Predictive Models of Recombination Rate Variation across the Drosophila melanogaster Genome

Abstract

In all eukaryotic species examined, meiotic recombination, and crossovers in particular, occur non‐randomly along chromosomes. The cause for this non-random distribution remains poorly understood but some specific DNA sequence motifs have been shown to be enriched near crossover hotspots in a number of species. We present analyses using machine learning algorithms to investigate whether DNA motif distribution across the genome can be used to predict crossover variation in Drosophila melanogaster, a species without hotspots. Our study exposes a combinatorial non-linear influence of motif presence able to account for a significant fraction of the genome-wide variation in crossover rates at all genomic scales investigated, from 20% at 5-kb to almost 70% at 2,500-kb scale. The models are particularly predictive for regions with the highest and lowest crossover rates and remain highly informative after removing sub-telomeric and -centromeric regions known to have strongly reduced crossover rates. Transcriptional activity during early meiosis and differences in motif use between autosomes and the X chromosome add to the predictive power of the models. Moreover, we show that population-specific differences in crossover rates can be partly explained by differences in motif presence. Our results suggest that crossover distribution in Drosophila is influenced by both meiosis-specific chromatin dynamics and very local constitutive open chromatin associated with DNA motifs that prevent nucleosome stabilization. These findings provide new information on the genetic factors influencing variation in recombination rates and a baseline to study epigenetic mechanisms responsible for plastic recombination as response to different biotic and abiotic conditions and stresses.

Introduction

Meiosis is a pervasive process among eukaryotes and the meiotic machinery is heavily conserved (Keeney 2001). Yet the rate of meiotic recombination, and crossover in particular, exhibits an astounding degree of variation across genomes as well as between closely related species, populations of the same species, and even among individuals of the same population (Neel 1941; Parsons 1988; Kim et al. 2007; Coop et al. 2008; Kulathinal et al. 2008; Mancera et al. 2008; Kong et al. 2010; Dumont et al. 2011; Fledel-Alon et al. 2011; Ross et al. 2011; Smukowski and Noor 2011; Comeron et al. 2012; McGaugh et al. 2012; Miller et al. 2012; Singh et al. 2013; Gossmann et al. 2014; Liu et al. 2015). Moreover, both the overall number of crossovers and their distribution across genomes are affected by other factors such as age, temperature, food, and stressors, indicating that a precise description of crossover distribution requires characterizing genetic and epigenetic factors (Stern 1926; Neel 1941; Redfield 1966; Brooks 1988; Parsons 1988; Kong et al. 2002; Hussin et al. 2011; Singh et al. 2015).

To gain insight into the factors involved in crossover localization much attention has been given to short DNA sequence motifs near crossovers. Computational analyses of high-resolution crossover maps can identify specific motifs enriched at hotspot regions, but analyses of motif presence are rarely predictive enough to forecast patterns of crossover variation at a whole-genome scale. One of these cases is the 13-mer DNA motif recognized by the histone methyltransferase PRDM9 in humans and mice, with PRDM9 promoting histone methylation and meiotic crossover around the motif (Baudat et al. 2010; Parvanov et al. 2010; Billings et al. 2013). The PRDM9-associated motif is very highly significantly enriched near human crossovers, being present in approximately 40–60% of crossover hotspots (Myers et al. 2008; Hinch, et al. 2011). The reverse is much less often true: the presence of the PRDM9-associated motif is not a strong predictor of crossover distribution across the genome (Ségurel et al. 2011). A recent analysis across the ape phylogeny supports this conclusion, with enrichment of putative PRDM9 binding in recombination hotspot regions but no association between PRDM9 presence and local increases in recombination rates when measured broadly across the genome (Stevison et al. 2015). An equivalent case is observed in the yeast Schizosaccharomyces pombe where motifs enriched near some hotspots are, nonetheless, very poor predictors of hotspot localization genome-wide (Fowler et al. 2014).

In Drosophila, high-resolution recombination maps have revealed that crossover rates can vary 20- to 40-fold across genomic regions traditionally assumed to exhibit limited variation in recombination rates (Kulathinal et al. 2008; Comeron et al. 2012; McGaugh et al. 2012; Miller et al. 2012; Singh et al. 2013). These studies describe peaks of crossover rates across Drosophila genomes that are far less extreme and physically discrete than in species with more traditional hotspots, where crossover rates are >100-fold higher than in adjacent regions (Ségurel et al. 2011). Moreover, Drosophila species, like other species including some placental mammals, do not have functional PRDM9 orthologs (Oliver et al. 2009; Parvanov et al. 2010; Muñoz-Fuentes et al. 2011; Heil and Noor 2012). Predictably, the 13-mer motif associated with human hotspots that is recognized by PRDM9 is not observed near crossover events in Drosophila (Comeron et al. 2012; Heil and Noor 2012). In fact, sequence analyses in Drosophila melanogaster have identified not one but many DNA motifs significantly enriched near crossover events (Comeron et al. 2012; Miller et al. 2012; Singh et al. 2013). Combined, current data suggest that Drosophila has no traditional hotspots and we hypothesized that crossover-associated DNA motifs could be more evolutionary stable than in primates where hotspots become inactive relatively young (Coop and Myers 2007).

Here, we investigated whether the genomic distribution of specific DNA motifs has predictive power in describing crossover landscapes across the genome of D. melanogaster. The motifs under study were recently identified as motifs enriched near crossover sites through analysis of experimentally genotyped recombinant offspring (Comeron et al. 2012). We have now generated genome-wide landscapes of motif presence taking into account the probabilistic nature of motif sequences, background composition and a FDR-based genome-wide motif detection approach. We have also obtained genome-wide landscapes of crossover rates based on population patterns of linkage disequilibrium (LD) in two D. melanogaster natural populations (Chan et al. 2012). Importantly, these LD-based landscapes of crossover rates are completely independent from the data used to identify the DNA motifs, thus allowing for an unbiased evaluation of a potential association of motif distribution with crossover landscapes.

We show that the variable presence of multiple motifs across the genome generate non-linear quantitative models that explain a significant fraction of the genome-wide variation in crossover rates at all genomic scales investigated, from 20% at 5-kb to almost 70% at 2,500-kb scale. Also across all scales analyzed, the models are particularly accurate at detecting the genomic regions with the highest and lowest 10% crossover rates. Interestingly, these models remain highly predictive of crossover rate variation after removing sub-telomeric and -centromeric regions known to have strongly reduced crossover rates, and predict minimal levels of crossover across the dot (fourth) chromosome, which is known to be achiasmatic in Drosophila female meioses. Moreover, we report that the effect of motif presence on crossover rates differs between autosomal arms and the X chromosome, and show that transcriptional activity during early meiosis adds predictive power to the models thus explicitly including a potential mechanistic explanation to the known plasticity in recombination rates. Finally, we show that the most informative motifs predicting high crossover rates share properties associated with highly localized genomic regions depleted of nucleosomes.

Results

Genome-Wide Landscapes of DNA Motifs

The study of almost 2,000 crossover events mapped with high-resolution in D. melanogaster uncovered many DNA motifs enriched within the 500-bp sequence encompassing these crossover events (Comeron et al. 2012). These motifs, therefore, were localized to less than 1% of the genome. To generate landscapes of motif presence across the whole genome, we used the position probability matrix (PPM) of these motifs and took into account the numerous false positives expected in any large-scale genomic study as well as background nucleotide composition (see “Methods” section for details). Unless otherwise indicated, we focused on the 12 motifs present more than 1,000 times genome-wide once a 1% false discovery rate (FDR) correction is applied (see supplementary table S1 and fig. S1, Supplementary Material online for motif sequences). Motif presence ranges up to over 18,000 motif hits (M5) and highlights the need for caution when interpreting the biological relevance of individual motifs at specific genomic locations, even when FDR is set to 1%. At first glance, several motifs show variation in their distribution on a chromosome scale that visually follows the traditional distribution of crossover rate variation in D. melanogaster (fig. 1), with motif presence reduced near centromeric and, to a lesser degree, telomeric regions (Morton et al. 1976; Lindsley and Zimm 1992; Fiston-Lavier et al. 2010; Comeron et al. 2012; Miller et al. 2012).

Fig. 1.—

Genomic landscape of motifs. Number of motifs per 100-kb for motif 3 (M3 in blue; [A]_n) and motif 4 (M4 in red; [CA]_n) across autosomal arms 2L, 2R, 3L, 3R and the X chromosome (see supplementary fig. S1 for motif sequence information). Presence shown after applying a 1% FDR (see “Methods” section).

Motif Presence Is Correlated with Crossover Rates across the Genome

To study genome-wide associations between variation in motif presence and crossover rates, we obtained estimates of crossover rates that are independent of the experimental genetic map used to find the initial motifs thus preventing any circularity. We used LDhelmet (Chan et al. 2012), a method that generates high-resolution population estimates of crossover rate (ρ_LD) across the genome based on patterns of nucleotide polymorphism and LD. LDhelmet was applied to the D. melanogaster African Rwanda (RG) population [(Pool et al. 2012; Lack et al. 2015); see “Methods” setcion for details] because this population shows very low levels of admixture and is from the sub-Saharan ancestral range of D. melanogaster, which minimizes the non-equilibrium effects caused by recent expansion observed in western Africa and non-African populations (Pool et al. 2012; Lack et al. 2015). To investigate potential intraspecific variation in the distribution of motifs and/or crossover rates, we applied LDhelmet to the D. melanogaster African Zambia (ZI) population, which also shows low levels of admixture (Pool et al. 2012; Lack et al. 2015). Unless noted, analyses are reported using LD-based crossover estimates ρ_LD and motif distribution for the RG population at 100-kb scale.

The direct comparison of ρ_LD and motif presence at 100-kb scale shows positive associations for all 12 motifs analyzed (P < 1 × 10⁻⁶), with Spearman’s r_s² higher than 0.10 (P < 5 × 10⁻³¹) for eight motifs (fig. 2 and supplementary fig. S1, Supplementary Material online). We also observe that some motifs show clear differences among chromosome arms in terms of association with ρ_LD (fig. 2 and supplementary fig. S2, Supplementary Material online ). Variation in M7 presence shows a very strong association with ρ_LD along the X chromosome (Spearman’s r_s²= 0.24, P = 4.1 × 10⁻¹⁵) whereas it shows no association along autosomal arms (P > 0.1 in all autosomal arms). A similar tendency can be seen for motifs M11 and M12 that also contain [TA]_n repeats. M2, on the other hand, shows a positive association with ρ_LD along all four autosomal arms but not in the X chromosome. These differences are unlikely to be caused by differences in statistical power alone, as M2 is more frequently observed on the X chromosome than on autosomes (average presence per 100 kb is 16.4 and 8.5 for the X and autosomes, respectively). Although some motifs (e.g. M1, M4, M5, and M6) show diverse degrees of association with ρ_LD among autosomal arms, the difference in potential effects of motif presence on crossover localization seems to be mostly influenced by a dichotomy between autosomal arms and the X chromosome (see below).

Fig. 2.—

Probability heatmap of correlation between presence of individual motifs and crossover rates ρ_LD. P-values of non-parametric correlation (Spearman’s r_s) of motif presence and LD-based crossover rates ρ_LD calculated genome-wide and for each chromosome arm. Only motifs showing correlations with P < 0.01 in genome-wide analyses are shown. Motifs are ordered based on Spearman’s correlation across the genome, with M5 (Spearman’s r_s²= 0.237, P = 1 × 10⁻⁷¹) showing the strongest correlation.

To obtain an initial model that considers multiple motifs to explain crossover distribution, we first performed Least Absolute Shrinkage and Selection Operator (LASSO) regression (see “Methods” section for details) (Tibshirani 1996; Hastie et al. 2009). LASSO regression is a technique that favors solutions with fewer parameter values under a linear model, simultaneously performing variable selection and simplifying model interpretation. LASSO exposes six heavily weighted motifs (in order of importance M3, M1, M7, M5, M6, and M2; supplementary fig. S3, Supplementary Material online), all positively associated with crossover rates ρ_LD. With these six motifs, LASSO fits a model of motif presence that explains more than 20% of the variation in ρ_LD genome-wide (R²_LASSO = 0.234, P < 2.2 × 10⁻¹⁶). Note, however, that non-parametric Spearman’s correlations between motif presence and ρ_LD suggest that some individual motifs (e.g. M3 and M5) explain crossover variation when analyzed independently almost as much as the more complex linear LASSO model that includes several motifs (fig. 2 and supplementary fig. S1, Supplementary Material online). Easing the constraints of LASSO (λ + 1 S.E; see “Methods” section) allows all 12 motifs under study to enter the model but this highly complex and likely over-parameterized model exhibits little improvement in overall performance (R²_LASSO= 0.252, P < 2.2 × 10⁻¹⁶).

Predictive Models of Variation in Crossover Rates across the Genome Based on Motif Presence

We applied two machine learning methods to investigate models of crossover rate variation using motif distribution as continuous predictors. We first used Random Forests (RF) (Breiman 2001; Lee et al. 2005; Banfield et al. 2007) as a form of supervised learning to discriminate between genomic regions (classes) with different crossover rates, particularly between low and high rates. We later constructed a quantitative predictive model using Multivariate Adaptive Regression Splines (MARS) (Friedman 1991; Friedman and Roosen 1995; Hastie et al. 2009) (see “Methods” section for details). MARS is an approach that allows multiple interactions among motifs and non-linear effects thus potentially capturing saturation/insensitivity and cooperative action of different motifs when describing crossover rates. Importantly, MARS allows obtaining a final explicit and continuous model of crossover rates based on the combined presence of multiple motifs.

Random Forests (RF) Categorical Modeling

We split all 100-kb regions into ten approximately equally sized bins, from the lowest (class A) to highest (class J) 10% ρ_LD, and applied random forests (RF) to classify crossover classes using a 10-fold cross-validation approach (see “Methods” section). The correctness of the RF models is measured by accuracy (true positive rate) and the area under the curve (AUC) that indicates the ability of the model to discriminate between the different classes, with AUC scores ranging from 0.5 (indicating that a model has no discriminatory ability) to 1 (indicating that the model can discriminate perfectly among all classes). Note that RF does not directly generate probability values associated with the whole model. We, therefore, obtained the statistical significance of RF models by comparing the accuracy and AUC generated by the model and the accuracy and AUC generated by RF when estimates of ρ_LD are randomized among 100-kb regions (250,000 randomizations per model).

Using the ten ρ_LD classes as our class variables, we applied RF with motif distribution across the genome as continuous predictors to later add transcription data and chromosome arm. Genome-wide, motif distribution allows RF to generate a model with an accuracy of 23.1% (vs. a random expectation of 10%, P < 3 × 10⁻⁶) and a mean AUC = 0.644 (P < 3 × 10⁻⁶). Although this RF model includes all 12 motifs with significant effects on the model, the six more important motifs based on information gain (M5, M4, M3, M1, M2, and M7) can explain more than 85% of the model. Overall, the model performs fundamentally well for the top and bottom classes (fig. 3A), with accuracy of 78.0 and 56.3%, respectively (more than 5-fold enriched, P < 3 × 10⁻⁶, in both cases). Enrichment based on AUC shows an equivalent pattern, with AUC of 0.876 and 0.814 for the top and bottom 10% classes, respectively (P < 3 × 10⁻⁶ in both cases). This study of motif presence correctly classifies ρ_LD class within one step of their true class 44% of the time, indicating that when our model fails to accurately predict a class, it often falls into the adjacent bin.

Fig. 3.—

Random Forest (RF) models. A) Accuracy (true positive rate) is given for 10 crossover classes, from class A (regions with lowest 10% crossover rate ρ_LD) to class J (regions with highest 10% crossover rate ρ_LD). Random accuracy (uninformative model) per class is 10% (horizontal dashed line). The model tested utilizes all 12 motifs to predict crossover classes (see “Methods” section for details). B) Accuracy when the model is trained with data from one autosomal arm and applied to either other autosomal arms or to the X chromosome (left) as testing set, or trained with data from the X chromosome and applied to either autosomal arms or to the X chromosome (right).

A RF model with motif distribution and information on transcribed genes during early meiosis (Adrian and Comeron 2013) increases the genome-wide accuracy to 24.4% and AUC to 0.678 (P < 3 × 10⁻⁶ in both cases), whereas motifs, transcription data and chromosome arm information generate an improved model with accuracy and AUC of 27% and 0.727, respectively (P < 3 × 10⁻⁶ in both cases). In contrast, genomic properties such as the number of annotated genes or proportion of exonic sequence in each window do not significantly affect model accuracy (data not shown) and these variables are never within the top ten variables in term of importance within the model. Similarly, GC content per window is neither ranked highly by information gain criteria nor does it have a substantial impact on classification accuracy.

The application of RF to each chromosomal arm separately reveals that the models are much more accurate predicting ρ_LD variation for the X chromosome (51.8% accuracy, a 5-fold enrichment relative to random expectations) than for autosomal arms (21.0% with accuracy, ranging between 16.5% for 2L and 24.5% for 3L) (fig. 3B). An equivalent conclusion is obtained based on AUC, with AUC of 0.68 for the X chromosome whereas AUC ranges between 0.51 (2L and 2R) and 0.62 (3L) for autosomes. In agreement with our initial analyses, RF also indicates that the influence of some motifs on crossover distribution is not equivalent genome-wide. M5 and M7 are more important motifs in the RF model for the X chromosome (combining 33% of the relative importance of all motifs) than in the model for autosomes (combining 18% of the relative importance). Conversely, M4 and M2 are ranked lower in models for the X chromosome than in models describing crossover across autosomes (14 and 28% of the relative importance of all motifs, respectively). To further test the difference between the X chromosome and autosomes we applied RF using data from individual chromosomal arms as a training set and tested the accuracy of the model describing crossover rates along other chromosomal arms (see “Methods” section). The results of this analysis evidence that autosomal arms are worse at predicting ρ_LD along the X chromosome than along other autosomal arms (fig. 3B). Equivalently, the use of X chromosome data as training set generates models of ρ_LD variation along autosomes with an average accuracy of only 14.8%.

MARS Modeling

We used the 10-fold cross-validation approach (see “Methods” section for details) and evaluated the quality of MARS models focusing on R²_CV scores (the MARS estimate of how well this model would perform on new data when using the 10-fold cross-validation approach; see “Methods” section). The simplest model that considers only the variable presence of motifs across the genome is able to explain ∼50% (R²_CV = 0.501) of the genome-wide variation in ρ_LD (fig. 4 and supplementary table S2, Supplementary Material online). This predictive model improves even further when including information on transcription (R²_CV = 0.512) or chromosome arm (R²_CV = 0.540).

Fig. 4.—

MARS predictive models of crossover rates. (A) Estimates of the predictive power of MARS models (R²_GCV) based on the presence of motifs across the genome, transcription data during early meiosis, and/or chromosome arms as predictive variables. Results shown for genome-wide analyses (red) and for trimmed (after removing sub-telomeric and -centromeric regions) genome (blue). (B) Relationship between crossover rates obtained from population genetic analyses of linkage disequilibrium (x-axis) and those predicted based on a MARS model (y-axis) including motif, transcription and chromosome arm data. The unit of crossover rate is ρ_LD (ρ_LD = 2 N_e r), where N_e is the effective population size and r is the rate of crossover per bp and generation in females (Chan et al. 2012). C) Examples of the linear and non-linear influence of motif presence on crossover rates. All results are shown for analyses of the RG population at 100-kb scale.

The most complete MARS model, which includes motif presence, transcription data and chromosome arms, explains 57% (R²_CV = 0.569) of the variation in crossover genome-wide. This most complex model identifies chromosome arm, number of actively transcribed genes and seven motifs as significantly important within the model (M5, M3, M4, M7, M2, M12, and M10), several of which exhibit non-linear effects on crossover rates (fig. 4B and C). Note that MARS estimates based on less conservative methods such as the legacy mode (R²_Legacy) would imply an even higher influence of motif presence on ρ_LD (R²_Legacy values always larger than R²_CV; supplementary table S2, Supplementary Material online) but caution should be applied to the interpretation of these high estimates due to overfitting (see “Methods” section).

Putative Influence of the Method to Estimate Crossover Rates

Supplementary figure S1, Supplementary Material online shows Spearman’s correlation between motif distribution and crossover rates across the genome based on either population estimates (ρ_LD) or from direct genotyping of offspring [i.e., experimentally identified crossovers; (Comeron et al. 2012)]. We observe that all 12 DNA motifs show significant correlations between presence across the genome and experimentally generated crossover landscapes, with the highest Spearman’s r_s² of 0.176 for M3 (P = 7 × 10⁻⁵²) at 100-kb scale. Additionally, MARS modeling shows an important predictive power of motifs explaining these crossover rates genome-wide (R²_CV ranging between 0.263 and 0.304). These data show that the observed significant contribution of motif distribution to variation in crossover rates across the genome is not exclusive to using ρ_LD. However, we also detect that the predictive power is higher when using population estimates ρ_LD and motif distribution from the same population than when using crossover rates estimated experimentally and motifs from either RG or ZI population (or reference genome). This difference can be interpreted as consequence of the admixed source of strains used to generate a recombination map for the D. melanogaster species and/or the environmental conditions when obtaining recombinants and associated epigenetic factors influencing crossover distribution.

Alternatively, one could argue that the difference between experimental and LD-based crossover landscapes exposes biases in LDhelmet when generating ρ_LD. In Drosophila, where males do not recombine, ρ_LD is formally equal to 2 N_e r, where N_eis the effective population size and r is the rate of crossover per bp and generation in females (see “Methods” section for details). Variation in ρ_LD could then reflect differences in N_e,additional to (or rather than) differences in r, due to demographic events or the interplay between selection and linkage (Wright 1938; Hill and Robertson 1966; Smith and Haigh 1974; Slatkin and Hudson 1991; Charlesworth et al. 1993; Gillespie 2000; Sella et al. 2009; Cutter and Payseur 2013; Charlesworth and Campos 2014; Comeron 2014). Chan et al. (2012) showed that LDhelmet generates estimates of ρ_LD that are good estimators of r under several demographic and selective conditions, although complex adaptive selective scenarios cause more noise in the estimates of ρ_LD and could, potentially, affect ρ_LD differentially across the genome. To investigate this possibility, we focused on the ratio of ρ_LD (2 N_e r) to the amount of silent nucleotide polymorphism (π_sil), which is also proportional to N_e (π_sil = 4N_eμ for autosomes and 3N_eμ for the X, where μ is the mutation rate per bp and generation). We show that the correlation between motif presence and ρ_LD/π_sil (which is independent of N_e) is equivalent to that observed when using ρ_LD, and this is the case at different genomic scales (supplementary table S3, Supplementary Material online). RF based on motif distribution generates models with 22.9% accuracy (AUC of 0.638) when assigning regions to their corresponding decile ρ_LD/π_sil class, with accuracy for the top and bottom 10% classes of 83.2 and 55.5%, respectively, thus with all results virtually equivalent to those obtained when using ρ_LD. Also equivalent is the increased accuracy (25.1%) and AUC (0.707) when including chromosome arm as variable. Furthermore, MARS generates models that explain as much of the variance in ρ_LD/π_sil across the genome as the models for ρ_LD, with R²_CV ranging between 0.513 (models using only motifs distribution) and 0.583 (when also including transcription and chromosome data) for analyses at 100-kb scale. Combined, these data indicate that our results and conclusions supporting a strong role of motifs in crossover distribution are unlikely to be caused by the use of ρ_LD.

The Centromere-Effect

In D. melanogaster, crossover frequency is severely reduced in euchromatic regions near centromeres and, to a lesser degree, near telomeres [the so-called “centromere effect” (Beadle 1932)]. Crossover in these large sub-centromeric and telomeric regions is likely influenced by mechanisms at least partially different to those acting along the central regions of chromosomal arms. In agreement, RF assigns all 100-kb regions correctly to their corresponding decile class (the majority of which are class A or B), and MARS models generate predictions of ρ_LD for these sub-centromeric and telomeric regions that are significantly lower than the rest of the euchromatic genome (Mann–Whitney U Test, P < 1 × 10⁻¹⁶). We, then, investigated whether motif distribution is also informative predicting variation in ρ_LD after removing sub-centromeric and -telomeric regions (i.e., trimmed genome) from the study (fig. 4A; see “Methods” section for details). RF across the trimmed genome shows 26.0% accuracy and 0.656 AUC. MARS generates models with R²_CV of 0.482 (only motif presence) and 0.517 (motifs + chromosome arms + transcription activity during early meiosis), respectively. These results evidence that variation in motif distribution maintains significant power explaining variation in crossover rates beyond the centromere effect.

The Achiasmate Fourth Chromosome

The fourth (or dot) chromosome in D. melanogaster represents approximately 3.5% of the genome, consists of interspersed heterochromatic and euchromatic DNA (Sun et al. 2000), and does not experience crossing over (Hochman 1973). We asked whether our models based on DNA motif presence predict low or no crossover along this chromosome by applying RF and MARS models that were trained on genome data that did not contain the fourth chromosome and then tested these models with the fourth chromosome. RF correctly classifies all thirteen 100-kb intervals of the fourth chromosome as belonging to class A, the lowest 10% ρ_LD genome-wide. The application of MARS modeling using motif presence generates predictions of ρ_LD for these thirteen 100-kb intervals that are significantly lower than the rest of the genome (Mann–Whitney U Test, P = 0.0022).

Influence of Genomic Scale on the Association between Motif Presence and Crossover Rates

To investigate whether the influence of motif presence on ρ_LD is scale-specific, we generated data at nine different genomic scales, from fine (5-kb) to broad (2,500-kb) non-overlapping intervals across the whole genome. Figure 5 shows Spearman’s r_s correlations and corresponding probability values for each of the 12 motifs analyzed at these different scales. At the finest scale of 5-kb, all motifs show a highly significant correlation between motif presence and ρ_LD (from P = 3 × 10⁻¹¹ for M12 to P < 1 × 10⁻³⁰⁰ for M5), with Spearman’s r_s ranging between 0.043 (M12) and 0.31 (M5). Motifs show increasing r_s with successively broader scales (with the only exceptions of M4 and M7 at or above 1,000-kb). Note, however, that there is a reduction in statistical significance with broader scales, at least in part expected due to the smaller number of intervals investigated, and four motifs (M7, M8, M11, and M12) show non-significant correlations with crossover at 2,500-kb scale. The application of RF and MARS at these different genomic scales shows equivalent patterns (fig. 6). There is a tendency for increased predictive power (accuracy in RF and R²_CV in MARS models) with successively broader scales between 5- and 1,000-kb, whereas RF shows a clear reduction in accuracy above the 1,000-kb scale evidencing the influence of larger chromosomal properties.

Fig. 5.—

Influence of genomic scale on the correlation between motif presence and crossover rates ρ_LD. Spearman’s non-parametric correlation (r_s) between motif presence and LD-based crossover rates ρ_LD is shown for intervals of 5-, 10-, 25-, 50-, 100-, 250-, 500-, 1,000-, and 2,500-kb. For each motif, the nine adjacent vertical bars indicate the different scales, from the finest scale (5-kb; left) to the broadest scale (2,500-kb; right). The color of each bar indicates the probability (P) of the correlation, with more significant correlations (lower probabilities) in darker red. Vertical bars with dashed borders indicate correlations with probabilities greater than 0.001. See supplementary figure S1 for motif sequence information.

Fig. 6.—

Influence of genomic scale on RF and MARS analyses. Predictive power (accuracy and R²_CV in RF and MARS models, respectively) for models using motif presence to predict crossover rates ρ_LD at nine different genomic scales across the genome.

Intra-Specific Variation in Motif Presence and Crossover Rates

In many species, including D. melanogaster, crossover rates are known to vary among individuals of the same species in terms of total rates as well as for crossover distribution along chromosomes (Brooks and Marks 1986; Neumann and Jeffreys 2006; Graffelman et al. 2007; Coop et al. 2008; Dumont et al. 2009; Kong et al. 2010; Comeron et al. 2012; Miller et al. 2012; Bauer et al. 2013; Hunter et al. 2016). All our previous analyses focused on motif presence calculated across the genomes of individuals of the African D. melanogaster RG population and estimates of crossover rates ρ_LD for this same population. Analyses based on motif presence and estimates of ρ_LD using the Zambia (ZI) population generate similar conclusions (supplementary fig. S1 and Table S2, Supplementary Material online), with variation in motif presence across ZI genomes being able to explain a large fraction of the observed intra-genomic variation in ρ_LD. MARS, for instance, generates models of ρ_LD variation when studying the ZI population with higher R²_CV than those obtained from the study of the RG population (R²_CV > 0.59 for analyses at 100-kb scale, supplementary table S2, Supplementary Material online).

The comparison of the RG and ZI populations reveals differences in ρ_LD landscapes (Spearman’s r_s²= 0.52 at 100-kb scale) as well as differences in motif distribution (Spearman’s r_s² ranges between 0.581 for M12 and 0.979 for M4 at 100-kb scale). To investigate whether inter-population variation in motif presence plays a role in the difference in crossover landscapes, we applied MARS using different source of motif data and at different genomic scales (fig. 7). MARS models generate greater R²_CV predicting ρ_LD variation in the RG population when using motif distribution from this same RG population than when using motif distribution across genomes of the ZI population at all scales, most noticeably at 100-kb or finer scales. The use of motif distribution of the D. melanogaster reference genome shows even more reduced power forecasting ρ_LD in the RG population, which would be consistent with its low percentage (9%) of African ancestry (Pool 2015). Combined, these analyses show that population-specific differences in crossover rates can be, to some degree, explained by population-specific differences in motif presence.

Fig. 7.—

Influence of intra-specific origin of motif data and genomic scale on MARS analyses. Predictive power (R²_CV) for MARS models of crossover rate ρ_LD across sequences of the RG population using motif distribution estimated from sequences of the same RG population, the ZI population or the D. melanogaster reference genome.

Predictive Motifs, Chromatin Accessibility and High-Resolution Crossover Rates

Nucleosome-depleted regions (NDR) in both S. pombe and Saccharomyces cerevisiae are strongly associated with crossovers hotspots and local patterns of double-strand break (DSB) distribution, evidencing an influence of chromatin accessibility on DSBs (Ohta et al. 1994; Wu and Lichten 1994; Hirota et al. 2007; Berchowitz et al. 2009; de Castro et al. 2012; Yamada and Ohta 2013). Importantly, however, nucleosome depletion is not informative enough to describe DSB distribution genome-wide in these yeast species (de Castro et al. 2012; Fowler et al. 2014). Most of the motifs with strong influence on crossover rates genome-wide within our RF and MARS models contain [CA]_n (M1 and M4), short poly-A/T (M3 and M5) and [AT]_n (M7) tracts. All these specific repeats have been proposed to prevent nucleosome stabilization, potentially increasing highly localized accessibility (Travers 1990; Perez-Martin and de Lorenzo 1997; Shimizu et al. 2000; Segal et al. 2006; Struhl and Segal 2013). We, thus, asked whether these motifs are indeed both enriched in highly accessible chromatin regions and show higher crossover rates at very local scale. We argue that, contrary to transcription-associated NDRs, accessible chromatin due to short sequences that prevent nucleosome stabilization should be constitutive and, as such, they should be a detectable component in different cells types, tissues and developmental stages. Therefore, we used publicly available high-resolution open chromatin profiles generated from four D. melanogaster samples, including eye-antennal imaginal discs and three different cell lines (S2, BG3 and Kc167) [(Kharchenko et al. 2011; Thomas et al. 2011; Davie et al. 2015); see “Methods” section for details].

We observe that there is a significant enrichment of these five motifs in open chromatin regions compared with random expectations in each of the four samples analyzed (P < 1 × 10⁻⁵³ in all cases). This enrichment is particularly evident for [CA]_n-related M1 and M4 motifs (P < 1 × 10⁻¹¹⁰ in all four samples) and, to a lesser degree, for the short poly-A/T M5 motif, which shows enrichment in three out of the four samples (P = 3.4 × 10⁻⁷ in eye-antennal imaginal discs, P = 6.2 × 10⁻ in Kc167 and P = 0.02 in S2). We then investigated crossover rates at the location of these motifs based on estimates of ρ_LD between informative SNPs encompassing the motif genomic position (the average distance between informative SNPs is only 43-bp thus this approach provides a very local estimates of crossover rates). Crossover rates are significantly higher at the location of these motifs than expected by random distribution (fig. 8), and this is the case whether the three types of motifs ([CA]_n, poly-A/T, and [AT]_n) are analyzed combined or separately (P < 1 × 10⁻¹⁹⁰ in all cases). Finally, we also report that not all accessible chromatin regions in the samples investigated are associated with increased crossover rates. In fact, only accessible regions containing [CA]_n, poly-A/T, and/or [AT]_n exhibit significantly increased crossover rates (P < 1 × 10⁻⁹ in all cases, fig. 8) as expected if they are associated with constitutive NDRs and thus relevant for female meiosis.

Fig. 8.—

Boxplots of local crossover rate (ρ_LD) at motifs. Crossover rates estimated by LDhelmet (Chan et al. 2012) between SNPs surrounding the motif location in the RG population. The average distance between SNPs surrounding motifs in the RG population is 41-bp. Median crossover rates are identified by the horizontal line inside each box and the length of the box and whiskers indicate 50% and 90% CI, respectively. The horizontal dashed line indicates the genome-wide median ρ_LD (ρ_LD= 0.0225). Asterisks below boxes indicate the probability of having crossover rates compatible with genome-wide estimates. For analyses of local crossover rates at accessible chromatin regions, ρ_LD was estimated at the center of the region. The study of all accessible chromatin regions (see “Methods” section) reveals median ρ_LD of 0.0234 at these regions (indistinguishable from genome-wide rates, P > 0.50). Asterisks above boxes of accessible chromatin regions containing specific motifs ([CA]_n, short poly-A and/or [TA]_n) indicate the probability of having crossover rates compatible with all accessible chromatin regions.

Discussion

In our study, we obtained FDR-corrected landscapes of motif presence across the genome using the likelihood of each k-mer sequence of nucleotides to correspond to a given position probability matrix (PPM) and taking into account genome size and nucleotide composition. The use of a FDR instead of a direct arbitrary probability is necessary to limit the extent of false positives and this parameter should be tuned appropriately for each study. We set FDR at 1% because it generates a large number of motif hits whereas still producing PPMs equivalent to those obtained under the most stringent FDR of 0.1%, thus suggesting that false positives do not seriously alter motif detection. We also confirmed that a single PPM per motif is adequate across the whole genome by comparing the top 50 and bottom 50 recombination-correlated regions by residual (which followed an approximately normal distribution). We found no significant differences between PPMs recovered from these two classes of regions indicating that a single PPM per motif can be used at genome-wide scale and that motif count, rather than motif sequence or quality, is a more important predictor of crossover in our data once FDR is applied.

Differences among Chromosome Arms

Our study has exposed that the association between motif presence and crossover rates differs depending on chromosome arm, mostly as a dichotomy between autosomal arms and the X chromosome. Our results obtained using either ρ_LD or ρ_LD/π_sil suggest that different genomic regions may utilize different combinations of DNA motifs as localizing factors for crossover formation (and potentially DSBs). Outside of differential gene expression patterns (Meisel and Connallon 2013; Llopart 2015) or average rates of crossover in females, it is not direct how the X chromosome and autosomes could be different in terms of motif utilization for meiotic DSB formation and resolution as crossovers. At this time, we hypothesize that such a potential mechanistic link could be associated with differences in chromatin exposure and transcription during early female meiosis (Adrian and Comeron 2013) and/or spatio-temporal compartmentalization of chromosome arms within the nucleus (Parvinen and Soderstrom 1976; Koszul et al. 2008; Shibuya et al. 2014) during early female meiosis. At a more practical level, our results also indicate that analyses of motif occurrence based on a single genomic region or chromosome may not be necessarily applicable genome-wide, thus explaining differences in motif detection among studies.

Crossover Localization across the Genome

Based on the knowledge obtained from this study and others, a general model is emerging where crossover distribution is determined by a combination of factors acting hierarchically at different physical scales, including motifs, transcription, and chromatin structures (Petes 2001; Kleckner 2006; Pan and Keeney 2007; Pan et al. 2011; Adrian and Comeron 2013; Borde and de Massy 2013; Smukowski Heil et al. 2015). In D. melanogaster, the centromere effect describes variation in crossover distribution at the largest scale (hundreds of kb), with a severe reduction in crossover rates at sub-centromeric/telomeric regions (Beadle 1932). We observe that regions proximal to telomeric and centromeric regions have fewer motifs positively associated with crossovers. Because crossovers near centromeres increase the probability of non-disjunction events at the second meiotic division (Koehler et al. 1996), it is tempting to speculate that natural selection may have played a role in the observed paucity of recombinogenic motifs in such genomic regions. Combined, our results indicate that the centromere-effect observed today in D. melanogaster may be the consequence of both direct mechanistic explanations as well as long-term evolutionary forces that have reduced the presence of crossover-associated motifs in these regions.

High-resolution crossover maps in a number of species (including D. melanogaster, S. cerevisiae, S. pombe, Plasmodium falciparum or Apis mellifera) have exposed multiple motifs significantly enriched near crossovers (Gerton et al. 2000; Cromie et al. 2007; Steiner et al. 2009; Jiang et al. 2011; Bessoltane et al. 2012; Comeron et al. 2012; Singh et al. 2013; Liu et al. 2015). Here, we have showed that variation in the presence of several motifs is in fact predictive of a significant fraction of the observed variation in crossover distribution across the genome of D. melanogaster, where traditional hotspots have not been detected, even after removing regions near centromeres and telomeres. Moreover, our study suggests that the difference in motif landscapes between populations may be associated with the observed difference in crossover landscapes between these populations, therefore exposing an important genetic component responsible for (or associated with) variation and evolution of recombination landscapes. Additionally, we observe that this influence of motif distribution on differences in crossover rates between populations is most evident at small scale (≤250-kb), thus potentially being an unappreciated aspect of the dichotomy between evolutionary conservation of recombination landscapes at very broad genomic scales and highly variable crossover rates at finer scales (Myers et al. 2005; Coop and Przeworski 2007; Coop et al. 2008; Smukowski and Noor 2011; Comeron et al. 2012; Smukowski Heil et al. 2015).

Individually, the motifs with the strongest effect could explain up to 24% (figs. 2 and 5 and supplementary fig. S1, Supplementary Material online) of the variance in crossover rates genome-wide when analyzing the RG population at the 100-kb scale (30% for the ZI population). Standard multiple linear and the more complex LASSO linear regression analyses generate models with little or no additional advantages when describing the observed variance in crossover rates across the genome. The application of more advanced techniques, however, exposes increased predictive power to describe crossover distribution when multiple motif variables are considered without the constraints of linear models. Our study shows that RF modeling is particularly accurate at predicting regions with the highest and lowest 10% crossover rates, and reliably predicts minimal crossover across the fourth chromosome based on motif distribution alone. The continuous models generated by MARS, on the other hand, are able to account for a large fraction of the variance in crossover rates across the D. melanogaster genome and identify significant interactions among motifs. We also show that variables describing transcriptional activity across the genome during early meiosis and, more unexpectedly, chromosome arm add to the predictive power of the models. Notably, the influence of motif distribution on crossover rates is detected at all genomic scales analyzed (from 5- to 2,500-kb) although it is most significant at or below the 1,000-kb scale.

Open Chromatin Sites

Several of the motifs with the strongest association with crossover rates share an enrichment of [CA]n, short poly-A/T and [AT]_n tracts. Gel-mobility and X-ray crystallographic studies have shown that repeated instances of A/T tracts produce a non-canonical bend in the DNA helix axis, with the in-phase repetition of these elements contributing to larger overall bends (Travers 1990; Dlakic and Harrington 1998; Hizver et al. 2001). Such unusual DNA conformation of poly-A/T tracts and other AA/TT/AT repeats is a significant factor altering protein-DNA binding specificities, prevents nucleosome formation and stabilization and can, ultimately, increase accessibility (Travers 1990; Perez-Martin and de Lorenzo 1997; Shimizu et al. 2000; Segal et al. 2006; Struhl and Segal 2013). The signal associated with [CA]n motifs across the D. melanogaster genome is also interesting because these motifs are markers for Z-DNA regions which are not easily wrapped into nucleosomes (Garner and Felsenfeld 1987; Herbert and Rich 1996).

In this study, we have showed that in D. melanogaster [CA]n, short poly-A/T tracts and [TA]n motifs are both enriched in open chromatin regions and show higher crossover rates than expected. Our results in Drosophila at a genome-wide scale, therefore, parallel those in yeast hotspots, where short poly-A/T and [CA]n tracts are also significantly enriched (Treco and Arnheim 1986; Mancera et al. 2008; Fowler et al. 2014). Worth mentioning, the association between A/T rich motifs and crossovers is motif-specific and not a consequence of variation in large-scale nucleotide composition because there is only a nominal and negative effect of overall nucleotide A + T content on the distribution of crossover rates [Spearman’s r_s = −0.057 (P = 0.006) at 100-kb scale (Comeron et al. 2012)]. Combined, our data strongly suggest that meiotic crossover localization in Drosophila is influenced by both chromatin dynamics associated with transcription and DNA motifs that cause constitutive open chromatin through unusual secondary and tertiary DNA structures at least partly independent of transcription, in qualitative agreement with data from S. cerevisiae (Berchowitz et al. 2009). Nevertheless, additional work is required in Drosophila to characterize nucleosome dynamics and/or higher-order chromatin domains specific to female early meiosis stages to fully ascertain similarities and differences between species (Ohta et al. 1994; Wu and Lichten 1994; Fan and Petes 1996; Mirouze et al. 2012; Yelina et al. 2012; Adrian and Comeron 2013; Soriano et al. 2013; Aymard et al. 2014).

Conclusions

Our results show that the presence of specific DNA motifs that prevent nucleosome stabilization add an important layer of information when considering genomic landscapes of crossover in Drosophila, likely through very local constitutive open chromatin. Additionally, we show that the distribution of these motifs varies between populations and likely play a role in the observed intra-specific differences in crossover landscapes. Beyond the presence of these specific motifs and the large-scale centromere-effect, we identify the additional influence of transcription activity during early meiosis that creates a mechanistic link between local recombination rates and epigenetic features in a manner similar to yeast hotspots (Petes 2001). We propose that our study provides a baseline for future analyses in Drosophila designed to characterize the genetic causes of intra- and interspecific variation in crossover rates and the epigenetic mechanisms responsible for the known variability in crossover rates as response to different biotic and abiotic conditions and stresses.

Methods

Motif Landscape Generation

We used the position probability matrix (PPM) of 20 DNA motifs identified as enriched near crossover events from (Comeron, et al. 2012) (see supplementary fig. S1 and table S4, Supplementary Material online). To generate motif frequency estimates across chromosomes (motif landscapes), we developed a suite of custom python scripts designed to take PPM generated by MEME (Bailey et al. 2009) as input, apply a sliding-windows approach to estimate the likelihood of each stretch of DNA of containing the motif, and finally apply a FDR-based threshold to classify a sequence as belonging to a motif or not. In more detail, and for each motif, we applied a genomic scan to assign a likelihood L to every k-mer sequence across the genome to fit the PPM (with k indicating the length of the motif). L_i at position i is estimated as the log₁₀-transformed product of individual probabilities of the observed nucleotide j (j=A, G, C, T) at position x in the k-mer being at the same position x in the PPM (1 ≤ x≤ k). Nucleotide probabilities of 0 within the PPM were replaced by 1 × 10⁻¹⁰. We then generated a genome-wide null distribution of L_i (RL_i) based on random shuffling of nucleotide and dinucleotide composition using an equivalent approach. Finally, we used the complete null distribution of RL_i to obtain a threshold for observed L_i that would represent a desired false discovery rate (FDR) or L_FDR. We call a motif to be present at position i only when L_i> L_FDR. This approach allows applying any arbitrary FDR and, importantly, takes into account the number of sites under study. We chose to use a conservative FDR of 1% as it maximizes dynamic range and allows recovering sequence motifs nearly indistinguishable from those produced using an FDR < 1%, all while restricting the fraction of false positives to an acceptable threshold.

We generated motif landscapes with 1% FDR for the D. melanogaster reference genome 5.47 (dm3 assembly; http://flybase.org/) and for the RG and ZI populations [(Pool et al. 2012; Lack et al. 2015); see below] separately. Supplementary table S4, Supplementary Material online details the PPM for all motifs investigated in this study when applied to the RG population. The set of FDR-corrected motifs generate PPMs that are similar but not an exact match to the initial set of seed PPMs, which is not unexpected due to the limited number and genomic distribution of the original set of sequences analyzed. Some of the motifs reported to be enriched near crossover sites in Comeron et al. (2012) show very limited presence once the 1% FDR-correction is applied and, as consequence, motifs M13-M20 in supplementary table S4, Supplementary Material online, with fewer than 1,000 counts genome-wide, show no significant correlation with ρ_LD and were not included in the analyses. Unless noted, all 12 motifs present more than 1,000 times genome-wide (M1–M12) were used in the analyses (supplementary tables S1 and S4, Supplementary Material online), and the RG population was used to estimate motif distribution and ρ_LD (see below). Analyses towards investigating ρ_LD for the ZI population used motif landscapes along chromosomes from the ZI population.

Using positional information of each motif location, we generated sliding-window estimates of FDR-corrected motif presence for non-overlapping regions at different genomic scales across the genome, including 5-, 10-, 25-, 50- 100-, 250-, 500-, 1,000-, and 2,500-kb. Chromosome positions and gene annotations were based on the D. melanogaster dm3 assembly and annotation release 5.47 (http://flybase.org/). Sequence logos were generated using WebLogo 3 [http://weblogo.threeplusone.com (Crooks et al. 2004)].

LD-Based High-Resolution Crossover Maps

We calculated the population-scaled recombination rate for two African populations of D. melanogaster using the program LDhelmet (Chan et al. 2012). LDhelmet is a statistical method that allows estimating fine-scale recombination rates across genomes based on patterns of linkage disequilibrium, where the parameter estimated is the population-scaled crossover rate per bp and generation (ρ_LD); ρ_LD = 2N_er, where N_e is the effective population size of the population and r is the rate of crossover per bp and generation in females. Note, therefore, that estimates of ρ_LD by LDhelmet represent historic averages of estimates of crossover for the population or species under analysis. Following Chan et al. (2012), we applied a block penalty of 50 and used the RG matrix. We applied effective mutation rates estimated from the RG and ZI sequences: 0.008 and 0.0071 for autosomes and the X chromosome, respectively, for the RG population, and 0.011 and 0.0087 for autosomes and the X chromosome, respectively, for the ZI population. The data was divided into overlapping blocks of 4400 SNPs, with 200 SNPs of overlap. For each block we ran LDhelmet for 3,000,000 iterations after 300,000 iterations of burn-in. Recombination maps for each chromosomal arm were analyzed as non-overlapping adjacent windows at nine different genomic scales (5-, 10-, 25-, 50-, 100-, 250-, 500-, 1,000, and 2,500-kb). To remove sub-centromeric and –telomeric regions with strongly reduced crossover rates, we classified a sub-centromeric region by starting at the centromere and moving into the chromosome arm until a minimum of 3 consecutive 100-kb windows showed ρ_LD > 0.02, and sub-telomeric regions were assigned in an equivalent manner [see (Comeron et al. 2012)].

We analyzed the Rwanda (RG) and Zambia (ZI) populations because both show very limited levels of admixture and allow analyzing a relatively large sample of strains with no chromosomal inversions (Pool et al. 2012; Lack et al. 2015). We obtained the genomic sequences from the Drosophila Genome Nexus [http://www.johnpool.net/genomes.html; (Lack et al. 2015)] and analyzed strains with no evidence of chromosomal inversions in any chromosomal arm. In total our analysis included 19 RG sequences (RG10, RG13N, RG15, RG19, RG22, RG24, RG28, RG2, RG32N, RG33, RG34, RG35, RG38N, RG39, RG4N, RG6N, RG7, and RG8) and 20 ZI sequences (ZI184, ZI250, ZI252, ZI271, ZI311N, ZI320, ZI324, ZI332, ZI344, ZI378, ZI386, ZI398, ZI402, ZI418N, ZI420, ZI455N, ZI457, ZI477, ZI517, and ZI85). Unless noted, our analyses use the RG population because the low levels of admixture have been well characterized (Pool et al. 2012) and we masked admixture regions following (Pool et al. 2012; Lack et al. 2015). At 100kb-scale, ρ_LD estimated across the sequences of the RG and ZI populations show a Spearman’s r_s of 0.76 (P < 1 × 10⁻¹⁶).

To investigate whether the main trends observed in this study were driven by estimates of the population parameter ρ_LD that, at least partially, reflect differences in N_e rather than in recombination rate r, we normalized ρ_LD by estimates of silent nucleotide diversity (π_sil; π_sil = 4N_eμ in autosomes and 3N_eμ in the X chromosome, where μ is the mutation rate per bp and generation). To obtain π_sil, we estimated pairwise nucleotide variation per site at intergenic sequences, introns and 4-fold degenerate sites in coding regions from sequences of the RG population. Finally, we studied the influence of variable motif presence across the genome on the ratio ρ_LD/π_sil, which should be independent of N_e when both ρ_LD and π_sil are estimated from the same population and at the same genomic scale.

Open Chromatin Profiles and Transcriptional Activity in Early Female Meiosis

We used high-resolution open chromatin profiles in D. melanogaster from four differences samples and with two different methods. High-magnitude DNase I hypersensitive sites (DHS) from three different cell lines were obtained from http://compbio.hms.harvard.edu/kharchenko-et-al-nature-2011 (Kharchenko et al. 2011; Thomas et al. 2011). The three cell lines investigated are: S2 (S2-DRSC; derived from late male embryonic tissues, stages 16–17), BG3 (ML-DmBG3-c2; derived from the central nervous system of male third instar larvae), and Kc167 (derived from disaggregated young embryos 8–12 h old). We also obtained information on accessible chromatin regions in the eye-antennal imaginal disc generated using the recently developed ATAC methodology [(Davie et al. 2015); NCBI GEO samples GSM1426254- GSM1426256]. ATAC [Assay for Transposase Accessible Chromatin; (Buenrostro et al. 2015; Sos et al. 2016)] is more sensitive and robust than DNase-seq for identifying sites of high chromatin accessibility and thus can provide information more relevant for in vivo DSB (Davie et al. 2015). Transcriptome information during early female meiosis in D. melanogaster was generated by Adrian and Comeron (2013) and RNA-seq data are available at NCBI SRA SRP032523.

Analyses, Model Generation and Attribute Selection

We applied LASSO (Tibshirani 1996; Hastie et al. 2009) as implemented in the WEKA v3.6.1 software package [(Hall et al. 2009); http://www.cs.waikato.ac.nz/ml/weka/]. LASSO is a data mining technique that favors solutions with fewer parameter values under a linear model, simultaneously performing variable selection and simplifying model interpretation. The intensity of regularization (or shrinkage) within LASSO is controlled by the regularization/shrinkage parameter (λ). Unless noted, we used a λ that minimizes the cross validated mean squared error plus 0.5 standard error. Cross-validation (CV), which we used within LASSO, RF, and MARS analyses (see below), simulates the process of separately developing a model on one set of data and predicting for a test set of data not used in developing the model, with all aspects of the model development process repeated for each loop of the cross-validation.

We also utilized the WEKA implementation of Random Forests (RF) for classification. RF is a non-parametric approach useful for detecting associations when there are large numbers of predictor variables with the possibility that each variable has relatively weak effects (Breiman 2001; Banfield et al. 2007). Briefly, RF classification constructs a collection of many independent decision trees, sampling both the data and attributes randomly with replacement. The remaining, unused data is classified using the collection of trees, with the classification of each item being based upon the result mode of the RF. Here, we generated 1,000 trees of unrestricted depth with Log₂(Attribute Number) +1 random attributes in each individual tree. RF models were evaluated using 10-fold cross validation (CV), which involves splitting the complete dataset into ten equal sets and training on nine sets while testing on the remaining set—this process is then repeated ten times to obtain an average accuracy for each class. An exception to the 10-CV evaluation method was applied when studying how a model trained with data from an individual chromosomal arm performed when applied to other chromosomal arms, in which cases we used the full data from the chromosome used as training set and the full data from the chromosome used to test the model.

Each model was tested versus a ZeroR null model which classifies all instances solely based on the majority (mode) class. In all cases, the RF model performed significantly better at classification (two-tailed t-test, P < 0.05) than the null model unless otherwise noted. In order to select the best features for use in model generation, we ranked all features by the information gain criterion implemented in WEKA. Information gain is the measure of the contribution of a particular feature to the model. When calculating probabilities for RF models, we performed 250,000 whole-genome randomizations per model. For each randomization (replicate), RF modeling was limited to 150 trees using 10-fold cross validation in order to speedup computation at the expense of increased variance, and therefore generates conservative estimates. Conversely, when testing RF on the fourth chromosome, we used the complete genomic data from 2L, 2R, 3L, 3R, and the X for training and tested on the whole chromosome as well as on the thirteen adjacent 100-kb regions of this small chromosome. Tests on the fourth chromosome were repeated 20,000 times with 150 trees on random seeds in order to evaluate reliability.

We applied multivariate adaptive regression splines (MARS) (Friedman 1991; Friedman and Roosen 1995; Hastie et al. 2009) using the software suite Salford Predictive Modeler (v.7) from Salford Systems (http://www.salford-systems.com). MARS is a form of regression analysis that splits predictive variables into several intervals, allows potential non-linear relationships over different intervals (basis functions) and combines individual models as a final quantitative and predictive model. Importantly, MARS allows for any degree of interaction between variables. The quality of MARS models can be ascertained using the generalized cross-validation (GCV) criterion, with small GCV scores being indicative of superior model fit (Craven and Wahba 1979). Because the number of data points is not very large (n = 1,191 non-overlapping 100-kb regions), we avoided portioning the data into training and test samples and, instead, we initially applied cross-validation and the MARS legacy modes to estimate the optimal model and its performance (Friedman 1991). Note, however, that under the legacy mode MARS builds a sequence of models using all available data and can overestimate the performance of the model. We, thus, show MARS results based on 10-fold cross-validation to train and test classifiers unless specifically noted. We use the notation R²_CV to describe the MARS estimate of how well this model would perform on new data when using the 10-fold cross validation mode. In all cases, a 10-fold cross-validation mode generates smaller (more conservative) R²_CV than when a legacy mode is applied (R²_Legacy> R²_CV). Alternative estimates of model quality such standard R² using the whole dataset can be subject to substantial overfitting and are not reported (we obtained R² > R²_CV in all cases). Finally, variable importance under MARS was measured by the Gini index (Breiman et al. 1984).

Supplementary Material

Supplementary tables S1–S4 and figures S1–S3 are available at Genome Biology and Evolution online (http://www.gbe.oxfordjournals.org/).