Estimating ethnic admixture from pedigree data

This paper introduces a likelihood method of estimating ethnic admixture that uses individuals, pedigrees, or a combination of individuals and pedigrees. For each founder of a pedigree, admixture proportions are calculated by conditioning on the pedigree-wide genotypes at all ancestry-informative markers. These estimates are then propagated down the pedigree to the nonfounders by a simple averaging process. The large-sample standard errors of the founders' proportions can be similarly transformed into standard errors for the admixture proportions of the descendants. These standard errors are smaller than the corresponding standard errors when each individual is treated independently. Both hard and soft information on a founder's ancestry can be accommodated in this scheme, which has been implemented in the genetic software package Mendel. The utility of the method is demonstrated on simulated data and a real data example involving Mexican families of mixed Amerindian and Spanish ancestry.     

Haplotypic QTL mapping in an outbred pedigree

An offspring genome can be viewed as a mosaic of chromosomal segments or haplotypes contributed by multiple founders in any quantitative trait locus (QTL) detection study but tracing these is especially complex to achieve for outbred pedigrees. QTL haplotypes can be traced from offspring back to individual founders in outbred pedigrees by combining founder-origin probabilities with fully informative flanking markers. This haplotypic method was illustrated for QTL detection using a three-generation pedigree for a woody perennial plant, Pinus taeda L. Growth rate was estimated using height measurements from ages 2 to 10 years. Using simulated and actual datasets, power of the experimental design was shown to be efficient for detecting QTLs of large effect. Using interval mapping and fully informative markers, a large QTL accounting for 11.3% of the phenotypic variance in the growth rate was detected. This same QTL was expressed at all ages for height, accounting for 7.9-12.2% of the phenotypic variance. A mixed-model inheritance was more appropriate for describing genetic architecture of growth curves in P. taeda than a strictly polygenic model. The positive QTL haplotype was traced from the offspring to its contributing founder, GP3, then the haplotypic phase for GP3 was determined by assaying haploid megagametophytes. The positive QTL haplotype was a recombinant haplotype contributed by GP3. This study illustrates the combined power of fully informative flanking markers and founder origin probabilities for (1) estimating QTL haplotype magnitude, (2) tracing founder origin and (3) determining haplotypic transmission frequency.     

A haplotypic approach to founder-origin probabilities and outbred QTL analysis

Founder-origin probability methods are used to trace specific chromosomal segments in individual offspring. A haplotypic method was developed for calculating founder-origin probabilities in three-generation outbred pedigrees suited to quantitative trait locus (QTL) analysis. Estimators for expected founder-origin proportions were derived for a linkage group segment, an entire linkage group and a complete haplotype. If the founders are truly outbred, the haplotypic method gives a close approximation when compared with the Haley et al. (1994) method that simultaneously uses all marker information for QTL analysis, and it is less computationally demanding. The chief limitation of the haplotypic method is that some information in two-allele intercross marker-type configurations is ignored. Informativeness of marker arrays is discussed in the framework of founder-origin probabilities and proportions. The haplotypic method can be extended to more complex pedigrees with additional generations.     

QTL analysis in arbitrary pedigrees with incomplete marker information

Mapping quantitative trait loci (QTL) in arbitrary outbred pedigrees is complicated by the combinatorial possibilities of allele flow relationships and of the founder allelic configurations. Exact methods are only available for rather short and simple pedigrees. Stochastic simulation using Markov chain Monte Carlo (MCMC) integration offers more flexibility. MCMC methods are less natural in a frequentist than in a Bayesian context, which we therefore adopt. Among the MCMC algorithms for updating marker locus genotypes, we implement the descent-graph algorithm. It can be used to update marker locus allele flow relationships and can handle arbitrarily complex pedigrees and missing marker information. Compared with updating marker genotypic information, updating QTL parameters, such as position, effects, and the allele flow relationships is relatively easy with MCMC. We treat the effect of each diploid combination of founder alleles as a random variable and only estimate the variance of these effects, ie, we model diploid genotypic effects instead of the usual partition in additive and dominance effects. This is a variant of the random model approach. The number of QTL alleles is generally unknown. In the Bayesian context, the number of QTL present on a linkage group can be treated as variable. Computer simulations suggest that the algorithm can indeed handle complex pedigrees and detect two QTL on a linkage group, but that the number of individuals in a single extended family is limited to about 50 to 100 individuals.     

Estimation of Epistatic Variance Components and Heritability in Founder Populations and Crosses

Genetic association studies have explained only a small proportion of the estimated heritability of complex traits, leaving the remaining heritability “missing.” Genetic interactions have been proposed as an explanation for this, because they lead to overestimates of the heritability and are hard to detect. Whether this explanation is true depends on the proportion of variance attributable to genetic interactions, which is difficult to measure in outbred populations. Founder populations exhibit a greater range of kinship than outbred populations, which helps in fitting the epistatic variance. We extend classic theory to founder populations, giving the covariance between individuals due to epistasis of any order. We recover the classic theory as a limit, and we derive a recently proposed estimator of the narrow sense heritability as a corollary. We extend the variance decomposition to include dominance. We show in simulations that it would be possible to estimate the variance from pairwise interactions with samples of a few thousand from strongly bottlenecked human founder populations, and we provide an analytical approximation of the standard error. Applying these methods to 46 traits measured in a yeast (Saccharomyces cerevisiae) cross, we estimate that pairwise interactions explain 10% of the phenotypic variance on average and that third- and higher-order interactions explain 14% of the phenotypic variance on average. We search for third-order interactions, discovering an interaction that is shared between two traits. Our methods will be relevant to future studies of epistatic variance in founder populations and crosses.     

A consensus map for loblolly pine (Pinus taeda L.). I. Construction and integration of individual linkage maps from two outbred three-generation pedigrees.

A consensus map for loblolly pine (Pinus taeda L.) was constructed from the integration of linkage data from two unrelated three-generation outbred pedigrees. The progeny segregation data from restriction fragment length polymorphism, random amplified polymorphic DNA, and isozyme genetic markers from each pedigree were recoded to reflect the two independent populations of parental meioses, and genetic maps were constructed to represent each parent. The rate of meiotic recombination was significantly greater for males than females, as was the average estimate of genome length for males (1983.7 cM [Kosambi mapping function (K)]) and females [1339.5 cM(K)]. The integration of individual maps allows for the synthesis of genetic information from independent sources onto a single consensus map and facilitates the consolidation of linkage groups to represent the chromosomes n = 12 of loblolly pine. The resulting consensus map consists of 357 unique molecular markers and covers approximately 1300 cM(K).     

Bayesian mapping of QTL in outbred F2 families allowing inference about whether F0 grandparents are homozygous or heterozygous at QTL

In this paper, we propose a new Bayesian method for QTL analysis in outbred F2 families based on Markov chain Monte Carlo (MCMC) estimation allowing inference about whether each of F0 founders (grandparents) is homozygous or heterozygous at QTL. This, in turn, allows us to select a model accurately explaining observations of phenotypes for F2 individuals. The proposed method performs the fitting a statistical model of the two possible QTL states in each F0 grandparent, that is, homozygous and heterozygous at QTL, and gives a posterior distribution for the QTL states in each F0 grandparent. We confine ourselves to the discrimination of two QTL states, homozygous or heterozygous, for each of the F0 grandparents without taking into consideration whether common alleles are shared by F0 grandparents. The statistical model includes allelic effects and dominance effects for each QTL. The number of parameters representing allelic effects and dominance effects is therefore changed depending on the QTL states. A Reversible Jump MCMC technique is used for transition between the models of different dimensions. The effectiveness of the proposed method was investigated using simulation experiments. It was practicable to estimate the QTL states of F0 grandparents as well as the number, the locations and the effects of QTL segregating in an outbred F2 family.     

Evaluating the genetic status of a closed colony of titi monkeys (Callicebus cupreus) using multigenerational pedigrees

Pedigree metrics are essential for investigating colony genetic structure. The genetic structure of a closed Callicebus cupreus colony was examined using multigenerational pedigrees. Inbreeding was low, but genetic drift caused the loss of founder genome representation. Pedigrees can be used to detect founder representation and prevent bottlenecks and allele loss.     

Marker imputation efficiency for genotyping-by-sequencing data in rice (<Emphasis Type="Italic">Oryza sativa</Emphasis>) and alfalfa (<Emphasis Type="Italic">Medicago sativa</Emphasis>)

Genotyping-by-sequencing (GBS) is a rapid and cost-effective genome-wide genotyping technique applicable whether a reference genome is available or not. Due to the cost-coverage trade-off, however, GBS typically produces large amounts of missing marker genotypes, whose imputation becomes therefore both challenging and critical for later analyses. In this work, the performance of four general imputation methods (K-nearest neighbors, Random Forest, singular value decomposition, and mean value) and two genotype-specific methods (“Beagle” and FILLIN) was measured on GBS data from alfalfa (Medicago sativa L., autotetraploid, heterozygous, without reference genome) and rice (Oryza sativa L., diploid, 100 % homozygous, with reference genome). Alfalfa SNP were aligned on the genome of the closely related species Medicago truncatula L.. Benchmarks consisted in progressive data filtering for marker call rate (up to 70 %) and increasing proportions (up to 20 %) of known genotypes masked for imputation. The relative performance was measured as the total proportion of correctly imputed genotypes, globally and within each genotype class (two homozygotes in rice, two homozygotes and one heterozygote in alfalfa). We found that imputation accuracy was robust to increasing missing rates, and consistently higher in rice than in alfalfa. Accuracy was as high as 90–100 % for the major (most frequent) homozygous genotype, but dropped to 80–90 % (rice) and below 30 % (alfalfa) in the minor homozygous genotype. Beagle was the best performing method, both accuracy- and time-wise, in rice. In alfalfa, KNNI and RFI gave the highest accuracies, but KNNI was much faster.     

Prediction of additive genetic effects for the QTL-cluster on the basis of data on surrounding markers in outbred populations

This paper described a method for predicting additive effects of a cluster of tightly linked QTLs for outbred populations of animals in the situation where the QTLs are located on a chromosome segment surrounded by multiple linked DNA markers. We present a mixed model method for best linear unbiased prediction (conditional to the marker data) of the additive effects of the QTL-cluster and of the remaining QTLs unlinked to the marker linkage group. This method takes into consideration the identity-by-descent proportion (IBDP) for the particular chromosomal segment, in contrast to some other methods which use IBD probabilities at one specific location. In this method, fully informative data on different flanking markers is used to calculate the values of the expectations of the IBDPs (EIBDPs) between gametes for animals to be evaluated. Then the expected values are used as the elements of the gametic relationship matrix required in the best linear unbiased prediction. Giving a small numerical example, we illustrate how the present method can be used for the prediction of the QTL-cluster effects and for genetic evaluation of animals in outbred populations. A computational strategy is discussed on the basis of the calculation of the EIBDPs and the inverted gametic relationship matrix in complex pedigrees.     

Genetic linkage mapping in Acacia mangium. 2. Development of an integrated map from two outbred pedigrees using RFLP and microsatellite loci

An integrated genetic linkage map, comprised of 219 RFLP and 33 microsatellite loci in 13 linkage groups, was constructed using two outbred pedigrees of Acacia mangium Willd. The linkage groups ranged in size from 23 to 103 cM and the total map length was 966 cM. Individual maps were made for each pedigree and the ordering of loci was consistent with the integrated map. The use of two independent pedigrees allowed a comparison of recombination rates between linked loci in male and female meioses as well as between parents. Differences were confined to specific regions and were not uniform across the male and female genomes or between genotypes. The heterogeneity in recombination frequencies did not result in major differences in the ordering of loci between pedigrees; hence, the integrated map provides a sound basis for QTL detection, leading to marker-assisted selection in A. mangium. It also provides a reference map for comparative genome analysis in acacias. The co-dominant markers used for mapping provide a useful resource in population studies and for quality control in acacia breeding programs. Detection of a relatively high proportion of selfs in pods derived from flowers which were not emasculated (30%), compared with emasculated flowers (0.01%), indicates that emasculation is desirable for efficient delivery of control-crossed seed in acacia breeding programs. Received: 25 March 2000 / Accepted: 30 April 2000     

Quantifying and managing the loss of genetic variation in a free-ranging population of takahe through the use of pedigrees

Pedigree analysis has clear benefits for the genetic management of threatened populations through the evaluation of inbreeding, population structure and genetic diversity. The use of pedigrees is usually restricted to captive populations and few examples exist of their exclusive use in managing free-ranging populations. One such example is the management of the takahe (Porphyrio hochstetteri), a highly endangered, flightless New Zealand rail at risk from introduced mammalian predators and habitat loss. During the 1980’s and 90’s, as part of the takahe recovery programme, birds were translocated from the sole remnant population in Fiordland to four offshore islands from which introduced predators had been eradicated. The subsequent “island” population, now numbering 83 and thought to be at carrying capacity, has been closely monitored since founding. Detailed breeding records allow us to analyse the island pedigree, which is up to 7 generations deep. Gene-drop analysis indicated that 7.5% of genetic diversity has been lost over the relatively short timeframe since founding (2.1 generations on average; total genetic founders = 31) due to both a failure to equalise founder representation early on and subsequent disproportionate breeding success (founder equivalents = 12.5; founder genome equivalents = 6.6). A high prevalence of close inbreeding will have also impacted on genetic diversity. Predictions from pedigree modelling suggest that 90% genetic diversity will be maintained for only 12 years, but by introducing a low level of immigration from the Fiordland population and permitting the population to grow, 90% GD could be maintained over the next 100 years. More generally, the results demonstrate the value of maintaining pedigrees for wild populations, especially in the years immediately after a translocation event.     

A simple method to approximate gene content in large pedigree populations: application to the myostatin gene in dual-purpose Belgian Blue cattle

Gene content is the number of copies of a particular allele in a genotype of an animal. Gene content can be used to study additive gene action of candidate gene. Usually genotype data are available only for a part of population and for the rest gene contents have to be calculated based on typed relatives. Methods to calculate expected gene content for animals on large complex pedigrees are relatively complex. In this paper we proposed a practical method to calculate gene content using a linear regression. The method does not estimate genotype probabilities but these can be approximated from gene content assuming Hardy-Weinberg proportions. The approach was compared with other methods on multiple simulated data sets for real bovine pedigrees of 1 082 and 907 903 animals. Different allelic frequencies (0.4 and 0.2) and proportions of the missing genotypes (90, 70, and 50%) were considered in simulation. The simulation showed that the proposed method has similar capability to predict gene content as the iterative peeling method, however it requires less time and can be more practical for large pedigrees. The method was also applied to real data on the bovine myostatin locus on a large dual-purpose Belgian Blue pedigree of 235 133 animals. It was demonstrated that the proposed method can be easily adapted for particular pedigrees.     

Detection of quantitative trait loci for backfat thickness and intramuscular fat content in pigs (Sus scrofa).

In an experimental cross between Meishan and Dutch Large White and Landrace lines, 619 F(2) animals and their parents were typed for molecular markers covering the entire porcine genome. Associations were studied between these markers and two fatness traits: intramuscular fat content and backfat thickness. Association analyses were performed using interval mapping by regression under two genetic models: (1) an outbred line-cross model where the founder lines were assumed to be fixed for different QTL alleles; and (2) a half-sib model where a unique allele substitution effect was fitted within each of the 19 half-sib families. Both approaches revealed for backfat thickness a highly significant QTL on chromosome 7 and suggestive evidence for a QTL at chromosome 2. Furthermore, suggestive QTL affecting backfat thickness were detected on chromosomes 1 and 6 under the line-cross model. For intramuscular fat content the line-cross approach showed suggestive evidence for QTL on chromosomes 2, 4, and 6, whereas the half-sib analysis showed suggestive linkage for chromosomes 4 and 7. The nature of the QTL effects and assumptions underlying both models could explain discrepancies between the findings under the two models. It is concluded that both approaches can complement each other in the analysis of data from outbred line crosses.     

Analysis of founder representation in pedigrees: Founder equivalents and founder genome equivalents

The concepts of “founder equivalent” and “founder genome equivalent” are introduced to facilitate analysis of the founding stocks of captive or other populations for which pedigrees are available. The founder equivalents of a population are the number of equally contributing founders that would be expected to produce the same genetic diversity as in the population under study. Unequal genetic contributions by founders decrease the founder equivalents, portend greater inbreeding in future generations than would be necessary, and reflect a greater loss of the genetic diversity initially present in the founders. The number of founder genome equivalents of a population is that number of equally contributing founders with no random loss of founder alleles in descendants that would be expected to produce the same genetic diversity as in the population under study. The number of founder genome equivalents is approximately that number of wild-caught animals that would be needed to obtain the same amount of genetic diversity as is in the descendant captive population. Founder equivalents and founder genome equivalents allow comparison of the genetic merits of adding new wild-caught stock vs. further equalizing founder representations in a captive population.     

Sequence analysis of the mitochondrial genomes from Dutch pedigrees with Leber hereditary optic neuropathy

The complete mitochondrial DNA (mtDNA) sequences for 63 Dutch pedigrees with Leber hereditary optic neuropathy (LHON) were determined, 56 of which carried one of the classic LHON mutations at nucleotide (nt) 3460, 11778, or 14484. Analysis of these sequences indicated that there were several instances in which the mtDNAs were either identical or related by descent. The most striking example was a haplogroup J mtDNA that carried the 14484 LHON mutation. Four different but related mitochondrial genotypes were identified in seven of the Dutch pedigrees with LHON, including six of those described by van Senus. The control region of the founder sequence for these Dutch pedigrees with LHON matches the control-region sequence that Macmillan and colleagues identified in the founder mtDNA of French Canadian pedigrees with LHON. In addition, we obtained a perfect match between the Dutch 14484 founder sequence and the complete mtDNA sequences of two Canadian pedigrees with LHON. Those results indicate that these Dutch and French Canadian 14484 pedigrees with LHON share a common ancestor, that the single origin of the 14484 mutation in this megalineage occurred before the year 1600, and that there is a 14484/haplogroup J founder effect. We estimate that this lineage--including the 14484 LHON mutation--arose 900-1,800 years ago. Overall, the phylogenetic analyses of these mtDNA sequences conservatively indicate that a LHON mutation has arisen at least 42 times in the Dutch population. Finally, analysis of the mtDNA sequences from those pedigrees that did not carry classic LHON mutations suggested candidate pathogenic mutations at nts 9804, 13051, and 14325.     

宽边黄粉蝶(Eurema hecabe)基因组Survey分析

宽边黄粉蝶(Eurema hecabe)是重要的传粉昆虫,广布于非洲热带区、东洋区、澳洲区及古北区东部,具有较高的学术价值和经济意义。为了深入研究其广泛适应性,确定适合该蝴蝶的全基因组的测序研究策略,我们首先做低覆盖度的基因组Survey测序,然后做大规模的全基因组深度测序。采用第二代高通量的测序技术作为该研究的研究方法,测定了宽边黄粉蝶基因组大小,并利用生物信息学方法估计该种的杂合率、重复序列和GC含量等基因组信息。结果表明:(1)宽边黄粉蝶的基因组大小估计为285.34 Mb,测序深度51×;(2)从K-mer分布曲线发现黄粉蝶基因组有明显的杂合峰,杂合率达1.97%,重复序列比例为35.37%。该研究结果对于揭示宽边黄粉蝶物种的起源和进化及适应性具有重要意义,为宽边黄粉蝶选择全基因组测序策略提供依据。     

The relevance of pedigrees in the conservation genomics era

Over the past 50 years conservation genetics has developed a substantive toolbox to inform species management. One of the most long-standing tools available to manage genetics—the pedigree—has been widely used to characterize diversity and maximize evolutionary potential in threatened populations. Now, with the ability to use high throughput sequencing to estimate relatedness, inbreeding, and genome-wide functional diversity, some have asked whether it is warranted for conservation biologists to continue collecting and collating pedigrees for species management. In this perspective, we argue that pedigrees remain a relevant tool, and when combined with genomic data, create an invaluable resource for conservation genomic management. Genomic data can address pedigree pitfalls (e.g., founder relatedness, missing data, uncertainty), and in return robust pedigrees allow for more nuanced research design, including well-informed sampling strategies and quantitative analyses (e.g., heritability, linkage) to better inform genomic inquiry. We further contend that building and maintaining pedigrees provides an opportunity to strengthen trusted relationships among conservation researchers, practitioners, Indigenous Peoples, and Local Communities.     

A Monte Carlo algorithm for computing the IBD matrices using incomplete marker information

Identity-By-Descent (IBD) is a general measurement of the relationship between two groups of genes. If the two groups consist of two homologous genes, one from each individual, the IBD is called the coancestry between the two individuals. Coancestry is an important concept in both population and quantitative genetics. It is the probability that both genes are copies of the same gene in the genealogy. The average coancestry value at a random locus in a population reflects the level of population diversity, effective population size, the level of inbreeding and other attributes. Coancestry is also the building block for the covariance structure used to estimate the additive genetic variance component for a quantitative trait. There are many other types of IBD matrices, depending on the natures of the genes included in each group, and these IBD matrices vary from locus to locus. Molecular markers distributed along the genome provide information that can be used to infer these locus-specific IBD matrices. As a result, we can estimate and test the variance components of a quantitative trait contributed by these loci using the inferred IBD matrices. In this study, we develop the concept of locus-specific epistatic IBD matrices and a Monte Carlo method to infer these IBD matrices. The method is suitable for large pedigrees with arbitrary complexity and various levels of missing marker information. With these locus-specific IBD matrices, we are ready to search for quantitative trait loci along the genome in complicated pedigrees.     

Combination of multipoint maximum likelihood (MML) and regression mapping algorithms to construct a high-density genetic linkage map for loblolly pine (Pinus taeda L.)

Genetic maps have been successfully applied to assist in the dissection of complex traits, provide insight on genome structure, and estimate recombination in conjunction with physical maps. Despite an extensive list of genetic maps developed for loblolly pine (Pinus taeda L.) over the past two decades, a high-density consensus map has not yet been constructed. In this study, we used two reference three-generation outbred pedigrees, base and qtl, obtained from the North Carolina State University Cooperative Tree Improvement Program, to obtain a high-density genetic consensus map. Both populations were genotyped with ≈ 7,000 different markers (restriction fragment length polymorphisms, expressed sequence tag polymorphisms, simple sequence repeats, SNPs). The grouping, ordering, and spacing of the markers on each linkage group were performed with JoinMap® 4.1, which implements the multipoint maximum likelihood algorithm for outbred populations. The final consensus map contains 2,466 markers, with a total length of 1,476 centimorgans (cM). The average marker density across the 12 linkage groups was 0.62 cM/marker. This high-density map provides an important resource for breeders and geneticists and will enable comparative studies across species, as well as improve the loblolly pine genome sequence assembly.