Genome-wide patterns of identity-by-descent sharing in the French Canadian founder population

Deciphering the genetic structure of the Quebec founder population using genealogies

Using genealogy to study the demographic history of a population makes it possible to overcome the models and assumptions often used in population genetics. The Quebec founder population is one of the few populations in the world having access to the complete genealogy of the last 400 years. The goal of this study is to follow the evolution of the Quebec population structure over time from the beginning of European colonization until the present day. To do so, we calculated the kinship coefficients of all ancestors' pairs in the ascending genealogy of 665 subjects from eight regional and ethnocultural groups per 25-year period. We show that the Quebec population structure appeared progressively in the St. Lawrence valley as early as 1750 with the distinction of the Saguenay and Gaspesian groups. At that time, the ancestors of two groups, the Sagueneans and the Acadians from the Gaspé Peninsula, experienced a marked increase in kinship and inbreeding levels which have shaped the structure and led to the contemporary population structure. Interestingly, this structure arose before the colonization of the Saguenay region and at the very beginning of the Gaspé Peninsula settlement. The resulting regional founder effects in these groups led to differences in the present-day identity-by-descent sharing, the Gaspé and North Shore groups sharing more large segments and the Sagueneans more short segments. This is also reflected by the distribution of the number of most recent common ancestors at different generations and their genetic contribution to the studied subjects.

Correspondence Between Genomic- and Genealogical/Coalescent-Based Inference of Homozygosity by Descent in Large French-Canadian Genealogies

Research on the genetics of complex traits overwhelmingly focuses on the additive effects of genes. Yet, animal studies have shown that non-additive effects, in particular homozygosity effects, can shape complex traits. Recent investigations in human studies found some significant homozygosity effects. However, most human populations display restricted ranges of homozygosity by descent (HBD), making the identification of homozygosity effects challenging. Founder populations give rise to higher HBD levels. When deep genealogical data are available in a founder population, it is possible to gain information on the time to the most recent common ancestor (MRCA) from whom a chromosomal segment has been transmitted to both parents of an individual and in turn to that individual. This information on the time to MRCA can be combined with the time to MRCA inferred from coalescent models of gene genealogies. HBD can also be estimated from genomic data. The extent to which the genomic HBD measures correspond to the genealogical/coalescent measures has not been documented in founder populations with extensive genealogical data. In this study, we used simulations to relate genomic and genealogical/coalescent HBD measures. We based our simulations on genealogical data from two ongoing studies from the French-Canadian founder population displaying different levels of inbreeding. We simulated single-nucleotide polymorphisms (SNPs) in a 1-Mb genomic segment from a coalescent model in conjunction with the observed genealogical data. We compared genealogical/coalescent HBD to two genomic methods of HBD estimation based on hidden Markov models (HMMs). We found that genomic estimates of HBD correlated well with genealogical/coalescent HBD measures in both study genealogies. We described generation time to coalescence in terms of genomic HBD estimates and found a large variability in generation time captured by genomic HBD when considering each SNP. However, SNPs in longer segments were more likely to capture recent time to coalescence, as expected. Our study suggests that estimating the coalescent gene genealogy from the genomic data to use in conjunction with observed genealogical data could provide valuable information on HBD.

Leveraging health systems data to characterize a large effect variant conferring risk for liver disease in Puerto Ricans

The integration of genomic data into health systems offers opportunities to identify genomic factors underlying the continuum of rare and common disease. We applied a population-scale haplotype association approach based on identity-by-descent (IBD) in a large multi-ethnic biobank to a spectrum of disease outcomes derived from electronic health records (EHRs) and uncovered a risk locus for liver disease. We used genome sequencing and in silico approaches to fine-map the signal to a non-coding variant (c.2784-12T>C) in the gene ABCB4. In vitro analysis confirmed the variant disrupted splicing of the ABCB4 pre-mRNA. Four of five homozygotes had evidence of advanced liver disease, and there was a significant association with liver disease among heterozygotes, suggesting the variant is linked to increased risk of liver disease in an allele dose-dependent manner. Population-level screening revealed the variant to be at a carrier rate of 1.95% in Puerto Rican individuals, likely as the result of a Puerto Rican founder effect. This work demonstrates that integrating EHR and genomic data at a population scale can facilitate strategies for understanding the continuum of genomic risk for common diseases, particularly in populations underrepresented in genomic medicine.

The Genetic Analyses of French Canadians of Quebec Facilitate the Characterization of New Cancer Predisposing Genes Implicated in Hereditary Breast and/or Ovarian Cancer Syndrome Families

The French Canadian population of the province of Quebec has been recognized for its contribution to research in medical genetics, especially in defining the role of heritable pathogenic variants in cancer predisposing genes. Multiple carriers of a limited number of pathogenic variants in BRCA1 and BRCA2, the major risk genes for hereditary breast and/or ovarian cancer syndrome families, have been identified in French Canadians, which is in stark contrast to the array of over 2000 different pathogenic variants reported in each of these genes in other populations. As not all such cancer syndrome families are explained by BRCA1 and BRCA2, newly proposed gene candidates identified in other populations have been investigated for their role in conferring risk in French Canadian cancer families. For example, multiple carriers of distinct variants were identified in PALB2 and RAD51D. The unique genetic architecture of French Canadians has been attributed to shared ancestry due to common ancestors of early settlers of this population with origins mainly from France. In this review, we discuss the merits of genetically characterizing cancer predisposing genes in French Canadians of Quebec. We focused on genes that have been implicated in hereditary breast and/or ovarian cancer syndrome families as they have been the most thoroughly characterized cancer syndromes in this population. We describe how genetic analyses of French Canadians have facilitated: (i) the classification of variants in BRCA1 and BRCA2; (ii) the identification and classification of variants in newly proposed breast and/or ovarian cancer predisposing genes; and (iii) the identification of a new breast cancer predisposing gene candidate, RECQL. The genetic architecture of French Canadians provides a unique opportunity to evaluate new candidate cancer predisposing genes regardless of the population in which they were identified.

Investigative genetic genealogy: Current methods, knowledge and practice

Investigative genetic genealogy (IGG) has emerged as a new, rapidly growing field of forensic science. We describe the process whereby dense SNP data, commonly comprising more than half a million markers, are employed to infer distant relationships. By distant we refer to degrees of relatedness exceeding that of first cousins. We review how methods of relationship matching and SNP analysis on an enlarged scale are used in a forensic setting to identify a suspect in a criminal investigation or a missing person. There is currently a strong need in forensic genetics not only to understand the underlying models to infer relatedness but also to fully explore the DNA technologies and data used in IGG. This review brings together many of the topics and examines their effectiveness and operational limits, while suggesting future directions for their forensic validation. We further investigated the methods used by the major direct-to-consumer (DTC) genetic ancestry testing companies as well as submitting a questionnaire where providers of forensic genetic genealogy summarized their operation/services. Although most of the DTC market, and genetic genealogy in general, has undisclosed, proprietary algorithms we review the current knowledge where information has been discussed and published more openly.

Ventricular Arrhythmia in Septal and Apical Hypertrophic Cardiomyopathy: The French-Canadian Experience

Background: Apical hypertrophic cardiomyopathy (aHCM) is thought to have a more benign clinical course compared to septal HCM (sHCM), but most data have been derived from Asian cohorts. Comparative data on clinical outcome in Caucasian aHCM cohorts are scarce, and the results are conflicting. The aim of this study was to estimate the prevalence and outcome of aHCM in French-Canadians of Caucasian descent.

Methods and results: We conducted a retrospective, single-center cohort study. The primary endpoint was a composite of documented sustained ventricular arrhythmia (VA), appropriate ICD therapy, arrhythmogenic syncope, cardiac arrest, or all-cause mortality. A total of 301 HCM patients (65% males) were enrolled including 80/301 (27%) with aHCM and 221/301 (73%) with sHCM. Maximal wall thickness was similar in both groups. Left ventricular apical aneurysm was significantly more common in aHCM (10 vs. 0.5%; p < 0.001). The proportion of patients with myocardial fibrosis ≥ 15% of the left ventricular mass was similar between aHCM and sHCM (21 vs. 24%; p = 0.68). Secondary prevention ICDs were more often implanted in aHCM patients (16 vs. 7%; p = 0.02). The primary endpoint occurred in 26% of aHCM and 10.4% of sHCM patients (p = 0.001) and was driven by an increased incidence of sustained VA (10 vs. 2.3%; p = 0.01). Multivariate analysis identified apical aneurysm and a phenotype of aHCM as independent predictors of the primary endpoint and the occurrence of sustained ventricular tachycardia. Unexplained syncope and a family history of sudden cardiac death were additional predictors for sustained VA. Apical HCM was associated with an increased risk of ventricular arrhythmia even when excluding patients with apical aneurysm.

Conclusions: The phenotype of apical HCM is much more common in French-Canadians (27%) of Caucasian descent compared to other Caucasian HCM populations. Apical HCM in French-Canadians is associated with an increased risk for ventricular arrhythmia.

Founder BRCA1/BRCA2/PALB2 pathogenic variants in French-Canadian breast cancer cases and controls

Inherited germline pathogenic variants are responsible for ~5% of breast cancer globally. Through rapid expansion and isolation since immigration in the early 17th century, French Canadians are a relatively genetically homogenous founder population and therefore represent a unique demographic for genetic contributions to disease. To date, twenty variants in BRCA1, BRCA2, and PALB2 that predispose families to breast and ovarian cancer have been identified as recurring in the French-Canadian founder population. Our objective was to evaluate the clinical efficacy and validity of targeted genetic testing for these variants in Montreal French Canadians. A total of 555 breast cancer cases unselected for family history or age of diagnosis were genotyped, along with 1940 controls without a personal or family history of cancer. A Sequenom genotyping assay identified a pathogenic variant in 0.2% (5 of 1940) of cancer-free controls, and 3.8% (21/555) of breast cancer cases. Almost 10% (12/113) of early onset cases were heterozygous for founder BRCA1 or BRCA2 pathogenic variant. Of twenty variants tested, only seven were identified in this study. The option of providing this test as population-based screening is discussed.

Inferring Transmission Histories of Rare Alleles in Population-Scale Genealogies

Learning the transmission history of alleles through a family or population plays an important role in evolutionary, demographic, and medical genetic studies. Most classical models of population genetics have attempted to do so under the assumption that the genealogy of a population is unavailable and that its idiosyncrasies can be described by a small number of parameters describing population size and mate choice dynamics. Large genetic samples have increased sensitivity to such modeling assumptions, and large-scale genealogical datasets become a useful tool to investigate realistic genealogies. However, analyses in such large datasets are often intractable using conventional methods. We present an efficient method to infer transmission paths of rare alleles through population-scale genealogies. Based on backward-time Monte Carlo simulations of genetic inheritance, we use an importance sampling scheme to dramatically speed up convergence. The approach can take advantage of available genotypes of subsets of individuals in the genealogy including haplotype structure as well as information about the mode of inheritance and general prevalence of a mutation or disease in the population. Using a high-quality genealogical dataset of more than three million married individuals in the Quebec founder population, we apply the method to reconstruct the transmission history of chronic atrial and intestinal dysrhythmia (CAID), a rare recessive disease. We identify the most likely early carriers of the mutation and geographically map the expected carrier rate in the present-day French-Canadian population of Quebec.

Estimating Lactase Nonpersistence Distributions in the Multi-Ethnic Canadian Demographic: A Population-Based Study

Objectives

The lactase persistence/nonpersistence (LP/LNP) phenotypes follow a geographic pattern that is rooted in the gene-culture coevolution observed throughout the history of human migrations. The immense size and relatively open immigration policy have drawn migrants of diverse ethnicities to Canada. Among the multicultural demographic, two-thirds of the population are derived from the British Isles and northwestern France. A recent assessment of worldwide lactase distributions found Canada to have an LNP rate of 59% (confidence interval [CI] 44%-74%). This estimate is rather high compared with earlier reports that listed Canada as a country with a 10% LNP rate; the authors had also noted that biases were likely because their calculations were based largely on Aboriginal studies. We hereby present an alternate LNP prevalence estimate at the national, provincial and territorial level.

Methods

We applied the referenced LNP frequency distribution data to the 2016 population census to account for the current multi-ethnic distributions in Canada. Prevalence rates for Canada, the provinces and territories were calculated.

Results

The national LNP rate is estimated at 44% (CI 41%-47%) after accounting for the 254 ethnic groups, with the lowest rates found in the eastern provinces and the highest rates in the Northwest Territories (57%) and Nunavut (66%), respectively.

Conclusion

Despite the heterogeneous nature of the referenced data and the inference measures taken, evidently, the validity of our LNP estimate is anchored on the inclusion of multi-ethnic groups representing the current Canadian demographic.

Exploring rare and low-frequency variants in the Saguenay-Lac-Saint-Jean population identified genes associated with asthma and allergy traits

The Saguenay–Lac-Saint-Jean (SLSJ) region is located in northeastern Quebec and is known for its unique demographic history and founder effect. As founder populations are enriched with population-specific variants, we characterized the variants distribution in SLSJ and compared it with four European populations (Finnish, Sweden, United Kingdom and France), of which the Finnish population is another founder population. Targeted sequencing of the coding and non-coding immune regulatory regions of the SLSJ asthma familial cohort and the four European populations were performed. Rare and low-frequency coding and non-coding regulatory variants identified in the SLSJ population were then investigated for variant- and gene-level associations with asthma and allergy-related traits (eosinophil percentage, immunoglobulin (Ig) E levels and lung function). Our data showed that (1) rare or deleterious variants were not enriched in the two founder populations as compared with the three non-founder European populations; (2) a larger proportion of founder population-specific variants occurred with higher frequencies; and (3) low-frequency variants appeared to be more deleterious. Furthermore, a rare variant, rs1386931, located in the 3ʹ-UTR of CXCR6 and intron of FYCO1 was found to be associated with eosinophil percentage. Gene-based analyses identified NRP2, MRPL44 and SERPINE2 to be associated with various asthma and allergy-related traits. Our study demonstrated the usefulness of using a founder population to identify new genes associated with asthma and allergy-related traits; thus better understand the genes and pathways implicated in pathophysiology.

Haplotype Sharing Provides Insights into Fine-Scale Population History and Disease in Finland

Finland provides unique opportunities to investigate population and medical genomics because of its adoption of unified national electronic health records, detailed historical and birth records, and serial population bottlenecks. We assembled a comprehensive view of recent population history (≤100 generations), the timespan during which most rare-disease-causing alleles arose, by comparing pairwise haplotype sharing from 43,254 Finns to that of 16,060 Swedes, Estonians, Russians, and Hungarians from geographically and linguistically adjacent countries with different population histories. We find much more extensive sharing in Finns, with at least one ≥ 5 cM tract on average between pairs of unrelated individuals. By coupling haplotype sharing with fine-scale birth records from more than 25,000 individuals, we find that although haplotype sharing broadly decays with geographical distance, there are pockets of excess haplotype sharing; individuals from northeast Finland typically share several-fold more of their genome in identity-by-descent segments than individuals from southwest regions. We estimate recent effective population-size changes through time across regions of Finland, and we find that there was more continuous gene flow as Finns migrated from southwest to northeast between the early- and late-settlement regions than was dichotomously described previously. Lastly, we show that haplotype sharing is locally enriched by an order of magnitude among pairs of individuals sharing rare alleles and especially among pairs sharing rare disease-causing variants. Our work provides a general framework for using haplotype sharing to reconstruct an integrative view of recent population history and gain insight into the evolutionary origins of rare variants contributing to disease.

Deep genealogical analysis of a large cohort of participants in the CARTaGENE project (Quebec, Canada)

BACKGROUND

Genealogical analysis helps to better understand the genetic structure of populations. The population of Quebec (Canada) often serves as a model for this type of analysis, having one of the world's most complete genealogical databases.

AIM

The main objective of this study was to reconstruct, analyse and compare the ascending genealogies of participants to CARTaGENE, a project that aims at building a database on various aspects of public health.

SUBJECTS AND METHODS

In total, 5110 genealogies from four Quebec regions were reconstructed. Distribution of ancestors, completeness and depth of the genealogies, characteristics of immigrant ancestors and kinship and inbreeding coefficients were analysed.

RESULTS

Most genealogies go back to the 17th century, with a mean genealogical depth of 10 generations. Origins of immigrant ancestors are more diverse in the Montreal region, resulting in lower inbreeding and kinship among the participants from this region. Inbreeding and kinship values are mainly explained by remote genealogical links (from 6 to 11 generations).

CONCLUSION

Deep genealogies allowed for a precise measurement of the geographic origins of the participants' immigrant ancestors, as well as inbreeding and kinship ties in the population, which may be crucial for studies aiming to identify genetic variations associated with Mendelian or complex diseases.

Clustering of 770,000 genomes reveals post-colonial population structure of North America

Despite strides in characterizing human history from genetic polymorphism data, progress in identifying genetic signatures of recent demography has been limited. Here we identify very recent fine-scale population structure in North America from a network of over 500 million genetic (identity-by-descent, IBD) connections among 770,000 genotyped individuals of US origin. We detect densely connected clusters within the network and annotate these clusters using a database of over 20 million genealogical records. Recent population patterns captured by IBD clustering include immigrants such as Scandinavians and French Canadians; groups with continental admixture such as Puerto Ricans; settlers such as the Amish and Appalachians who experienced geographic or cultural isolation; and broad historical trends, including reduced north-south gene flow. Our results yield a detailed historical portrait of North America after European settlement and support substantial genetic heterogeneity in the United States beyond that uncovered by previous studies.

Whole-genome sequencing in French Canadians from Quebec

Genome-wide association studies (GWAS) have had a tremendous success in the identification of common DNA sequence variants associated with complex human diseases and traits. However, because of their design, GWAS are largely inappropriate to characterize the role of rare and low-frequency DNA variants on human phenotypic variation. Rarer genetic variation is geographically more restricted, supporting the need for local whole-genome sequencing (WGS) efforts to study these variants in specific populations. Here, we present the first large-scale low-pass WGS of the French-Canadian population. Specifically, we sequenced at ~5.6× coverage the whole genome of 1970 French Canadians recruited by the Montreal Heart Institute Biobank and identified 29 million bi-allelic variants (31 % novel), including 19 million variants with a minor allele frequency (MAF) <0.5 %. Genotypes from the WGS data are highly concordant with genotypes obtained by exome array on the same individuals (99.8 %), even when restricting this analysis to rare variants (MAF <0.5, 99.9 %) or heterozygous sites (98.9 %). To further validate our data set, we showed that we can effectively use it to replicate several genetic associations with myocardial infarction risk and blood lipid levels. Furthermore, we analyze the utility of our WGS data set to generate a French-Canadian-specific imputation reference panel and to infer population structure in the Province of Quebec. Our results illustrate the value of low-pass WGS to study the genetics of human diseases in the founder French-Canadian population.

Rapidly Registering Identity-by-Descent Across Ancestral Recombination Graphs

The genomes of remotely related individuals occasionally contain long segments that are identical by descent (IBD). Sharing of IBD segments has many applications in population and medical genetics, and it is thus desirable to study their properties in simulations. However, no current method provides a direct, efficient means to extract IBD segments from simulated genealogies. Here, we introduce computationally efficient approaches to extract ground-truth IBD segments from a sequence of genealogies, or equivalently, an ancestral recombination graph. Specifically, we use a two-step scheme, where we first identify putative shared segments by comparing the common ancestors of all pairs of individuals at some distance apart. This reduces the search space considerably, and we then proceed by determining the true IBD status of the candidate segments. Under some assumptions and when allowing a limited resolution of segment lengths, our run-time complexity is reduced from O(n(3) log n) for the naïve algorithm to O(n log n), where n is the number of individuals in the sample.

Estimation of Recent and Ancient Inbreeding in a Small Endogamous Tunisian Community Through Genomic Runs of Homozygosity

Runs of homozygosity (ROHs) are extended genomic regions of homozygous genotypes that record populations' mating patterns in the past. We performed microarray genotyping on 15 individuals from a small isolated Tunisian community. We estimated the individual and population genome-wide level of homozygosity from data on ROH above 0.5 Mb in length. We found a high average number of ROH per individual (48.2). The smallest ROH category (0.5-1.49 Mb) represents 0.93% of the whole genome, while medium-size (1.5-4.99 Mb) and long-size ROH (≥5 Mb) cover 1.18% and 0.95%, respectively. We found that genealogical individual inbreeding coefficients (Fped ) based on three- to four-generation pedigrees are not reliable indicators of the current proportion of genome-wide homozygosity inferred from ROH (FROH ) either for 0.5 or 1.5 Mb ROH length thresholds, while identity-by-descent sharing is a function of shared coancestry. This study emphasizes the effect of reproductive isolation and a prolonged practice of consanguinity that limits the genetic heterogeneity. It also provides evidence of both recent and ancient parental relatedness contribution to the current level of genome-wide homozygosity in the studied population. These findings may be useful for evaluation of long-term effects of inbreeding on human health and for future applications of ROHs in identifying recessive susceptibility genes.

GENLIB: an R package for the analysis of genealogical data

BACKGROUND

Founder populations have an important role in the study of genetic diseases. Access to detailed genealogical records is often one of their advantages. These genealogical data provide unique information for researchers in evolutionary and population genetics, demography and genetic epidemiology. However, analyzing large genealogical datasets requires specialized methods and software. The GENLIB software was developed to study the large genealogies of the French Canadian population of Quebec, Canada. These genealogies are accessible through the BALSAC database, which contains over 3 million records covering the whole province of Quebec over four centuries. Using this resource, extended pedigrees of up to 17 generations can be constructed from a sample of present-day individuals.

RESULTS

We have extended and implemented GENLIB as a package in the R environment for statistical computing and graphics, thus allowing optimal flexibility for users. The GENLIB package includes basic functions to manage genealogical data allowing, for example, extraction of a part of a genealogy or selection of specific individuals. There are also many functions providing information to describe the size and complexity of genealogies as well as functions to compute standard measures such as kinship, inbreeding and genetic contribution. GENLIB also includes functions for gene-dropping simulations. The goal of this paper is to present the full functionalities of GENLIB. We used a sample of 140 individuals from the province of Quebec (Canada) to demonstrate GENLIB's functions. Ascending genealogies for these individuals were reconstructed using BALSAC, yielding a large pedigree of 41,523 individuals. Using GENLIB's functions, we provide a detailed description of these genealogical data in terms of completeness, genetic contribution of founders, relatedness, inbreeding and the overall complexity of the genealogical tree. We also present gene-dropping simulations based on the whole genealogy to investigate identical-by-descent sharing of alleles and chromosomal segments of different lengths and estimate probabilities of identical-by-descent sharing.

CONCLUSIONS

The R package GENLIB provides a user friendly and flexible environment to analyze extensive genealogical data, allowing an efficient and easy integration of different types of data, analytical methods and additional developments and making this tool ideal for genealogical analysis.

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.

Identity-by-descent mapping in a Scandinavian multiple sclerosis cohort

In an attempt to map chromosomal regions carrying rare gene variants contributing to the risk of multiple sclerosis (MS), we identified segments shared identical-by-descent (IBD) using the software BEAGLE 4.0's refined IBD analysis. IBD mapping aims at identifying segments inherited from a common ancestor and shared more frequently in case–case pairs. A total of 2106 MS patients of Nordic origin and 624 matched controls were genotyped on Illumina Human Quad 660 chip and an additional 1352 ethnically matched controls typed on Illumina HumanHap 550 and Illumina 1M were added. The quality control left a total of 441 731 markers for the analysis. After identification of segments shared by descent and significance testing, a filter function for markers with low IBD sharing was applied. Four regions on chromosomes 5, 9, 14 and 19 were found to be significantly associated with the risk for MS. However, all markers but for one were located telomerically, including the very distal markers. For methodological reasons, such segments have a low sharing of IBD signals and are prone to be false positives. One marker on chromosome 19 reached genome-wide significance and was not one of the distal markers. This marker was located within the GNA11 gene, which contains no previous association with MS. We conclude that IBD mapping is not sufficiently powered to identify MS risk loci even in ethnically relatively homogenous populations, or that alternatively rare variants are not adequately present.

A renewal theory approach to IBD sharing

A long genomic segment inherited by a pair of individuals from a single, recent common ancestor is said to be identical-by-descent (IBD). Shared IBD segments have numerous applications in genetics, from demographic inference to phasing, imputation, pedigree reconstruction, and disease mapping. Here, we provide a theoretical analysis of IBD sharing under Markovian approximations of the coalescent with recombination. We describe a general framework for the IBD process along the chromosome under the Markovian models (SMC/SMC'), as well as introduce and justify a new model, which we term the renewal approximation, under which lengths of successive segments are independent. Then, considering the infinite-chromosome limit of the IBD process, we recover previous results (for SMC) and derive new results (for SMC') for the mean number of shared segments longer than a cutoff and the fraction of the chromosome found in such segments. We then use renewal theory to derive an expression (in Laplace space) for the distribution of the number of shared segments and demonstrate implications for demographic inference. We also compute (again, in Laplace space) the distribution of the fraction of the chromosome in shared segments, from which we obtain explicit expressions for the first two moments. Finally, we generalize all results to populations with a variable effective size.