Incorporating genotypes of relatives into a test of linkage disequilibrium.

Genetic data from autosomal loci in diploids generally consist of genotype data for which no phase information is available, making it difficult to implement a test of linkage disequilibrium. In this paper, we describe a test of linkage disequilibrium based on an empirical null distribution of the likelihood of a sample. Information on the genotypes of related individuals is explicitly used to help reconstruct the gametic phase of the independent individuals. Simulation studies show that the present approach improves on estimates of linkage disequilibrium gathered from samples of completely independent individuals but only if some offspring are sampled together with their parents. The failure to incorporate some parents sharply decreases the sensitivity and accuracy of the test. Simulations also show that for multiallelic data (more than two alleles) our testing procedure is not as powerful as an exact test based on known haplotype frequencies, owing to the interaction between departure from Hardy-Weinberg equilibrium and linkage disequilibrium.     

Blood groups of anthropoid apes and their relationship to human blood groups

Affinity between blood groups of man and those of anthropoid apes is reflected not only in similarities or identities of reactions of the red cells with many specific typing reagents, but also in overall structures of some of the main blood group systems defined in man and in apes.Besides specificities of human-type, such as A-B-O, M-N, Rh-Hr, I-i, etc. known to be present on the red cells of various species of apes, specific reagents were produced by iso- or cross-immunization of chimpanzees that detect red cell specificities characteristic for apes only. Some of those specificities were found to be shared by several ape species and to fall into separate blood group systems that are counterparts of the human blood group systems. Recently obtained serological, as well as population data, indicate that the chimpanzee R-C-E-F blood group system is the counterpart of the human Rh-Hr system. Similarly to the Rh-Hr system, it is built around a main antigen, the R^c antigen, to which secondary specificities are attached by means of multiple allelic genes. The R^c is not only the principal factor of the chimpanzee R-C-E-F group system, but also constitutes a direct link with the human Rh-Hr blood group system, since anti-R^c reagents also detect Rh₀ specificity on the human red cells. Another chimpanzee blood group system, the V-A-B-D system, is counterpart of the M-N-S-s system, and is built around the central antigen V^c. the V^c is not only the principal specificity of the chimpanzee V-A-B-D system, but it also constitutes the direct link with the human M-N-S-s system since anti-V^c reagent gives with chimpanzee red cells reactions parralleling those obtained with anti-N lectin (N^v) while in tests with human red cells it detects specificity identical or closely related to the Mi^a specificity.     

NM+: software implementing parentage-based models for estimating gene dispersal and mating patterns in plants

NM+ is computer software designed for making inferences on plant gene dispersal and mating patterns by modelling parentage probabilities of offspring based on the spatially explicit neighbourhood model. NM+ requires a sample of mapped and genotyped candidate parents and offspring; however, offspring may optionally be assigned to single maternal parents (forming so-called half-sib progeny arrays). Using maximum likelihood, NM+ estimates a number of parameters, including proportions of offspring due to self-fertilization, pollen immigration from outside of a defined study site, parameters of pollen (and/or seed) dispersal kernels (exponential-power, Weibull, geometric or 2Dt) and selection gradients relating covariates (phenotypic traits) with male (and/or female) reproductive success. NM+ allows for missing data both in parents and in offspring. It accounts for null alleles and their frequencies can optionally be considered as estimable parameters. Data files are formatted in a table-like structure so they can be easily prepared in a spreadsheet software. By default NM+ is for studying plant populations, however, it can be used for any organism as long as data requirements and model assumptions are met. NM+ runs under Windows, but it can be launched under Linux using WINE emulator. NM+ can be downloaded free of charge from http://www.genetyka.ukw.edu.pl/index_pliki/software.htm.     

Assessing parent numbers from offspring genotypes: the importance of marker polymorphism

Methods to infer parent numbers from offspring genotypes either determine the minimum number of parents required to explain alleles and multilocus genotypes detected in the offspring or use models to incorporate information on population allele frequencies and allele segregation. Disparate results by different approaches suggest that one or perhaps all methods are subject to bias. Here, we investigate the performance of minimum parent number estimates, maximum likelihood, and Bayesian analyses (programs COLONY and PARENTAGE) with respect to marker information content in simulated data sets without knowledge of parental genotypes. Offspring families of different sizes were assumed to share one parent and to be sired by 1 or 5 additional parents. All methods committed large errors in terms of underestimation (minimum value) and overestimation (COLONY), or both (PARENTAGE) of parent numbers, unless the data were highly informative, and their relative performances depended on full-sib group sizes and sire numbers. Increasing the number of markers with low gene diversity (H(e) < or = 0.68) yielded only slow improvement of the results, but all 3 methods performed well with 5-7 markers of H(e) = 0.84. We emphasize the importance of high marker polymorphism for inferring parent numbers and individual parent contributions, as well as for the detection of monogamous reproduction.     

Angiotensin‐Converting Enzyme Gene Polymorphisms and Obesity: An Examination of Three Black Populations

We examined the association between obesity and 13 angiotensin‐converting enzyme (ACE) gene polymorphisms, including the presence (I) or absence (D) of an Alu element in intron 16 (I/D polymorphism), and performed haplotype analysis using data collected from participants of a community survey of hypertension among blacks living in Ibadan, Nigeria; Spanish Town, Jamaica; and Chicago, IL. Transmission distortion of ACE gene polymorphisms and haplotypes from heterozygous parents to affected offspring was examined in each study population. To estimate haplotypes, polymorphisms were divided into three groups based on their position on the ACE gene. No ACE gene polymorphism was consistently overtransmitted from parents to obese offspring among the three populations. However, the haplotype ACE1‐ACE5 TACAT, located in the promoter region, was significantly overtransmitted from parents to obese offspring in both the U.S. and Nigerian populations. No haplotype was significantly overtransmitted from parents to obese offspring among the Jamaicans. In conclusion, we noted the overtransmission of a particular ACE gene promoter region haplotype from parents to obese offspring in two separate black populations. These data suggest that ACE gene polymorphisms may influence the development of weight gain.     

Analysis of the diallelic model for the prevalence of epilepsy in families and populations

The initial data for the analysis have resulted in epidemiologic (547 patients) and genetic-epidemiologic (365 patients) study of patients with diagnosis of epilepsy living in five districts of the Khabarovsk Territory. The population frequency of epilepsy was equal to 0.288%. With the use of data on numbers of sick and healthy first-third-degree relatives, and the method of maximum likelihood, the monolocus diallelic model (MDM) parameters of the family and population epilepsy prevalence were estimated. For each of 9 MDM variants two decisions were obtained, depending on the use of population probability of the feature. The analysis of 8 sets of initial data allowed to ascertain the influence of information about the first-third-degree relatives on parameter estimates. The calculation results are presented for one of initial data sets (set A). Three MDM variants were shown to predict the values of the relative affection probability, these being rather close to frequencies observed. The arguments are presented in favour of quasi-dominant variant with following parameters: frequency of mutant allele in a population - 5.28%, homozygote penetrance - 21.5% and that for heterozygote - 2.6%. According to parameter estimates within this model, the probability of offspring disease in the family with the known number of sick and healthy parents was calculated.     

Comparison of year-of-exam- and age-matched estimates of heritability in the Framingham Heart Study data

Several different approaches can be used to examine generational and temporal trends in family studies. The measurement of offspring and parents can be made over a short period of time with parents and offspring having quite different ages, or measurements can be made at the same ages but with decades between parent and offspring measures. A third approach, used in the Framingham Heart Study, has repeated examinations across a broad range of age and time, and provides a unique opportunity to compare these approaches. Parents and offspring were matched both on (year of exam) and on age. Heritability estimates for systolic blood pressure, body mass index, height, weight, cholesterol, and glucose were obtained by regressing offspring on midparent values with and without adjustment for age. Higher estimates of heritability were obtained for age-matched than for year-of-exam-matched data for all traits considered. For most traits, estimates of the heritability of the change over time (slope) of the trait were near zero. These results suggest that the optimal design to identify genetic effects in traits with large age-related effects may be to measure parents and offspring at similar ages and not to rely on age-adjustment or longitudinal measures to account for these temporal effects.     

Testing for unequal paternal contributions using nuclear and chloroplast SSR markers in polycross families of radiata pine

The lack of male pedigree control is the major limitation of an otherwise very useful and cost effective mating design, namely, the polycross. This study was conducted to investigate the relative contribution of different pollen parents to the sound-seeds stage, and also in a field progeny trial. Pollen from 15 radiata pine (Pinus radiata D. Don) parents was mixed in equal volume and applied to the same 15 parents, potentially allowing selfing. Samples of 8-year-old offspring were genotyped from five polycross families, and available seed from three of these five families was tested for unequal paternal contributions. The total paternal exclusion probability of five chloroplast markers and four microsatellite markers in our study was 99.1%. Overall, 81% of the offspring (both seeds and 8-year-old offspring) were assigned to 1 out of the 15 potential male parents, but a surprisingly high proportion (about 13%) was evidently fathered by pollen not included in the pollen-mix. Inconclusive evidence of unequal paternal contribution was observed in some families, but it did not influence the general combining ability (GCA) estimates appreciably, as evident from a high degree of correspondence between GCA estimates obtained from polycross and female-tester mating designs. A non-significant negative correlation was observed between the relative reproductive success (across polycross families) and predicted breeding values for diameter growth.     

Genotyping‐free parentage assignment using RAD‐seq reads

Parentage assignment is defined as the identification of the true parents of one focal offspring among a list of candidates and has been commonly used in zoological, ecological, and agricultural studies. Although likelihood‐based parentage assignment is the preferred method in most cases, it requires genotyping a predefined set of DNA markers and providing their population allele frequencies. In the present study, we proposed an alternative method of parentage assignment that does not depend on genotype data and prior information of allele frequencies. Our method employs the restriction site‐associated DNA sequencing (RAD‐seq) reads for clustering into the overlapped RAD loci among the compared individuals, following which the likelihood ratio of parentage assignment could be directly calculated using two parameters—the genome heterozygosity and error rate of sequencing reads. This method was validated on one simulated and two real data sets with the accurate assignment of true parents to focal offspring. However, our method could not provide a statistical confidence to conclude that the first ranked candidate is a true parent.     

Joint modeling of linkage and association: identifying SNPs responsible for a linkage signal

Once genetic linkage has been identified for a complex disease, the next step is often association analysis, in which single-nucleotide polymorphisms (SNPs) within the linkage region are genotyped and tested for association with the disease. If a SNP shows evidence of association, it is useful to know whether the linkage result can be explained, in part or in full, by the candidate SNP. We propose a novel approach that quantifies the degree of linkage disequilibrium (LD) between the candidate SNP and the putative disease locus through joint modeling of linkage and association. We describe a simple likelihood of the marker data conditional on the trait data for a sample of affected sib pairs, with disease penetrances and disease-SNP haplotype frequencies as parameters. We estimate model parameters by maximum likelihood and propose two likelihood-ratio tests to characterize the relationship of the candidate SNP and the disease locus. The first test assesses whether the candidate SNP and the disease locus are in linkage equilibrium so that the SNP plays no causal role in the linkage signal. The second test assesses whether the candidate SNP and the disease locus are in complete LD so that the SNP or a marker in complete LD with it may account fully for the linkage signal. Our method also yields a genetic model that includes parameter estimates for disease-SNP haplotype frequencies and the degree of disease-SNP LD. Our method provides a new tool for detecting linkage and association and can be extended to study designs that include unaffected family members.     

A general program for estimation of haplotype frequencies from population diploid data.

The program which is written in FORTRAN estimates haplotype frequencies in two-locus and three-locus genetic systems from population diploid data. It is based on the gene counting method which leads to maximum likelihood estimates, and can be used whenever the possible antigens (one or more) on each chromosome can be specified for each person and for each locus, i.e., ABO-like systems and inclusions are permitted. The number of alleles per locus may be rather large, and both grouped and ungrouped data can be used. Log likelihoods are calculated on the basis of various assumptions, so that likelihood ratio tests can be carried out.     

Association test algorithm between a qualitative phenotype and a haplotype or haplotype set using simultaneous estimation of haplotype frequencies, diplotype configurations and diplotype-based penetrances

Analysis of the association between haplotypes and phenotypes is becoming increasingly important. We have devised an expectation-maximization (EM)-based algorithm to test the association between a phenotype and a haplotype or a haplotype set and to estimate diplotype-based penetrance using individual genotype and phenotype data from cohort studies and clinical trials. The algorithm estimates, in addition to haplotype frequencies, penetrances for subjects with a given haplotype and those without it (dominant mode). Relative risk can thus also be estimated. In the dominant mode, the maximum likelihood under the assumption of no association between the phenotype and presence of the haplotype (L(0max)) and the maximum likelihood under the assumption of association (L(max)) were calculated. The statistic -2 log(L(0max)/L(max)) was used to test the association. The present algorithm along with the analyses in recessive and genotype modes was implemented in the computer program PENHAPLO. Results of analysis of simulated data indicated that the test had considerable power under certain conditions. Analyses of two real data sets from cohort studies, one concerning the MTHFR gene and the other the NAT2 gene, revealed significant associations between the presence of haplotypes and occurrence of side effects. Our algorithm may be especially useful for analyzing data concerning the association between genetic information and individual responses to drugs.     

An analytical model for the estimation of chromosome substitution effects in the offspring of individuals heterozygous at a segregating marker locus

Summary Use of marker genes for quantitative traits has been suggested as a supplement to selection for livestock species. Linkage relationships can be estimated by using data from offspring of a heterozygous parent, if offspring can be positively assigned segregation of one or the other of the marker alleles. In field data, some data on offspring can be characterized and used to estimate the difference in chromosome substitution effects, but other matings result in uncertain transfer of the marker alleles. In this study, an alternative estimation procedure is proposed that would allow incorporation of data on all offspring of a heterozygous parent, even those where chromosome segregation is ambiguous. If the frequency of the marker alleles is known in the population of mates of a heterozygous individual, the mean and variance of the heterozygous offspring can be used in a generalized leastsquares model to estimate the chromosome substitution effect. When gene frequencies are not known, maximum likelihood estimates can be obtained from the data for use in a conditional estimate. Monte Carlo simulations of data following the assumed genetic model were analyzed as proposed, and parameter estimates were characterized. Estimates of chromosome substitution effects were reasonable approximations of input values. Distributions of t-statistics testing the null hypothesis of no difference between marked chromosome segments were unbiased, with only slightly larger variance than expected. Addition of data from heterozygous offspring improved the efficiency of detection of chromosome substitution effects by more than four times when marker gene frequencies were low.     

HAPLOFREQ--estimating haplotype frequencies efficiently.

A commonly used tool in disease association studies is the search for discrepancies between the haplotype distribution in the case and control populations. In order to find this discrepancy, the haplotypes frequency in each of the populations is estimated from the genotypes. We present a new method HAPLOFREQ to estimate haplotype frequencies over a short genomic region given the genotypes or haplotypes with missing data or sequencing errors. Our approach incorporates a maximum likelihood model based on a simple random generative model which assumes that the genotypes are independently sampled from the population. We first show that if the phased haplotypes are given, possibly with missing data, we can estimate the frequency of the haplotypes in the population by finding the global optimum of the likelihood function in polynomial time. If the haplotypes are not phased, finding the maximum value of the likelihood function is NP-hard. In this case, we define an alternative likelihood function which can be thought of as a relaxed likelihood function. We show that the maximum relaxed likelihood can be found in polynomial time and that the optimal solution of the relaxed likelihood approaches asymptotically to the haplotype frequencies in the population. In contrast to previous approaches, our algorithms are guaranteed to converge in polynomial time to a global maximum of the different likelihood functions. We compared the performance of our algorithm to the widely used program PHASE, and we found that our estimates are at least 10% more accurate than PHASE and about ten times faster than PHASE. Our techniques involve new algorithms in convex optimization. These algorithms may be of independent interest. Particularly, they may be helpful in other maximum likelihood problems arising from survey sampling.     

Estimation of transmission probabilities in families ascertained through a proband with variable age-at-onset disease: application to the HLA A, B and DR loci in Finnish families with type 1 diabetes. The DiMe Study Group

An open problem of some interest in the study of HLA has been the possible existence of transmission distortion in the human HLA complex. In this paper, transmission probabilities are estimated and tested using data on HLA A, B and DR loci genotypes of parents and offspring ascertained from the entire population of Finland (Childhood Diabetes in Finland Study) through one or more offspring diagnosed with insulin-dependent diabetes mellitus (IDDM) during the recruitment period from September 1986 to July 1989. First, we show how to get unbiased estimates of transmission probabilities from the family data collected in the disease registry of incident cases. This is accomplished by assuming that transmission of HLA genes to children in the general population is conditionally independent given the parents' genotypes, and the birth dates of all offspring. Based on the sampling (ascertainment) process in the study on Childhood Diabetes in Finland, younger siblings of the index child (the oldest proband) are independent of the ascertainment and therefore give rise to unbiased inference regarding allele transmission. The hypothesis of Mendelian transmission of alleles at each locus was tested using the standard chi(2) test. Goodness-of-fit of the Mendelian inheritance model to the individual locus data is calculated by maximizing the likelihood function over allele transmission intensities at each locus. The existence of a strong transmission distortion is not supported by this study at the loci considered.     

Blood groups as genetic markers in chimpanzees: Their importance for the national chimpanzee breeding program

Severe restrictions on the importation of chimpanzees emphasize the importance and urgency of domestic breeding as a sole means to assure an uninterrupted supply of animals for medical research. An insight into the genetic structure of the self-sustained captive population of animals is indispensable to prevent the effects of inbreeding and to preserve the animals' reproductive capacity. This can be achieved by study of sets of genetic markers in the form of heritable molecular or antigenic variations detectable by relatively simple methods. Among chimpanzee blood components so far identified as possible genetic markers, red cell antigens appear to be the most useful and most readily available. The amount of information concerning blood groups of chimpanzees, their serology and genetics, number of polymorphic types, etc, surpasses data on other heritable traits in this species. A concise review of the present status of knowledge of chimpanzee blood groups and, particularly, of serology and genetics of two complex blood group systems, V-A-B-D and R-C-E-F, is given together with a few examples of their application in cases of disputed parentage. Finally, a list of practical steps is suggested dealing with introduction and use of genetic markers as elements of the national chimpanzee breeding program.     

APIS: An auto‐adaptive parentage inference software that tolerates missing parents

In the context of parentage assignment using genomic markers, key issues are genotyping errors and an absence of parent genotypes because of sampling, traceability or genotyping problems. Most likelihood‐based parentage assignment software programs require a priori estimates of genotyping errors and the proportion of missing parents to set up meaningful assignment decision rules. We present here the R package APIS, which can assign offspring to their parents without any prior information other than the offspring and parental genotypes, and a user‐defined, acceptable error rate among assigned offspring. Assignment decision rules use the distributions of average Mendelian transmission probabilities, which enable estimates of the proportion of offspring with missing parental genotypes. APIS has been compared to other software (CERVUS, VITASSIGN), on a real European seabass (Dicentrarchus labrax) single nucleotide polymorphism data set. The type I error rate (false positives) was lower with APIS than with other software, especially when parental genotypes were missing, but the true positive rate was also lower, except when the theoretical exclusion power reached 0.99999. In general, APIS provided assignments that satisfied the user‐set acceptable error rate of 1% or 5%, even when tested on simulated data with high genotyping error rates (1% or 3%) and up to 50% missing sires. Because it uses the observed distribution of Mendelian transmission probabilities, APIS is best suited to assigning parentage when numerous offspring (>200) are genotyped. We have demonstrated that APIS is an easy‐to‐use and reliable software for parentage assignment, even when up to 50% of sires are missing.     

Relative efficiency of haplotype frequency estimation in sibships and nuclear families compared to unrelated individuals

The problem of estimating haplotype frequencies from unphased single nucleotide polymorphism (SNP) genotype data in sibships with and without parents is considered. We focus on the Fisher information of the haplotype frequencies of the parents in order to correctly deal with the dependence of haplotypes within sibships. We compare these Fisher information matrices with those obtained for unrelated individuals and study the relative efficiency of sibships with and without parents compared to unrelated individuals in estimating haplotype frequencies. Crudely summarizing, the second sib contributes half the information of the first, except for rare haplotypes, when the second sib counts almost as one. We argue that the relative efficiencies can also be used to correct for dependence in the calculation of standard errors after initially ignoring the dependence in the estimation phase.     

Molecular genetics of chimpanzee Rh-related genes: Their relationship with the R-C-E-F blood group system,the chimpanzee counterpart of the human rhesus system

As the chimpanzee R-C-E-F blood group system appears to be the chimpanzee counterpart of the human Rhesus (RH) system, we have tried to determine whether chimpanzee Rh-like genes encode R-C-E-F-related proteins. Chimpanzee genomic DNA, digested by any of eight endonucleases and hybridized with three Rh exon-specific probes, exhibits a high degree of polymorphism. Analysis of DNA from unrelated individuals of different R-C-E-F types revealed that the presence of some restriction fragments is correlated with particular R-C-E-F types. The cosegregation of these fragments with R-C-E-F haplotypes was confirmed by family studies. Oligonucleotides complementary to regions flanking human exons were used as PCR primers on chimpanzee DNA; the resulting amplified fragments were identical in size to their human counterparts. Moreover, the nucleotide sequences of the fragments present a high degree of similarity to the corresponding human regions.     

Relationship between chimpanzee Rh-like genes and the R-C-E-F blood group system

The antigenic closeness between the chimpanzee alloantigen R^c of the R-C-E-F system, and the human alloantigen Rh_o(D) suggests a phylogeconnection between their genes. To confirm at the molecular level the common origin of these genes, genomic DNA from 16 unrelated chimpanzees of various R-C-E-F phenotypes were digested by three restriction enzymes and analyzed by Southern blot using a human Rh cDNA probe and three exon-specific probes. Restrictions profiles displayed reach polymorphism. Correlations between some bands and certain R-C-E-F phenotypes demonstrate that the human Rh cDNA probe defines in chimpanzee genomic DNA some genes of the R-C-E-F system.