Inter-chromosomal Linkage Disequilibrium Research Articles

Postzygotic barriers persist despite ongoing introgression in hybridizing Mimulus species.

The evolution of postzygotic isolation is thought to be a key step in maintaining species boundaries upon secondary contact, yet the dynamics and persistence of hybrid incompatibilities in naturally hybridizing species are not well understood. Here, we explore these issues using genetic mapping in three independent populations of recombinant inbred lines between naturally hybridizing monkeyflowers, Mimulus guttatus and Mimulus nasutus, from the sympatric Catherine Creek population. We discover that the three M. guttatus founders differ dramatically in admixture history, with nearly a quarter of one founder's genome introgressed from M. nasutus. Comparative genetic mapping in the three RIL populations reveals three new putative inversions, each one segregating among the M. guttatus founders, two due to admixture. We find strong, genome-wide transmission ratio distortion in all RILs, but patterns are highly variable among the three populations. At least some of this distortion appears to be explained by epistatic selection favouring parental genotypes, but tests of inter-chromosomal linkage disequilibrium also reveal multiple candidate Dobzhansky-Muller incompatibilities. We also map several genetic loci for hybrid pollen viability, including two interacting pairs that coincide with peaks of distortion. Remarkably, even with this limited sample of three M. guttatus lines, we discover abundant segregating variation for hybrid incompatibilities with M. nasutus, suggesting this population harbours diverse contributors to postzygotic isolation. Moreover, even with substantial admixture, hybrid incompatibilities between Mimulus species persist, suggesting postzygotic isolation might be a potent force in maintaining species barriers in this system.

Efficient estimation for large-scale linkage disequilibrium patterns of the human genome.

In this study, we proposed an efficient algorithm (X-LD) for estimating linkage disequilibrium (LD) patterns for a genomic grid, which can be of inter-chromosomal scale or of small segments. Compared with conventional methods, the proposed method was significantly faster, dropped from O(nm2) to O(n2m)-n the sample size and m the number of SNPs, and consequently we were permitted to explore in depth unknown or reveal long-anticipated LD features of the human genome. Having applied the algorithm for 1000 Genome Project (1KG), we found (1) the extended LD, driven by population structure, universally existed, and the strength of inter-chromosomal LD was about 10% of their respective intra-chromosomal LD in relatively homogeneous cohorts, such as FIN, and to nearly 56% in admixed cohort, such as ASW. (2) After splitting each chromosome into upmost of more than a half million grids, we elucidated the LD of the HLA region was nearly 42 folders higher than chromosome 6 in CEU and 11.58 in ASW; on chromosome 11, we observed that the LD of its centromere was nearly 94.05 folders higher than chromosome 11 in YRI and 42.73 in ASW. (3) We uncovered the long-anticipated inversely proportional linear relationship between the length of a chromosome and the strength of chromosomal LD, and their Pearson's correlation was on average over 0.80 for 26 1KG cohorts. However, this linear norm was so far perturbed by chromosome 11 given its more completely sequenced centromere region. Uniquely chromosome 8 of ASW was found most deviated from the linear norm than any other autosomes. The proposed algorithm has been realized in C++ (called X-LD) and is available at https://github.com/gc5k/gear2, and can be applied to explore LD features in any sequenced populations.

Efficient estimation for large-scale linkage disequilibrium patterns of the human genome

In this study, we proposed an efficient algorithm (X-LD) for estimating linkage disequilibrium (LD) patterns for a genomic grid, which can be of inter-chromosomal scale or of small segments. Compared with conventional methods, the proposed method was significantly faster, dropped from O(nm2) to O(n2m)—n the sample size and m the number of SNPs, and consequently we were permitted to explore in depth unknown or reveal long-anticipated LD features of the human genome. Having applied the algorithm for 1000 Genome Project (1KG), we found (1) the extended LD, driven by population structure, universally existed, and the strength of inter-chromosomal LD was about 10% of their respective intra-chromosomal LD in relatively homogeneous cohorts, such as FIN, and to nearly 56% in admixed cohort, such as ASW. (2) After splitting each chromosome into upmost of more than a half million grids, we elucidated the LD of the HLA region was nearly 42 folders higher than chromosome 6 in CEU and 11.58 in ASW; on chromosome 11, we observed that the LD of its centromere was nearly 94.05 folders higher than chromosome 11 in YRI and 42.73 in ASW. (3) We uncovered the long-anticipated inversely proportional linear relationship between the length of a chromosome and the strength of chromosomal LD, and their Pearson’s correlation was on average over 0.80 for 26 1KG cohorts. However, this linear norm was so far perturbed by chromosome 11 given its more completely sequenced centromere region. Uniquely chromosome 8 of ASW was found most deviated from the linear norm than any other autosomes. The proposed algorithm has been realized in C++ (called X-LD) and is available at https://github.com/gc5k/gear2, and can be applied to explore LD features in any sequenced populations.

Genomic mechanisms and consequences of diverse postzygotic barriers between monkeyflower species.

The evolution of genomic incompatibilities causing postzygotic barriers to hybridization is a key step in species divergence. Incompatibilities take two general forms - structural divergence between chromosomes leading to severe hybrid sterility in F1 hybrids and epistatic interactions between genes causing reduced fitness of hybrid gametes or zygotes (Dobzhansky-Muller incompatibilities). Despite substantial recent progress in understanding the molecular mechanisms and evolutionary origins of both types of incompatibility, how each behaves across multiple generations of hybridization remains relatively unexplored. Here, we use genetic mapping in F2 and RIL hybrid populations between the phenotypically divergent but naturally hybridizing monkeyflowers Mimulus cardinalis and M. parishii to characterize the genetic basis of hybrid incompatibility and examine its changing effects over multiple generations of experimental hybridization. In F2s, we found severe hybrid pollen inviability (< 50% reduction vs. parental genotypes) and pseudolinkage caused by a reciprocal translocation between Chromosomes 6 and 7 in the parental species. RILs retained excess heterozygosity around the translocation breakpoints, which caused substantial pollen inviability when interstitial crossovers had not created compatible heterokaryotypic configurations. Strong transmission ratio distortion and inter-chromosomal linkage disequilibrium in both F2s and RILs identified a novel two-locus genic incompatibility causing sex-independent gametophytic (haploid) lethality. The latter interaction eliminated three of the expected nine F2 genotypic classes via F1 gamete loss without detectable effects on the pollen number or viability of F2 double heterozygotes. Along with the mapping of numerous milder incompatibilities, these key findings illuminate the complex genetics of plant hybrid breakdown and are an important step toward understanding the genomic consequences of natural hybridization in this model system.

GWLD: an R package for genome-wide linkage disequilibrium analysis.

Linkage disequilibrium (LD) analysis is fundamental to the investigation of the genetic architecture of complex traits (e.g. human disease, animal and plant breeding) and population structure and evolution dynamics. However, until now, studies primarily focus on LD status between genetic variants located on the same chromosome. Moreover, genome (re)sequencing produces unprecedented numbers of genetic variants, and fast LD computation becomes a challenge. Here, we have developed GWLD, a parallelized and generalized tool designed for the rapid genome-wide calculation of LD values, including conventional D/D', r2, and (reduced) mutual information (MI and RMI) measures. LD between genetic variants within and across chromosomes can be rapidly computed and visualized in either an R package or a standalone C++ software package. To evaluate the accuracy and speed of LD calculation, we conducted comparisons using 4 real datasets. Interchromosomal LD patterns observed potentially reflect levels of selection intensity across different species. Both versions of GWLD, the R package (https://github.com/Rong-Zh/GWLD/GWLD-R) and the standalone C++ software (https://github.com/Rong-Zh/GWLD/GWLD-C++), are freely available on GitHub.

Population Structure and Association Mapping for Agronomical and Biochemical Traits of a Large Spanish Apple Germplasm.

A basic knowledge of linkage disequilibrium and population structure is necessary in order to determine the genetic control and identify significant associations with agronomical and phytochemical compounds in apple (Malus × domestica Borkh). In this study, 186 apple accessions (Pop1), representing both Spanish native accessions (94) and non-Spanish cultivars (92) from the EEAD-CSIC apple core collection, were assessed using 23 SSRs markers. Four populations were considered: Pop1, Pop2, Pop3, and Pop4. The initial Pop1 was divided into 150 diploid (Pop2) and 36 triploid accessions (Pop3), while for the inter-chromosomal linkage disequilibrium and the association mapping analysis, 118 phenotype diploid accessions were considered Pop4. Thus, the average number of alleles per locus and observed heterozygosity for the overall sample set (Pop1) were 15.65 and 0.75, respectively. The population structure analysis identified two subpopulations in the diploid accessions (Pop2 and Pop4) and four in the triploids (Pop3). Regarding the Pop4, the population structure with K = 2 subpopulations segregation was in agreement with the UPGMA cluster analysis according to the genetic pairwise distances. Moreover, the accessions seemed to be segregated by their origin (Spanish/non-Spanish) in the clustering analysis. One of the two subpopulations encountered was quite-exclusively formed by non-Spanish accessions (30 out of 33). Furthermore, agronomical and basic fruit quality parameters, antioxidant traits, individual sugars, and organic acids were assessed for the association mapping analysis. A high level of biodiversity was exhibited in the phenotypic characterization of Pop4, and a total of 126 significant associations were found between the 23 SSR markers and the 21 phenotypic traits evaluated. This study also identified many new marker-locus trait associations for the first time, such as in the antioxidant traits or in sugars and organic acids, which may be useful for predictions and for a better understanding of the apple genome.

Interchromosomal linkage disequilibrium and linked fitness cost loci associated with selection for herbicide resistance.

The adaptation of weeds to herbicide is both a significant problem in agriculture and a model of rapid adaptation. However, significant gaps remain in our knowledge of resistance controlled by many loci and the evolutionary factors that influence the maintenance of resistance. Here, using herbicide-resistant populations of the common morning glory (Ipomoea purpurea), we perform a multilevel analysis of the genome and transcriptome to uncover putative loci involved in nontarget-site herbicide resistance (NTSR) and to examine evolutionary forces underlying the maintenance of resistance in natural populations. We found loci involved in herbicide detoxification and stress sensing to be under selection and confirmed that detoxification is responsible for glyphosate (RoundUp) resistance using a functional assay. We identified interchromosomal linkage disequilibrium (ILD) among loci under selection reflecting either historical processes or additive effects leading to the resistance phenotype. We further identified potential fitness cost loci that were strongly linked to resistance alleles, indicating the role of genetic hitchhiking in maintaining the cost. Overall, our work suggests that NTSR glyphosate resistance in I. purpurea is conferred by multiple genes which are potentially maintained through generations via ILD, and that the fitness cost associated with resistance in this species is likely a by-product of genetic hitchhiking.

Postzygotic isolation drives genomic speciation between highly cryptic Hypocnemis antbirds from Amazonia.

How species evolve reproductive isolation in the species-rich Amazon basin is poorly understood in vertebrates. Here, we sequenced a reference genome and used a genome-wide sample of SNPs to analyze a hybrid zone between two highly cryptic species of Hypocnemis warbling-antbirds-the Rondonia warbling-antbird (H. ochrogyna) and Spix's warbling-antbird (H. striata)-in a headwater region of southern Amazonia. We found that both species commonly hybridize, producing F1 s and a variety of backcrosses with each species but we detected only one F2 -like hybrid. Patterns of heterozygosity, hybrid index, and interchromosomal linkage disequilibrium in hybrid populations closely match expectations under strong postzygotic isolation. Hybrid zone width (15.4 km) was much narrower than expected (211 km) indicating strong selection against hybrids. A remarkably high degree of concordance in cline centers and widths across loci, and a lack of reduced interspecific Fst between populations close to versus far from the contact zone, suggest that genetic incompatibilities have rendered most of the genome immune to introgression. These results support intrinsic postzygotic isolation as a driver of speciation in a moderately young cryptic species pair from the Amazon and suggest that species richness of the Amazon may be grossly underestimated.

Inter-chromosomal coupling between vision and pigmentation genes during genomic divergence

Recombination between loci underlying mate choice and ecological traits is a major evolutionary force acting against speciation with gene flow. The evolution of linkage disequilibrium between such loci is therefore a fundamental step in the origin of species. Here, we show that this process can take place in the absence of physical linkage in hamlets—a group of closely related reef fishes from the wider Caribbean that differ essentially in colour pattern and are reproductively isolated through strong visually-based assortative mating. Using full-genome analysis, we identify four narrow genomic intervals that are consistently differentiated among sympatric species in a backdrop of extremely low genomic divergence. These four intervals include genes involved in pigmentation (sox10), axial patterning (hoxc13a), photoreceptor development (casz1) and visual sensitivity (SWS and LWS opsins) that develop islands of long-distance and inter-chromosomal linkage disequilibrium as species diverge. The relatively simple genomic architecture of species differences facilitates the evolution of linkage disequilibrium in the presence of gene flow.

Evidence for Strong Kinship Influence on the Extent of Linkage Disequilibrium in Cultivated Common Beans.

Phaseolus vulgaris is an important grain legume for human consumption. Recently, association mapping studies have been performed for the species aiming to identify loci underlying quantitative variation of traits. It is now imperative to know whether the linkage disequilibrium (LD) reflects the true association between a marker and causative loci. The aim of this study was to estimate and analyze LD on a diversity panel of common beans using ordinary and extensions which correct bias due to population structure (), kinship (), and both (). A total of 10,362 single nucleotide polymorphisms (SNPs) were identified by genotyping by sequencing (GBS), and polymorphisms were found to be widely distributed along the 11 chromosomes. In terms of , high values of LD (over 0.8) were identified between SNPs located at opposite chromosomal ends. Estimates for were lower than those for . Results for and were similar, suggesting that kinship may also include information on population structure. Over genetic distance, LD decayed to 0.1 at a distance of 1 Mb for . Inter-chromosomal LD was also evidenced. This study showed that LD estimates decay dramatically according to the population structure, and especially the degree of kinship. Importantly, the LD estimates reported herein may influence our ability to perform association mapping studies on P. vulgaris.

Genome-wide association analysis of agronomic traits in wheat under drought-stressed and non-stressed conditions.

This study determined the population structure and genome-wide marker-trait association of agronomic traits of wheat for drought-tolerance breeding. Ninety-three diverse bread wheat genotypes were genotyped using the Diversity Arrays Technology sequencing (DArTseq) protocol. The number of days-to-heading (DTH), number of days-to-maturity (DTM), plant height (PHT), spike length (SPL), number of kernels per spike (KPS), thousand kernel weight (TKW) and grain yield (GYLD), assessed under drought-stressed and non-stressed conditions, were considered for the study. Population structure analysis and genome-wide association mapping were undertaken based on 16,383 silico DArTs loci with < 10% missing data. The population evaluated was grouped into nine distinct genetic structures. Inter-chromosomal linkage disequilibrium showed the existence of linkage decay as physical distance increased. A total of 62 significant (P < 0.001) marker-trait associations (MTAs) were detected explaining more than 20% of the phenotypic variation observed under both drought-stressed and non-stressed conditions. Significant (P < 0.001) MTA event(s) were observed for DTH, PHT, SPL, SPS, and KPS; under both stressed and non-stressed conditions, while additional significant (P < 0.05) associations were observed for TKW, DTM and GYLD under non-stressed condition. The MTAs reported in this population could be useful to initiate marker-assisted selection (MAS) and targeted trait introgression of wheat under drought-stressed and non-stressed conditions, and for fine mapping and cloning of the underlying genes and QTL.

Genetic differentiation and evolutionary adaptation in Cryptomeria japonica.

Local adaptation of plant species is a central issue for survival during global climate change, especially for long-lived forest trees, with their lengthy regeneration time and spatially limited gene flow. Identification of loci and/or genomic regions associated with local adaptation is necessary for knowledge of both evolution and molecular breeding for climate change. Cryptomeria japonica is an important species for forestry in Japan; it has a broad natural distribution and can survive in a range of different environments. The genetic structure of 14 natural populations of this species was investigated using 3930 SNP markers. Populations on the Pacific Ocean side of Japan are clearly different from those on the Japan Sea side, as discussed in previous studies. Structure analysis and population network trees show that peripheral populations, including the most northerly and southerly ones, have unique features. We found that the genetic differentiation coefficient is low, FST = 0.05, although it must account for the presence of important genes associated with adaptation to specific environments. In total, 208 outlier loci were detected, of which 43 were associated with environmental variables. Four clumped regions of outlier loci were detected in the genome by linkage analysis. Linkage disequilibrium (LD) was quite high in these clumps of outlier loci, which were found in linkage groups (LGs) 2, 7, 10, and 11, especially between populations of two varieties, and when interchromosomal LD was also detected. The LG7 region is characteristic of the Yakushima population, which is a large, isolated, peripheral population occupying a specific environment resulting from isolation combined with volcanic activity in the region. The detected LD may provide strong evidence for selection between varieties.

Long Distance Linkage Disequilibrium and Limited Hybridization Suggest Cryptic Speciation in Atlantic Cod

Hybrid zones provide unprecedented opportunity for the study of the evolution of reproductive isolation, and the extent of hybridization across individuals and genomes can illuminate the degree of isolation. We examine patterns of interchromosomal linkage disequilibrium (ILD) and the presence of hybridization in Atlantic cod, Gadus morhua, in previously identified hybrid zones in the North Atlantic. Here, previously identified clinal loci were mapped to the cod genome with most (∼70%) occurring in or associated with (<5 kb) coding regions representing a diverse array of possible functions and pathways. Despite the observation that clinal loci were distributed across three linkage groups, elevated ILD was observed among all groups of clinal loci and strongest in comparisons involving a region of low recombination along linkage group 7. Evidence of ILD supports a hypothesis of divergence hitchhiking transitioning to genome hitchhiking consistent with reproductive isolation. This hypothesis is supported by Bayesian characterization of hybrid classes present and we find evidence of common F1 hybrids in several regions consistent with frequent interbreeding, yet little evidence of F2 or backcrossed individuals. This work suggests that significant barriers to hybridization and introgression exist among these co-occurring groups of cod either through strong selection against hybrid individuals, or genetic incompatibility and intrinsic barriers to hybridization. In either case, the presence of strong clinal trends, and little gene flow despite extensive hybridization supports a hypothesis of reproductive isolation and cryptic speciation in Atlantic cod. Further work is required to test the degree and nature of reproductive isolation in this species.

Detection of molecular signatures of selection at microsatellite loci in the South African abalone (Haliotis midae) using a population genomic approach

Identifying genomic regions that may be under selection is important for elucidating the genetic architecture of complex phenotypes underlying adaptation to heterogeneous environments. A population genomic approach, using a classical neutrality test and various Fst-outlier detection methods was employed to evaluate genome-wide polymorphism data in order to identify loci that may be candidates for selection amongst six populations (three cultured and three wild) of the South African abalone, Haliotis midae. Approximately 9% of the genome-wide microsatellite markers were putatively subject to directional selection, whilst 6–18% of the genome is thought to be influenced by balancing selection. Genetic diversity estimates for candidate loci under directional selection was significantly reduced in comparison to candidate neutral loci, whilst candidate balancing selection loci demonstrated significantly higher levels of genetic diversity (Kruskal–Wallis test, P<0.05). Pairwise Fst estimates based on candidate directional selection loci also demonstrated increased levels of differentiation between study populations. Various candidate loci under selection showed significant inter-chromosomal linkage disequilibrium, suggesting possible gene-networks underling adaptive phenotypes. Furthermore, several loci had significant hits to known genes when performing BLAST searches to NCBI's non-redundant databases, whilst others are known to be derived from expressed sequences even though homology to a known gene could not be established. A number of loci also demonstrated relatively high similarity to transposable elements. The association of these loci to functional and genomically active sequences could in part explain the observed signatures of selection.

Inter-chromosomal level of genome organization and longevity-related phenotypes in humans.

Studies focusing on unraveling the genetic origin of health span in humans assume that polygenic, aging-related phenotypes are inherited through Mendelian mechanisms of inheritance of individual genes. We use the Framingham Heart Study (FHS) data to examine whether non-Mendelian mechanisms of inheritance can drive linkage of loci on non-homologous chromosomes and whether such mechanisms can be relevant to longevity-related phenotypes. We report on genome-wide inter-chromosomal linkage disequilibrium (LD) and on chromosome-wide intra-chromosomal LD and show that these are real phenomena in the FHS data. Genetic analysis of inheritance in families based on Mendelian segregation reveals that the alleles of single nucleotide polymorphisms (SNPs) in LD at loci on non-homologous chromosomes are inherited as a complex resembling haplotypes of a genetic unit. This result implies that the inter-chromosomal LD is likely caused by non-random assortment of non-homologous chromosomes during meiosis. The risk allele haplotypes can be subject to dominant-negative selection primary through the mechanisms of non-Mendelian inheritance. They can go to extinction within two human generations. The set of SNPs in inter-chromosomal LD (N=68) is nearly threefold enriched, with high significance (p=1.6 × 10(-9)), on non-synonymous coding variants (N=28) compared to the entire qualified set of the studied SNPs. Genes for the tightly linked SNPs are involved in fundamental biological processes in an organism. Survival analyses show that the revealed non-genetic linkage is associated with heritable complex phenotype of premature death. Our results suggest the presence of inter-chromosomal level of functional organization in the human genome and highlight a challenging problem of genomics of human health and aging.

Complex phenotypes and phenomenon of genome-wide inter-chromosomal linkage disequilibrium in the human genome

Studies of non-human species show that loci on non-homologous chromosomes can be in linkage disequilibrium (LD). I focus on the Framingham Heart Study (FHS) participants to explore whether the phenomenon of inter-chromosomal LD can be caused by non-stochastic bio-genetic mechanisms in the human genome and be associated with complex, polygenic phenotypes. This paper documents remarkably strong and extensive LD among SNPs at loci on multiple non-homologous chromosomes genotyped using two independent (Affymetrix 50 K and 500 K) arrays. The analyses provided compelling evidences that the observed inter-chromosomal LD was unlikely generated by stochasticity, population or family structure, or mis-genotyping. The analyses show that this LD is associated with complex heritable phenotypes characterizing poor health. The inter-chromosomal LD was observed in parental and offspring generations of the FHS participants. These findings suggest that inter-chromosomal LD can be caused by bio-genetic mechanisms possibly associated with favorable or unfavorable epistatic evolution. This phenomenon can challenge our understanding of the role of genes and gene networks in regulating complex, polygenic phenotypes in humans.

Linkage disequilibrium and population structure in wild and domesticated populations of Phaseolus vulgaris L.

Together with the knowledge of the population structure, a critical aspect for the planning of association and/or population genomics studies is the level of linkage disequilibrium (LD) that characterizes the species and the population used for such an analysis. We have analyzed the population structure and LD in wild and domesticated populations of Phaseolus vulgaris L. using amplified fragment length polymorphism markers, most of which were genetically mapped in two recombinant inbred populations. Our results reflect the previous knowledge of the occurrence of two major wild gene pools of P. vulgaris, from which two independent domestication events originated, one in the Andes and one in Mesoamerica. The high level of LD in the whole sample was mostly due to the gene pool structure, with a much higher LD in domesticated compared to wild populations. In relation to association studies, our results also suggest that whole-genome-scan approaches are feasible in the common bean. Interestingly, an excess of inter-chromosomal LD was found in the domesticated populations, which suggests an important role for epistatic selection during domestication. Moreover, our results indicate the occurrence of a strong bottleneck in the Andean wild population before domestication, suggesting a Mesoamerican origin of P. vulgaris. Finally, our data support the occurrence of a single domestication event in Mesoamerica, and the same scenario in the Andes.

Cytonuclear Genic Incompatibilities Cause Increased Mortality in Male F2 Hybrids of Nasonia giraulti and N. vitripennis

The haplodiploid wasp genus Nasonia is a promising model for studying the evolution of genic incompatibilities due to the existence of interfertile species and haploid males. The latter allows for significantly reducing the sample size required to detect and map recessive dysfunctional genic interactions. We exploited these features to study the genetics of intrinsic hybrid inviability in male F2 hybrids of Nasonia giraulti and N. vitripennis. Analyzing marker segregation in 225 hybrid embryos, we inferred a linkage map with 38 framework markers. The markers were tested for marker transmission ratio distortion (MTRD) and interchromosomal linkage disequilibrium in populations of embryonic and adult hybrids. We found evidence for four transmission ratio distorting loci (TRDL). Three TRDL showed a deficit of the N. giraulti allele in hybrids with N. vitripennis cytoplasm. A separate TRDL exhibited a deficiency of the N. vitripennis allele in hybrids with N. giraulti cytoplasm. We ascribe the observed MTRD in adult hybrids to cytonuclear genic incompatibilities causing differential mortality during development since hybrid embryos did not show MTRD. The identified cytonuclear genic incompatibilities in F2 hybrids with N. vitripennis cytoplasm account for most of the intrinsic hybrid inviability in this cross. The high mortality rate in F2 hybrids with N. giraulti cytoplasm cannot be explained by the single identified TRDL alone, however.