The Statistics of Bulk Segregant Analysis Using Next Generation Sequencing
[['Bulk segregant analysis ( BSA; [1] ) is a QTL mapping technique for identifying genomic regions containing genetic loci affecting a trait of interest .', 'Starting with a segregating population from a genetic cross , individuals are assayed for the focal trait and two pools ( bulks ) of segregants are created by selecting individuals from the tails of the phenotypic distribution ( other sampling designs can also be used as discussed below ) .', 'Genotype frequencies are estimated for the two bulks , either via genotyping of individuals or via the creation of pooled DNA samples from which allele frequencies are estimated .', 'Allele frequencies should be approximately equal between the two bulks in genomic regions without loci affecting the trait .', 'Regions of the genome containing causal loci should exhibit allele frequency differences between bulks .', 'BSA is most effective with high marker density and accurate allele frequency estimation within bulks [2] .', 'The former was effectively addressed with the application of microarray based genotyping to BSA [3]–[8] .', 'More recently , investigators have begun to use massively parallel sequencing methods to estimate allele frequencies for BSA studies [9]–[11] , which has a number of advantages .', 'For organisms with moderately sized genomes , next generation sequencing can provide essentially single base-pair resolution .', 'In such cases rather than simply observing markers in linkage with causal loci the BSA-sequencing approach should allow one to observe allelic biases at the causal loci themselves .', 'For larger genomes where high coverage of the entire genome is less practical , BSA-sequencing still has many potential advantages .', 'For example , it does not require the design of new genotyping arrays for new crosses and may provide greater resolution than array based genotyping .', 'Furthermore , sequencing data yields counts of alleles at polymorphic loci and thus provides a simple and intuitive way of estimating allele frequencies .', 'In bulk segregant studies based on high-throughput sequencing there are two sources of variation that affect allele frequency estimates .', 'The first is variation due to the sampling of segregants that constitute the bulks themselves .', 'This source of variation can be minimized by increasing both the size of the segregant population and the size of the bulk samples .', 'The second source of variation is a consequence of the measurement technique used to estimate allele frequencies in the bulks .', 'In the case of sequencing of pooled DNA samples , the sources of variation of this second type include , but are not limited to , library preparation , sequencing chemistry , sequencing coverage , post-sequencing alignment of reads , and base/allele calling algorithms .', 'Here again , some of these sources of variation can be minimized by standardization of experimental protocols and analysis pipelines .', 'However some of these sources of variation , particularly stochasticity in sequencing coverage , are an inherent property of short-read sequencing methods .', 'In this paper , we develop explicit statistical models to describe the sources of variation that should be considered in the analysis of BSA-sequencing data .', 'We first develop test statistics based on the classic -statistic accounting for the two phase sampling inherent to BSA .', 'We then propose an analysis pipeline for whole-genome studies and present a proof-of-concept example with data from yeast .', 'A combination of simulation and empirical application demonstrate the utility of this analytical framework .'], ['Based on the arguments developed above , we propose the following analytical pipeline for the analysis of BSA-sequencing data sets .', 'We assume that sequencing reads have been aligned to a reference genome where physical distances between polymorphic sites and ( approximate ) rates of recombination are known .', 'We assume that all sites are biallelic .', 'Following alignment of reads to a reference genome , per site counts of each allele are generated from the reads .', 'Our recommended analysis pipeline for estimating QTLs is as follows: We used simulations to conduct a simple power analysis of our proposed methodology .', 'In this analysis we used the mean at a causal site as measure of power for given values of , , , window size ( ) , SNP density , and for different magnitudes of QTL effect on phenotype .', 'Figure 2 summarizes results for two different values of , corresponding to large ( ) and very large ( ) F populations .', 'We find that increasing coverage , , is advantageous until , but has minimal effect beyond that .', 'A somewhat counterintuitive result is that larger bulk size , , is generally beneficial as long as sequencing coverage is modest to high .', 'This is despite the fact that larger bulks imply weaker selection for a given ( and hence a smaller allele frequency divergence among bulks ) .', 'Based on these findings we recommend bulks consisting of at least 10% and as perhaps as high as 20% of the F segregant population in order to maximize power to detect QTLs .', 'To demonstrate the correspondence between theory and data we here draw on a BSA-sequencing data set generated to identify loci that contribute to variation in colony morphology in the budding yeast Saccharomyces cerevisiae [27] .', 'A full description and analysis of these data will appear elsewhere ( Granek et al . , in prep ) .', 'Here , these data serve to illustrate the utility of both our theoretical framework and the associated robust estimators for data analysis .', 'The yeast data consist of a low and high bulk , each composed of 288 homozygous diploid segregants drawn from an F population of size generated by sporulating a naturally heterozygous diploid strain [28] .', 'The low bulk consists of segregants with simple colony morphology , while the high bulk consists of segregants with complex colony morphology ( see [27] for a description of morphology scoring ) .', 'Creation of DNA pools , sequencing , and mapping of reads is described in the Methods section .', 'Because each segregant is homozygous , the effective number of alleles sampled for each bulk is instead of 2 .', 'In total 44 , 066 polymorphic sites were analyzed with a mean interval between sites of approximately 280 bp .', 'Below we refer to the two sequencing runs for the low bulks as and , and those for the high bulks as and .', 'The coverage per SNP ( ) for each sequencing run was as follows: , , , and .', 'For each of the analyses below , we used a smoothing window width of ( 30 cM ) , and took the average coverage of each bulk being compared as the estimate of coverage , .', 'Because there are two sequencing runs per DNA pool , variation in allele frequency estimates between sequencing runs from the same segregant bulk should be exclusively due to stochastic aspects of the sequencing reaction and primary bioinformatics analyses ( base calling , read alignment ) .', 'The structure of this data set is thus useful for dissecting the impact of sequencing variation on estimates of and , and the subsequent impact of this variability on the inference of QTL regions and peaks .', 'We use these data to explore both the null model ( no QTL; by analyzing the low-vs-low and high-vs-high comparisons ) as well as the case where QTLs are expected ( comparing low-vs-high bulks ) .', 'In the null case , the differences in allele frequencies are subject to only one source of variation because the bulks are fixed but sequencing is variable .', 'The non-null analyses are individually affected by both sources of variation ( bulking and sequencing ) , but when comparing the results from comparable analyses ( e . g . comparing QTL peak locations between the -vs- and -vs- analyses ) , the differences are again simply a function of sequencing variation .'], ['Our simulations suggest that for the experimental design considered here using bulk sizes as large as 15–20% of the phenotyped segregant population increases power to detect causal QTLs despite the fact that this means relatively smaller allele frequency differences between bulks .', 'This is due to tradeoffs between bulk-size , selection intensity , and the variance of allele frequencies under the hierarchical sampling .', 'Consider , for example , a single locus with alleles and , where the effect of is additive and the two homozygotes differ by units on average .', 'Assuming no segregation distortion , and an population generated from inbred lines , the change in the allele frequency of in the high bulk after truncation selection is approximately [30] , [31] where is the intensity of selection , and is the ‘standardized effect of the locus’ ( these quantities can be related to the selection coefficient , , by ) .', 'Given truncation selection on a normal distribution , the intensity of selection is given by where is the proportion of selected individuals and is the probability density function at the truncation point [31] .', 'Since the intensity of selection increases at a rate much less than ( e . g . see [31] , Fig . 11 . 3 ) , an -fold decrease in results in a much less than -fold change in the intensity of selection .', 'For example , let and consider truncation on the upper 20% , 10% , and 1% , of the phenotypic distribution .', 'The increase in the frequency of in the high bulk given these truncation points is approximately 3 . 5% , 4 . 4% , and 6 . 7% respectively ( translating to allele frequency differences of 7% , 8 . 8% , and 13 . 4% in the two-bulk case ) .', 'On the other hand , the variance of the realized frequencies of the alleles in each bulk is inversely proportional to bulk size ( ) .', 'Thus , a twenty-fold decrease in bulk size translates to less than a two-fold increase in allele frequency divergence , but a twenty-fold increase in the variance of allele frequencies .', 'As long as average coverage , , is moderate to large , the benefit of increasing offsets the relatively smaller penalty resulting from a decrease in selection intensity .', 'However , there is little benefit to increasing sequencing coverage beyond the size of the bulks .', 'Sequencing can introduce complications such as biases toward particular nucleotide calls; however in general this should effect both segregant bulks in the same direction .', 'Due to the averaging affect of , unless such biased sites are common over very large map distances they are unlikely to have substantial affects on results derived under our proposed framework .', 'Similarly , a low percentage of mismapped reads or miscalled SNP calling are unlikely to be problematic for our framework , again because of the averaging affect of .', 'However caution should be exercised in genomic regions that are particularly problematic in this regard , such as repeat rich regions .', 'In this paper we have focused on QTL mapping with an F experimental design , but clearly our framework can be extended to other designs .', 'Common alternatives include mapping populations produced by imposing one or more generations of inbreeding on an F , such as Recombinant Inbred Lines ( RILs ) .', 'The increased homozygosity of such populations should also be taken into consideration , as it increases the expected change in allele frequency due to selection but it also decreases the number of independent chromosomes that are sampled for a given number of selected individuals .', 'Chromosomes in such RILs experience as much as twice the number of crossovers as do F populations so the physical size of the smoothing window should be reduced to take this reduced linkage disequilibrium into account .', 'Even greater reductions of linkage disequilibrium can be accomplished by an alternative design that imposes additional generations of random mating , rather than inbreeding , on an F , resulting in more precise localization of QTLs .', 'Additional generations of outcrossing ( beyond the F ) will likely magnify deviations of the null allele frequency from 0 . 5 owing to segregation distortion and/or inadvertent selection .', 'This can be accommodated by application of formulas in Text S1 with estimated from all sites within a genomic window .', 'Other experimental designs , such as backcrosses , will not have allele frequencies of 0 . 5 .', 'For these situations the null expected distributions of and can be approximated using the equations presented in Text S1 , although in this case it will be necessary to know the parental origin of the SNP alleles .', 'Similarly , since can be generalized to an arbitrary number of classes [12] , one-tailed scenarios ( e . g . [9] ) involving comparison to either a theoeretical population or a random sampling of segregants can be addressed in this framework .'], ['To create the bulked DNA pools each segregant was grown overnight in liquid medium to saturation ( cells/ml ) and equal volumes of each culture were mixed to form cell bulks .', 'Genomic DNA was isolated from the cell bulks and single Illumina DNA sequencing libraries were prepared from each bulk , using standard protocols as described in [28] .', 'Each bulk DNA pool was sequenced twice using 50 bp reads on an Illumina GAII sequencing instrument .', 'Approximately 15 M reads were generated in each sequencing run .', 'Reads were aligned to the yeast reference genome ( obtained from the Saccharomyces Genome Database , January 2010 ) using the program BWA [32] and polymorphic sites were called using SAMtools [33] .', 'For each sequencing run , SAMtools was used to create a pileup file giving the alleles at each polymorphic site , from which allele counts were derived using scripts written in Python .']]
['Introduction', 'Results', 'Discussion', 'Methods']
['We describe a statistical framework for QTL mapping using bulk segregant analysis ( BSA ) based on high throughput , short-read sequencing .', 'Our proposed approach is based on a smoothed version of the standard statistic , and takes into account variation in allele frequency estimates due to sampling of segregants to form bulks as well as variation introduced during the sequencing of bulks .', 'Using simulation , we explore the impact of key experimental variables such as bulk size and sequencing coverage on the ability to detect QTLs .', 'Counterintuitively , we find that relatively large bulks maximize the power to detect QTLs even though this implies weaker selection and less extreme allele frequency differences .', 'Our simulation studies suggest that with large bulks and sufficient sequencing depth , the methods we propose can be used to detect even weak effect QTLs and we demonstrate the utility of this framework by application to a BSA experiment in the budding yeast Saccharomyces cerevisiae .']
['Quantitative or complex phenotypes are traits that are under the control of multiple genes and environmental factors .', 'Identifying the parts of the genome that contribute to variation in complex traits ( Quantitative Trait Loci or QTLs ) , and ultimately the genes and alleles that are mechanistically responsible for trait variation , is a primary challenge in animal and plant breeding , population studies of human health and disease , and evolutionary genetics .', 'In this study we describe an analytical framework that allows investigators to marry a QTL mapping approach called “bulk segregant analysis” ( BSA ) with high-throughput genome sequencing methodologies in order to map traits quickly , efficiently , and in a relatively inexpensive manner .', 'This framework provides a statistical basis for analyzing BSA experiments that use next-generation sequencing and will help to accelerate the identification of QTLs in both model and non-model organisms .']
['genome sequencing', 'genomics', 'mathematics', 'statistics', 'genetics', 'statistical methods', 'population genetics', 'biology', 'evolutionary biology', 'evolutionary genetics', 'genetics and genomics']