Indel candidate detection

We performed a custom split read alignment method to retrieve indel candidates from the Arabidopsis thaliana strain ICE111 from phase I of the 1001 Genomes Project [2]. The read lengths ranged from 36 to 64 bp with an average sequencing depth of 21x. All mapped-unmapped read pairs (MURs) were retrieved from the available alignments from Cao et al.[2], which allowed 4 base pair differences between read and reference, of which at most 3 could be gaps. The mapped partner may have multiple alignment positions across the whole genome. Because of many ambiguous alignments due to the high repetitivity of centromeric sequences, all MURs within centromeres were excluded. The unmapped partners of the MURs were mapped against Col-0 (TAIR8) in a 5,000 bp window downstream of the mapped partner using Gotoh’s alignment algorithm [27], allowing for long-range gaps as well as additional SNPs or few base pair-sized indels (Additional file 1). All best-scoring alignments were reported and indels with a minimum support of two reads constituted the indel candidate set to be further evaluated.

Feature selection

The split read alignment approach identified 14,155 potential indel candidates for the Arabidopsis thaliana strain ICE111. We randomly selected 219 deletion and 43 insertion candidates across all chromosomes from this set and labeled them as true or false after Sanger sequencing. Thus, we retrieved two training sets. The training corpus for deletions consisted of 172 correctly and 47 falsely labeled examples and the training corpus for insertions of 33 true and 10 false ones. These sets were used to train a SVM [26].

Pindel [22] uses the number of split-read alignments supporting an indel with identical genomic coordinates as the only evidence for an indel. In a first study, only this alignment feature was used for classification (named f1 training hereafter). The f1-based training was contrasted to the use of several alignment characteristics, 13 for insertions (f13) and 17 for deletions (f17). These features can be grouped into four main categories (Figure 1). The first considers the number of uniquely mapped reads (UMRs) and non-uniquely mapped reads (N-UMRs) overlapping the sequence space within a deletion. Since this is not determinable for insertion signatures, this feature is only available for deletions. The second group comprises the number of UMRs and N-UMRs 60 bp downstream as well as 60 bp upstream of the indel candidate to represent the coverages to the right and left where 60 bp reflects approximately the maximum read length. A ‘true’ deletion should show either zero or a low number of UMRs within the deleted region compared to the UMR-coverage up- and downstream thereof, whereas a certain number of N-UMRs might be tolerated. The third group of features examines the concordance of SNP and short indel calls detected by the two mapping passes (the short read mapping tool and our split read alignment step). Since these variations are compared to each other position-wise, short indels are considered as consecutive single position variants (SPVs). These features can be interpreted as a check if the aligned reads of the first mapping pass in the vicinity of an indel derive from the same haplotype as the split reads spanning the indel. The last category includes general attributes such as the indel length and the split read alignment support of identically-located indels.

Discriminative training

We trained a SVM [26] using a simple-to-interpret linear kernel on all three sets of features (f1, f13, f17) performing a 10-fold cross-validation for deletions and a 5-fold cross-validation for insertions and repeated each cross-validation 100 times (Additional file 2). The resulting average area under the receiver operating characteristic curves (AUC) and average specificity-sensitivity-break-even-points (Spec-Sens-BEP) (Figure 2) suggest that the f1-based classification did not notably exceed the performance of a random guess for deletions (AUC = 49.3% ± 8.8%, Spec-Sens-BEP = 49.4%±7.5%) and performs slightly better for insertions (AUC = 67.0% ± 7.7%, Spec-Sens-BEP = 60.5% ± 7.7%), whereas the use of 13 (AUC = 93.5% ± 2.6%, Spec-Sens-BEP = 91.2% ± 5.0%) and 17 features (AUC = 95.1% ± 1.3%, Spec-Sens-BEP = 89.7% ± 2.2%) reveal high concordance with the true classification.

The training of the SVM based on a linear kernel enabled us to identify the contributions of each feature to an indel prediction. Positive weights contribute to the support, and negative to the rejection of a candidate (Figure 3). Interestingly, the criteria for deletions and insertions notably differ from each other. While the strongest argument in favor for deletions is the number of SV supporting reads, it is the sequence length for insertions. Furthermore, the agreement of SPVs between the first and the second mapping pass contributes more to the acceptance of insertions, but is used as an indication against the trustworthiness of deletions. This effect might be explained by alignment errors by the first mapping pass close to deletions causing false positive SPV calls. Our classifier for insertions is trained on a dataset including 43 true insertions. Due to the limited size of this training dataset, it is to be expected that larger training datasets will further improve the prediction performance.

Indel prediction

Applying our machine learning approach with the f13/f17 feature set to indel candidates of strain ICE111 positively classified 10,256 out of 13,547 deletions in total (76%), and 373 from 608 insertions (61%), respectively. The length of deletions ranged from 2 to 4,880 bp with a mean of 334 bp and a median of 12 bp. For insertions the length ranged from 2 to 5 bp with a mean and median of 4 bp. Thus, the SVM was capable to extract information from the defined features leading to falsifications of indel candidates. ’False’ SVs can be attributed to spurious mappings dependent on the length of the split read fragments or to multiple best-scoring alignments across the reference.

Next, we compared our predictions of indels in the strain ICE111 to those identified by two versions of Pindel [22] (v0.1 and v0.24). The minimum length of deletions was set to 5 bp for all three sets, and the maximum deletion size constituted 5,000 bp due to the adjustable restriction of the alignment space. Pindel detected a total of 2,087 (v0.1) and 3,272 (v0.24) deletions larger than 5 bp. 99.8% (v0.1 and v0.24) of Pindel’s deletions were shared among all unclassified deletions of our approach. The SVM classification identified 220 (11%, v0.1) and 309 (10%, v0.24) false positive deletions among the Pindel candidates. Further, our Gotoh approach detected an additional set of 6,890 (v0.1) and 5,706 (v0.24) positively classified deletions. This can be explained by different mapping strategies. Pindel [22] in version 0.1 requires uniquely and error-free mapped reads and allows only split read alignments where the read partners are aligned within two times the average insertion size. On the contrary, our SVM approach follows a less conservative re-alignment strategy by analyzing non error-free and multiple best-scoring alignments of the same read. Moreover, we tolerated split read mappings anywhere within the alignment window, which results in a larger candidate set by allowing the detection of SVs in highly divergent regions. The subsequent classification compensates for these introduced levels of uncertainty. Indeed, Sanger sequencing revealed 14 (out of 219 validated) deletions, where the read partners showed discordant insert sizes. Furthermore, a 61bp deletion, which was included in the training set and falsified by Sanger sequencing, was reported by Pindel, but correctly classified as false by our SVM. This deletion would have proposed a potential frameshift in a coding region.

Due to general alignment restrictions, detecting insertions is limited in terms of their length. Aligning a short sequence against a long one by introducing a series of gaps into the long sequence at the same time leads necessarily to an inferior alignment score. Thus, Pindel (v0.1) and our approach share merely 15% of all insertions. Abyzov et al.[28] investigated exactly this problem and proposed an improved alignment algorithm called AGE. Applying this algorithm we could increase the number of shared insertions to 35%.

Indel detection and prediction on 80 genomes

Next, we detected and classified indels in 80 accessions of Arabidopsis thaliana from the first phase of the 1001 Genomes Project [2]. The average coverage of strains was 17x. By using a 5,000 bp alignment window, on average ∼2,116 positive deletions and ∼69 positive insertions were reported per strain, the largest being 4,916 bp long. Combining similarly localized indels of identical length in different strains revealed 169,246 non-redundant deletions and 5,500 insertions in this population. Altogether, they span over 25 Mb in total. Almost half, ∼44%, were shared among more than one strain (Additional file 3).

We found 829 long-range deletions spanning at least one complete gene sequence of the TAIR8 annotation with an average allele frequency of ∼2.7 (ranging from 1 to 65). Of those deletions 101 were classified as whole gene losses if there was no unique read coverage within the deletion (at least 90% zero-covered positions) and sufficient coverage in the same-sized flanking regions (at least 90% non-zero-covered positions), as determined by the first mapping pass. Their average allele frequency was ∼4.4 (ranging up to 29). Spurious read mapping within the deletion, ambiguous split read alignments, gene translocations or heterozygous deletions could explain long-range deletions not meeting the aforementioned criteria.

As expected, only a minority (< 10%) of indels overlap with coding regions and have a potential deleterious effect on proteins (Additional file 4). Indels that do not alter the open reading frame of a gene outnumber those that do by almost two to one (Additional file 4). However, the prediction of amino acid or framshift changes has been performed for each SV separately without considering potential nearby SVs. It is known that additional nearby variants can compensate for frameshifts [29], thus the number of protein-changing SVs reported here might still be an overestimate.

Population structure

To further assess our method, we attempted to recover the population structure of the 80 genomes with the predicted indels. To this end, three principal component analyses (PCA) [30] were performed: PCA1) on our 97,967 positively classified, non-private (shared by at least two different strains) indels (Figure 4A), PCA2) on the 37,294 non-private indels identified by the program Pindel [22] (v0.1) (Figure 4B), and PCA3) on the 53,417 non-private indels identified by the program Pindel (Figure 4C). PCA1 can successfully reconstruct the population structure, even slightly more distinctive as a PCA with non-private SNPs [2]. The first principal component distinguished the western and middle European accessions from the Caucasian and Russian individuals, explaining a variance of 20%. The second principle component with a variance of 6% was – as in Cao et al.[2] – not completely aligned with the latitude of the accessions. Interestingly, the outlier Yeg-1 from the Caucasus found by Cao et al. was positioned near the South Russian and East Asian cluster in our analysis as well. PCA2 and PCA3 revealed that the reported indels of the program Pindel contain less information about population structure compared to our method. Furthermore, the clustering of the subpopulations in PCA1 is much more differentiable as in PCA2 and PCA3. The larger set of indels due to the more non-conservative re-alignment strategy and the removal of false indels (PCA1) seem to reflect the population structure more clearly, suggesting low rates of both false positives and false negatives.

Support Vector Machine

A Support Vector Machine (SVM) [26] is a classifier which uses a hyperplane for classification. A SVM deals with a binary classification problem. We assume that we are given a set of data points $\mathcal{D}=\left\{\right(x_1,y_1),\dots ,(x_m,y_m\left)\right\}$, where $x_i\in {\mathbb{R}}^d$. The label y _i of a point x _i describes whether the point is in the negative (y _i = −1) or the positive class (y _i = 1). A SVM tries to separate the set $\mathcal{D}$ into a positive and a negative class by using a hyperplane. The process of finding the hyperplane is referred to as training. The hyperplane then defines a decision function to find the unknown label y _i for a new data point x _i . We use a soft-margin variant of the SVM, the C-SVM which is maximizing the margin and is minimizing the training error at the same time. The C-SVM uses a penalty factor C, which penalizes wrongly classified points in the training set. Our developed software is written in C/C++ and uses libsvm [31], a library for Support Vector Machines.

Classifier training

To train a classifier using a C-SVM and a linear kernel we labeled a set of detected indel candidates by reliable Sanger sequencing as true (positive class) and false indels (negative class). We split the validated corpus into a training and testing set. The training set was used to learn the discriminative model whereas the testing set measured the accuracy of the model. We counted a correctly classified test point as a true positive (TP) if the test point corresponded to the positive class and as true negative (TN) if the test point corresponded to the negative class. A false negative (FN) is a positive test point that is classified into the negative class. Correspondingly, a false positive (FP) is a negative test point that is classified into the positive class. For the actual training we selected 13 features for insertions and 17 for deletions derived from the split read alignment profiles (Figure 1). To train the SVM with these features, we normalized the data within the interval [0,1] and used a 10-fold cross-validation for deletions and a 5-fold cross-validation for insertions (Additional file 2). We repeated each cross-validation experiment 100 times. After cross-validation the best performing soft-margin parameter C value is 10 for deletions and 0.10 for insertions. To measure the performance we computed the area under (AUC) the receiver operation characteristic (ROC) curve and the specificity-sensitivity-break-even point (Spec-Sens-BEP). The ROC curve is the fraction of the TP over all positives TP + FN(sensitivity or true positive rate (TPR)) against the fraction of TN over all negatives TN + FP(specificity or true negative rate (TNR)). The Spec-Sens-BEP is the point where the TPR is equal to the TNR.

Split read alignment

To detect indels we used the short read alignments of 80 strains from Arabidopsis thaliana against its reference genome Col-0 provided by Cao et al.[2]. We parsed all read pairs, from which only one partner could be mapped (MURs). The mapped partner of a MUR may contain mismatches and may have multiple mapping positions across the whole genome. The mapped partner served as an anchor point. We considered a sequence window of length 5000 bp downstream of the anchor. Depending on whether the mapped read is located at the forward or backward strand we have to span the alignment window upstream or downstream. Using an exact Gotoh [27] alignment we aligned the unmapped read within this window against the reference (Additional file 1). The Gotoh [27] alignment is based on the Smith-Waterman [32] algorithm to compute a local pair-wise alignment between two sequences a and b using affine gap costs. Gotoh described in his work how to use dynamic programming to compute an alignment with affine gap costs in $\mathcal{O}\left(\mathit{\text{mn}}\right)$, where m and n are the lengths of sequences a and b. As alignment matrix we used the NUC4.2 scoring matrix (ftp://ftp.ncbi.nih.gov/blast/matrices/), which scores a match with 5 and a mismatch with -4. A gap opening is scored with -10, whereas a gap extension scores with zero. Alignments with a score less than the maximal alignment score minus 30 were discarded allowing for up to 7 mismatches or 3 gap openings. If the alignment contains a sequence of at least two consecutive gaps either in the unmapped read or in the reference, a possible indel location was reported. For short reads this single split read alignment is not a strong indicator of an indel due to similar regions and alignment errors. Hence we considered a location as a possible indel candidate only if we found a second independent split read alignment that supported the same location. Furthermore, each fragment of the split read alignment (left and right part of the read compared to the indel) had to be at least 8 bp long. We then used a pre-trained SVM [26] to predict whether an indel candidate is a true indel.

Population structure

Novembre et al.[30] showed that the eigenvectors of the SNP covariance matrix reflect the population structure. We here used an indel covariance matrix. For this purpose, we combined identical or few base pair-shifted indels of the same length among different strains into an MxN matrix, where M is the number of strains and N the number of indels. All deletions and insertions with an SV frequency of at least two among all strains were encoded with 1 and -1, respectively. The absence of an indel was specified with zero. To compute the underlying population structure for all eighty genomes for the first phase of the 1001 genomes project for Arabidopsis thaliana[2] we conducted a principle component analysis (PCA) using a custom Matlab script.