Genotype by random environmental interactions gives an advantage to non-favored minor alleles.

Fixation probability, the probability that the frequency of a newly arising mutation in a population will eventually reach unity, is a fundamental quantity in evolutionary genetics. Here we use a number of models (several versions of the Moran model and the haploid Wright-Fisher model) to examine fixation probabilities for a constant size population where the fitness is a random function of both allelic state and spatial position, despite neither allele being favored on average. The concept of fitness varying with respect to both genotype and environment is important in models of cancer initiation and progression, bacterial dynamics, and drug resistance. Under our model spatial heterogeneity redefines the notion of neutrality for a newly arising mutation, as such mutations fix at a higher rate than that predicted under neutrality. The increased fixation probability appears to be due to rare alleles having an advantage. The magnitude of this effect can be large, and is an increasing function of the spatial variance and skew in fitness. The effect is largest when the fitness values of the mutants and wild types are anti-correlated across environments. We discuss results for both a spatial ring geometry of cells (such as that of a colonic crypt), a 2D lattice and a mass-action (complete graph) arrangement.

Estimation of population heterozygosity and library construction-induced mutation rate from expressed sequence tag collections.

Unigene alignments obtained from cDNA libraries made using multiple individuals are not currently used to estimate population heterozygosity, as they are known to harbor mutations created during library construction. We describe an estimator of population heterozygosity that utilizes only SNPs unlikely to be library construction artifacts.

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, Tajima's 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.

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.

Improved statistical inference from DNA microarray data using analysis of variance and a Bayesian statistical framework. Analysis of global gene expression in Escherichia coli K12.

We describe statistical methods based on the t test that can be conveniently used on high density array data to test for statistically significant differences between treatments. These t tests employ either the observed variance among replicates within treatments or a Bayesian estimate of the variance among replicates within treatments based on a prior estimate obtained from a local estimate of the standard deviation. The Bayesian prior allows statistical inference to be made from microarray data even when experiments are only replicated at nominal levels. We apply these new statistical tests to a data set that examined differential gene expression patterns in IHF(+) and IHF(-) Escherichia coli cells (Arfin, S. M., Long, A. D., Ito, E. T., Tolleri, L., Riehle, M. M., Paegle, E. S., and Hatfield, G. W. (2000) J. Biol. Chem. 275, 29672-29684). These analyses identify a more biologically reasonable set of candidate genes than those identified using statistical tests not incorporating a Bayesian prior. We also show that statistical tests based on analysis of variance and a Bayesian prior identify genes that are up- or down-regulated following an experimental manipulation more reliably than approaches based only on a t test or fold change. All the described tests are implemented in a simple-to-use web interface called Cyber-T that is located on the University of California at Irvine genomics web site.

Genetic architecture of thermal adaptation in Escherichia coli.

Elucidating the genetic basis of adaptation on a genomewide scale has evaded biologists, but complete genome sequences and DNA high-density array technology make genomewide surveys more tractable. Six lines of Escherichia coli adapted for 2,000 generations to a stressful high temperature of 41.5 degrees C were examined on a genomewide scale for duplication/deletion events by using DNA high-density arrays. A total of five duplication and deletion events were detected. These five events occurred in three of the six lines, whereas the remaining three lines contained no detectable events. Three of the duplications were at 2.85 Mb of the E. coli chromosome, providing evidence for the replicability of the adaptation to high temperature. Four candidate genes previously shown to play roles in stress and starvation survival were identified in the region of common duplication. Expression of the two candidate genes examined is elevated over expression levels in the ancestral lines or the lines without the duplication. In the two cases where the duplication at 2.85 Mb has been further characterized, the timing of the genome reorganization is coincident with significant increases in relative fitness. In both of these cases, the model for the origin of the duplication is a complex recombination event involving insertion sequences and repeat sequences. These results provide additional evidence for the idea that gene duplication plays an integral role in adaptation, specifically as a means for gene amplification.

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.

Both naturally occurring insertions of transposable elements and intermediate frequency polymorphisms at the achaete-scute complex are associated with variation in bristle number in Drosophila melanogaster.

A restriction enzyme survey of a 110-kb region including the achaete scute complex (ASC) examined 14 polymorphic molecular markers in a sample of 56 naturally occurring chromosomes. Large insertions as a class were associated with a reduction in both sternopleural and abdominal bristle number, supporting deleterious mutation-selection equilibrium models for the maintenance of quantitative genetic variation. Two polymorphic sites were independently associated with variation in bristle number measured in two genetic backgrounds as assessed by a permutation test. A 6-bp deletion near sc alpha is associated with sternopleural bristle number variation in both sexes and a 3.4-kb insertion between sc beta and sc gamma is associated with abdominal bristle number variation in females. Under an additive genetic model, the small deletion polymorphism near sc alpha accounts for 25% of the total X chromosome genetic variation in sternopleural bristle number, and the 3.4 kb insertion accounts for 22% of the total X chromosome variation in female abdominal bristle number. The observation of common polymorphisms associated with variation in bristle number is more parsimoniously explained by models that incorporate balancing selection or assume variants affecting bristle number are neutral, than mutation-selection equilibrium models.

The power of association studies to detect the contribution of candidate genetic loci to variation in complex traits.

The statistical power of five association study test statistics (two haplotype-based tests, two marker-based tests, and the Transmission Disequilibrium Test-Q5) to detect single nucleotide polymorphism (SNP)/phenotype associations in a linkage-disequilibrium-based candidate gene scan employing a number of SNPs is examined. Power is estimated as a function of realistic parameters expected to affect the likelihood of detecting a significant association: the number of SNPs examined, the scaled recombination size of the region examined, the proportion of variance in the trait attributable to a hidden causative polymorphism within the region, and the number of individuals or families examined. For the different combinations of parameter values, power is estimated from a large number of realizations of a simulated coalescent describing a single random mating population with mutation, random genetic drift, and recombination. This explicit population genetics model results in a distribution of DNA marker heterozygosities and linkage disequilibria that are likely to resemble those expected in actual population samples. The study concludes that (1) marker-based permutation tests are more powerful than simple haplotype-based tests, (2) there is sufficient power to detect the presence of causative polymorphisms of small effect if on the order of 500 individuals are sampled, (3) greater power is achieved by increasing the sample size than by increasing the number of polymorphisms, (4) association studies are generally more powerful than transmission disequilibrium-based tests, and (5) for the range of parameters considered association studies have a low repeatability unless sample sizes are on the order of 500 individuals. Estimates of 4Nc for a number of gene regions and human populations will be of use in determining the density of SNPs that are likely to be required for successful association studies.

Two sites in the Delta gene region contribute to naturally occurring variation in bristle number in Drosophila melanogaster.

A restriction enzyme survey of a 57-kb region including the gene Delta uncovered 53 polymorphic molecular markers in a sample of 55 naturally occurring chromosomes. A permutation test, which assesses the significance of the molecular marker with the largest effect on bristle variation in four genetic backgrounds relative to permuted data-sets, found two sites that were independently associated with variation in bristle number. A common site in the second intron of Delta affected only sternopleural bristle number, and another common site in the fifth intron affected only abdominal bristle number in females. Under an additive genetic model, the polymorphism in the second intron may account for 12% of the total genetic variation in sternopleural bristle number due to third chromosomes, and the site in the fifth intron may account for 6% of the total variation in female abdominal bristle number due to the third chromosomes. These results suggest the following: (1) models that incorporate balancing selection are more consistent with observations than deleterious mutation-selection equilibrium models, (2) mapped quantitative trait loci of large effect may not represent a single variable site at a genetic locus, and (3) linkage disequilibrium can be used as a tool for understanding the molecular basis of quantitative variation.

Genetic interactions between naturally occurring alleles at quantitative trait loci and mutant alleles at candidate loci affecting bristle number in Drosophila melanogaster.

Previously, we mapped quantitative trait loci (QTL) affecting response to short-term selection for abdominal bristle number to seven suggestive regions that contain loci involved in bristle development and/or that have adult bristle number mutant phenotypes, and are thus candidates for bristle number QTL in natural populations. To test the hypothesis that the factors contributing to selection response genetically interact with these candidate loci, high and low chromosomes from selection lines were crossed to chromosomes containing wild-type or mutant alleles at the candidate loci, and the numbers of bristles were recorded in trans heterozygotes. Quantitative failure to complement, detected as a significant selection line*cross effect by analysis of variance, can be interpreted as evidence for allelism or epistasis between the factors on selected chromosomes and the candidate loci. Mutations at some candidate loci (bb, emc, h, Dl, Hairless) showed strong interactions with selected chromosomes, whereas others interacted weakly (ASC, abd, Scr) or not at all (N, mab, E(spl)). These results support the hypothesis that some candidate loci, initially identified through mutations of large effect on bristle number, either harbor or are close members in the same genetic pathway as variants that contribute to standing variation in bristle number.

Molecules versus morphology: the detection of selection acting on morphological characters along a cline in Drosophila melanogaster.

This work examines the nature of north-south clinal variation in morphological characters in Drosophila melanogaster. Isofemale lines were established from flies collected along a transect extending from Winnipeg, Manitoba (Canada) to Tampa Bay, Florida (U.S.A.). Offspring from different lines within each location were then cultured under standardized conditions and used to examine phenotypic variation in seven morphological characters along the cline. In addition, allozyme variation at seven polymorphic loci was examined for the same set of clinal populations. Scutellum length and wing length show the strongest clinal trends. Clinal variation is nonmonotonic, with larger flies in the middle latitudes and smaller flies in the north and south. This result contrasts with other studies which have shown monotonic clines. Patterns of population subdivision were different for the different characters. This implies that there are different selective forces acting on the different morphological characters. Based on a comparison of morphological and molecular population subdivision for adjacent populations it is inferred that natural selection is operating to maintain a high level of population subdivision for wing width and the first principal component between one of the sets of populations. A combined approach using molecules and morphology may provide an alternative to retrospective selection analysis for detecting selection in nature.

High resolution mapping of genetic factors affecting abdominal bristle number in Drosophila melanogaster.

Factors responsible for selection response for abdominal bristle number and correlated responses in sternopleural bristle number were mapped to the X and third chromosome of Drosophila melanogaster. Lines divergent for high and low abdominal bristle number were created by 25 generations of artificial selection from a large base population, with an intensity of 25 individuals of each sex selected from 100 individuals of each sex scored per generation. Isogenic chromosome substitution lines in which the high (H) X or third chromosome were placed in an isogenic low (L) background were derived from the selection lines and from the 93 recombinant isogenic (RI) HL X and 67 RI chromosome 3 lines constructed from them. Highly polymorphic neutral roo transposable elements were hybridized in situ to the polytene chromosomes of the RI lines to create a set of cytogenetic markers. These techniques yielded a dense map with an average spacing of 4 cM between informative markers. Factors affecting bristle number, and relative viability of the chromosome 3 RI lines, were mapped using a multiple regression interval mapping approach, conditioning on all markers > or = 10 cM from the tested interval. Two factors with large effects on abdominal bristle number were mapped on the X chromosome and five factors on the third chromosome. One factor with a large effect on sternopleural bristle number was mapped to the X and two were mapped to the third chromosome; all factors with sternopleural effects corresponded to those with effects on abdominal bristle number. Two of the chromosome 3 factors with large effects on abdominal bristle number were also associated with reduced viability. Significant sex-specific effects and epistatic interactions between mapped factors of the same order of magnitude as the additive effects were observed. All factors mapped to the approximate positions of likely candidate loci (ASC, bb, emc, h, mab, Dl and E(spl), previously characterized by mutations with large effects on bristle number.

Naturally occurring variation in bristle number and DNA polymorphisms at the scabrous locus of Drosophila melanogaster.

The association between quantitative genetic variation in bristle number and molecular variation at a candidate neurogenic locus, scabrous, was examined in Drosophila melanogaster. Approximately 32 percent of the genetic variation in abdominal bristle number (21 percent for sternopleural bristle number) among 47 second chromosomes from a natural population was correlated with DNA sequence polymorphisms at this locus. Several polymorphic sites associated with large phenotypic effects occurred at intermediate frequency. Quantitative genetic variation in natural populations caused by alleles that have large effects at a few loci and that segregate at intermediate frequencies conflicts with the classical infinitesimal model of the genetic basis of quantitative variation.

Single-strand conformation polymorphism analysis coupled with stratified DNA sequencing reveals reduced sequence variation in the su(s) and su(wa) regions of the Drosophila melanogaster X chromosome.

Single-strand conformation polymorphism (SSCP) analysis followed by DNA sequencing of stratified sub-samples was used to survey DNA polymorphism in the su(s) and su(wa) regions in a natural population of Drosophila melanogaster. su(s) and su(wa) are located near the telomere of the X chromosome, where the rate of crossing over per kilobase of DNA monotonically decreases toward the tip. SSCP was assessed in 12 noncoding segments amplified from the su(s) region (3213 bp) and in 8 noncoding segments amplified from the su(wa) region (1955 bp). Sets of segments were multiplexed in a single electrophoretic lane to increase the number of base pairs assayed per lane. Eight segments were monomorphic, and the other 12 segments exhibited two to four SSCP classes. Only four within-SSCP-class DNA sequence differences (a single nucleotide substitution) were observed among 24,360 bp compared within classes. The between-SSCP-class DNA sequence comparisons revealed 27 substitutions and 9 insertion/deletion polymorphisms. The average numbers of substitutional differences per site were 0.0010 and 0.0021 for su(s) and su(wa), respectively. These values are intermediate between those reported for the more distal y-ASC region (0.0004) and the more proximal Pgd locus (0.0024). This observation is consistent with the prediction of the hitchhiking-effect model-i.e., a monotonic increase in polymorphism as a function of crossing over per kilobase.

A correction for allele frequency estimates derived from isofemale lines.

Isofemale lines are commonly used in Drosophila and other genera for the purpose of assaying genetic variation. Isofemale lines can be kept in the laboratory for many generations before genetic work is carried out, and permit the confirmation of newly discovered alleles. A problem not realized by many workers is that the commonly used estimate of allele frequency from these lines is biased. This estimation bias occurs at all times after the first laboratory generation, regardless of whether single individuals or pooled samples are used in each well of an electrophoretic gel. This bias can potentially affect the estimation of population genetic parameters, and in the case of rare allele analysis it can cause gross overestimates of gene flow. This paper provides a correction for allele frequency estimates derived from isofemale lines for any time after the lines are established in the laboratory. When pooled samples are used, this estimator performs better than the standard estimator at all times after the first generation. The estimator is also insensitive to multiple inseminations. After the lines have drifted one Ne generations, multiple inseminations actually make the new estimator perform better than it does in singly inseminated females. Simulations show that estimates made using either estimator after the lines have drifted to fixation have a much greater error associated with their use than do those estimates made earlier in time using the correction. In general it is better to use corrected estimates of gene frequency soon after lines are established than to use uncorrected estimates made after the first laboratory generation.

Geographic variation in Drosophila: From molecules to morphology and back.

The examination of spatial variation can act as a substitute for temporal variation in population studies. Of particular use in the effort to understand the selective forces that govern spatial variation are the sibling species Drosophila melanogaster and D. simulans. Recent work at the level of both molecules and morphology has uncovered a great deal of spatial variation within and between these two species. Here we summarize these data, with reference to what they tell us about the history and nature of selection operating in these species.