How to select a satisfying typing program for paternity testing

The efficiency of a typing program for paternity testing concerns three specific aspects: first, what is the percentage of non-fathers that cannot be excluded from paternity; second, what is the percentage of true fathers that cannot be recognized as probable fathers, and third, what is the percentage of non-fathers that will be assigned as probale fathers. When extensive materials for observation with any specific typing program are not directly available, only the chance of non-exclusion of non-fathers can be calculated in a relatively simple way.The aim of the present study was to find a relationship between this and the other two criteria. It was found that the variance of the distribution of natural logarithms of paternity index values is approximated rather well by the formula var. $\text{I = 0.65 ×}\text{(n(}\text{ln 1}\text{ne}\text{3}\text{)}{}^2\text{)}$ (n = the number of genetic systems of the typing program and ne = the chance of non-exclusion of non-fathers). This allows the estimation of the two other critical percentages: the percentage of true fathers that cannot be assigned, and the percentages: the percentage of true fathers that cannot be assigned, and the percentage of non-fathers that will be assigned as probably true fathers.     

ISFG: Recommendations on biostatistics in paternity testing

The Paternity Testing Commission (PTC) of the International Society for Forensic Genetics has taken up the task of establishing the biostatistical recommendations in accordance with the ISO 17025 standards and a previous set of ISFG recommendations specific to the genetic investigations in paternity cases. In the initial set, the PTC recommended that biostatistical evaluations of paternity are based on a likelihood ratio principle – yielding the paternity index, PI. Here, we have made five supplementary biostatistical recommendations. The first recommendation clarifies and defines basic concepts of genetic hypotheses and calculation concerns needed to produce valid PIs. The second and third recommendations address issues associated with population genetics (allele probabilities, Y-chromosome markers, mtDNA, and population substructuring) and special circumstances (deficiency/reconstruction and immigration cases), respectively. The fourth recommendation considers strategies regarding genetic evidence against paternity. The fifth recommendation covers necessary documentation, reporting details and assumptions underlying calculations. The PTC strongly suggests that these recommendations should be adopted by all laboratories involved in paternity testing as the basis for their biostatistical analysis.     

The problem of single parent/child paternity analysis--practical results involving 336 children and 348 unrelated men

In a certain amount of paternity investigations, only DNA from child and alleged father is analyzed, thus increasing the possibility of false paternity inclusions. The aim of this study was to determine how many wrong paternity inclusions could be detected in a rather small geographical area comparing empirical results from 336 children and 348 men (13-15 STRs were investigated per person). This comparison between each child and all unrelated men (i.e. all putative fathers from the other cases) with an especially designed computer program resulted in 116,004 man/child pairs. Less than three excluding STRs were found in 1666 child/unrelated man pairs (1.44% of the comparisons). At least one unrelated man with only two or less STR mismatches could be determined for 322 children (95.8% of all investigated children). In 26 comparisons no STR mismatches between a child and an unrelated man were detected, thus at least one and up to three "second father(s)" under 350 men could be found for 23 children, if the mother is excluded. Paternity probabilities between 95.475% and 99.996% were calculated. Our results underline the difficulties in motherless paternity cases using only STR analysis and advise great precaution in assigning verbal predicates such as "paternity proven" in those investigations.     

Possible pitfalls in motherless paternity analysis with related putative fathers

Nowadays, more and more paternity cases are carried out investigating only child and putative father, mostly for economical or private reasons. Usually, reliable results can be obtained and the putative father can be included or ruled out with a high certainty. Considerable problems might arise when a relative of the biological father is investigated as being the putative father. In this study, we investigated 164 persons from 27 families creating artificial deficiency cases using the AmpFlSTRIdentifiler kit, which amplifies 15 STRs simultaneously. We analyzed 93 child/biological father pairs and the corresponding uncles, respectively the brothers of the biological fathers. The average paternity probability for the biological father was 99.9699% (paternity index (PI): 3321.26); only in three cases the results were under 99.9%. In five out of 125 child/uncle pairs no STR mismatches were found and paternity probabilities between 99.9726% (PI 3652) and 99.9970% (PI 33,545) were calculated. The average number of excluding loci was 3.4, but in 31.2% of the cases only zero, one or two mismatches were found. When both putative fathers were genetically typed, the biological father usually had a statistically higher paternity probability. Nevertheless, the differences between probabilities for father and uncle were only small. These results show that a reliable investigation of deficiency cases (i.e. child and putative father) seems to be more difficult than generally assumed. Especially in cases with an unknown familiar background and/or when investigating foreigners for immigration purposes, the laboratory expert should include the mother, increase the number of investigated loci or include a second method such as RFLP-analysis, some serological systems or typing of X-chromosome specific STRs to further ascertain the results.     

双亲皆疑亲子鉴定STR分型亲权指数计算方法探讨

计算标准三联体亲子鉴定的PI值及探讨双亲皆疑亲子鉴定PI值计算的可靠方法 ,对常规STR分型鉴定结果 ,根据Eseen M ller计算理论 ,总结出标准三联体亲子鉴定计算PI值的 4个公式 :1/ p ,1/ ( 2 p) ,1/ (p +q) ,1/ ( 2p +2 q)。提出适用于双亲皆疑亲子鉴定的一种新的PI值计算方法 ,并与其他方法进行比较。认为该方法取值Y时 ,既考虑随机男女生孩子的可能性 ,也考虑假设父 (或假设母 )与随机个体生孩子的可能性 ,更符合随机原则。     

The decision theory of paternity disputes: optimization considerations applied to multilocus DNA fingerprinting.

The solution of paternity disputes using results from scientific analyses is studied from a decision-theoretical viewpoint. Two alternative approaches to decision making, the so-called 'Bayes' and 'Minimax' strategies, are described and discussed. If prior probabilities of paternity are exactly known, then Bayes decisions are (a) independent of the source of evidence and (b) optimal with respect to average losses caused by wrong decisions. However, it is concluded that Minimax decisions, which depend upon the employed test system but not upon prior probabilities, are more appropriate in paternity cases if equal prior good will towards disclaimed children and alleged fathers is demanded. It is further demonstrated that, when major evidence about paternity comes from multilocus DNA fingerprinting, prior probabilities must be known quite accurately for Bayes decisions to be superior with respect to average losses. Finally, we are able to show that 'quasi' Bayes decision making, that is, adopting a neutral prior probability of 0.5 but leaving thresholds for decision making unchanged, coincides with Minimax decision making if multilocus DNA fingerprinting is employed.     

Resolving paternity relationships using X-chromosome STRs and Bayesian networks

X-chromosomal short tandem repeats (X-STRs) are very useful in complex paternity cases because they are inherited by male and female offspring in different ways. They complement autosomal STRs (as-STRs) allowing higher paternity probabilities to be attained. These probabilities are expressed in a likelihood ratio (LR). The formulae needed to calculate LR depend on the genotype combinations of suspected pedigrees. LR can also be obtained by the use of Bayesian networks (BNs). These are graphical representations of real situations that can be used to easily calculate complex probabilities. In the present work, two BNs are presented, which are designed to derive LRs for half-sisters/half-sisters and mother/daughter/paternal grandmother relationships. These networks were validated against known formulae and show themselves to be useful in other suspect pedigree situations than those for which they were developed. The BNs were applied in two paternity cases. The application of the mother/daughter/paternal grandmother BN highlighted the complementary value of X-STRs to as-STRs. The same case evaluated without the mother underlined that missing information tends to be conservative if the alleged father is the biological father and otherwise nonconservative. The half-sisters case shows a limitation of statistical interpretations in regard to high allelic frequencies.     

DNA数据库9个STR基因座比中认定亲权的可靠性分析

目的探讨Profiler plus试剂盒9个常染色体STR基因座用于DNA数据库中双亲亲缘关系比中结果认定亲权的可靠性。方法在DNA数据库中搜集无关个体与已知母子（或父子）在9个STR基因座不排除亲缘关系的比中记录54例，组成54例假定的三联体家庭，计算其PI值与RCP值；应用Identifiler试剂盒加做到15个常染色体STR基因座，观察其排除情况。结果在54例假定三联体中PI值最低为178．598597（RCP=99．443203％），最高为97318．085812（RCP=99．998972％）。加做到15个STR基因座后，54例假定三联体中每个三联体至少出现2个基因座排除，最多5个基因座出现排除的现象，平均排除基因座数为3．52个。结论Profilerplus试剂盒9个STR基因座用于亲缘关系鉴定可能出现错误结论；单纯利用RCP值来认定亲缘关系是不安全的；建议应用16个或更多的基因座建设DNA数据库和进行亲缘关系判定。     

Optimization and validation studies of the Mentype Argus X-8 kit for paternity cases

The use of ChrX-STRs is enormous in forensic case as these have proven to be powerful tools, mainly in deficiency paternity cases when the disputed child is female, and also some special cases involving blood relatives, incest cases, fetal typing in abortion material. The Mentype^® Argus X-8 kit is a commercial multiplex system which contains Amelogenin for gender determination as well as gonosomal STR markers (DXS8378, HPRTB, DXS7423, DXS7132, DXS10134, DXS10074, DXS10101 and DXS10135). Validation studies were being performed on blood obtained from the volunteers in Turkish population. In this study, some parameters were taken under consideration for validation like DNA extraction using different protocols, quantitated by using commercially available Invitrogen Qubit Fluorometer, reaction volume validation of Master Mix and the analysis of female/male, female/female and male/male mixtures were performed. The conditions were optimized and validated using GenAmp 9700 and reducing reaction volume from 25 μl to 12.5 μl and 6.5 μl. After reducing the total volume of the reaction, the results were same and there was no effect on peak height and quality when analyzed on ABI 310 genetic analyzer. 2 paternity cases were also performed which gave the same power of discrimination as has been mentioned in Mentype^® Argus X-8 kit.     

The effect of differences in gene frequency on probability of paternity

Knowledge of gene frequencies in populations is required for the calculation of probability of paternity. The question remains open as to the degree of accuracy of gene frequency estimates required to give accurate probability of paternity figures. This is of special concern in the HLA system, which has haplotype frequencies known to vary in populations. This paper presents computer simulation data comparing probability of paternity calculations using HLA data from California and North Carolina. Comparisons were made between geographic regions, and between blacks and whites within a geographic region. It was found that when the absolute probability of paternity is high, the average differences induced were small, but at lower probabilities the changes can be large. Differences were most pronounced between black and white populations. Examples of individual cases are given to illustrate the huge differences that can be induced in some cases by changing gene frequency.     

Subject index : Volume 25 (1984)

Biostatistical Parameters such as the paternal markers in the child (PM), individual exclusion change (IEC) probability of incidental involvement (Z), probability of paternity (POP), plausibility of paternity according to Essen-Möller (PLEM) and paternity index (PI) are defined and discussed in respect to their application in cases of disputed paternity. In order to calculate these parameters for up to 24 marker systems, including HLA under strict observation of the linkage disequilibrium, a computer programme in BASIC has been developed.     

The expected performance of single nucleotide polymorphism loci in paternity testing

We discuss the utility of single nucleotide polymorphism loci for full trio and mother-unavailable paternity testing cases, in the presence of population substructure and relatedness of putative and actual fathers. We focus primarily on the expected number of loci required to gain specified probabilities of mismatches, and report the expected proportion of paternity indices greater than three threshold values for these loci.     

Computer analysis of parentage in relation to maternity and paternity

General formulas for statistical calculations of parentage by means of blood group analysis are presented in relation to those of maternity and paternity. Based on these formulas, a computer program has been devised to calculate plausibilities, exclusion probabilities, and distributions of log (Y/X) of parentage for any blood groups. The program also gives numerical values of these quantities of maternity and paternity. The values of plausibility and exclusion probability are highest for parentage, and decrease in the order of paternity and maternity. Concerning the distribution of log (Y/X) for true families, a simple relation holds for the ratio of the mean value of log (Y/X) in parentage ap, to that in paternity af, and to that in maternity am as, ap: af: am = 1: 0.6: (0.6)2 This relation holds for all 14 blood groups examined.     

二联体亲权鉴定风险分析

目的探讨二联体亲权鉴定时存在的风险。方法选取22组经Goldeneye~(TM) 20A试剂盒检测后只有一个或没有不符合基因座的无关个体对构建假想家系。对其增加检测STRtyper-10G和/或AGCU 21+1 STR系统直至所有组不符合基因座个数大于3个,累积父权指数(CPI)不大于0.000 1。以三种规则:(1)不符合基因座数大于3个;(2)CPI值小于0.000 1;(3)同时满足(1)和(2),作为排除依据,使用不同数量的基因座(19个、26个、39个和46个)进行检测,讨论无关个体对的排除情况是否存在差异。结果 22组无关个体对,使用19个基因座和39个基因座以上的检测系统达到排除结果的分别为0组和22组。结论二联体亲子鉴定,使用19个基因座进行检测仍存在结果错判,39个基因座以上的检测系统能更有效的避免二联体的鉴定风险。     

Performance of the SNPforID 52 SNP-plex assay in paternity testing

The performance of a multiplex assay with 52 autosomal single nucleotide polymorphisms (SNPs) developed for human identification was tested on 124 mother–child–father trios. The typical paternity indices (PIs) were 10⁵–10⁶ for the trios and 10³–10⁴ for the child–father duos. Using the SNP profiles from the randomly selected trios and 700 previously typed individuals, a total of 83,096 comparisons between mother, child and an unrelated man were performed. On average, 9–10 mismatches per comparison were detected. Four mismatches were genetic inconsistencies and 5–6 mismatches were opposite homozygosities. In only two of the 83,096 comparisons did an unrelated man match perfectly to a mother–child duo, and in both cases the PI of the true father was much higher than the PI of the unrelated man. The trios were also typed for 15 short tandem repeats (STRs) and seven variable number of tandem repeats (VNTRs). The typical PIs based on 15 STRs or seven VNTRs were 5–50 times higher than the typical PIs based on 52 SNPs. Six mutations in tandem repeats were detected among the randomly selected trios. In contrast, there was not found any mutations in the SNP loci. The results showed that the 52 SNP-plex assay is a very useful alternative to currently used methods in relationship testing. The usefulness of SNP markers with low mutation rates in paternity and immigration casework is discussed.     

SNPs in paternity investigation: The simple future

Based on the 52 SNP-plex developed by the SNPforID Consortium, we designed two 10-plex to study single nucleotide polymorphisms (SNPs) for human identification and to establish its usefulness in paternity casework. This 20 autosomal SNP set was studied in 56 paternity investigation cases from South Portuguese resident population, also analyzed with 17 Short Tandem Repeats (STRs). Results obtained with both methodologies were consistent with each other, except for one case where the alleged father could not be excluded by SNPs. No mutation was found in the SNP loci, whereas a mismatch in STRs was detected. The use of SNPs as a complement to the analysis of autosomal STRs in paternity casework can result in paternity index and paternity probability values equivalent or higher than those obtained with more STR loci, but with lower costs. This study shows that instead of using additional STR loci, the analysis of 20 autosomal SNPs, as a complement technique to standard methodologies, is an appealing alternative in paternity investigation cases.     

A Windows-based software for common paternity and sibling analyses

A new Windows-based freeware for kinship analysis from DNA data is presented. This software can be used to calculate likelihood ratios and probabilities of paternity in trio and motherless cases, as well as in cases when a parent is lacking but there are data from the grandparents. It can also be used to compute the probability of two subjects being full-brothers or half-brothers.     

Maximum range of pellets fired from a shotgun

A mathematical model to determine the maximum range of pellets fired from a shotgun has been suggested. It has been assumed that the air resistance experienced by a pellet is proportional to the square of its velocity (?μV²) where $\text{μ =}\text{A}\text{C}$ with

$\text{C=0.061}\text{86}\text{N}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}$

and

$\text{A=}\text{1}\text{[17 696+2N+10 000(0.2?d)]}$

N is the number of pellets/ounce and d is the diameter of the pellets in inches. A method for calculating the maximum range has been suggested, and the values obtained for Buck 00, size 8 and size 9 American pellets are very close to the reported experimental observations. The maximum ranges for other sizes of pellets have also been calculated. The angle of projection decreases with increase in velocity and increases with increase in the weight of the pellet. It varies between 26° to 32° for common sizes of pellets and standard shotgun velocity. The maximum range in air is only 1 – 3% of the range attained by a pellet in vacuum.     

STR等位基因频率对父权指数的影响

目的观察中国汉族不同人群STR等位基因频率对联合父权指数(CPI)的影响。方法随机取108例13个CODIS基因座分型结果不排除父权关系的三联体案和二联体案,用5个不同地区人群的等位基因频率计算CPI值。结果三联体案的CPI值在2077.63～50897711626.46之间,同一案例的最大CPI与最小值CPI之比大于100者有20例(19.52%);二联体案的CPI值在25.12～2998685141之间,同一案例的最大CPI与最小值CPI之比大于100者有13例(12.04%)。结论不同人群等位基因频率计算CODIS基因座所得的CPI值在部分亲权鉴定案中有很大的差异。为了防止等位基因频率不确定性带来的误差,建议在亲权鉴定中用保守法计算CPI值。     

Deduction of paternity index from DNA mixture

Determination of individual genotypes in DNA mixture remains a challenge in forensic science. Using an approach of mixture of distributions, this article provides formula for calculation of paternity index (PI) in cases where only tissue mixture of the mother and alleged father, the genotypes of the mother and child, but not that of the alleged father are available. The formula has been used to solve a real case using mother's vaginal tissue contaminated with semen from alleged father.