Genetics: Published Articles Ahead of Print, published on January 31, 2012 as 10.1534/genetics.111.137075 1 A test for selection employing quantitative trait locus and mutation accumulation data Daniel P. Rice*,§§ and Jeffrey P. Townsend*,§ *Department of Ecology and Evolutionary Biology, and §Program in Computational Biology and Bioinformatics, Yale University, New Haven, CT 06520 §§Current address: Department of Organismic and Evolutionary Biology, Harvard University, 26 Oxford St., Cambridge, MA 02138 Copyright 2012. 2 Running Head: QTL, mutation accumulation, and selection Keywords: Phenotype / Selection / Statistical Tests / QTL / Neutrality Corresponding Author: Jeffrey P. Townsend, Department of Ecology and Evolutionary Biology, Yale University, Osborne Memorial Labs 226, 165 Prospect Street, PO Box 208106, New Haven, CT 06520 Tel: (203) 432 4646 Fax: (203) 432-5176 Email: [email protected] 3 Abstract Evolutionary biologists attribute much of phenotypic diversity observed in nature to the action of natural selection. However, for many phenotypic traits, and especially quantitative phenotypic traits, it has been challenging to test for the historical action of selection. An important challenge for biologists studying quantitative traits, therefore, is to distinguish between traits that have evolved under the influence of strong selection and those that have evolved neutrally. Most existing tests for selection employ molecular data, but selection also leaves a mark on the genetic architecture underlying a trait. In particular, the distribution of quantitative trait locus (QTL) effect sizes and the distribution of mutational effects together provide information regarding the history of selection. Despite the increasing availability of QTL and mutation accumulation data, such data have not yet been effectively exploited for this purpose. We present a model of the evolution of QTL and employ it to formulate a test for historical selection. To provide a baseline for neutral evolution of the trait, we estimate the distribution of mutational effects from mutation accumulation experiments. We then apply a maximum likelihood-based method of inference to estimate the range of selection strengths under which such a distribution of mutations could generate the observed QTL. Our test thus represents the first integration of population genetic theory and QTL data to measure the historical influence of selection. 4 Introduction Identifying which quantitative traits have been subject to strong selection and which have evolved under neutral or nearly neutral conditions is a challenging and important task for evolutionary biologists (Boake et al., 2002). To this end, biologists are devoting increased attention to the genetic basis and evolutionary causes of quantitative variation (Barton and de Vladar, 2009, Barton and Keightley, 2002, Lai et al., 2007). On one hand, substantial progress has been made in revealing the genetic architecture of quantitative traits (Mackay, 2001, Mackay and Lyman, 2005, Brem and Kruglyak, 2005, Lai et al., 2007, Verhoeven et al., 2004, Zimmerman et al., 2000, Ashton et al., 2001, Gleason et al., 2009, Gleason et al., 2002). On the other hand, it has been difficult to connect the action of microevolutionary forces detected in studies of contemporary populations to their macroevolutionary effects (Grant and Grant, 2002). Consequently, few attempts to detect natural selection currently exploit the growing body of knowledge about the sizes and directions of quantitative trait locus (QTL) effects (for counter- examples, see Rieseberg et al., 2002, Albertson et al., 2003, and Lexer et al., 2005). Progress toward understanding the basis of quantitative genetic variation is likely to come from studying allelic variation at specific QTL (Barton and Keightley, 2002). Identifying the genetic architecture of quantitative traits begins with mapping QTL to broad genomic regions and ends with the molecular definition of quantitative trait loci alleles. This high degree of resolution has been achieved, for instance, for some QTL in Drosophila (Palsson et al., 2005, Mackay, 2001, Zimmerman et al., 2000, Palsson and Gibson, 2004). QTL mapping may be coupled with further genetic dissection (e.g. fine- 5 scale mapping, disequilibrium mapping, transgenic manipulation; Mackay, 2001) to characterize the specific loci targeted by selection. Weinig et al. (2003) demonstrated that the QTL architecture behind herbivory tolerance was one of many loci of small effect, and simultaneously elucidated locus-specific evolutionary constraints, demonstrating that linking molecular genetic tools to quantitative genetic analysis and field studies in ecologically relevant settings can clarify the role of specific loci in the evolution of quantitative traits. These QTL studies not only generate maps from genotype to phenotype, but also yield information that may be applied to the study of phenotypic evolution (Erickson et al., 2004). Behind every genetically based phenotypic difference lies an evolutionary history. Despite the evident relevance of QTL data to the study of the evolutionary process, very little theory has been developed to link data from QTL studies to population genetic parameters via the methods of molecular evolution. This lack of theoretical tools has inhibited progress in explaining the process underlying the evolution of phenotypes that are genetically dissected in empirical QTL studies. While most tests for selection depend directly on molecular data (McDonald and Kreitman, 1991, Depaulis et al., 2003, Mousset et al., 2004, Nurminsky et al., 2005, Schlenke and Begun, 2003, Schlenke and Begun, 2004, Schlenke and Begun, 2005), Orr (1998a) presented two innovative attempts to integrate QTL data and population genetic theory into tests for selection: the QTL sign test and the QTL effect size test. These tests employ a null model of the evolutionary process that produces QTL. They have been applied multiple times to empirical data (Rieseberg et al., 2002, Albertson et al., 2003, Lexer et al., 2005, Orr, 2010). However, the QTL sign test has been deemed 6 substantially flawed by its high false-positive rate (Anderson and Slatkin, 2003) and the QTL effect size test has been shown to provide very low power to detect selection (Anderson and Slatkin, 2003). Moreover, the tests neither model selection explicitly nor account for the distribution of mutational effects, both of which are important to accurately model the “filtering” action of natural selection (Orr 1998b). Accordingly, understanding the evolutionary significance of QTL observations requires evaluation of both the origin and fate of heritable variation. In particular, the evolutionary forces that result in the genetic differences we observe must be estimated (Barton and Keightley, 2002). Here we develop a test for a history of directional selection on quantitative traits and a method for estimation of the strength of that selection. Using mutation accumulation (MA) data and the QTL effect distribution derived from a cross between two divergent populations, we infer the selective history of the trait. While existing tests (Orr, 1998) only model neutral evolution and assume selection to be at work whenever data does not fit the model’s predictions under neutrality, we model selection explicitly and consider neutrality as one potential inference on a continuum. Such a flexible model is a key first step toward unraveling the complex link between molecular evolution and quantitative trait variation. Theory Overview: Our framework for inference integrates information from mutation accumulation experiment (Figure 1A-B), population genetic theory on selection (Figure 1G-J), the consequent expected outcome of selection (Figure 1K-N), and the empirically obtained QTL effect size distribution (Figure 1O-R). In our schematic example, mutation 7 accumulation is depicted as resulting in increased variance of the phenotype with no directional bias (Figure 1A), or, alternatively, as resulting in an increased variance in phenotype with a downward bias (Figure 1B). From phenotypic observations obtained along the time course of a mutation accumulation experiment (Figure 1A-B), the distribution of mutational effects on phenotype can be inferred (Figure 1C-F). Data as in Figure 1A yields an inferred distribution of mutational effects that is symmetrical around no change (Figure 1C and Figure 1D); in contrast, data as in Figure 1B yields asymmetry (Figure 1E and Figure 1F). We multiply the mutation effect distribution by the calculated probability of fixation as a function of the strength of selection corresponding to the phenotypic effect (Figure 1G-J). For a neutral phenotype, fixation probabilities are equivalent across all phenotypes (Figure 1G and Figure 1I), whereas under selection, fixation probabilities depend upon the phenotype conferred (Figure 1H and Figure 1J). The product of the mutation effect distribution and the fixation probability distribution is the probability distribution of fixed phenotypic differences resulting from substitutions at quantitative trait loci (Figure 1K-N). Sampling a number of substitutions from this distribution and summing their effects (e.g. Figure 1O-R, boxes), we compare the cumulative effects with those of the observed QTL (Figure 1O-R, bars). The accord between the sampled effects and the observed effects varies with the estimated mutation effect distribution and selective regime considered: the accord will be better when the level of