The importance of HLA typing in cases of disputed paternity

In dispute paternity, the biologists must reply to two questions: 1. Is the paternity excluded or possible? 2. If it is possible, what is its probability? Valid answers can be given, using several genetic markers, among which HLA genes are specially interesting. Looking at HLA-A, B, C, DR typing of child, mother and presumed father, we propose a method which allows a direct calculation of paternity probability. Crossing over between HLA genes in presumed father and in mother are also considered in this method. In our experience, adding the date provided by the HLA genes and other genetic markers, we obtained, either formal exclusions, or possible paternities with a probability almost always higher than 90%.     

Probability of paternity exclusion when relatives are involved.

In diagnosis of paternity by means of polymorphic markers, the proportion of men excluded on the basis of the phenotypes of the mother and child is the best index for controlling information. Its expected value, the probability of exclusion of a male chosen at random with respect to a random child-mother couple, calculated from gene frequencies of every genetic system, may be modified by a close relationship between the mother, the real father, and the presumptive father. The father and even more the brother of the mother, if he is the father of the child, diminishes the probability of exclusion of an individual chosen at random in the population, and if he is falsely accused, he has a higher probability of being excluded. On the other hand, the brother of the real father chosen at random in the population has the least chance of being excluded. The two different rules of exclusion are involved in the calculations, the first one being the more reliable.     

Exclusion probabilities for single-locus paternity analysis when related males compete for matings

The statistical power of single-locus paternity analyses has previously been assessed by calculating an expected exclusion probability ( E ), the probability of excluding a randomly chosen nonfather. This E -statistic assumes that putative sires are a random selection of individuals from a panmictic study population. In species that display male natal philopatry, closely related individuals may be the principal competitors for paternity. In such structured populations, the E statistic will overestimate exclusion probability because males competing for paternity are more closely related than males chosen randomly from the population. A suite of loci thought to be sufficient for a panmictic population may frequently incorrectly assign paternity to close relatives of true sires. This study provides equations for calculating the expected probability of excluding a close male relative of the genetic sire ( Erel ) for any genotyping system that uses codominant markers. We also describe the use of Monte Carlo modelling to estimate exclusion probabilities when multiple male relatives compete for paternity. We show that the utility of a set of codominant markers will depend on the breeding behaviour and social system of the species in question.     

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.     

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.     

Do marker‐based paternity assignments favour heterozygous and unrelated males?

Genetic marker‐based parentage analyses are widely applied to studies of natural populations in the fields of evolutionary biology, conservation biology and ecology. When the same markers used in a parentage analysis are used together with the inferred parentage in a downstream analysis, such as the analysis of mate choice in terms of heterozygosity or relatedness, a bias may be incurred because a subset of the genotypes are favoured in parentage assignments or non‐exclusions. A previous simulation study shows that exclusion‐based paternity analyses are biased in favour of heterozygous males, and males less related to the mothers than expected under random mating. In this study, I investigated the biases of genetic paternity analyses achieved by both exclusion‐ and likelihood‐based methods, using both analytical and simulation approaches. It is concluded that while both exclusion‐ and likelihood‐based methods can lead to biased paternity assignments or non‐exclusions in favour of a subset of genotypes, the bias is not consistently towards heterozygous males or males apparently less related to mothers. Both the direction and extent of the bias depend heavily on the allele frequency distribution and the number of markers, the methods used for paternity assignments, and the estimators of relatedness. There exist important differences in the patterns of the biases between exclusion‐ and likelihood‐based paternity analysis methods. It is concluded that the markers, except when they are highly informative to yield accurate paternity assignments or exclusions, should be split into two subsets which are used separately in the paternity and downstream analyses.     

Probability and paternity testing.

A probability can be viewed as an estimate of a variable that is sometimes 1 and sometimes 0. To have validity, the probability must equal the expected value of that variable. To have utility, the average squared deviation of the probability from the value of that variable should be small. It is shown that probabilities of paternity calculated by the use of Bayes' theorem under appropriate assumptions are valid, but they can vary in utility. In particular, a recently proposed probability of paternity has less utility than the usual one based on the paternity index. Using an arbitrary prior probability in the calculation cannot lead to a valid probability unless, by chance, the chosen prior probability happens to be appropriate. Appropriate assumptions regarding both the prior probability and gene or genotypic frequencies can be estimated from prior experience.     

Parentage Analysis with Genetic Markers in Natural Populations. I. the Expected Proportion of Offspring with Unambiguous Paternity

Recent studies indicate that polymorphic genetic markers are potentially helpful in resolving genealogical relationships among individuals in a natural population. Genetic data provide opportunities for paternity exclusion when genotypic incompatibilities are observed among individuals, and the present investigation examines the resolving power of genetic markers in unambiguous positive determination of paternity. Under the assumption that the mother for each offspring in a population is unambiguously known, an analytical expression for the fraction of males excluded from paternity is derived for the case where males and females may be derived from two different gene pools. This theoretical formulation can also be used to predict the fraction of births for each of which all but one male can be excluded from paternity. We show that even when the average probability of exclusion approaches unity, a substantial fraction of births yield equivocal mother-father-offspring determinations. The number of loci needed to increase the frequency of unambiguous determinations to a high level is beyond the scope of current electrophoretic studies in most species. Applications of this theory to electrophoretic data on Chamaelirium luteum (L.) shows that in 2255 offspring derived from 273 males and 70 females, only 57 triplets could be unequivocally determined with eight polymorphic protein loci, even though the average combined exclusionary power of these loci was 73%. The distribution of potentially compatible male parents, based on multilocus genotypes, was reasonably well predicted from the allele frequency data available for these loci. We demonstrate that genetic paternity analysis in natural populations cannot be reliably based on exclusionary principles alone. In order to measure the reproductive contributions of individuals in natural populations, more elaborate likelihood principles must be deployed.     

Empirical validation of the Essen-Möller probability of paternity.

The validity of the Essen-Möller formulation probability of paternity is supported by demonstrating its correctness in a model genetic system--the ABO system. An analysis was made of 1,393 paternity cases typed uniformly for HLA-A and -B, ABO, Rh, and MNSs, in which the mother named one man only as the child''s father and in which both mother and putative father identified themselves as Caucasian. For purposes of analysis, putative fathers not excluded from paternity by the four systems tested were regarded as actual fathers. The joint distribution of observed triplets of ABO phenotypes is shown to be statistically consistent with expected values, and the fractions of "true" fathers for a given triplet closely approximated the probability of paternity calculated using a realistic prior probability. Recent allegations of fallaciousness of the method by Li and Chakravarty and Aickin are discussed in terms of the results presented.     

Trade up polygyny and breeding synchrony in avian populations

The advent of the molecular techniques used to assign paternity has focused attention on the differences between the social and the genetic mating systems of sexual species. In particular, the interrelations between breeding synchrony-the degree to which the fertility periods of individual females in a population overlap and the degree of extra pair paternity (EPP) in that population, has became a subject of a lively debate. Investigation of the subject can be facilitated by examining the criteria that females use in choosing extra pair partners. These preferences constitute a continuum ranging between two extremes. At one end, there are situations wherein all the females in a population exhibit a preference for males with particular phenotypic markers, and females mated to males lacking such "quality" markers seek extra pair fertilizations from males that do -trade up polygyny. At the other extreme, there are situations wherein females seek to maximize the total number of male partners, rather than secure fertilization by males of particular type -indiscriminate polygyny. Previously, we used game theoretical methods to model the interrelations between breeding synchrony and EPP in the context of indiscriminate polygyny. Here we present an analogous investigation in the context of trade up polygyny. Our results for the two cases, which delimit the range of the possible behavior, are similar. That is, we see that it is the pursuit of extra pair fertilizations opportunities that determines breeding synchrony of populations, rather than the vice versa as has been previously suggested.     

Establishment of paternity testing system using microsatellite markers in Chinese Holstein

To estimate the efficiency of microsatellite markers in paternity testing among Chinese Holstein, 30 microsatellite loci were used to differentiate 330 Chinese Holstein genotypes, according to the calculation of the allele frequency, number of alleles, effective number of alleles, genetic heterozygosity, polymorphic information content (PIC), and the exclusion probability in this cattle population. The results demonstrated that the exclusion probability ranged from 0.620 in locus BM1818 to 0.265 in locus INRA005 with the average of 0.472 and 11 microsatellite markers exceeding 0.5. The combined exclusion probability of nine microsatellite markers was over 0.99. The result showed that paternity testing of Chinese Holstein was basically resolved using the nine microsatellite markers selected.     

Genetic Patterns of Paternity and Testes Size in Mammals

Background

Testes size is used as a proxy of male intrasexual competition, with larger testes indicative of greater competition. It has been shown that in some taxa, social mating systems reflect variance in testes size, but results are not consistent, and instead it has been suggested that genetic patterns of mating may reflect testes size. However, there are different measures of genetic patterns of mating. Multiple paternity rates are the most widely used measure but are limited to species that produce multi-offspring litters, so, at least for group living species, other measures such as loss of paternity to males outside the social group (extra group paternity) or the proportion of offspring sired by the dominant male (alpha paternity) might be appropriate. This study examines the relationship between testes size and three genetic patterns of mating: multiple paternity, extragroup paternity and alpha paternity.

Methodology/Principal Findings

Using data from mammals, phylogenetically corrected general linear models demonstrate that both multiple paternity and alpha paternity, but not extra group paternity, relate to testes size. Testes size is greater in species with high multiple paternity rates, whereas the converse is found for alpha paternity. Additionally, length of mating season, ovulation mode and litter size significantly influenced testes size in one model.

Conclusions/Significance

These results demonstrate that patterns of mating (multiple paternity and alpha paternity rates) determined by genetic analysis can provide reliable indicators of male postcopulatory intrasexual competition (testes size), and that other variables (length of mating season, ovulation mode, litter size) may also be important.     

A High Throughput Single Nucleotide Polymorphism Multiplex Assay for Parentage Assignment in New Zealand Sheep

Accurate pedigree information is critical to animal breeding systems to ensure the highest rate of genetic gain and management of inbreeding. The abundance of available genomic data, together with development of high throughput genotyping platforms, means that single nucleotide polymorphisms (SNPs) are now the DNA marker of choice for genomic selection studies. Furthermore the superior qualities of SNPs compared to microsatellite markers allows for standardization between laboratories; a property that is crucial for developing an international set of markers for traceability studies. The objective of this study was to develop a high throughput SNP assay for use in the New Zealand sheep industry that gives accurate pedigree assignment and will allow a reduction in breeder input over lambing. This required two phases of development- firstly, a method of extracting quality DNA from ear-punch tissue performed in a high throughput cost efficient manner and secondly a SNP assay that has the ability to assign paternity to progeny resulting from mob mating. A likelihood based approach to infer paternity was used where sires with the highest LOD score (log of the ratio of the likelihood given parentage to likelihood given non-parentage) are assigned. An 84 “parentage SNP panel” was developed that assigned, on average, 99% of progeny to a sire in a problem where there were 3,000 progeny from 120 mob mated sires that included numerous half sib sires. In only 6% of those cases was there another sire with at least a 0.02 probability of paternity. Furthermore dam information (either recorded, or by genotyping possible dams) was absent, highlighting the SNP test’s suitability for paternity testing. Utilization of this parentage SNP assay will allow implementation of progeny testing into large commercial farms where the improved accuracy of sire assignment and genetic evaluations will increase genetic gain in the sheep industry.     

Statistical confidence for likelihood-based paternity inference in natural populations

Paternity inference using highly polymorphic codominant markers is becoming common in the study of natural populations. However, multiple males are often found to be genetically compatible with each offspring tested, even when the probability of excluding an unrelated male is high. While various methods exist for evaluating the likelihood of paternity of each nonexcluded male, interpreting these likelihoods has hitherto been difficult, and no method takes account of the incomplete sampling and error-prone genetic data typical of large-scale studies of natural systems. We derive likelihood ratios for paternity inference with codominant markers taking account of typing error, and define a statistic Δ for resolving paternity. Using allele frequencies from the study population in question, a simulation program generates criteria for Δ that permit assignment of paternity to the most likely male with a known level of statistical confidence. The simulation takes account of the number of candidate males, the proportion of males that are sampled and gaps and errors in genetic data. We explore the potentially confounding effect of relatives and show that the method is robust to their presence under commonly encountered conditions. The method is demonstrated using genetic data from the intensively studied red deer ( Cervus elaphus ) population on the island of Rum, Scotland. The Windows-based computer program, CERVUS , described in this study is available from the authors. CERVUS can be used to calculate allele frequencies, run simulations and perform parentage analysis using data from all types of codominant markers.     

Confidence of paternity,divorce, and investment in children by Albuquerque men

Using a sample of men living in Albuquerque, NM, we examined the relationship between paternity confidence and men's investment in children. In humans, men may reduce their investment in a child in two ways: indirectly, by ending their relationship with the child's mother and ceasing to cohabit with the child (e.g., divorce), and directly, by allocating less time and fewer resources to the child. In this article, we tested two hypotheses regarding the effect of paternity confidence on investment in children: (1) men will be more likely to divorce women if they suspect or are sure that they are not the father of their wife's child, and (2) controlling for divorce, men will reduce direct investments in low paternity confidence children relative to high paternity confidence children. The first hypothesis was supported by the data. The second hypothesis was supported for two out of three measures of paternal investment we examined; low paternity confidence reduces the time men spend with a child in a group with other children or adults, and it reduces extensive involvement with the child's educational progress; there was no effect of paternity confidence on the amount of time men spend with children in one-on-one interactions. We also examined the effects of unstated paternity confidence (e.g., when men decline to answer the question) on divorce and paternal investment. Overall, the results suggested that paternity confidence plays an important role in shaping men's relationships with women and with their putative genetic children.     

Genotype Reconstruction of Paternity in European Lobsters (Homarus gammarus)

Decapod crustaceans exhibit considerable variation in fertilisation strategies, ranging from pervasive single paternity to the near-ubiquitous presence of multiple paternity, and such knowledge of mating systems and behaviour are required for the informed management of commercially-exploited marine fisheries. We used genetic markers to assess the paternity of individual broods in the European lobster, Homarus gammarus, a species for which paternity structure is unknown. Using 13 multiplexed microsatellite loci, three of which are newly described in this study, we genotyped 10 eggs from each of 34 females collected from an Atlantic peninsula in the south-western United Kingdom. Single reconstructed paternal genotypes explained all observed progeny genotypes in each of the 34 egg clutches, and each clutch was fertilised by a different male. Simulations indicated that the probability of detecting multiple paternity was in excess of 95% if secondary sires account for at least a quarter of the brood, and in excess of 99% where additional sire success was approximately equal. Our results show that multiple paternal fertilisations are either absent, unusual, or highly skewed in favour of a single male among H. gammarus in this area. Potential mechanisms upholding single paternal fertilisation are discussed, along with the prospective utility of parentage assignments in evaluations of hatchery stocking and other fishery conservation approaches in light of this finding.     

A note on positive identification of paternity by using genetic markers

To see the efficiency of the statistical methods for positive identification of fathers using genetic markers, the statistical properties of the paternity index are studied algebraically and numerically. It is found that the currently used statistical methods are not powerful enough to discriminate between true fathers and non-excluded non-fathers, and, more often than not, may lead to false attributions of paternity. It is, therefore, suggested that exclusion of paternity is the only conclusive evidence that can be accepted by courts of law until better methods are devised.     

Population genetic data and forensic parameters of 30 autosomal InDel markers in Santa Catarina State population,Southern Brazil

The application of DNA technology in forensic investigations has grown rapidly in the last 25 years and with an exponential increase of short tandem repeats (STRs) data, usually presented as allele frequencies, that may be later used as databases for forensic and population genetics purposes. Thereby, classes of molecular markers such as single nucleotide polymorphisms and insertions/deletions (InDels) have been presented as another option of genetic marker sets. These markers can be used in paternity cases, when mutations in STR polymorphisms are present, as well as in highly degraded DNA analysis. In the present study, the allele frequencies and heterozygosity (H) of a 30 InDel markers set were determined and the forensic efficacy was evaluated through estimation of discrimination power (DP), match probability, typical paternity index and power of paternity exclusion in 108 unrelated volunteers from the State of Santa Catarina (South Brazil). The observed H per locus showed a range between 0.370 and 0.574 (mean = 0.479). HLD128 was the locus with the highest DP (DP = 0.656). DP for all markers combined was greater than 99.9999999999646 % which provides satisfactory levels of information for forensic demands. Genetic comparisons (exact tests of population differentiation and pairwise genetic distances) revealed that the population of Santa Catarina State differs from Korea and USA Afro-American populations but is similar to the Portuguese, German, Polish, Spanish and Basque populations.     

On the number of reproductives contributing to a half-sib progeny array

We address various statistical aspects of biological parentage in multi-offspring broods that arise via multiple paternity or multiple maternity and, hence, consist of mixtures of full- and half-sibs. Conditioned on population genetic parameters, computer simulations described herein permit estimation of: (1) the mean number of offspring needed to detect all parental gametes in a brood and (2) the relationship between the number of distinct parental gametes found in a brood and the number of parents. Results are relevant to the design of empirical studies employing molecular markers to assess genetic parentage in polygynous or polyandrous species with large broods, such as are found in many fishes, amphibians, insects, plants and other groups. The utility of this approach is illustrated using two empirical data sets.     

Constraints on control: factors influencing reproductive success in male mandrills (Mandrillus sphinx)

Over the last decade, paternity analysis using molecular markershas revealed that observed mating systems do not necessarilycorrelate with reproductive systems and thus cannot providereliable information about male reproductive success (RS). Thisis especially true for primate species with a complex multimale-multifemalesocial organization, such as mandrills (Mandrillus sphinx).Using molecular markers for the measurement of individual RSand a comprehensive data set comprising 193 offspring from 27birth cohorts over a 20-year period of sampling, we investigatedthe social, genetic, and demographic factors that may influencethe probability of paternity by dominant male mandrills, livingin a semi–free-ranging colony. We observed a significantskew in RS towards dominant males, with their probability ofpaternity increasing as the number of adult males in the groupincreased, and when they were closely related to subordinateadolescent males. Conversely, the probability of dominant malessiring infants decreased when the number of simultaneously tumescentfemales increased. Fewer offspring were sired by dominant maleswhen female partners were closely related to them and when therelatedness between dominant and subordinate adult males increased.These two last points suggests particularly that mechanismsof kin recognition are operating to avoid the costs of inbreedingand may also reflect the lower costs to dominant males of losingconception opportunities to more closely related subordinateadult males. This study is, to our knowledge, one of the firstin primates to use an integrative approach and multivariateanalysis to show that multiple factors are involved in determiningthe probability of paternity by dominant males.