Anthony D. Long

A Bayesian framework for the analysis of microarray expression data: regularized t -test and statistical inferences of gene changes

MOTIVATION DNA microarrays are now capable of providing genome-wide patterns of gene expression across many different conditions. The first level of analysis of these patterns requires determining whether observed differences in expression are significant or not. Current methods are unsatisfactory due to the lack of a systematic framework that can accommodate noise, variability, and low replication often typical of microarray data. RESULTS We develop a Bayesian probabilistic framework for microarray data analysis. At the simplest level, we model log-expression values by independent normal distributions, parameterized by corresponding means and variances with hierarchical prior distributions. We derive point estimates for both parameters and hyperparameters, and regularized expressions for the variance of each gene by combining the empirical variance with a local background variance associated with neighboring genes. An additional hyperparameter, inversely related to the number of empirical observations, determines the strength of the background variance. Simulations show that these point estimates, combined with a t -test, provide a systematic inference approach that compares favorably with simple t -test or fold methods, and partly compensate for the lack of replication.

Patterns of DNA sequence polymorphism along chromosome 1 of maize (Zea mays ssp. mays L.)

We measured sequence diversity in 21 loci distributed along chromosome 1 of maize (Zea mays ssp. mays L.). For each locus, we sequenced a common sample of 25 individuals representing 16 exotic landraces and nine U.S. inbred lines. The data indicated that maize has an average of one single nucleotide polymorphism (SNP) every 104 bp between two randomly sampled sequences, a level of diversity higher than that of either humans or Drosophila melanogaster. A comparison of genetic diversity between the landrace and inbred samples showed that inbreds retained 77% of the level of diversity of landraces, on average. In addition, Tajimas D values suggest that the frequency distribution of polymorphisms in inbreds was skewed toward fewer rare variants. Tests for selection were applied to all loci, and deviations from neutrality were detected in three loci. Sequence diversity was heterogeneous among loci, but there was no pattern of diversity along the genetic map of chromosome 1. Nonetheless, diversity was correlated (r = 0.65) with sequence-based estimates of the recombination rate. Recombination in our sample was sufficient to break down linkage disequilibrium among SNPs. Intragenic linkage disequilibrium declines within 100–200 bp on average, suggesting that genome-wide surveys for association analyses require SNPs every 100–200 bp.

Global gene expression profiling in Escherichia coli K12. The effects of integration host factor.

We have used nylon membranes spotted in duplicate with full-length polymerase chain reaction-generated products of each of the 4,290 predicted Escherichia coli K12 open reading frames (ORFs) to measure the gene expression profiles in otherwise isogenic integration host factor IHF+ and IHF−strains. Our results demonstrate that random hexamer rather than 3′ ORF-specific priming of cDNA probe synthesis is required for accurate measurement of gene expression levels in bacteria. This is explained by the fact that the currently available set of 4,290 unique 3′ ORF-specific primers do not hybridize to each ORF with equal efficiency and by the fact that widely differing degradation rates (steady-state levels) are observed for the 25-base pair region of each message complementary to each ORF-specific primer. To evaluate the DNA microarray data reported here, we used a linear analysis of variance (ANOVA) model appropriate for our experimental design. These statistical methods allowed us to identify and appropriately correct for experimental variables that affect the reproducibility and accuracy of DNA microarray measurements and allowed us to determine the statistical significance of gene expression differences between our IHF+ and IHF− strains. Our results demonstrate that small differences in gene expression levels can be accurately measured and that the significance of differential gene expression measurements cannot be assessed simply by the magnitude of the fold difference. Our statistical criteria, supported by excellent agreement between previously determined effects of IHF on gene expression and the results reported here, have allowed us to identify new genes regulated by IHF with a high degree of confidence.

The Molecular Diversity of Adaptive Convergence

Natural Selection Caught in the Act Understanding how new functions evolve has been of long-standing interest. However, the number of mutations needed to evolve a key innovation is rarely known, or whether other sets of mutations would also suffice, whether the intermediate steps are driven by natural selection, or how contingent the outcome is on steps along the way. Meyer et al. (p. 428; see the Perspective by Thompson) answer these questions for a case in which phage lambda evolved the ability to infect its host Escherichia coli through a novel receptor. This shift required four mutations, which accumulated under natural selection in concert with coevolution of the host. However, when Tenaillon et al. (p. 457) exposed 115 lines of E. coli to high temperature and sequenced them, adaptation occurred through many different genetic paths, showing parallelism at the level of genes and interacting protein complexes, but only rarely at the nucleotide level. Thus, epistasis—nonadditive genetic interaction—is likely to play an important part in the process of adaptation to this environment. Replicate Escherichia coli lines show multiple convergent adaptations via different mutations in response to high temperature. To estimate the number and diversity of beneficial mutations, we experimentally evolved 115 populations of Escherichia coli to 42.2°C for 2000 generations and sequenced one genome from each population. We identified 1331 total mutations, affecting more than 600 different sites. Few mutations were shared among replicates, but a strong pattern of convergence emerged at the level of genes, operons, and functional complexes. Our experiment uncovered a set of primary functional targets of high temperature, but we estimate that many other beneficial mutations could contribute to similar adaptive outcomes. We inferred the pervasive presence of epistasis among beneficial mutations, which shaped adaptive trajectories into at least two distinct pathways involving mutations either in the RNA polymerase complex or the termination factor rho.

Genome-wide analysis of a long-term evolution experiment with Drosophila

Experimental evolution systems allow the genomic study of adaptation, and so far this has been done primarily in asexual systems with small genomes, such as bacteria and yeast. Here we present whole-genome resequencing data from Drosophila melanogaster populations that have experienced over 600 generations of laboratory selection for accelerated development. Flies in these selected populations develop from egg to adult ∼20% faster than flies of ancestral control populations, and have evolved a number of other correlated phenotypes. On the basis of 688,520 intermediate-frequency, high-quality single nucleotide polymorphisms, we identify several dozen genomic regions that show strong allele frequency differentiation between a pooled sample of five replicate populations selected for accelerated development and pooled controls. On the basis of resequencing data from a single replicate population with accelerated development, as well as single nucleotide polymorphism data from individual flies from each replicate population, we infer little allele frequency differentiation between replicate populations within a selection treatment. Signatures of selection are qualitatively different than what has been observed in asexual species; in our sexual populations, adaptation is not associated with ‘classic’ sweeps whereby newly arising, unconditionally advantageous mutations become fixed. More parsimonious explanations include ‘incomplete’ sweep models, in which mutations have not had enough time to fix, and ‘soft’ sweep models, in which selection acts on pre-existing, common genetic variants. We conclude that, at least for life history characters such as development time, unconditionally advantageous alleles rarely arise, are associated with small net fitness gains or cannot fix because selection coefficients change over time.

The Lowdown on Linkage Disequilibrium

Flowering time varies among Arabidopsis accessions. Some of the genes that contribute to this polygenic trait have been localized using quantitative trait loci (QTL) mapping, eventually leading to the identification of genetic variants that contribute to observed differences in flowering time ([El-

Contribution of Distal-less to quantitative variation in butterfly eyespots.

The colour patterns decorating butterfly wings provide ideal material to study the reciprocal interactions between evolution and development. They are visually compelling products of selection, often with a clear adaptive value, and are amenable to a detailed developmental characterization. Research on wing-pattern evolution and development has focused on the eyespots of the tropical butterfly Bicyclus anynana. There is quantitative variation for several features of eyespot morphology but the actual genes contributing to such variation are unknown. On the other hand, studies of gene expression patterns in wing primordia have implicated different developmental pathways in eyespot formation. To link these two sets of information we need to identify which genes within the implicated pathways contribute to the quantitative variation accessible to natural selection. Here we begin to bridge this gap by demonstrating linkage between DNA polymorphisms in the candidate gene Distal-less (Dll) and eyespot size in B. anynana.

Diversification of complex butterfly wing patterns by repeated regulatory evolution of a Wnt ligand

Although animals display a rich variety of shapes and patterns, the genetic changes that explain how complex forms arise are still unclear. Here we take advantage of the extensive diversity of Heliconius butterflies to identify a gene that causes adaptive variation of black wing patterns within and between species. Linkage mapping in two species groups, gene-expression analysis in seven species, and pharmacological treatments all indicate that cis-regulatory evolution of the WntA ligand underpins discrete changes in color pattern features across the Heliconius genus. These results illustrate how the direct modulation of morphogen sources can generate a wide array of unique morphologies, thus providing a link between natural genetic variation, pattern formation, and adaptation.

Experimental evolution reveals natural selection on standing genetic variation

Evolution depends on genetic variation generated by mutation or recombination from standing genetic variation. In sexual organisms, little is known about the molecular population genetics of adaptation and reverse evolution. We carry out 50 generations of experimental reverse evolution in populations of Drosophila melanogaster, previously differentiated by forward evolution, and follow changes in the frequency of SNPs in both arms of the third chromosome. We characterize the effects of sampling finite population sizes and natural selection at the genotype level. We demonstrate that selection has occurred at several loci and further that there is no general loss or gain of allele diversity. We also observe that despite the complete convergence to ancestral levels of adaptation, allele frequencies only show partial return.

Genetic dissection of a model complex trait using the Drosophila Synthetic Population Resource

Genetic dissection of complex, polygenic trait variation is a key goal of medical and evolutionary genetics. Attempts to identify genetic variants underlying complex traits have been plagued by low mapping resolution in traditional linkage studies, and an inability to identify variants that cumulatively explain the bulk of standing genetic variation in genome-wide association studies (GWAS). Thus, much of the heritability remains unexplained for most complex traits. Here we describe a novel, freely available resource for the Drosophila community consisting of two sets of recombinant inbred lines (RILs), each derived from an advanced generation cross between a different set of eight highly inbred, completely resequenced founders. The Drosophila Synthetic Population Resource (DSPR) has been designed to combine the high mapping resolution offered by multiple generations of recombination, with the high statistical power afforded by a linkage-based design. Here, we detail the properties of the mapping panel of >1600 genotyped RILs, and provide an empirical demonstration of the utility of the approach by genetically dissecting alcohol dehydrogenase (ADH) enzyme activity. We confirm that a large fraction of the variation in this classic quantitative trait is due to allelic variation at the Adh locus, and additionally identify several previously unknown modest-effect trans-acting QTL (quantitative trait loci). Using a unique property of multiparental linkage mapping designs, for each QTL we highlight a relatively small set of candidate causative variants for follow-up work. The DSPR represents an important step toward the ultimate goal of a complete understanding of the genetics of complex traits in the Drosophila model system.