Linkage disequilibrium in European elite maize germplasm investigated with SSRs

Information about the extent and genomic distribution of linkage disequilibrium (LD) is of fundamental importance for association mapping. The main objectives of this study were to (1) investigate genetic diversity within germplasm groups of elite European maize (Zea mays L.) inbred lines, (2) examine the population structure of elite European maize germplasm, and (3) determine the extent and genomic distribution of LD between pairs of simple sequence repeat (SSR) markers. We examined genetic diversity and LD in a cross section of European and US elite breeding material comprising 147 inbred lines genotyped with 100 SSR markers. For gene diversity within each group, significant (P<0.05) differences existed among the groups. The LD was significant (P<0.05) for 49% of the SSR marker pairs in the 80 flint lines and for 56% of the SSR marker pairs in the 57 dent lines. The ratio of linked to unlinked loci in LD was 1.1 for both germplasm groups. The high incidence of LD suggests that the extent of LD between SSR markers should allow the detection of marker-phenotype associations in a genome scan. However, our results also indicate that a high proportion of the observed LD is generated by forces, such as relatedness, population stratification, and genetic drift, which cause a high risk of detecting false positives in association mapping.     

Extent and genome-wide distribution of linkage disequilibrium in commercial maize germplasm

Association mapping is based on linkage disequilibrium (LD) resulting from historical recombinations and helps understanding the genetic basis of complex traits. Many factors affect LD and, therefore, it must be determined empirically in the germplasm under investigation to examine the prospects of successful genome-wide association mapping. The objectives of our study were to (1) examine the extent of LD with simple sequence repeat (SSR) and single nucleotide polymorphism (SNP) markers in 1,537 commercial maize inbred lines belonging to four heterotic pools, (2) compare the LD patterns determined by these two marker types, (3) evaluate the number of SNP markers needed to perform genome-wide association analyses, and (4) investigate temporal trends of LD. Mean values of the squared correlation coefficient ( $ \bar{R} $ ) were almost identical for unlinked, linked, and adjacent SSR marker pairs. In contrast, $ \bar{R} $ values were lowest for the unlinked SNP loci and highest for the SNPs within amplicons. LD decay varied across the different heterotic pools and the individual chromosomes. The SSR markers employed in the present study are not adequate for association analysis, because of insufficient marker density for the germplasm evaluated. Based on the decay of LD in the various heterotic pools, we would need between 4,000 and 65,000 SNP markers to detect with a reasonable power associations with rather large quantitative trait loci (QTL). A much higher marker density is required to identify QTL with smaller effects. However, not only the total number of markers but also their distribution among and along the chromosomes are primordial for undertaking powerful association analyses.     

High levels of linkage disequilibrium and associations with forage quality at a Phenylalanine Ammonia-Lyase locus in European maize (Zea mays L.) inbreds

Forage quality of maize is influenced by both the content and structure of lignin in the cell wall. Phenylalanine Ammonia-Lyase (PAL) catalyzes the first step in lignin biosynthesis in plants; the deamination of L-phenylalanine to cinnamic acid. Successive enzymatic steps lead to the formation of three monolignols, constituting the complex structure of lignin. We have cloned and sequenced a PAL genomic sequence from 32 maize inbred lines currently employed in forage maize breeding programs in Europe. Low nucleotide diversity and excessive linkage disequilibrium (LD) was identified at this PAL locus, possibly reflecting selective constrains resulting from PAL being the first enzyme in the monolignol, and other, pathways. While the association analysis was affected by extended LD and population structure, several individual polymorphisms were associated with neutral detergent fiber (not considering population structure) and a single polymorphism was associated with in vitro digestibility of organic matter (considering population structure).     

Testing for linkage disequilibrium in the New Zealand radiata pine breeding population

Linkage analysis is commonly used to find marker-trait associations within the full-sib families of forest tree and other species. Study of marker-trait associations at the population level is termed linkage-disequilibrium (LD) mapping. A female-tester design comprising 200 full-sib families generated by crossing 40 pollen parents with five female parents was used to assess the relationship between the marker-allele frequency classes obtained from parental genotypes at SSR marker loci and the full-sib family performance (average predicted breeding value of two parents) in radiata pine (Pinus radiata D. Don). For alleles (at a marker locus) that showed significant association, the copy number of that allele in the parents was significantly correlated, either positively or negatively, with the full-sib family performance for various economic traits. Regression of parental breeding value on its genotype at marker loci revealed that most of the markers that showed significant association with full-sib family performance were not significantly associated with the parental breeding values. This suggests that over-representation of the female parents in our sample of 200 full-sib families could have biased the process of detecting marker-trait associations. The evidence for the existence of marker-trait LD in the population studied is rather weak and would require further testing. The exact test for genotypic disequilibrium between pairs of linked or unlinked marker loci revealed non-significant LD. Observed genotypic frequencies at several marker loci were significantly different from the expected Hardy-Weinberg equilibrium. The possibilities of utilising marker-trait associations for early selection, among-family selection and selecting parents for the next generation of breeding are also discussed.     

A program to test linkage disequilibrium between loci in autotetraploid species

No software currently implements a test of linkage disequilibrium in autotetraploid species. We propose a program, LD4X that performs a Fisher's exact test between pairs of alleles at two loci. All combinations of alleles from two loci are treated in turn. If two alleles of a pair of loci have a nonrandom distribution, the markers are considered as linked. The program was tested on a set of microsatellite markers in synthetic alfalfa populations.     

Population structure and linkage disequilibrium of a mini core set of maize inbred lines in China

Understanding genetic diversity, population structure, and the level and distribution of linkage disequilibrium (LD) in target populations are of great importance and the prerequisite for association mapping. In the present study, 145 genome-wide SSR markers were used to assess the genetic diversity, population structure, and LD of a set of 95 maize inbred lines which represented the Chinese maize inbred lines. Results showed that the population included a diverse genetic variation. A model-based population structure analysis subdivided the inbred lines into four subgroups that correspond to the four major empirical germplasm origins in China, i.e., Lancaster, Reid, Tangsipingtou and P. Among all of the inbred lines, 65.3% were assigned into the corresponding subgroups; others were assigned into a “mixed” subgroup. LD was significant at a 0.01 level between 63.89% of the SSR pairs in the entire sample and with a range of 18.75–40.28% in the subgroups. Among factors influencing LD, linkage was the major cause for LD of SSR loci. The results suggested that the population may be used in the detection of genome-wide SSR marker–phenotype association. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users. R. Wang and Y. Yu contributed equally to the work.     

SNP frequency, haplotype structure and linkage disequilibrium in elite maize inbred lines

Background  

Recent studies of ancestral maize populations indicate that linkage disequilibrium tends to dissipate rapidly, sometimes within 100 bp. We set out to examine the linkage disequilibrium and diversity in maize elite inbred lines, which have been subject to population bottlenecks and intense selection by breeders. Such population events are expected to increase the amount of linkage disequilibrium, but reduce diversity. The results of this study will inform the design of genetic association studies.     

Extent and consistency across generations of linkage disequilibrium in commercial layer chicken breeding populations

Recent studies report a surprisingly high degree of marker-to-marker linkage disequilibrium (LD) in ruminant livestock populations. This has important implications for QTL mapping and marker-assisted selection. This study evaluated LD between microsatellite markers in a number of breeding populations of layer chickens using the standardized chi-square (chi(2')) measure. The results show appreciable LD among markers separated by up to 5 cM, decreasing rapidly with increased separation between markers. The LD within 5 cM was strongly conserved across generations and differed among chromosomal regions. Using marker-to-marker LD as an indication for marker-QTL LD, a genome scan of markers spaced 2 cM apart at moderate power would have good chances of uncovering most QTL segregating in these populations. However, of markers showing significant trait associations, only 57% are expected to be within 5 cM of the responsible QTL, and the remainder will be up to 20 cM away. Thus, high-resolution LD mapping of QTL will require dense marker genotyping across the region of interest to allow for interval mapping of the QTL.     

DSLINK: a computer program for gene-centromere linkage analysis in families with a trisomic offspring.

Trisomic individuals provide information for gene-centromere mapping, since two of the four chromatids in a meiotic tetrad can be recovered. When centromeric markers are available, linkage analysis between the centromere and any marker locus can be performed in nuclear families having one or more trisomic offspring. Since conventional linkage programs consider only disomic individuals, we have written a FORTRAN computer program, DSLINK, that performs gene-centromere linkage analysis on the basis of information on trisomic and disomic offspring. This program makes it possible to study the relationship between recombination and chromosome segregation.     

ldne: a program for estimating effective population size from data on linkage disequilibrium

ldne is a program with a Visual Basic interface that implements a recently developed bias correction for estimates of effective population size (N(e) ) based on linkage disequilibrium data. The program reads genotypic data in standard formats and can accommodate an arbitrary number of samples, individuals, loci, and alleles, as well as two mating systems: random and lifetime monogamy. ldne calculates separate estimates using different criteria for excluding rare alleles, which facilitates evaluation of data for highly polymorphic markers such as microsatellites. The program also introduces a jackknife method for obtaining confidence intervals that appears to perform better than parametric methods currently in use.     

Towards linkage analysis with markers in linkage disequilibrium by graphical modelling

We review recent developments of MCMC integration methods for computations on graphical models for two applications in statistical genetics: modelling allelic association and pedigree based linkage analysis. We discuss and illustrate estimation of graphical models from haploid and diploid genotypes, and the importance of MCMC updating schemes beyond what is strictly necessary for irreducibility. We then outline an approach combining these methods to compute linkage statistics when alleles at the marker loci are in linkage disequilibrium. Other extensions suitable for analysis of SNP genotype data in pedigrees are also discussed and programs that implement these methods, and which are available from the author's web site, are described. We conclude with a discussion of how this still experimental approach might be further developed.     

Accuracy of genomic selection in European maize elite breeding populations

Genomic selection is a promising breeding strategy for rapid improvement of complex traits. The objective of our study was to investigate the prediction accuracy of genomic breeding values through cross validation. The study was based on experimental data of six segregating populations from a half-diallel mating design with 788 testcross progenies from an elite maize breeding program. The plants were intensively phenotyped in multi-location field trials and fingerprinted with 960 SNP markers. We used random regression best linear unbiased prediction in combination with fivefold cross validation. The prediction accuracy across populations was higher for grain moisture (0.90) than for grain yield (0.58). The accuracy of genomic selection realized for grain yield corresponds to the precision of phenotyping at unreplicated field trials in 3–4 locations. As for maize up to three generations are feasible per year, selection gain per unit time is high and, consequently, genomic selection holds great promise for maize breeding programs.     

Genetic variability in a genomic region with long-range linkage disequilibrium reveals traces of a bottleneck in the history of the European population

The inference of the demographic history of populations from genetic variability data is not only of academic interest. It also provides background information for the identification of genes which may have played a role in human evolution or in the aetiology of human disease. To obtain a clear picture of this background, it is necessary to compare data obtained from a number of genomic loci. Due to its very low recombination rate, the NF1 gene region can be regarded as a further suitable locus. A combined resequencing and SNP typing project in a European population disclosed the presence of only two well separated subgroups of NF1 sequences. Statistical analysis revealed a bimodal distribution of the pairwise differences, a positive value of Tajima’s D and a TMRCA of 700,000 years for the whole sample, and pairwise differences indicative for a growing population and TMRCAs of 130,000 to 150,000 years for the subgroups. Together, the data lead to a model that the recent European population went through a bottleneck during the last 150,000 years of its history. Regarding the given timeframe, this bottleneck could either reflect a speciation event which led to the anatomically modern human (AMH), or a severe reduction of the population size during the emigration of AMHs out of Africa or the immigration into Europe.     

Levels of linkage disequilibrium in a wild bird population

Population-based mapping approaches are attractive for tracing the genetic background to phenotypic traits in wild species, given that it is often difficult to gather extensive and well-defined pedigrees needed for quantitative trait locus analysis. However, the feasibility of association or hitch-hiking mapping is dependent on the degree of linkage disequilibrium (LD) in the population, on which there is yet limited information for wild species. Here we use single nucleotide polymorphism (SNP) markers from 23 genes in a recently established linkage map of the Z chromosome of the collared flycatcher, to study the extent of LD in a natural bird population. In most but not all cases we find SNPs within the same intron (less than 500 bp) to be in perfect LD. However, LD then decays to background level at a distance 1cM or 400-500 kb. Although LD seems more extensive than in other species, if the observed pattern is representative for other regions of the genome and turns out to be a general feature of natural bird populations, dense marker maps might be needed for genome scans aimed at identifying association between marker and trait loci.     

Extent of linkage disequilibrium in chicken

Many of the economically important traits in chicken are multifactorial and governed by multiple genes located at different quantitative trait loci (QTLs). The optimal marker density to identify these QTLs in linkage and association studies is largely determined by the extent of linkage disequilibrium (LD) around them. In this study, we investigated the extent of LD on two chromosomes in a white layer and two broiler chicken breeds. Pairwise levels of LD were calculated for 33 and 36 markers on chromosomes 10 and 28, respectively. We found that useful LD (i.e. an r(2) value higher than 0.3) in Nutreco chicken breed E5 (inbred) can extend to around 1 cM on chromosomes 10 and 28, although in a second region on chromosome 28 it extends to about 2.5 cM. The extent in breed Nutreco E3 (outbred) was very short in chromosome 10 (15 kb) but very much larger on chromosome 28, particularly in one region of depressed heterozygosity. The layer breed E2 (inbred) showed an extent of useful LD up to 4 cM on chromosome 10; the extent on chromosome 28 could not be assessed due to an erratic pattern of LD on that chromosome, although in one region LD appears to be in the order of 0.8 cM. This indicates that there may be very large differences in patterns of LD between different chicken breeds and different genomic regions.     

A FORTRAN program for the calculation and analysis of two-locus linkage disequilibrium coefficients

Summary A FORTRAN program was written that calculates composite linkage disequilibrium coefficients from genotypic data. Chi-square tests determine whether coefficients calculated for allele and locus pairs are significantly greater than zero. A subroutine is provided that partitions the variance in linkage disequilibrium into within- and between-subpopulation components. Output obtained from analysis of allozyme data collected from natural subpopulations of the house fly (Musca domestica L.) are included to illustrate features of the program.Journal Paper No. J-11345 of the Iowa Agriculture and Home Economics Experiment Station, Ames, Iowa. Project No. 2411     

The posterior probability of linkage allowing for linkage disequilibrium and a new estimate of disequilibrium between a trait and a marker

The posterior probability of linkage (PPL) statistic has been developed as a method for the rigorous accumulation of evidence for or against linkage allowing for both intra- and inter-sample heterogeneity. To date, the method has assumed linkage equilibrium between alleles at the trait locus and the marker locus. We now generalize the PPL to allow for linkage disequilibrium (LD), by incorporating variable phase probabilities into the underlying linkage likelihood. This enables us to recover the marginal posterior density of the recombination fraction, integrating out nuisance parameters of the trait model, including the locus heterogeneity (admixture) parameter, as well as a vector of LD parameters. The marginal posterior density can then be updated across data subsets or new data as they become available, while allowing parameters of the trait model to vary between data sets. The method applies immediately to general pedigree structures and to markers with multiple alleles. In the case of SNPs, the likelihood is parameterized in terms of the standard single LD parameter D'; and it therefore affords a mechanism for estimation of D' between the marker and the trait, again, without fixing the parameters of the trait model and allowing for updating across data sets. It is even possible to allow for a different associated allele in different populations, while accumulating information regarding the strength of LD. While a computationally efficient implementation for multi-allelic markers is still in progress, we have implemented a version of this new LD-PPL for SNPs and evaluated its performance in nuclear families. Our simulations show that LD-PPLs tend to be larger than PPLs (stronger evidence in favor of linkage/LD) with increased LD level, under a variety of generating models; while in the absence of linkage and LD, LD-PPLs tend to be smaller than PPLs (stronger evidence against linkage). The estimate of D' also behaves well even in relatively small, heterogeneous samples.     

PSEUDOMARKER: a powerful program for joint linkage and/or linkage disequilibrium analysis on mixtures of singletons and related individuals

A decade ago, there was widespread enthusiasm for the prospects of genome-wide association studies to identify common variants related to common chronic diseases using samples of unrelated individuals from populations. Although technological advancements allow us to query more than a million SNPs across the genome at low cost, a disappointingly small fraction of the genetic portion of common disease etiology has been uncovered. This has led to the hypothesis that less frequent variants might be involved, stimulating a renaissance of the traditional approach of seeking genes using multiplex families from less diverse populations. However, by using the modern genotyping and sequencing technology, we can now look not just at linkage, but jointly at linkage and linkage disequilibrium (LD) in such samples. Software methods that can look simultaneously at linkage and LD in a powerful and robust manner have been lacking. Most algorithms cannot jointly analyze datasets involving families of varying structures in a statistically or computationally efficient manner. We have implemented previously proposed statistical algorithms in a user-friendly software package, PSEUDOMARKER. This paper is an announcement of this software package. We describe the motivation behind the approach, the statistical methods, and software, and we briefly demonstrate PSEUDOMARKER's advantages over other packages by example.