Interplay between large low-recombining regions and pseudo-overdominance in a plant genome

Abstract

To what extent overdominance might contribute to the maintenance of genetic diversity within genomes is still an ongoing research question. Pseudo-overdominance created by the complementation of deleterious alleles in heterozygotes has recently become a subject of particular interest. Simulations and theory suggest that pseudo-overdominance may occur in low recombining regions. Here, we conduct a comprehensive investigation of large low-recombining (LLR) regions in cultivated populations of pearl millet, an outcrossing diploid African cereal. We examine seven large regions ranging from 5 to 88 Mb and six of them are pericentromeric. These LLR regions exhibit an excess of heterozygotes, a distinctive hallmark of overdominance. They display a tendency toward a higher diversity and a larger ratio of non-synonymous and deleterious variants. We conduct a more in-depth study of the largest 88 Mb region, identified on chromosome 3. Interestingly, haplotypes of this region have been introgressed from wild relatives. Using long read sequencing, we confirm their strong divergence and the presence of inversions across one of them. One of the haplotypes seems to be highly deleterious in the homozygous state. A total of 17% of the cultivated pearl millet genome exhibit a local population structure suggestive of overdominance or possibly pseudo-overdominance. Our empirical results contribute to the accumulation of knowledge, which will enhance our understanding of the potential role of overdominance or pseudo-overdominance in maintaining genetic diversity, particularly in low recombining regions.

Introduction

Understanding how molecular polymorphism is maintained in populations is a longstanding question^1,2 in evolutionary biology. Initially, selection was thought to be a major driving force¹, with selective processes like overdominance favoring the maintenance of polymorphism in the population. Overdominance—a form of balancing selection³—is a selective mechanism whereby heterozygotes have higher fitness than both homozygotes at a given locus. Yet true overdominance is relatively uncommon^4,5,6 and, as such, cannot therefore account alone for the genome-wide diversity patterns observed in populations. Although natural selection was initially considered to be a major driver in shaping diversity, theory and evidence suggest neutral processes have a considerable impact on the genetic diversity that prevails in any population². Recently, there has been a renewed interest^7,8,9,10 in another overdominance pattern, namely so-called pseudo-overdominance (POD)⁸.

POD is defined by Gilbert et al.¹⁰ as a ‘form of balancing selection that maintains complementary deleterious haplotypes, effectively masking the effects of recessive deleterious mutations’. Consequently, the complementation of deleterious alleles in repulsion results in a heterozygote advantage^4,7,8. There is considerable confusion in the literature regarding the distinction between POD and associative overdominance^11,12,13. True overdominant alleles and deleterious alleles involved in POD can lead through hitchhiking to associative overdominance (AOD)^14,15, i.e., an apparent heterozygote advantage to nearby neutral loci^10,12,16.

To take place, POD requires linkage disequilibrium (LD) between partially recessive deleterious alleles^8,9. Strong LD can result from demographic factors, such as small population sizes, inbreeding^17,18, as well as from genomic factors, such as low recombination rates. Low recombination rates can be expected in centromeric regions or when structural variants like inversions are present. Sturtevant and Mather proposed a mechanism by which POD might arise and posited the occurrence of an inversion, which allows accumulation of deleterious alleles in LD in two haplotypes¹⁹. Regions subject to POD should harbor an excess of heterozygotes compared to the rest of the genome^8,9, and may contribute to higher-than-expected diversity across low-recombining regions^10,20. This mechanism is particularly interesting, as genomic regions with a low recombination rate are generally expected to display lower neutral diversity due to linkage with loci under selection against deleterious (background selection^21,22) or for beneficial (selective sweep²³) variants^10,20.

Recent simulations and theoretical studies have not allowed researchers to reach a consensus on the conditions required for the emergence of POD, its pervasiveness and the significance of its impact on variability^{8,9,10,12,24,25,26,27}. Additionally, there is not yet sufficient empirical evidence to help answer these questions^10,20,28. As a result, there is an urgent need to investigate POD patterns more frequently in genomic analyses, particularly since this phenomenon could be mistaken for other forms of balancing selection or could interfere with the detection of local adaptation¹⁰.

Here, we undertake a comprehensive study to identify large low-recombining (LLR) regions in a plant genome and to investigate whether true overdominance or POD processes might be at play in these regions. Pearl millet (Pennisetum glaucum (L.)) R. Br. syn. Cenchrus americanus (L.) Morrone, an allogamous diploid African cereal, has a genome size of 1.76 Gb with 7 metacentric chromosomes (2n = 14)²⁹. We use local PCA³⁰, a recent effective population genomics approach to detect LLR regions^30,31,32,33 in Senegalese pearl millet landraces. We then characterize these regions’ diversity patterns, which include heterozygote excess, increased diversity and accumulation of deleterious mutations. Our findings demonstrate a potential interplay between overdominance (i.e., true and POD) and LLR regions. These regions cover at least 17% of the pearl millet genome. We conduct a thorough investigation of the largest region. By combining several datasets, we find that this region, which includes one apparently lethal haplotype, shows signatures of introgression from wild populations.

Results

Multiple divergent haplotypes in the Senegalese pearl millet population

Pearl millet is a diploid allogamous cereal with high genetic diversity and a complex demographic history with gene flow from wild population³⁴. We applied local PCA³⁰, a population genomics approach that seeks outlier regions in terms of population structure compared to the rest of the genome^30,32. We used a dataset, referred to as the Senegalese dataset, composed of 126 cultivated pearl millet accessions from Senegal genotyped by exome capture sequencing (n = 76,018 filtered SNPs). The population was structured into early- and late-flowering landraces, as previously reported^35,36 (Supplementary Fig. 1). The local PCA analyses allowed us to identify seven regions ranging from 5.3 to 87.6 Mb (Table 1 and Supplementary Fig. 2). Six out of seven of the identified regions exhibit a population structure that deviated from the genome-wide pattern (early- vs late-flowering, Supplementary Fig. 1), where genetic diversity is organized into three to six distinct clusters. A population structure with three clusters distributed along the first PCA axis, with higher heterozygosity for the middle one, is expected when two non-recombining haplotypes are present in the population³² (Fig. 1a). We observed this pattern in the region identified on chromosomes 7 and 4 (Fig. 1b and Supplementary Fig. 2). When three non-recombining haplotypes: H₁, H₂ and the reference one, are present in the population, their combination results in six genotypic clusters³⁷ (Fig. 1d: clusters RR, RH₁, H₁H₁, RH₂, H₁H₂ and H₂H₂). This pattern was observed in the candidate regions identified on chromosomes 2, 3 and 6 (Fig. 1e and Supplementary Fig. 2). Because no or low recombination is expected between haplotypes, the average heterozygosity within an individual is expected to be higher in heterokaryotic individuals³². We indeed observed significantly higher heterozygosity in heterokaryotic clusters (Fig. 1c, f, Supplementary Fig. 2 and Supplementary Data 1). The six regions with a clear local population structure deviating from that of the rest of the genome collectively spanned 307.9 Mb. All but one of these regions included the putative centromere (Table 1). These regions represented approximately 17% of the genome and encompassed 3163 genes (Supplementary Fig. 3). The number of genes across these regions ranged from 95 to 688 (Table 1, Supplementary Data 2, and Supplementary Fig. 3).

Fig. 1: Local population structure and heterozygosity patterns associated with non-recombining haplotypes.

a Schematic representation of principal component analysis (PCA) expected pattern in the presence of two non-recombining haplotypes, the reference haplotype R and a single divergent alternate haplotype H₁, in a population. The population structure is characterized by three clusters separated on the first PC axis. Each cluster aligns with one of the three possible genotypes: two homozygotes (RR and H₁H₁) and one heterozygote (RH₁). b Results of a PCA analysis conducted in the LLR region identified on chromosome 7 from 129 to 178 Mb. Assignment of the accessions to the three clusters was performed with a kmean approach (red and blue circles represent likely homozygous genotypes, purple triangles likely heterozygous genotypes). c Observed heterozygosity pattern of the three clusters on chromosome 7. Each point displays mean individual heterozygosity with the confidence interval corresponding to ± 1.96 × the standard error of the mean (SEM). Sample sizes for clusters RR, RH₁, H₁H₁: n = 59, 50, 17. d Schematic representation of PCA in the presence of a reference haplotype R and of two alternate haplotypes H₁ and H₂ in a population. The population structure is characterized by up to six clusters. Each cluster aligns with one of the six possible genotypes associated with the different haplotypes. Three clusters of homozygotes (clusters RR, H₁H₁ and H₂H₂) and three clusters of heterozygotes (RH₁, RH₂ and H₁H₂) are expected. e Results of a PCA analysis conducted on chromosome 2 from 131 to 187 Mb. The accessions were assigned to clusters using the kmean approach (dark, blue and red circles for the three likely homozygous genotypes, purple triangles for the three likely heterozygous genotypes). f Observed heterozygosity pattern of the six clusters on chromosome 2. Each point displays mean individual heterozygosity with the confidence interval corresponding to ± 1.96 × SEM. Sample sizes for clusters RR, RH₁, H₁H₁, RH₂, H₁H₂, H₂H₂: n = 17, 21, 10, 33, 24, 21.

Table 1 Candidate regions identified across the genome

Moreover, these regions harbored SNPs with higher linkage disequilibrium (LD) when studying the whole population, but a tendency to a lower LD when considering only the cluster of the most frequent homokaryotype (Supplementary Fig. 2). They also displayed lower estimated recombination rates compared to the rest of the genome (Supplementary Fig. 4).

Signatures of overdominance and pseudo-overdominance

We tested whether the candidate regions displayed genetic hallmarks that could be associated with true overdominance or POD⁸: heterozygote excess, accumulation of deleterious mutations, and maintenance of higher genetic diversity. We first assessed if those regions harbored higher heterozygote excess than expected from the average observed in the rest of the genome. The six regions with a clear local population structure pattern (i.e., all but the one on chromosome 1) displayed significantly lower F_IS in comparison with the rest of the genome. Five of them were significantly negative, i.e., a signature of heterozygote excess compared to HWE expectations (Fig. 2, Table 1). Negative F_IS is relatively uncommon and can notably be indicative of a selective heterozygote advantage³⁸ (Supplementary Method 1, Supplementary Tables 1–3, and Supplementary Figs. 5, 6).

Fig. 2: Mean F_IS for the whole genome and the seven candidate regions.

The mean F_IS is represented by the dot, and the bar represents ± 1.96 × SEM confidence intervals. The dashed line indicates a zero F_IS value. The F_IS fixation coefficient is a metric of departure from Hardy-Weinberg equilibrium (HWE) departure. Values around zero meet a neutral expectation. Positive values indicate a heterozygote deficit, while negative values indicate a heterozygote excess compared to HWE expectations. Values were calculated for each region and for the whole genome, excluding these regions. The number of SNPs for each category is: all genome 76,018; Chr1 100–162 Mb 800, Chr2 131–187 Mb 800, Chr3 101–189 Mb 1000, Chr4 118–160 Mb 700, Chr6 133–201 Mb 800, Chr6 224–229 Mb 300, Chr7 129–178 Mb 700.

A second hallmark is an increase in diversity. However, five of the six candidate regions contain the centromeres, which are expected to exhibit low diversity^39,40. Indeed, as in other species^{39,40,41,42,43,44,45}, we observed a positive correlation between diversity (π, π_S) and recombination (Supplementary Figs. 7c, 8c). Based on the diversity-recombination rate relationship, one would expect a significant decrease in diversity in the candidate regions. Contrary to this expectation, almost all regions showed no significant reduction neither in π or π_S (Supplementary Table 4, Supplementary Figs. 7a, 8a), as if the negative effect of low recombination on diversity was compensated by overdominance or associative overdominance.

In an attempt to disentangle the effects of overdominance and low recombination, we also estimate π and π_S for the most frequent homokaryotypes. For the six regions we could test, diversity values for π and π_S for the most frequent homokaryotypes are reduced by almost 40% on average compared to when all karyotypes are considered (Supplementary Figs. 7b, 8b and Supplementary Table 5). Reductions were significant for four regions for π and three regions for π_S. We verified that these lower diversity estimates were not simply a consequence of reduced sample size. Such an effect has been ruled out for almost all estimates, except for π_S in candidate regions on chromosomes 2 and 6 (Supplementary Figs. 7e, 8e and Supplementary Table 6). Overall, these results suggested that π and π_S were maintained in the regions despite low recombination^39,40. Compared to the rest of the genome, we also found a tendency for higher values of π_N that were significant for regions on chromosomes 1, 2 and 7 and almost significant on chromosome 3 (Supplementary Fig. 9a and Supplementary Table 4). The increase was not correlated with low recombination rates (Supplementary Fig. 9c, d). When only homokaryotes are considered, π_N was reduced by 45% on average (Supplementary Fig. 9b and Supplementary Table 5). This reduction was significant for three regions, even though a small effect of sample size may occur as for π_S (Supplementary Fig. 9e and Supplementary Table 6). A tendency for higher deleterious load in the LLR regions in terms of the π_N /π_S ratio was observed (Supplementary Fig. 10, Table 1 and Supplementary Table 7). When we used the pN/pS ratio, all six regions exhibited a higher ratio compared to the rest of the genome, with three of these regions showing statistically significant differences (Table 1). We further used SIFT^46,47 and revealed a higher ratio of deleterious to tolerated mutations across the regions compared to that of the rest of the genome, with two of them being statistically significant (Table 1 and Supplementary Table 8). Overall, depending on the metric used, many of the regions showed the hallmark, suggesting possible true overdominance or POD in action.

In-depth study of the largest candidate region on chromosome 3

We delved deeper into the examination of the largest region on chromosome 3, spanning from 101 to 189 Mb (Table 1, Fig. 3 and Supplementary Fig. 2). Instead of the six expected clusters (Fig. 1d, and Supplementary Fig. 11c), this region was found to harbor only five distinct clusters (Fig. 3a and Supplementary Fig. 11a). The high heterozygosity noted for three of the clusters (Fig. 3b, and Supplementary Fig. 11b) suggested that one of the expected homozygous clusters (Fig. 1d and Supplementary Fig. 11c) was missing. We performed a PCAdapt analysis on the 1000 SNPs of the chromosome 3 candidate region on the Senegalese dataset to identify the SNPs that are responsible for the population structure. Visualizing genotypes for those 238 SNPs that had the most impact on the population structure enabled us to identify the haplotypes shaping the five clusters (Fig. 3c and Supplementary Fig. 11). The first divergent haplotype H₁, spanned an area from around 120 to 175 Mb, and was found at both homozygous and heterozygous states in clusters (H₁H_1, RH₁ and H₁H₂, Fig. 3c and Supplementary Fig. 11d). A second larger haplotype H₂, spanning the whole 88 Mb region, was only found at heterozygous states (RH₂ and H₁H_2, Fig. 3c and Supplementary Fig. 11d).

Fig. 3: Analysis of the chromosome 3 region.

a Local PCA performed on 1000 SNPs from 101 to 189 Mb. The 126 accessions were assigned to five clusters using a kmeans approach: RR (blue), RH₁ (purple), RH₂ (brown), H₁H₂ (orange), and H₁H₁ (red). b Mean heterozygosity in the five clusters (RR, RH₁, H₁H₁, RH₂ and H₁H₂) and ± 1.96 × SEM. Sample sizes for clusters RR, RH₁, H₁H₁, RH₂, H₁H₂: n = 23, 53, 30, 8, 12. c Visualization of the genotypes for the 238 SNPs identified by PCAdapt analysis as the ones contributing the most to local population structure along the candidate region of chromosome 3. Positions of the 238 SNPs are displayed on the x-axis. On the y-axis, the 126 accessions are ordered in accordance with their respective cluster (RR, RH₁, H₁H₁, RH₂ and H₁H₂). The genotypes are colored in blue for the homozygous reference genotypes (0/0), red for the homozygous alternate genotypes (1/1) and purple for the heterozygous genotypes (0/1). Missing genotypes are indicated in gray. d Scaffolds of an individual from the cluster H₁H₂ (Autof-Pod103sr8) aligned to chromosome 3 of the reference genome. Three hybrid scaffolds (sorted as Super-Scaffold_100020, Super-Scaffold_100024, Super-Scaffold_100015) are aligned to the chromosome 3 region from 100 to 200 Mb. Green coloring corresponds to alignments with an identity above 50%, while orange corresponds to alignments with an identity of 25 to 50%. The two arrows indicate possible breakpoints of a main inversion from around 155 to 175 Mb.

We sequenced and assembled one heterozygous individual, Autof-Pod103sr8, belonging to cluster H₁H_2, using long-read sequencing and optical mapping (Supplementary Table 9). This assembled individual confirmed the presence of at least one large inversion on H₁ with putative breakpoints at 155 and 175 Mb (Fig. 3d and Supplementary Fig. 12c). Other smaller inversions were present between 125 and 150 Mb (Fig. 3d and Supplementary Fig. 12c). The second haplotype H₂ spans the entire candidate region from approximately 101 to 189 Mb and aligns with the reference genome with low sequence identity ranging from 25 to 50% across this region (orange dots in Supplementary Fig. 12c). The two largest scaffolds obtained from optical mapping showed good alignment to the reference genome at the beginning and end of the chromosome, but showed low congruence in the central region, approximately from 100 to 200 Mb (highlighted in yellow in Supplementary Figs. 12b, 13a), in contrast to an inbred line used as a control (Supplementary Fig. 13b). The low sequence identity observed in the central region of the chromosome, as indicated by both synteny plots and optical mapping, suggested substantial sequence divergence of H₁ and H₂ with the reference genome. This genetic divergence was also supported by F_ST estimates. All pairwise F_ST between clusters were significantly higher in the region than in the rest of the genome (Supplementary Fig. 14 and Supplementary Table 10). Notably, this was also the case between the two haplotypes H₁ and H₂ since F_ST between RH₁-H₁H₂ and between H₁H₁-H₁H₂ were of the same order of magnitude. Although less pronounced, the same trend was observed when using D_XY (Supplementary Fig. 15 and Supplementary Table 11).

Origin of the divergent haplotypes of chromosome 3

The divergence of the chromosome 3 haplotypes observed when comparing the optical maps and the scaffolds of Autof-Pod103sr8 with the reference genome (Supplementary Figs. 12, 13) as well as the genetic distances estimates (Supplementary Figs. 14, 15) led us to hypothesize that the variant may have been derived from introgression. Pearl millet domestication initially took place in the central Sahelian region and, following its geographical spreading, cultivated pearl millet underwent introgression from Western wild populations in Senegal³⁴. We investigated the potential introgressed origin of the chromosome 3 haplotypes using an African dataset hosting data on 117 cultivated and 55 wild whole genomes distributed across Africa (Supplementary Fig. 16a). We first showed that the H₁ haplotype was predominantly present, while the H₂ haplotype was exclusively observed in cultivated pearl millet populations in Senegal (Supplementary Fig. 16b). Only Senegalese cultivated accessions from this African dataset were found within clusters RH₂, H₁H₂ and H₂H₂ (Supplementary Fig. 16b: dark circles). Of the 238 SNPs identified by the PCAdapt analysis (Fig. 3), 158 SNPs were shared with the African dataset. Visualizing those SNP genotypes using accessions from Western and Central wild populations, we could see that H₁ and H₂ haplotypes in the cultivated Senegalese accessions were highly similar to those found in the wild Western population (Fig. 4a), suggesting that they might have been the result of introgression. We estimated f_dM values⁴⁸ to statistically assess this finding and found a signature supporting introgression between the wild Western population and the cultivated population (positive f_dM values, Fig. 4b).

Fig. 4: Signature of introgression from Western wild populations on chromosome 3.

a Visualization of the SNP genotypes. Of the 238 SNPs depicted in Fig. 3, 158 SNPs were shared with the African dataset. Genotypes are shown in blue for the homozygous reference genotypes (0/0), red for the homozygous alternative genotypes (1/1) and purple for the heterozygous genotypes (0/1). Missing genotypes are shown in gray. Positions of the 158 SNPs are displayed on the x-axis. On the y-axis, 126 accessions are ordered as follows: clusters RR, RH₁, H₁H₁, RH₂ and H₁H₂ from top to bottom, as in Fig. 3, and the 47 wild accessions from Western Africa, then from Central Africa. b f_dM values along chromosome 3. f_dM, a statistic derived from ABBA-BABA tests, was calculated on non-overlapping 200 kb windows containing at least 200 SNPs. The f_dM values ranged from −1 to 1. In a (((P1, P2) P3) Outgroup) topology, values around zero suggest no gene flow, positive values suggest gene flow between P3 and P2, while negative values indicate gene flow between P3 and P1. Here the analysis was performed using ((Cultivated_center, Cultivated_west), Wild_west, Outgroup), thus positive f_dM values within the 101 to 189 Mb range indicate gene flow between wild and cultivated Western populations.

Segregation analysis of the divergent haplotypes of chromosome 3

A non-Mendelian segregation pattern was observed for two heterozygous SNPs in the progenies of three selfed individuals harboring the divergent chromosome 3 haplotype H₂ found only in the heterozygous state (Supplementary Data 3, Fig. 5). The H₂ homozygote genotypes expected at a frequency of 25%, were absent in two selfed progenies, and only found at 3% frequency in the third progeny. For these three populations, we also analyzed three other SNPs displaying strong linkage disequilibrium (r² 0.51 to 0.81, mean: 0.66, Supplementary Data 3) with the divergent haplotype outside the central region, and also observed the same non-Mendelian segregation pattern (Supplementary Data 3).

Fig. 5: Segregation analysis of one SNP diagnostic marker of the variant.

Segregation analysis of one SNP diagnostic marker of the chromosome 3 divergent haplotype H₂ at the position 116,359,949 for three selfed-breeding parents (Pod 103-4, Pod 113-7 and Pod 74-3). Gray bars correspond to the expected frequencies of each genotype (Ref/Ref, Ref/Alt and Alt/Alt) under Mendelian segregation. Black bars are the observed genotype frequencies in the progeny. The homozygous alternate genotype was missing or only detected at very low frequency (<1%) in the progeny of each parent (p < 1.1.10⁻⁷ for Pod 103-4, p < 3.5.10⁻⁹ for Pod 113-7, p < 1.4.10⁻⁷ for Pod 74-3; these p-values are still significant with Bonferroni correction for three tests). Source data are provided as a Source Data file.

In contrast, we noted Mendelian segregation for four out of five SNPs in progenies from reference homozygote individuals, i.e., the control experiment (Supplementary Data 3). Experimental assessment of the recombination rate in progenies from heterozygote parents revealed lower recombination compared to that from homozygote parents (Supplementary Data 4). Overall, these results suggested that the H₂ alternate haplotype behaved as highly deleterious at the homozygous state, which was in line with the absence of the H₂H₂ cluster observed earlier (Fig. 3a–c). With this extent of segregation bias, the H₂ haplotype would likely disappear rapidly from the population.

Temporal evolution of the divergent haplotypes of chromosome 3

We used the temporal dataset of pearl millet landraces sampled 40 years apart, i.e., in 1976 and 2016 (Supplementary Fig. 17a) in Senegal, to assess how the frequencies of the different chromosome 3 haplotypes have evolved over time. A total of 377 accessions and 39,672 filtered SNPs were retained after filtering and used to perform a PCA analysis of the region from 101 to 189 Mb on chromosome 3. Over the 40-year sampling period, we found the same structure, with five clusters containing accessions from both 1976 and 2016 datasets (Supplementary Fig. 17a, b) and a sixth cluster represented by only three accessions (<1% of the population). This sixth cluster displayed high homozygosity and was only found in 2016 (Supplementary Fig. 17a, b). Visualization of the genotypes of SNPs confirmed that the sixth cluster contains the H₂H₂ homozygotes (Supplementary Fig. 17b, c). The number of accessions carrying the haplotype H₂ (accessions of clusters RH₂, H₂H₂ and H₁H₂) increased significantly between 1976 and 2016 (p-value of Fisher test = 0.003, Supplementary Table 12) whereas the number of accessions carrying the haplotype H₁ (accessions of clusters RH₁, H₁H₁ and H₁H₂) decreased (p-value of Fisher test = 0.038, Supplementary Table 12). At the cluster level, a significant decrease in the number of accessions was observed for cluster H₁H₁ (p-value: 0.032, Supplementary Table 12), whereas there was a trend toward an increase in cluster RH₂ (p-value: 0.078, Supplementary Table 12). The maintenance of the haplotype H₂ in heterozygotes, despite its very low frequency in the homozygous state, could be explained by a higher relative fitness of heterokaryotypes.

Association of the divergent haplotypes of chromosome 3 with phenotypic traits

We tested the association between the divergent haplotypes H₁ and H₂ of chromosome 3 and phenotypic traits. A total of 11 traits related to plant morphology and flowering time³⁶ were assessed and obtained from three field experiments involving the 126 accessions of the Senegalese dataset. We found that the five clusters were significantly different with regard to fitness-related traits, including flowering time, total number of productive tillers, main panicle length, diameter and weight, and total seed weight (Supplementary Table 13). Heterozygote accessions with the 88 Mb divergent haplotype H₂ displayed an earlier flowering time, and a greater number of productive tillers, but a smaller main panicle weight and diameter (Supplementary Table 13, clusters RH₂ and H₁H₂). These phenotypes are characteristic of wild pearl millet and thus could be a phenotypic signature of introgression. However, GWAS analysis did not highlight any SNP associations with phenotypic traits across the chromosome 3 region (Supplementary Figs. 18, 19). Associations were only found between flowering time and SNPs at the beginning of chromosome 2 (Supplementary Figs. 18, 19), in accordance with the findings of a previous study³⁶.

Discussion

With the increasing availability of high-quality genomes, there is mounting evidence suggesting that large structural variants such as inversions play a crucial role in the evolution of animals and plants^49,50.

We employed a population genomics-based strategy, since approach of this type are known for their efficacy in detecting large low-recombining variants such as inversions^30,32,33,49 or highly divergent sequences^32,49. Among the seven regions flagged, six exhibited distinct patterns indicative of the presence of non-recombining haplotypes: a three to six clusters pattern, heightened heterozygosity, and increased LD across the entire set of individuals compared to a set of homozygotes only^31,32,49. In our study, those genomic regions were large, ranging from 5 to 88 Mb, encompassing 17% of the genome. Considering the efficiency of genomics-based approaches and the growing availability of genomic data, we anticipate that an increasing number of studies will reveal the prevalence and diversity of LLR regions. We conducted a detailed analysis of the candidate region on chromosome 3. Our findings suggest that this region likely originated through introgression from a divergent wild relative population. The two haplotypes, H₁ and H₂, exhibit significant divergence from the reference genome and some evidence of a low recombination rate. The H₁ haplotype carries an inversion and appears to have resulted from a double crossover event between 120 and 175 Mb, involving the reference haplotype and a divergent one. However, it remains unclear whether this latter haplotype corresponds to the H₂ currently segregating in the population. F_ST values between H₁ and H₂ are high within the region, suggesting substantial genetic differentiation. Therefore, H₁ and H₂ might both originate from introgression events.

Low-recombining regions leading to a six clusters pattern have been observed across various taxa, including marine snails^37,51, deer mice³³, stick insects⁵² and zebra finches⁵³. This pattern is anticipated when multiple rearrangements are present in the population. Our results highlight that haplotype diversity—featuring at least three non-recombining haplotypes—is more the rule than the exception, as evidenced by four out of the six genomic regions analyzed in this study. If the LLR involves an inversion, the emergence of multiple haplotypes may be further facilitated by the tendency of inversions to cluster in close proximity⁵⁴. A notable example is observed in Heliconius, where consecutive nearby inversions resulted in the second inverted haplotype, responsible for a variety of wing morphotypes^55,56.

Six of the candidate regions include the pericentromeric regions. Comparable patterns were observed in plants⁵⁷ and in birds⁵⁸, with regions notably conserved within genera. Centromeres, which are recognized as flexible and unstable regions⁵⁹, typically exhibit lower gene density and are characterized by high repeat content⁵⁴. In addition, substantial impacts of rearrangements such as inversions on centromere drive have been observed⁵⁴. Notably, the pivotal role of inversions in centromere evolution has been extensively demonstrated across various clades, including primates⁶⁰ and Fabaceae species such as Vigna⁶¹ and soybean⁶². Large structural variants associated with the centromere are likely to evade more effectively any negative selection processes, with a reduced probability of breakpoints exerting a negative impact or of the elimination of recombinant gametes⁶³. In addition, due to the near absence of recombination in centromeric regions, large structural variants such as inversion could also accumulate by a purely neutral process.

Another common hallmark of our candidate regions was their negative F_IS values, which were significantly pronounced in five of them. In empirical studies, positive F_IS values are observed more frequently than negative F_IS values³⁸. Negative F_IS values can suggest overdominance. The selective advantage in heterozygotes was confirmed for chromosome 3 candidate region, where the H₂ haplotype has been maintained for 40 years, despite its apparently strong deleterious effect in the homozygous state. However, negative F_IS values can also be observed in cases of asexuality, disassortative mating, or very small populations³⁸. Given the biology of pearl millet, these hypotheses to explain negative F_IS values seem less likely.

True overdominance is generally regarded as rare^4,5,6. The conditions for the occurrence of POD in natural populations have been theoretically studied^26,64,65. Distinguishing between true overdominance and POD remains a significant challenge⁴. Conventional approaches, such as GWAS, are often confounded by strong linkage disequilibrium within POD zones or the presence of large structural variants, making it difficult to pinpoint the beneficial alleles associated with true overdominance. Consequently, the absence of significant associations between SNPs and fitness-related traits on chromosome 3 does not necessarily exclude true overdominance.

In contrast to true overdominance, POD requires regions of strong linkage between deleterious loci. Hence, the role of inversions in POD was theoretically proposed from the outset¹⁹, but inversions are unlikely to be maintained by POD alone in random mating populations¹². Centromeres were also later identified as potential contributors to POD due to their low recombination rates⁹. All candidate regions exhibited low recombination rates, with six of them overlapping centromeric regions. POD is characterized by the presence of recessive or partially recessive deleterious mutations in repulsion with each other, resulting in haplotypes carrying distinct complements of mutations that enhance diversity and heterozygosity. We observed significantly higher π_N values in four regions, suggesting that POD could emerge or is already taking place. Non-recombining haplotypes tend to accumulate deleterious mutations due to reduced recombination in heterozygotes⁹, unless they capture strongly selected beneficial alleles³³. Hard selective sweep will facilitate their rapid rise to high frequencies, thereby limiting the accumulation of deleterious mutations³³. In our case, interpreting π_N/π_S ratios is particularly challenging, as a reduction in effective population size due to any cause will lead to an increase in π_N/π_S¹². For certain regions, metrics such as pN/pS ratios or the deleterious-to-tolerated mutation ratio indicate a tendency toward the expected accumulation of deleterious mutations in non-recombining haplotypes. Notably, one of the two haplotypes H₂ appears to be strongly deleterious at homozygous state. The accumulation of deleterious mutations may partially account for this apparent lethality²⁷, but other phenomena leading to half-lethal systems have been observed, such as gene disruption created by rearrangements⁶⁶.

While some necessary conditions for POD to emerge—such as low recombination and deleterious mutations in repulsion—are now well established in simulation studies^9,10, many uncertainties remain. Notably, questions persist regarding how much genetic load must accumulate or which demographic scenarios favor the emergence of POD. Most studies have focused on the emergence of structural variants and genetic load within a single population^10,12,24,26. Recent simulation studies^9,27 explored scenarios in which POD emerge through introgression. The heterozygote advantage was found to be positively associated with the divergence between populations and the deleterious load of the recipient population, provided that the deleterious loads of the two haplotypes are not too dissimilar²⁷. Under very restricted conditions, the two haplotypes are maintained over an extended period²⁷. In such cases, one of the probable fates is the evolution toward a half-lethal system²⁷. Some of these favorable conditions align with the scenario observed for the region on chromosome 3, which likely originated through introgression from a divergent wild relative population.

What are the evolutionary consequences of maintaining polymorphism of non-recombining haplotypes when POD is involved? POD could be viewed as an ‘evolutionary trap’, where the relative advantage of heterozygotes perpetuates haplotypes within populations despite their deleterious effects at homozygous state. Conversely, POD might act as an ‘evolutionary escape’ from the steady accumulation of genetic load in regions of low recombination, such as those near centromeres, by partitioning the load between haplotypes, ultimately fixing half of the deleterious mutations in each haplotype. Simulations suggest that states where both homokaryotypes are maintained are typically transient but can persist for thousands of generations^9,27. Evolutionary outcomes such as half-lethal systems (where one homokaryotype is lost) or balanced-lethal systems (where arrangements persist only at the heterozygous state) may persist longer but occur only under specific conditions for the latter one. In this latter case, population fitness decreases. Overall, simulation studies indicate that POD alone is unlikely to maintain polymorphism over long evolutionary timescales^9,24,27. However, many parameters remain unexplored, such as the number of migrants or introgression events, whether involving the same rearrangement or a novel one. More generally, we would argue that cultivated plant species may be prone to POD because: (1) cultivated species, in particular annual species, often undergo severe population bottlenecks^67,68 leading to a high cultivated genetic load⁶⁹ and (2) cultivated species show frequent hybridization in secondary contact zones propelled by human migrations^70,71,72.

Our empirical study revealed a significant excess of heterozygotes in a substantial portion of the pearl millet genome, coinciding with regions characterized by: (1) reduced recombination and (2) elevated diversity of deleterious mutations. While true overdominance cannot be ruled out, all conditions necessary for POD to play a role were observed in these regions. We postulate that POD might be one of the primary mechanisms for maintaining diversity across these expansive non-recombining genomic regions. In concordance with recent simulations and theoretical inquiries^9,10, we suggest that this phenomenon could be more widespread than previously recognized, with gene flow and hybridization potentially contributing to its prevalence. We advocate for a reevaluation, through the lens of POD, of patterns identified in recent genomic studies, anticipating that such patterns will become increasingly apparent with the increase of genomic data availability and the advancement of long-read sequencing techniques. More generally, we believe that future theoretical studies should delve deeper into the role of gene flow and divergence in the emergence of POD. A comprehensive understanding of selection processes involving POD, background selection^21,22 and positive selection will enrich our comprehension of how diversity in neutral and selected regions of the genome is shaped.

Methods

Sampling, sequencing and SNPs detection

SNPs detection is fully described in Supplementary Method 2. We used a previously published whole exome sequencing dataset³⁶, which we then referred to as the Senegalese dataset (Supplementary Data 5). It consisted of 130 pearl millet (Cenchrus americanus glaucum) individuals from early- (87 accessions) and late-flowering Senegalese landraces (43 accessions).

We studied temporal variations using an exome sequencing dataset of 384 accessions. This dataset was referred to as the temporal dataset (Supplementary Data 5). Two early-flowering Senegalese landraces were sampled 40 years apart, i.e., in 1976 and 2016. A total of 96 plants were sampled per year and per landrace. We designed a specific capture approach⁷³ targeting 1900 genes, including 1043 randomly picked genes, and 857 genes with a potential selection signature³⁴.

We also generated a full genome high-depth sequencing dataset referred to as the African dataset, composed of 172 individuals, including 117 cultivated (Cenchrus americanus glaucum) and 55 wild (Cenchrus americanus monodii) plants distributed across the African continent (Supplementary Data 5, Supplementary Fig. 16a), with 31 being cultivated accessions from Senegal. One additional cultivated sample was generated as a replicate to assess the SNP calling accuracy. A mean read depth of 30X was targeted per sample. A replicate was used to estimate the SNP detection accuracy and indicated that approximately 93.4% of the SNPs had been correctly called. Moreover, optical mapping and long-read sequencing data were generated for one of the accessions, Autof-Pod103sr8 (accession SAMN26040898, see “Genome assembly” section).

Identification of large low-recombining regions

Putative chromosomal rearrangements were detected in the Senegalese dataset, using a population genomic approach named local PCA^30,31,32. The method aims to detect regions with a population structure that differs from that of the rest of the genome and which could be candidates for the presence of non-recombining haplotypes. The method uses the R package lostruct³⁰ (v. 0.0.0.9000) and is implemented in an R pipeline (https://forge.ird.fr/diade/dynadiv/inversions_detection_code/-/tree/main/localPCA). Briefly, the genome was divided into non-overlapping genomic windows composed of 100 SNPs, and a PCA was performed on each window. The first two principal components of the PCA were used to calculate the distance between each pair of windows and to compute the distance matrix. This distance matrix was used to perform a multidimensional scaling (MDS) analysis with 40 dimensions and to display the dissimilarity between windows across the genome. Outlier windows were identified using a 5% false discovery rate. For each dimension, we only considered chromosomes with significantly higher outlier windows compared to the rest of the genome (Gtest function from R library DescTools, v. 0.99.49, threshold p-value 0.05) and with a minimum of four outlier windows. We then clustered outlier windows to define candidate regions using a correlation value of 0.6³¹.

Structure and diversity analysis

PCAs were performed with SNPRelate⁷⁴ (v. 1.28.0). Population structure analysis of the Senegalese cultivated dataset was performed with the R package LEA⁷⁵ (v. 3.6.0) and the snmf() function. Cross-entropy was calculated with 1 to 10 K clusters. To obtain further evidence that the candidate regions might harbor non-recombining haplotypes, we first visualized the population structure by performing PCAs separately on each candidate region (SNPRelate⁷⁴ v. 1.28.0). When the population was clearly structured, we assigned accessions to each cluster using a k-means clustering approach⁷⁶ and the R function kmeans (). The number of k clusters in the population was chosen visually on the PCA plots. We conducted k-means clustering 100 times and selected the result with the lowest total within-cluster sum of squares. Then for each cluster we calculated the mean heterozygosity using vcftools (v. 0.1.17, --het parameter), by dividing the number of heterozygous sites by the total number of sites. We conducted Wilcoxon tests (wilcox.test () R function, v. 4.2.1) to statistically assess the difference in heterozygosity between clusters.

For each SNP, we computed the observed number of heterozygotes (Ho) and the corresponding expected number (He) under Hardy-Weinberg equilibrium using vcftools (v.0.1.17, --hardy option). We then calculated the F_IS inbreeding coefficient for each SNP as follows: (He-Ho)/He. We calculated the mean F_IS for each candidate region and compared it to the rest of the genome using Wilcoxon tests (wilcox.test () R function, v. 4.2.1). We also used t-test to compare the mean F_IS for each candidate region with a value of 0, to assess departure from HWE expectation. We calculated the total number of genes within each candidate region using the annotation file of the new genome⁷⁷ (ENA accession ERZ15184682). We plotted the number of genes along the chromosomes within non-overlapping genomic windows of 200 kb.

We assessed linkage disequilibrium between pairs of SNPs along each chromosome. The analysis was performed on the Senegalese dataset. We randomly picked SNPs using vcftools with the --thin parameter (v. 0.1.16, --thin 1000). We then used plink⁷⁸ (v. 1.90, -- r2 parameter) to obtain intra-chromosomal r² values for all pairs of SNPs and plotted them across the chromosomes. The analysis was performed for the whole population and for a cluster of the most frequent homokaryotypes.

We used the ReLERNN⁷⁹ (v.1.0.0, default parameters) method to calculate the recombination parameter ρ = 4Nc, where N is the effective size and c is the recombination rate per nucleotide. ReLERNN⁷⁹ generates simulations under the assumption of demographic equilibrium to train a recurrent neural network (RNN) that will later estimate the recombination landscape of the empirical dataset. This approach exhibits low sensitivity to demographic bias, and it demonstrates strong performance in fitting the esimates to inversions frequency. We assigned windows to each candidate region on the condition that at least half of the window covered the region. For each candidate region, we used Wilcoxon tests (wilcox.test () R function, v. 4.2.1) to assess if the mean recombination rate across the region was lower compared to the rest of the genome, excluding the candidate regions. The analysis was performed on the Senegalese dataset.

Study of deleterious mutations on the Senegalese dataset

SIFT^46,47 (https://github.com/rvaser/sift4g) was used to predict the effect of the mutations on protein functions. We first created the SIFT database for the pearl millet reference genome (https://github.com/pauline-ng/SIFT4G_Create_Genomic_DB). SNPs were annotated using SIFT4G Annotator (https://github.com/pauline-ng/SIFT4G_Annotator) by assigning a SIFT score ranging from 0 (most deleterious) to 1 (most tolerated). We used a default threshold of 0.05, i.e., an SNP was annotated as deleterious if the SIFT score <0.05. We then calculated the ratio of deleterious to tolerated mutations for each candidate region and for the whole genome. We used G-tests (GTest() function from R library DescTools, v. 0.99.49) and a resampling procedure to assess if the ratio of deleterious to tolerated mutations of each candidate region was different from the rest of the whole genome. We computed the ratio for 1000 regions distributed randomly along the genome.

Diversity analysis of the candidate regions

Since diversity π is weighted by sequence length, we wanted to ensure that we were estimating the true sequenced length, i.e., the one for which we had sufficient sequencing depth and quality for polymorphic and non-polymorphic sites. Pixy handles missing data and uses invariant sites to calculate unbiased estimation of nucleotide diversity and divergence⁸⁰. To obtain the invariant sites for the Senegalese dataset, we used the --include-non-variant-sites option of the module GenotypeGVCFs of gatk (v.4.2.0.0). We removed invariant sites with ‘LowQual’ annotation. We then applied similar filters as for the SNPs. We masked as missing data the genotypes with DP < 5 and DP > 100, and only kept the invariant sites with less than 50% of missing data. Diversity π was estimated using pixy⁸⁰ (v. 1.2.10.beta2) within non-overlapping genomic windows of 10 Mb. The mean diversity π was then calculated for the whole genome and for each candidate region.

To estimate diversity at synonymous π_S and non-synonymous π_N sites, we used the script dNdSpiNpiS (v. 3 with the default parameters (https://kimura.univ-montp2.fr/PopPhyl/index.php?section=tools)). First, we generated a GFF file (ENA accession: ERZ24912374) using Liftoff ⁸¹ and the annotation files of the Tift 23D2B1-P1-P5 reference genome (https://doi.org/10.5524/100192). The -polish option was employed to re-align exons and ensure proper restoration of coding sequences. To extract phase information for the coding sequence (CDS) features, we used GenomeTools (gt gff3 -sort -tidy -retainids). Based on the VCF file, we then generate the diploid fasta sequence for each individual using the FastaAlternateReferenceMaker module from GATK⁸² (v. 4.2.3.0). We then intersect these fasta sequences with the GFF file generated to keep only CDS with SNPs, leading to a total of 6453 CDS. For each CDS, individuals with missing data were excluded when estimating π_N and π_S. As for π, these estimates should be corrected to account for truly invariant sites versus those resulting from insufficient sequencing depth. We used the invariant sites file generated in the previous section to estimate the expected percentage of bases called per CDS and applied this measure as a correction factor for the π_N and π_S estimates. The mean diversities π_N and π_S of the CDS were then calculated for the whole genome and for each candidate region. We used bootstraps to set 95% confidence intervals.

We used Wilcoxon tests or resampling procedures (1000 tests) to compare diversity estimates (π, π_N, π_S) between candidate regions and the rest of the genome. We additionally computed diversity estimates using only individuals from the most frequent homokaryotype for each candidate region identified with k-means clustering. The aim was to estimate the population diversity along pericentromeric and low-recombining regions without the effect of the presence of multiple haplotypes. For each candidate region, we used Wilcoxon tests to compare the mean estimate between the entire population and the most frequent homokaryotype. To evaluate the potential artifact of subsampling on the significance of these comparisons, we applied the same approach to the rest of the genome, excluding the candidate regions. We further assessed the correlation between the estimated recombination rate computed with ReLERNN⁷⁹ and diversity estimates. To do so, we computed the nucleotide diversity estimates within genomic windows of the same size as imposed by ReLERNN⁷⁹, from 15 Mb to 19 Mb, depending on the chromosomes.

In addition, π_N/π_S ratios were obtained by dividing the mean diversities π_N and π_S for the whole genome and for each candidate region. We compared π_N/π_S ratios between candidate regions and the rest of the genome excluding each candidate region using a resampling procedure with 1000 tests. We also computed pN and pS using the script dNdSpiNpiS (v. 3 with the default parameters, https://kimura.univ-montp2.fr/PopPhyl/index.php?section=tools). We computed the ratio pN/pS for the genome and for the candidate regions. We used a resampling procedure and 1000 tests to assess if the ratio pN/pS of each candidate region was different in comparison with the rest of the genome excluding the region tested.

In-depth study of the largest 88 Mb candidate region on chromosome 3

We conducted a PCAdapt⁸³ analysis (pcadapt package, version 4.3.3) on SNPs within the candidate region on chromosome 3. We performed the analysis with the Senegalese dataset using k = 2. We applied a 5% false discovery rate (Benjamin–Hochberg method) and identified SNPs exhibiting the highest differentiation on the first two PCA axes. Genotypes for these SNPs were visualized across the candidate region with the accessions ordered according to clusters previously identified in the population.

We used pixy⁸⁰ (v. 1.2.10.beta2) to estimate the statistics D_xy and F_ST⁸⁴ between the clusters of accessions harboring the different haplotypes on chromosome 3. We computed the statistics D_xy and F_ST within non-overlapping genomic windows of 100 kb. We plotted D_xy and F_ST values of the windows along the chromosomes. We used Wilcoxon tests and a resampling procedure to compare the mean F_ST and the mean D_xy found within each haplotype with the rest of the genome and for all pairs of clusters of accessions. We used the region between 125 and 175 Mb for the clusters harboring only the first alternate haplotype, and the region from 101 to 189 Mb for the clusters harboring the second alternate haplotype.

Optical maps were generated for the Autof-Pod103sr8 heterozygote Senegalese cultivated sample from the E group (see “Results”). Optical maps were generated by the French Plant Genomic Resources Centre (CNRGV) of the French National Research Institute for Agriculture, Food and Environment (INRAE)⁷⁷. De novo assembly was performed with the Bionano Solve pipeline⁸⁵ (v. 3.5.1) using molecules longer than 150 kb and with more than nine labels. We compared the optical maps of Autof-Pod103sr8 to the pearl millet reference genome (GCA_947561735.1). The seven chromosomes were first converted into optical maps using the fa2cmap_multi_color.pl script of Bionano Solve⁸⁵ (v3.3). We aligned the Autof-Pod103sr8 optical maps to the chromosomes using the runCharacterize.py script of Bionano Solve with RefAligner (v3.3, default parameters). Alignments were visualized with Bionano Access^85,86 (v 3.7). As a control, we also aligned other optical maps of the PMiGAP257 (ENA accession ERZ14864807) Senegalese cultivated inbred accession.

We generated long reads based on Oxford Nanopore for the same individual Autof-Pod103sr8, which carried the variant on chromosome 3. High molecular weight DNA was extracted from isolated plant nuclei and used to prepare RAD004 and LSK109 libraries for Nanopore sequencing (https://www.protocols.io/view/high-molecular-weight-dna-extraction-from-plant-nu-83shyne)⁸⁷. DNA was quantified by fluorometry (Qubit) and qualitatively assessed using pulsed field electrophoresis to ensure that the fragment sizes ranged from 40 to 150 kb. Libraries were constructed using the SQK-RAD004 Rapid Sequencing or SQK-LSK109 1D ligation genomic DNA kits (Oxford Nanopore Technologies) according to the supplier’s recommendations, with minor modifications: 4 µg of initial DNA without shearing, 7 min incubation for DNA repair and 13 min incubation for ligation for SQK-LSK109 library preparation, while only 1.5 µL of fragmentase was used versus 2.5 µL for RAD004 library preparation.

Base calling on ONT reads was performed with guppy (v. 6.0.6, dna_r9.4.1_450bps_hac.cfg model). SMARTdenovo⁸⁸ (v. 1.0) and reads longer than 1 kb were used for the assembly. Three rounds of Medaka (v. 1.7, https://github.com/nanoporetech/medaka) were performed to polish and correct contigs with high-quality long reads (longer than 2 kb and with a quality score Q above 10, filtered with NanoFilt⁸⁹ v. 1.0). Polishing with high-quality Illumina short reads (21X of coverage, accession SAMN26040898, bioproject PRJNA805042) was also performed using Hapo-G⁹⁰ (v 1.3 default parameters). We used BUSCO⁹¹ (Benchmarking Universal Single-Copy Orthologs, v. 5.4.3) and the Poales dataset (odb10, 4896 genes) to assess the contig quality. We ordered and oriented the ONT contigs using the assembled optical maps and the hybrid scaffolding pipeline of Bionano Solve⁸⁵ (v. 3.3, hybridScaffold.pl script with --B2 --N2 parameters). Scaffold alignments to chromosome 3 of the reference genome were visualized with D-genies⁹² (v. 1.4, enabling the ‘hide noises’ and ‘sorted contigs’ options and displaying alignments with more than 25% of identity). We performed annotation transfer to the scaffolds using Liftoff ⁸¹ (v 1.6.3, – copies – sc 0.50) using the annotation files of the previous Tift 23 D2B1-P1-P5 reference genome (https://doi.org/10.5524/100192)²⁹. We calculated the total number of genes spanning the candidate region on chromosome 3.

To study changes in the frequency of the chromosome 3 haplotypes, the temporal dataset was used over a span of 40 generations. We first confirmed the characteristic clustering of the population on chromosome 3 in both 1976 and 2016 using PCAs (SNPRelate⁷⁴ v. 1.28.0). We then identified SNPs with the highest differentiation using PCAdapt (k = 2), and visualized their genotypes. We applied a 5% false discovery rate (Benjamin–Hochberg method) and identified SNPs exhibiting the highest differentiation on the first two PCA axes. We examined whether the frequencies of the different haplotypes or clusters changed between 1976 and 2016 using a Fisher’s exact test with the R function fisher.test ().

We assessed segregation of individuals carrying the chromosome 3 haplotypes by selecting 10 SNPs distributed along the chromosome. These SNPs were chosen from the 1500 SNPs with the highest contribution to the second component axis according to Faye et al.³⁶ and are referred to here as diagnostic SNPs of the chromosome 3 haplotypes. We selfed 130 accessions in a phenotyping experiment carried out in 2016. From this set, a random sample of 95 parental plants was genotyped using the 10 diagnostic SNPs. We only retained five SNPs that met two criteria, namely: (1) they had fewer than 20% missing data for genotyping; and (2) they were polymorphic within at least one of the progenies. Subsequently, we selected three parents among those heterozygous for the five diagnostic SNPs. The progeny of each of these three parents—totaling 94 individuals per progeny—was genotyped using the five diagnostic SNPs. In addition, we chose two homozygous-reference progenies for the diagnostic SNPs as a control. For these segregations, we designed a new set selected from among all SNPs, excluding the one identified by Faye et al.³⁶ (see above). Given the expectation of greater homozygosity than observed in the previous set, the decision was taken to select 24 SNPs. They were distributed in regions and at intervals similar to those of the diagnostic SNPs. We applied the same filters as above, and one of the SNPs was disregarded due to its presence only in the heterozygous state, indicating a potential duplicated region. After filtering, the final SNP control set consisted of five SNPs. We conducted a Chi-square test to assess Mendelian segregation and estimated recombination rates based on offspring genotyping. We computed pairwise r² values between each of the five filtered SNPs using plink⁷⁸ (v. 1.90, -- r2 parameter) to obtain intra-chromosomal r² values for all SNP pairs all along the chromosomes.

To investigate associations between the chromosome 3 haplotypes and phenotypic traits, we used 11 phenotypic trait measurements described in Faye et al.³⁶ were used for the Senegalese cultivated dataset. Briefly, three field experiments were performed: one in Senegal in 2016 and two in Niger and Senegal in 2017. Three fully randomized repetitions were performed per trial, while 8 and 10 individuals per accession for each repetition were phenotyped in Niger and Senegal, respectively. A total of 11 traits associated with fitness were measured: date when half of flowers were in bloom (later referred to as flowering time); main panicle length; main panicle diameter; main panicle weight; main stem length; main stem diameter; total seed weight and 1000 seed weight of the main panicle; total number of tillers; and total number of productive and non-productive tillers. For each trait, the minimal and maximal measures were eliminated, and the mean trait value was calculated.

We tested the association of chromosome 3 haplotypes with each phenotypic trait. We first tested the relationship between each trait and the sample clusters identified across the candidate region. We used the R function lm () to fit a linear model and test the effects of the nine repetitions, the two flowering types and the clusters on each trait (formula: trait ~ repetitions + types + clusters). We then tested the association between the genotypes of each SNP and the phenotypic traits. Genotypes with missing values were imputed using the impute () function of the LEA R package⁷⁵ (v. 3.8). We tested the effects of the nine repetitions using the lm () function (formula: trait ~ repetitions) based on the mean residual values for each trait and each sample. We used emma⁹³  (v.1.1.2) and LFMM⁹⁴ (v. 1.0) for association mapping between the residual values and genotypes. LFMM corrects for population structure while emma corrects for the genetic relatedness between the accessions. We used k = 2 for the population structure correction. We applied a Bonferroni correction to the p-value significance threshold to account for multiple testing.

To study the geographic distribution of the chromosome 3 haplotypes, we used the African dataset, which included accessions distributed across Africa, to study the geographic distribution of the chromosome 3 haplotypes. PCA (SNPRelate⁷⁴, v. 1.28.0) was first performed with the full dataset. We intersected SNPs from the Senegalese and the African datasets. A local PCA was performed (SNPRelate⁷⁴, v. 1.28.0) with SNPs shared between the two datasets across the candidate region on chromosome 3 for cultivated accessions.

We further investigate the introgressed origin of the chromosome 3 haplotypes. We used Illumina short reads of two Cenchrus pedicellatus accessions (accessions: srx4310736 and srx4310737) as an outgroup. The methods of identification of SNPs and genotypes are fully described in Supplementary Method 2. We then tested for introgression between wild and cultivated pearl millet populations using the f_dM statistic based on the ABBA-BABA test⁴⁸. For the ((P1, (P2, P3)), O) genealogy, where O is the outgroup species, f_dM uses frequencies of the derived allele to estimate gene flow from P3 to P2 (positive values) or from P3 to P1 (negative values). We used sNMF⁹⁵ (v 2.0) software implemented in the R package LEA⁷⁵ (v 3.14) to verify the assignment to wild vs cultivated and geographical subgroups. We first ran the analyses on all accessions to distinguish wild vs cultivated and then only on the cultivated accessions. The procedure was as follows: 10 analyses with K ranging from 1 to 10, with 5 repetitions for each K and 5 million SNPs randomly sampled along the genome for each of the 10 analyses. We only used accessions that could be assigned to the following respective groups with a threshold above 0.7 and in line with the sampling geographic coordinates: WILD_West (27 accessions from Senegal-Mauritania); WILD_Center (22 accessions from Niger, Mali and Chad); CULT_West (27 accessions from Senegal); CULT_Center (20 accessions from Mali, Burkina Faso and Niger); and CULT_East_South  (29 accessions from the rest of Africa). Then we calculated f_dM values using the following topology ((CULT_Center, (CULT_West, WILD_West)), Out) along 200 kb non-overlapping windows using scripts from Martin et al.⁹⁶.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.