The effectiveness of using co-dominant polymorphic allelic series for (1) checking pedigrees and (2) distinguishing full-sib pair members

Formulae express the effectiveness of parentage exclusion tests and differences separating full-sib pairs by compounding genotypic information on discrete examples of co-dominant alleles segregating at gene loci on different autosomes. Such polymorphisms occur among structural genes and polymorphic DNA sequences. Two general formulae state the theoretical effectiveness of using co-dominant alleles for (1) testing parentage and (2) distinguishing sibs. The formula for parentage exclusion tates the probability (P_E) that a given series of co-dominant alleles of known frequency should detect a falsely recorded father (or mother). The other formula describes how genetic polymorphism can distinguished closely related individuals. It states the probability (P_S) that alleles distinguish the members of full-sib pairs, dizygotic twins and tissue chimeras. To derive the two general formulae, particular formulae were calculated for n = 2,3 and 4 co-dominant alleles. By increasing the numbers of alleles, the formulae were seen to contain recurrent patterns which were then expressed in the two general formulae for n alleles. Some examples demonstrate applications of the two formulae in problems concerning parentage and sibship.     

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.     

Exclusion probabilities obtainable by biochemical polymorphisms in dogs

General formulae are given to calculate the exclusion probabilities in false paternity and parentage cases by means of gene loci with an arbitrary number of alleles whereas in paternity cases an arbitrary number of offspring per litter is considered additionally.
By aid of these formulae and on the basis of the allele frequencies of four blood protein and enzyme systems the probabilities of excluding incorrect paternity and parentage are calculated in seven German dog breeds. The results are tabulated and discussed.
It can be shown that the exclusion probability in false paternity cases increases distinctly with an increasing number of offspring per litter and its maximum is nearly attained if 5 offspring are examined. Therefore it is of value to consider entire litters in paternity controls in dogs.     

Exclusion probabilities of 22 bovine microsatellite markers in fluorescent multiplexes for semiautomated parentage testing

Six multiplexes developed for semiautomated fluorescence genotyping were evaluated for parentage testing. These multiplexes contained primer pairs for the amplification of 22 microsatellites on 17 bovine autosomes. Exclusion probabilities were determined from genotypes of 1022 Holstein cattle and 311 beef cattle belonging to five breeds. Two cases were considered: case 1, genotypes are known for an alleged parent and an offspring but genotypes of a confirmed parent are unknown; and case 2, genotypes are known for an alleged parent, a confirmed parent and an offspring. If the alleged parent is not the true parent, then the 22 markers will exclude the alleged parent with a probability of >0·9986 for case 1 and with a probability of >0·99999 for case 2. On the basis of these exclusion probabilities, the probability that an alleged parent will be falsely included as a parent is in the range of 1/716 to 1/2845 for case 1 and 1/1·2 million to 1/159753 for case 2. In addition to these results, a rapid and efficient non-organic method for extraction of DNA from semen is described.     

Single nucleotide polymorphisms for DNA typing in the domestic horse

Genetic markers are important resources for individual identification and parentage assessment. Although short tandem repeats (STRs) have been the traditional DNA marker, technological advances have led to single nucleotide polymorphisms (SNPs) becoming an attractive alternative. SNPs can be highly multiplexed and automatically scored, which allows for easier standardization and sharing among laboratories. Equine parentage is currently assessed using STRs. We obtained a publicly available SNP dataset of 729 horses representing 32 diverse breeds. A proposed set of 101 SNPs was analyzed for DNA typing suitability. The overall minor allele frequency of the panel was 0.376 (range 0.304–0.419), with per breed probability of identities ranging from 5.6 × 10^?35 to 1.86 × 10^?42. When one parent was available, exclusion probabilities ranged from 0.9998 to 0.999996, although when both parents were available, all breeds had exclusion probabilities greater than 0.9999999. A set of 388 horses from 35 breeds was genotyped to evaluate marker performance on known families. The set included 107 parent–offspring pairs and 101 full trios. No horses shared identical genotypes across all markers, indicating that the selected set was sufficient for individual identification. All pairwise comparisons were classified using ISAG rules, with one or two excluding markers considered an accepted parent–offspring pair, two or three excluding markers considered doubtful and four or more excluding markers rejecting parentage. The panel had an overall accuracy of 99.9% for identifying true parent–offspring pairs. Our developed marker set is both present on current generation SNP chips and can be highly multiplexed in standalone panels and thus is a promising resource for SNP‐based DNA typing.     

Association studies of QTL for multi-allele markers by mixed models

In this paper, we extend association study methods of both Fan et al. [Hum Hered 2002;53:130-145], in which a quantitative trait locus (QTL) and a multi-allele marker are considered for trio families, and Fan and Xiong [Biostatistics 2003, in press], in which a QTL and a bi-allelic marker are considered for nuclear families. The objective is to build mixed models for association study between a QTL and a multi-allelic marker for nuclear families with any number of offspring. Two types of nuclear family data are considered: the first is genetic data of offspring from at least one heterozygous parents, and the second is genetic data of offspring of nuclear family. (1) For the data of offspring from at least one heterozygous parents, we assume that at least one parent is heterozygous at the marker locus, and we may infer clearly the transmission of parental marker alleles to the offspring. We show that it can be used in association study in the presence of linkage. The theoretical basis is the difference between the conditional mean of trait value given an allele is transmitted and the conditional mean of trait value given the allele is not transmitted from a heterozygous parent. To build valid models, we calculate the variance covariance structure of trait values of offspring. Besides, the reduction of the number of parameters is discussed under an assumption of tight linkage between the trait locus and the marker. (2) For the data of offspring of nuclear family, we show that it can be used in general association study. In this case, the theoretical basis is the difference between the conditional mean of trait values given an allele is transmitted from a parent and the population mean. Then, we calculate variance-covariance structure of trait values of offspring. (3) Based on the theoretical analysis, mixed models are built for each type of the data, and related test statistics are proposed for association study. By power calculation and comparison, we show that, in some instances, the proposed test statistics have higher power than that by collapsing alleles to be new ones. The proposed models are used to analyze chromosomes 4 and chromosome 16 data of the Oxford asthma data, Genetic Analysis Workshop 12.     

Power of exclusion of 19 microsatellite markers for parentage testing in river buffalo (Bubalus bubalis)

In the present study, 19 microsatellite markers were assessed for their power of exclusion to test parentage in river buffalo. Microsatellite genotypes of 216 unrelated buffaloes belonging to five different breeds were utilized for the study. The probabilities of exclusion were calculated for three hypothetical situations viz. paternity testing (PE1), one parental genotype unavailable (PE2) and exclusion of both parents i.e. substituted offspring (PE3). The mean probability of exclusion across 19 investigated markers in buffalo was 0.578 (PE1), 0.405 (PE2) and 0.764 (PE3) respectively. The probability of exclusion for paternity (PE1) ranged between 0.297 and 0.814 across different markers. The exclusion probability for the cases one parent unavailable (PE2) and substituted offspring (PE3) varied from 0.143 to 0.688 and 0.465 to 0.946 respectively. Polymorphism information content and expected heterozygosity were found to have significantly high correlation with probability of exclusion of microsatellite markers. The cumulative PE1 of nine marker loci was estimated to be 0.9999 while in case of absence of one of the parental genotypes, a minimum of 11 markers were required to achieve a cumulative PE2 of 0.999. In conclusion, the present study proposes two multiplex sets with four and five markers respectively for routine parentage testing in buffalo and an additional set of four markers for doubtful cases of paternity.     

Parentage testing of racing camels (Camelus dromedarius) using microsatellite DNA typing

The camel racing industry would have added value in being able to assign parentage with high certainty. This study was aimed at assessing and applying microsatellite multiplexes to construct a parentage testing system for camels. An efficient system of 17 loci from 700 camel samples was used to construct a database of unrelated adults. Based on this, we estimated measures of polymorphism among the markers. In three multiplex reactions, we detected a total of 224 alleles, with 5–23 alleles/locus (mean = 13.18 ± 6.95 SD) and an average heterozygosity (H_E) of 0.54 (range 0.032–0.905). The total parentage exclusion probability was 0.99999 for excluding a candidate parent from parentage of an arbitrary offspring, given only the genotype of the offspring, and 0.9999 for excluding a candidate parent from parentage of an arbitrary offspring, given the genotype of the offspring and the other parent. We used 15 juveniles for parentage testing, as well as 17 sires (bull camels) and 21 dams (cows). In the case of parentage assignment, the microsatellite panel assigned all 15 offspring parentage with high confidence. Overall, these findings offer a set of microsatellite markers that are easy, simple and highly informative for parentage testing in camels.     

Detection of linkage between marker loci and loci affecting quantitative traits in crosses between segregating populations

Summary By making use of pedigree information and information on marker-genotypes of the parent and F-1 individuals crossed to form an F-2 population, it is possible to carry out a linkage analysis between marker loci and loci affecting quantitative traits in a cross between segregating parent populations that are at fixation for alternative alleles at the QTL, but share the same alleles at the marker loci. For two-allele systems, depending on marker allele frequencies in the parent populations, 2–4 times as many F-2 offspring will have to be raised and scored for markers and quantitative traits in order to provide power equivalent to that obtained in a cross between fully inbred lines. Major savings in number of F-2 offspring raised can be achieved by scoring each parent pair for a large number of markers in each chromosomal region and scoring F-1 and F-2 offspring only for those markers for which the parents were homozygous for alternative alleles. For multiple allele systems, particularly when dealing with hypervariable loci, only 10%–20% additional F-2 offspring will have to be raised and scored to provide power equivalent to that obtained in a cross between inbred lines. When a resource population contains novel favorable alleles at quantitative trait loci that are not present (or rare) in a commercial population, analyses of this sort will enable the loci of interest to be identified, mapped and manipulated effectively in breeding programs.Contribution no. 2124-E, 1987 series from The Agricultural Research Organization, The Volcani Center, Bet Dagan, Israel     

Linkage analysis for mapping genes of sex-influenced traits

Abstract Statistical methods are developed to estimate gender-specific and gender-average recombination frequencies between a biallelic or multiallelic marker and a sex-influenced gene. Iterative solutions are developed for intercross (or F-2 design). For biallelic markers, two iterative solutions are required, one for coupling and repulsion parental linkage phases and one for mixed parental linkage phases. For multiallelic markers, one set of iterative equations applies to all possible parental linkage phases. The resulting formulae for estimating recombination frequency use the full data set and yield estimates that are exactly the same as the true parameters if the observed and expected phenotypic distributions are equal. When one parent is homozygous for the sex-influenced gene as is expected with the backcross design, simple solutions exist for estimating recombination frequencies. However, offspring of one gender (male or female) do not have linkage information depending on whether the homozygous parent has two male-dominant or male-recessive alleles. Consequently, an F-2 design is more efficient than a backcross design for mapping a sex-influenced gene. Knowing each parental linkage phase is important to apply the methods developed in this article. It is shown that an individual's linkage phase of the sex-influenced locus can be determined based on allele transmission from the parents for all crosses except under the mating between an expressed male and an unexpressed female.     

Use of near-isogenic lines derived by backcrossing or selfing to map qualitative traits

Near-isogenic lines (NILs) are a valuable resource for detecting linkages between qualitative trait loci and molecular markers. Molecular marker studies are expensive and methods that require genotyping fewer individuals, such as the NIL-analysis method, are desirable. We present a theory for using sets of NILs to detect linkages between molecular markers and introgressed loci. The probability that a marker a specific distance from the introgressed gene will have a donor parent allele in a near-isogenic line is a function of the distance between the marker and the gene, and the number of back-crosses and/or selfs used in deriving the NIL. The binomial probability formula is used to calculate the probability of having a donor parent allele at a given marker when sets of NILs are used. The formulae given allow calculation of the probability that a marker is linked to the introgressed gene, as well as the probability that a gene will be successfully detected when using given numbers of NILs, backcrosses, and molecular markers.     

Parentage testing in alpacas (Vicugna pacos) using semi-automated fluorescent multiplex PCRs with 10 microsatellite markers

The aim of this study was to assess and apply a microsatellite multiplex system for parentage determination in alpacas. An approach for parentage testing based on 10 microsatellites was evaluated in a population of 329 unrelated alpacas from different geographical zones in Perú. All microsatellite markers, which amplified in two multiplex reactions, were highly polymorphic with a mean of 14.5 alleles per locus (six to 28 alleles per locus) and an average expected heterozygosity ( H _E) of 0.8185 (range of 0.698–0.946). The total parentage exclusion probability was 0.999456 for excluding a candidate parent from parentage of an arbitrary offspring, given only the genotype of the offspring, and 0.999991 for excluding a candidate parent from parentage of an arbitrary offspring, given the genotype of the offspring and the other parent. In a case test of parentage assignment, the microsatellite panel assigned 38 (from 45 cases) offspring parentage to 10 sires with LOD scores ranging from 2.19 × 10⁺¹³ to 1.34 × 10⁺¹⁵ and Δ values ranging from 2.80 × 10⁺¹² to 1.34 × 10⁺¹⁵ with an estimated pedigree error rate of 15.5%. The performance of this multiplex panel of markers suggests that it will be useful in parentage testing of alpacas.     

基于微卫星标记的圆口铜鱼亲子鉴定技术

为快速有效地鉴别不同的圆口铜鱼家系及来源, 研究从已发表的40个微卫星标记中筛选出20个多态性较高且稳定扩增的微卫星位点, 通过对8个圆口铜鱼家系339尾个体进行微卫星基因分型检测, 建立了圆口铜鱼荧光微卫星标记与多重毛细管电泳相结合的亲子鉴定技术。遗传多样性分析结果显示, 圆口铜鱼8个家系群体的平均等位基因数(N_a)为9个, 平均多态信息含量(PIC)为0.616, 平均期望杂合度(H_e)为0.659, 平均观测杂合度(H_o)为0.691, 其中子一代群体的遗传多样性水平明显低于亲本群体。亲子鉴定分析结果显示, 当双亲基因型未知时其单亲累积排除概率(CE-1P)为0.99954473, 当单亲基因型已知时其累积排除概率(CE-2P)为0.99999825, 当双亲基因型未知时其双亲累积排除概率(CE-PP)为1.00000000, 当使用20个微卫星位点进行亲子鉴定时, 297尾子一代均能正确找到其父母本, 亲子鉴定准确率为100%。由此可见, 研究建立的圆口铜鱼亲子鉴定技术是可靠的, 能为圆口铜鱼的家系管理、种群遗传管理和增殖放流效果评估提供科学依据     

Difficulties in parentage analysis: the probability that an offspring and parent have the same heterozygous genotype.

Parentage studies often estimate the number of parents contributing to half-sib progeny arrays by counting the number of alleles attributed to unshared parents. This approach is compromised when an offspring has the same heterozygous genotype as the shared parent, for then the contribution of the unshared parent cannot be unambiguously deduced. To determine how often such cases occur, formulae for co-dominant markers with n alleles are derived here for Ph, the probability that a given heterozygous parent has an offspring with the same heterozygous genotype, and Pa, the probability that a randomly chosen offspring has the same heterozygous genotype as the shared parent. These formulae have been derived assuming Mendelian segregation with either (1) an arbitrary mating system, (2) random mating or (3) mixed mating. The maximum value of Pa under random mating is 0.25 and occurs with any two alleles each at a frequency of 0.5. The behaviour with partial selfing (where reproduction is by selfing with probability s, and random mating otherwise) is more complex. For n < or = 3 alleles, the maximum value of Pa occurs with any two alleles each at a frequency of 0.5 if s < 0.25, and with three equally frequent alleles otherwise. Numerically, the maximum value of Pa for n > or = 4 alleles occurs with n* < or = n alleles at equal frequencies, where the maximizing number of alleles n* is an increasing function of the selfing rate. Analytically, the maximum occurs with all n alleles present and equally frequent if s > or = 2/3. In addition, the potential applicability of these formulae for evolutionary studies is briefly discussed.     

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.     

基于微卫星多重PCR技术的兰州鲇亲子鉴定

针对目前兰州鲇(Silurus lanzhouensis)种质资源救护保存和良种选育等研究工作中面临的亲子鉴定及系谱管理等问题,研究应用微卫星荧光标记多重PCR与自动测序分型技术,建立了2组四重PCR和2组三重PCR体系,并成功应用于3个家系亲子鉴定中。利用Cervus v.3.0软件对110尾兰州鲇进行遗传多样性分析,结果显示:研究筛选的14个微卫星标记的平均观测杂合度(H_o)为0.750,平均期望杂合度(H_e)为0.667,平均多态信息含量(PIC)为0.624,具有丰富的遗传多样性。对已知系谱信息的3个兰州鲇家系的90尾子代和20尾候选亲本进行亲子鉴定分析,结果表明,双亲基因型未知累积排除概率(CE-1P)、单亲基因型已知累积排除概率(CE-2P)和双亲基因型已知累积排除概率(CE-PP)分别为0.99753092、0.99983971和0.99999964。4组多重PCR累积模拟鉴定率为100%,累积实际鉴定率为83%。采用50尾个体进行双盲验证,利用MEGA7.0对3个家系50尾个体进行聚类分析,结果表明同一家系94%的个体聚类分析...     

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.     

Using blocks of linked single nucleotide polymorphisms as highly polymorphic genetic markers for parentage analysis

Single nucleotide polymorphisms (SNPs) are plentiful in most genomes and amenable to high throughput genotyping, but they are not yet popular for parentage or paternity analysis. The markers are bi-allelic, so individually they contain little information about parentage, and in nonmodel organisms the process of identifying large numbers of unlinked SNPs can be daunting. We explore the possibility of using blocks of between three and 26 linked SNPs as highly polymorphic molecular markers for reconstructing male genotypes in polyandrous organisms with moderate (five offspring) to large (25 offspring) clutches of offspring. Haplotypes are inferred for each block of linked SNPs using the programs Haplore and Phase 2.1. Each multi-SNP haplotype is then treated as a separate allele, producing a highly polymorphic, 'microsatellite-like' marker. A simulation study is performed using haplotype frequencies derived from empirical data sets from Drosophila melanogaster and Mus musculus populations. We find that the markers produced are competitive with microsatellite loci in terms of single parent exclusion probabilities, particularly when using six or more linked SNPs to form a haplotype. These markers contain only modest rates of missing data and genotyping or phasing errors and thus should be seriously considered as molecular markers for parentage analysis, particularly when the study is interested in the functional significance of polymorphisms across the genome.     

Reproductive Effort and Reproductive Values in Periodic Environments

Life-history theory concerns the optimal spread of reproduction over an organism's life span. In variable environments, there may be extrinsic differences between breeding periods within an organism's life, affecting both offspring and parent and giving rise to intergenerational trade-offs. Such trade-offs are often discussed in terms of reproductive value for parent and offspring. Here, we consider parental life-history optimization in response to varying offspring values of a population regulated by territoriality, where the quality of the environment varies periodically. Periods are interpreted as either within-year (seasonality) or between-years variation (cyclicity). The evolutionarily stable strategy in a general model with two-phased periodicity in the environment can generate either higher or lower effort in the more favorable of the two phases; hence knowing survival prospects of offspring does not suffice for predicting reproductive effort-the future of all descendants and the parent must be tracked. We also apply our method to data on the Ural owl Strix uralensis, a species preying on cyclically fluctuating voles. The observed dynamics are best predicted by assuming delayed reproductive costs and Type II functional response. Accounting for varying offspring values can lead to cases where both reproductive effort and recruitment of offspring are higher in the phase when voles are not maximally abundant, a pattern supported by our data.