Exclusion probabilities for pedigree testing farm animals

Pedigree testing, using genetic markers, may be undertaken for a variety of situations, of which the classical paternity testing is only one. This has not always been made clear in the literature. Exclusion probabilities associated with various testing situations, including the use of autosomal or X-linked codominant marker systems with any number of alleles, are presented. These formulae can be used to determine the appropriate exclusion probability for the situation being investigated. One such situation is where sire groups of progeny are to be verified without knowledge of the dams' genotypes, in which case the classical paternity exclusion probability is too high, and if used may result in an optimistic declaration about the progeny that have not been excluded. On the other hand, if mating pairs are known then incorrect progeny can be excluded at a higher rate than suggested by paternity exclusion calculations. The formulae also assist in determining the usefulness of X-linked markers, particularly if the pedigree checks involve progeny of only one sex. A system of notation that is useful for the algebraic manipulation of genetic probabilities, including exclusion probabilities as presented here, is also given.     

基于微卫星标记的斑点叉尾鮰家系鉴定技术及应用

研究旨在建立准确、高效且经济的斑点叉尾鮰(Ictalures punctatus)家系亲缘鉴定体系, 以期为斑点叉尾鮰的遗传评估及家系育种提供科学依据。选用10对具有较高多态性SSR标记, 建立两个5重PCR反应体系。应用建立的斑点叉尾鮰家系亲缘鉴定体系对来源于13个全同胞家系和8个半同胞家系的333尾个体进行亲权鉴定。结果表明: 10个位点平均等位基因数为9.8、平均观测杂合度0.8591、平均期望杂合度0.8092、平均多态信息含量0.7845; 3种情况下的累积排除概率分别为: 0.99996806、0.99833267和0.99999998; 验证群体的鉴定结果与系谱高度一致, 真实鉴定率达到99.1%, 子代与父母本三者之间配对平均LOD值介于13.30—24.70, 且置信度均达到95%。研究选择的微卫星位点等位基因数目较多, 多态性较高, 可以快速、准确地对斑点叉尾鮰混养群体进行家系鉴定。     

Comparison of Biochemical Polymorphisms and Short Tandem Repeat (STR) DNA Markers for Paternity Testing in Rhesus Monkeys (Macaca mulatta)

Genetic markers are indispensable for molecular and statistical genetic research involving nonhuman primates. Genetic markers must be used to ascertain parentage and to confirm the accuracy of pedigrees based solely on housing or demographic records; otherwise, the results of pedigree, linkage, or quantitative genetic analyses may be unreliable. Until recently, most genetic markers used in nonhuman primates were plasma proteins or isozyme polymorphisms, which were required in large numbers, because levels of genetic variation revealed by these markers were rather low. We compared the newer, PCR-amplified short tandem repeat markers (STRs) with a panel of classical biochemical polymorphic markers, for paternity determination among captive-bred rhesus monkeys. The STR markers exhibited an average genetic diversity of 64% and an expected paternity exclusion probability of 0.443. Both of these were greater than the average 54.5% genetic diversity and 0.298 exclusion probability exhibited by the biochemical markers. The STRs were much more efficient than the biochemical markers for parentage determination, since they required only half the amount of genetic typing data to resolve an average paternity case. Thus, the results of applying these two classes of genetic markers in paternity tests were somewhat different than expected on the basis of theoretical exclusion probabilities. These differences were probably due to inbreeding and other genetic differences among breeding colonies. Because they are more informative and provide rapid and efficient genetic data, STRs are now the method of choice for parentage determination and pedigree corroboration among nonhuman primates.     

Sampling genotypes in large pedigrees with loops

Markov chain Monte Carlo (MCMC) methods have been proposed to overcome computational problems in linkage and segregation analyses. This approach involves sampling genotypes at the marker and trait loci. Scalar-Gibbs is easy to implement, and it is widely used in genetics. However, the Markov chain that corresponds to scalar-Gibbs may not be irreducible when the marker locus has more than two alleles, and even when the chain is irreducible, mixing has been observed to be slow. These problems do not arise if the genotypes are sampled jointly from the entire pedigree. This paper proposes a method to jointly sample genotypes. The method combines the Elston-Stewart algorithm and iterative peeling, and is called the ESIP sampler. For a hypothetical pedigree, genotype probabilities are estimated from samples obtained using ESIP and also scalar-Gibbs. Approximate probabilities were also obtained by iterative peeling. Comparisons of these with exact genotypic probabilities obtained by the Elston-Stewart algorithm showed that ESIP and iterative peeling yielded genotypic probabilities that were very close to the exact values. Nevertheless, estimated probabilities from scalar-Gibbs with a chain of length 235 000, including a burn-in of 200 000 steps, were less accurate than probabilities estimated using ESIP with a chain of length 10 000, with a burn-in of 5 000 steps. The effective chain size (ECS) was estimated from the last 25 000 elements of the chain of length 125 000. For one of the ESIP samplers, the ECS ranged from 21 579 to 22 741, while for the scalar-Gibbs sampler, the ECS ranged from 64 to 671. Genotype probabilities were also estimated for a large real pedigree consisting of 3 223 individuals. For this pedigree, it is not feasible to obtain exact genotype probabilities by the Elston-Stewart algorithm. ESIP and iterative peeling yielded very similar results. However, results from scalar-Gibbs were less accurate.     

Reconstructing pedigrees: some identifiability questions for a recombination-mutation model

Pedigrees are directed acyclic graphs that represent ancestral relationships between individuals in a population. Based on a schematic recombination process, we describe two simple Markov models for sequences evolving on pedigrees—Model R (recombinations without mutations) and Model RM (recombinations with mutations). For these models, we ask an identifiability question: is it possible to construct a pedigree from the joint probability distribution of extant sequences? We present partial identifiability results for general pedigrees: we show that when the crossover probabilities are sufficiently small, certain spanning subgraph sequences can be counted from the joint distribution of extant sequences. We demonstrate how pedigrees that earlier seemed difficult to distinguish are distinguished by counting their spanning subgraph sequences.     

No sitting on the fence: protecting wetlands from feral pig damage by exclusion fences requires effective fence maintenance

Feral pigs damage the significant ecological and cultural values of tropical Australian wetlands. Control measures such as culling, baiting, and trapping can reduce overall pig populations, but do not eliminate the substantial physical damage to wetlands that can occur from just a few individuals. Exclusion fences have been adopted as a potential technique to prevent damage to selected wetlands. To test the effectiveness of exclusion fences we measured the physical damage caused by pigs to multiple wetlands in the Archer River catchment of tropical northern Australia. Wetlands were fenced using a typical cattle exclusion fence, a specific pig exclusion fence or had no fence. Initial analyses of these fence treatments showed no significant difference in the intensity of physical pig damage to exposed wetland sediments and fringing vegetation. However, several of the pig exclusion fences were found to have been compromised. Reanalysis indicated wetlands with functioning pig exclusion fences had no physical pig damage and this was significantly less damage than in all other treatments. In contrast, wetlands with compromised pig exclusion fences had damage that was statistically equivalent to sites without fences or with cattle exclusion fences, but in individual cases had the worst damage recorded in any of the treatments. Compromised pig exclusion fencing of wetlands can thus be worse than having no fencing at all. This suggests that the successful prevention of pig damage to wetlands by exclusion fences requires ongoing and effective fence monitoring and maintenance regimes.

     

Pedigree Analysis of the Sika Deer (Cervus nippon) using Microsatellite Markers

The usefulness of microsatellite markers in pedigree analysis of the sika deer (Cervus nippon) was tested in a herd in which the maternal lineages were recorded. Eighteen sets of microsatellite primers originally designed for bovine, ovine, and cervine loci successfully amplified polymorphic DNA in the deer. The numbers of alleles per locus ranged from two to seven, and the observed heterozygosity ranged from 0.350 to 0.900. The resolution power of the markers in paternity testing was then determined by calculating exclusion probabilities and paternity indices. Parentages of the study population were efficiently discriminated by genotyping 17 microsatellite loci. The microsatellite data were also used to calculate the genetic relatedness between individuals, which significantly correlated with coancestry coefficients for the pairs. Our results demonstrate that the microsatellite markers are efficient tools in studying the social structure and behavior of the sika deer, as well as in monitoring the inbreeding status.     

Single nucleotide polymorphisms for pig identification and parentage exclusion

Single nucleotide polymorphisms (SNPs) have become an important type of marker for commercial diagnostic and parentage genotyping applications as automated genotyping systems have been developed that yield accurate genotypes. Unfortunately, allele frequencies for public SNP markers in commercial pig populations have not been available. To fulfil this need, SNP markers previously mapped in the USMARC swine reference population were tested in a panel of 155 boars that were representative of US purebred Duroc, Hampshire, Landrace and Yorkshire populations. Multiplex assay groups of 5-7 SNP assays/group were designed and genotypes were determined using Sequenom's massarray system. Of 80 SNPs that were evaluated, 60 SNPs with minor allele frequencies >0.15 were selected for the final panel of markers. Overall identity power across breeds was 4.6 x 10(-23), but within-breed values ranged from 4.3 x 10(-14) (Hampshire) to 2.6 x 10(-22) (Yorkshire). Parentage exclusion probability with only one sampled parent was 0.9974 (all data) and ranged from 0.9594 (Hampshire) to 0.9963 (Yorkshire) within breeds. Sire exclusion probability when the dam's genotype was known was 0.99998 (all data) and ranged from 0.99868 (Hampshire) to 0.99997 (Yorkshire) within breeds. Power of exclusion was compared between the 60 SNP and 10 microsatellite markers. The parental exclusion probabilities for SNP and microsatellite marker panels were similar, but the SNP panel was much more sensitive for individual identification. This panel of SNP markers is theoretically sufficient for individual identification of any pig in the world and is publicly available.     

Computation of identity by descent probabilities conditional on DNA markers via a Monte Carlo Markov Chain method

The accurate estimation of the probability of identity by descent (IBD) at loci or genome positions of interest is paramount to the genetic study of quantitative and disease resistance traits. We present a Monte Carlo Markov Chain method to compute IBD probabilities between individuals conditional on DNA markers and on pedigree information. The IBDs can be obtained in a completely general pedigree at any genome position of interest, and all marker and pedigree information available is used. The method can be split into two steps at each iteration. First, phases are sampled using current genotypic configurations of relatives and second, crossover events are simulated conditional on phases. Internal track is kept of all founder origins and crossovers such that the IBD probabilities averaged over replicates are rapidly obtained. We illustrate the method with some examples. First, we show that all pedigree information should be used to obtain line origin probabilities in F2 crosses. Second, the distribution of genetic relationships between half and full sibs is analysed in both simulated data and in real data from an F2 cross in pigs.     

Prediction of identity by descent probabilities from marker-haplotypes

The prediction of identity by descent (IBD) probabilities is essential for all methods that map quantitative trait loci (QTL). The IBD probabilities may be predicted from marker genotypes and/or pedigree information. Here, a method is presented that predicts IBD probabilities at a given chromosomal location given data on a haplotype of markers spanning that position. The method is based on a simplification of the coalescence process, and assumes that the number of generations since the base population and effective population size is known, although effective size may be estimated from the data. The probability that two gametes are IBD at a particular locus increases as the number of markers surrounding the locus with identical alleles increases. This effect is more pronounced when effective population size is high. Hence as effective population size increases, the IBD probabilities become more sensitive to the marker data which should favour finer scale mapping of the QTL. The IBD probability prediction method was developed for the situation where the pedigree of the animals was unknown (i.e. all information came from the marker genotypes), and the situation where, say T, generations of unknown pedigree are followed by some generations where pedigree and marker genotypes are known.     

Pedigree and genotype errors in the Framingham Heart Study

The pedigree and genotype data from the Framingham Heart Study were examined for errors. Errors in 21 of 329 pedigrees were detected with the program PREST, and of these the errors in 16 pedigrees were resolved. Genotyping errors were then detected with SIMWALK2. Five Mendelian errors were found following the pedigree corrections. Double-recombinant errors were more common, with 142 being detected at mistyping probabilities of 0.25 or greater.     

Detection and Integration of Genotyping Errors in Statistical Genetics

Detection of genotyping errors and integration of such errors in statistical analysis are relatively neglected topics, given their importance in gene mapping. A few inopportunely placed errors, if ignored, can tremendously affect evidence for linkage. The present study takes a fresh look at the calculation of pedigree likelihoods in the presence of genotyping error. To accommodate genotyping error, we present extensions to the Lander-Green-Kruglyak deterministic algorithm for small pedigrees and to the Markov-chain Monte Carlo stochastic algorithm for large pedigrees. These extensions can accommodate a variety of error models and refrain from simplifying assumptions, such as allowing, at most, one error per pedigree. In principle, almost any statistical genetic analysis can be performed taking errors into account, without actually correcting or deleting suspect genotypes. Three examples illustrate the possibilities. These examples make use of the full pedigree data, multiple linked markers, and a prior error model. The first example is the estimation of genotyping error rates from pedigree data. The second-and currently most useful-example is the computation of posterior mistyping probabilities. These probabilities cover both Mendelian-consistent and Mendelian-inconsistent errors. The third example is the selection of the true pedigree structure connecting a group of people from among several competing pedigree structures. Paternity testing and twin zygosity testing are typical applications.     

An efficient algorithm to compute the posterior genotypic distribution for every member of a pedigree without loops

This paper describes a non-iterative, recursive method to compute the likelihood for a pedigree without loops, and hence an efficient way to compute genotype probabilities for every member of the pedigree. The method can be used with multiple mates and large sibships. Scaling is used in calculations to avoid numerical problems in working with large pedigrees.     

Parallel computations on pedigree data through mapping to configurable computing devices

Pedigree data structures have a number of applications in genetics, including the estimation of allelic or haplotype probabilities in humans and agricultural species, and the estimation of breeding values in agricultural species. Sequential algorithms for general purpose CPU-based computers are commonly used, but are inadequate for some tasks on large data sets. We show that pedigree data can be directly represented on Field Programmable Gate Arrays (FPGA), allowing highly efficient massively parallel simulation of the flow of genes. Operating on the whole pedigree in parallel, the transmission of genes can occur for all individuals in a single clock cycle. By using FPGA, the algorithms to estimate inbreeding coefficients and allelic probabilities are shown to operate hundreds to thousands of times faster than the corresponding sequentially based algorithms. Where problems can be largely represented in an integer form, FPGA provide an efficient platform for computations on pedigree data.     

Detecting deletions in families affected by a dominant disease by use of marker data

A method of testing for whether inherited deletions are a cause of a single-locus dominant disease was derived, involving analysis of the marker segregation within the pedigree of a single family that segregates for the disease. It is shown that markers can be used to test deductively for the presence of an inherited deletion. The probabilities of confirming or rejecting the presence of a deletion in an arbitrary pedigree without inbreeding are then derived. The power of the test is shown to be limited in single trios but to increase rapidly as the size of the pedigree increases. For larger pedigrees, the probabilities of confirming or rejecting a deletion are higher than 0.9 for SNPs having a minor allele frequency greater than 0.4. The probabilities are higher using multiallelic markers such as microsatellites, reaching levels as high as 0.9 in even rather small pedigrees. In certain cases the test outcome is not deductive, a deletion being neither confirmed nor rejected. It is shown to still be possible then to employ a statistical test for the presence of a deletion by use of an a priori probability for a deletion.     

GMCheck: Bayesian error checking for pedigree genotypes and phenotypes

GMCheck uses graphical modeling to find the posterior probabilities of data errors given genotypes or phenotypes in a specified pedigree structure.     

Isolation and characterization of microsatellite loci in Acer opalus (Aceraceae), a sexually-polymorphic tree, through an enriched genomic library

An enrichment protocol was used to isolate and characterize microsatellite loci in Acer opalus, a Mediterranean tree species. Highly polymorphic microsatellite loci were required for paternity analyses in a population of this species. Eight microsatellite loci were amplified and a total of 87 alleles were detected in a sample of 142 individuals from one population, allowing the identification of each individual with a unique multilocus genotype. The paternity exclusion probabilities varied from 0.261 for locus Aop820 to 0.806 for locus Aop450, and the parent-pair exclusion probabilities varied from 0.433 for Aop820 to 0.940 for Aop450. The cumulative probabilities of exclusion for paternity and parentage of the eight loci were both higher than 0.999, supporting the usefulness of these microsatellite loci for future paternity and parentage analyses in A. opalus. Cross-species transferability was also assayed, supporting their potential use in other eight Acer species.     

Estimation of the number of SNP genetic markers required for parentage verification

Formulae were developed to compute exclusion probabilities for parentage confirmation for any number of diallelic markers under the assumption that the minor allele frequency (MAF) varied among markers, but has a uniform distribution. Three scenarios were analysed: a progeny with (1) a single putative parent; (2) two putative parents; and (3) one actual parent and one putative parent. Exclusion probabilities were computed for minimum values for the MAFs of 0.1, 0.2 and 0.3, and required either one or at least two conflicts for exclusion. The numbers of markers required to obtain 99% exclusion probabilities based on a single conflict for the three minimum MAFs were 54, 45 and 39 for scenario 1; 17, 16 and 15 for scenario 2; and 28, 25 and 24 for scenario 3. The requirement of at least two conflicts for exclusion increased the number of markers required by approximately 45% for all three scenarios and all three minimum MAFs. The results obtained by the analytical formulae were very close to results obtained by simulation and to values in the literature for specific marker sets.     

Modeling of identity-by-descent processes along a chromosome between haplotypes and their genotyped ancestors

Identity-by-descent probabilities are important for many applications in genetics. Here we propose a method for modeling the transmission of the haplotypes from the closest genotyped relatives along an entire chromosome. The method relies on a hidden Markov model where hidden states correspond to the set of all possible origins of a haplotype within a given pedigree. Initial state probabilities are estimated from average genetic contribution of each origin to the modeled haplotype while transition probabilities are computed from recombination probabilities and pedigree relationships between the modeled haplotype and the various possible origins. The method was tested on three simulated scenarios based on real data sets from dairy cattle, Arabidopsis thaliana, and maize. The mean identity-by-descent probabilities estimated for the truly inherited parental chromosome ranged from 0.94 to 0.98 according to the design and the marker density. The lowest values were observed in regions close to crossing over or where the method was not able to discriminate between several origins due to their similarity. It is shown that the estimated probabilities were correctly calibrated. For marker imputation (or QTL allele prediction for fine mapping or genomic selection), the method was efficient, with 3.75% allelic imputation error rates on a dairy cattle data set with a low marker density map (1 SNP/Mb). The method should prove useful for situations we are facing now in experimental designs and in plant and animal breeding, where founders are genotyped with relatively high markers densities and last generation(s) genotyped with a lower-density panel.     

Conditional probability methods for haplotyping in pedigrees

Efficient haplotyping in pedigrees is important for the fine mapping of quantitative trait locus (QTL) or complex disease genes. To reconstruct haplotypes efficiently for a large pedigree with a large number of linked loci, two algorithms based on conditional probabilities and likelihood computations are presented. The first algorithm (the conditional probability method) produces a single, approximately optimal haplotype configuration, with computing time increasing linearly in the number of linked loci and the pedigree size. The other algorithm (the conditional enumeration method) identifies a set of haplotype configurations with high probabilities conditional on the observed genotype data for a pedigree. Its computing time increases less than exponentially with the size of a subset of the set of person-loci with unordered genotypes and linearly with its complement. The size of the subset is controlled by a threshold parameter. The set of identified haplotype configurations can be used to estimate the identity-by-descent (IBD) matrix at a map position for a pedigree. The algorithms have been tested on published and simulated data sets. The new haplotyping methods are much faster and provide more information than several existing stochastic and rule-based methods. The accuracies of the new methods are equivalent to or better than those of these existing methods.