's law.
The broad availability of sequence data for construction of accurate phylogenies and the development of a quantitative framework for inference of character evolution opened up new avenues for testing Dollo's law. Early phylogenetic studies of irreversibility based on parsimony reconstructions (Hennig 1966; reviewed in Maddison and Maddison 1992) often initially inferred reversal, but then found that this conclusion could be overturned by even a modest asymmetry in the difficulty of gain of a complex state over its loss (Cunningham et al. 1998; Cunningham 1999). Paradoxically, the limitations of parsimony methods (see Harvey and Pagel 1991; Cunningham et al. 1998) were in some ways advantageous in tests of Dollo's law in that they elicited explicit statements about assumptions, critical interpretation of results, and adjustments of methods (Kohn et al. 1996; Wray 1996; Omland 1997; Lee and Shine 1998; Cunningham 1999). The statistical model-based methods for character change in a maximum likelihood (Felsenstein 1981; Harvey and Pagel 1991; Sanderson 1993; Pagel 1994; Schluter et al. 1997) or Bayesian (Huelsenbeck et al. 2000, 2003; Pagel et al. 2004) framework were subsequently introduced and widely adopted. Applications of these methods to test Dollo's law recently yielded several spectacular claims of reversion to complex states (e.g., Oakley and Cunningham 2002; Collin and Cipriani 2003; Whiting et al. 2003; Nosil and Mooers 2005; Cruickshank and Paterson 2006; Domes et al. 2007; Ferrer and Good-Avila 2007; Brandley et al. 2008). Accordingly, criticism of Dollo's law shifted from debate about what constitutes a reversal to purported evidence of true reversals, leading to the prevailing view that Dollo's law was invalidated through the use of phylogenetic methods (recently reviewed in Pagel 2004; Kohlsdorf and Wagner 2006; Domes et al. 2007).
Here, we show that phylogenetic tests of Dollo's law are frequently misled by violations of at least two standard model assumptions. First, reconstructions are almost exclusively attempted only on clades that are variable at the focal character, leading to “acquisition bias” (Felsenstein 1992; Frumhoff and Reeve 1994; Lewis 2001) and inappropriate assignment of the character state distribution at the root. Second, association of character states with different net diversification rates (species-level selection) can lead to a strong bias in both transition rate and ancestral state estimation (Janson 1992; Strathmann and Eernisse 1994; Oakley and Cunningham 2000; Igic et al. 2006; Maddison 2006; Maddison et al. 2007; Paradis 2008). By applying existing models of character evolution (Pagel 1994; Lewis 2001; Mk2, Maddison et al. 2007, BiSSE) to simulated trees, we show that commonly used methods frequently incorrectly reject Dollo's law, but that more appropriate model comparisons do not. We also reanalyze data from two empirical studies that rejected irreversibility, and we discuss how extensions of phylogenetic methods and incorporation of additional data may improve tests of directionality in character evolution and ancestral state reconstructions.