Applications of the Dirichlet distribution to forensic match probabilities

The Dirichlet distribution provides a convenient conjugate prior for Bayesian analyses involving multinomial proportions. In particular, allele frequency estimation can be carried out with a Dirichlet prior. If data from several distinct populations are available, then the parameters characterizing the Dirichlet prior can be estimated by maximum likelihood and then used for allele frequency estimation in each of the separate populations. This empirical Bayes procedure tends to moderate extreme multinomial estimates based on sample proportions. The Dirichlet distribution can also be employed to model the contributions from different ancestral populations in computing forensic match probabilities. If the ancestral populations are in genetic equilibrium, then the product rule for computing match probabilities is valid conditional on the ancestral contributions to a typical person of the reference population. This fact facilitates computation of match probabilities and tight upper bounds to match probabilities.Editor's commentsThe author continues the formal Bayesian analysis introduced by Gjertson & Morris in this voluem. He invokes Dirichlet distributions, and so brings rigor to the discussion of the effects of population structure on match probabilities. The increased computational burden this approach entails should not be regarded as a hindrance.     

Validation of 15 microsatellites for parentage testing in North American bison, Bison bison and domestic cattle

Fifteen bovine microsatellites were evaluated for use in parentage testing in 725 bison from 14 public populations, 178 bison from two private ranches and 107 domestic cattle from five different breeds. The number of alleles per locus ranged from five to 16 in bison and from five to 13 in cattle. On average, expected heterozygosity, polymorphism information content (PIC) and probability of exclusion values were slightly lower in bison than in cattle. A core set of 12 loci was further refined to produce a set of multiplexed markers suitable for routine parentage testing. Assuming one known parent, the core set of markers provides exclusion probabilities in bison of 0.9955 and in cattle of 0.9995 averaged across all populations or breeds tested. Tests of Hardy-Weinberg and linkage equilibrium showed only minor deviations. This core set of 12 loci represent a powerful and efficient method for determining parentage in North American bison and domestic cattle.     

Genetic structure analyses and ancestral information inference of Chinese Kyrgyz group via a panel of 39 AIM-DIPs

Ancestry informative markers have extensive uses and advantages in inferring ancestral origins and estimating ancestral genetic information components of admixed populations. With the characteristics of highly cultural exchange and the admixed genetic structure of the Kyrgyz group, it is essential to enrich the genetic data of the Kyrgyz group. In this study, we used a self-developed ancestry informative marker-deletion/insertion polymorphic (AIM-DIP) panel to explore ancestral components of Chinese Kyrgyz group and population genetic relationships between the Kyrgyz group and reference populations. Results showed that all AIM-DIP loci were conformed to Hardy-Weinberg equilibrium. There were 36 AIM-DIP loci that contributed significantly to genetic information inference. Multiple statistical analyses revealed that Chinese Kyrgyz group had a closer genetic relationship with Chinese Uyghur group. The ancestral components of the Kyrgyz group, being mostly composed of genetic components of European and East Asian populations, were more similar to the ancestral components of Chinese Uyghur group.     

Migration, selection and histocompatibility

The extreme polymorphism of the HLA system allows a very precise definition of populations by gene frequencies. The existence of several linked loci (HLA-A, B, C, D, DR) induces the possibility of detection of preferential chromosomes in populations (particular associations of alleles or linkage disequilibria). These linkage disequilibria indicate that the conditions required for Hardy-Weinberg equilibrium are not met. The linkage disequilibria can be used as indicators for the evaluation of genetic dift, founder effect and inbreeding in small populations or for the detection of selection and migration in larger populations.     

Isolation and characterization of 11 microsatellite primers for a temperate reef fish, the California sheephead (Semicossyphus pulcher)

Eleven microsatellites were characterized for Semicossyphus pulcher (California sheephead) using an enrichment protocol. The number of alleles varied from three to 14 for a sample of 40 individuals from two populations. Expected heterozygosities ranged from 0.311 to 0.891. All loci but one were in Hardy-Weinberg equilibrium. No evidence for linkage disequilibrium was observed. These polymorphic microsatellites will be useful for genetic diversity and connectivity analyses of S. pulcher.     

Genetic analysis of 30 InDel markers for forensic use in five different Chinese populations

Allele frequencies of 30 insertion/deletion polymorphism (InDel) markers previously selected and validated for forensic purposes were assessed in 419 unrelated individuals originating from five different populations of P.R. China, including Chinese Han, Chinese Hui, Uighur, Mongolians, and Tibetans. Hardy-Weinberg equilibrium tests and linkage disequilibrium analysis were performed; the allele frequency distributions of the 30 InDel markers met the conditions for genetic equilibrium in all five populations and the InDel markers on the same chromosome did not generate any linkage blocking. Analysis of molecular variance indicated that genetic variation among the five populations represents only 4% of the total genetic diversity. We determined the cumulative power of discrimination for each population: 0.99999999999841 in Chinese Han, 0.99999999999690 in Chinese Hui, 0.99999999999709 in Uighur, 0.99999999999772 in Mongolians, and 0.99999999999854 in Tibetans.     

Isolation and characterization of 15 nuclear microsatellite markers for Baillonella toxisperma Pierre (Sapotaceae), a low-density tree species of Central Africa

Baillonella toxisperma is a scattered endemic species of the Guineo-Congolian forest. We developed 15 nuclear microsatellite markers specifically for B. toxisperma to analyse the genetic diversity of 188 individuals distributed in two natural populations in Gabon. On average, 8.3 alleles per locus were identified; observed heterozygosity ranged from 0.056 to 0.872 and expected heterozygosity from 0.282 to 0.823 among populations. Only three loci showed a significant departure to Hardy-Weinberg equilibrium, but no linkage disequilibrium was observed for any pair of loci.     

Sweet drinks are made of this: conservation genetics of an endemic palm species from the Dominican Republic

Pseudophoenix ekmanii is a threatened palm species endemic to the Dominican Republic. Sap from trees is extracted to make a local drink; once they are tapped the individual usually dies. Plants are also illegally harvested for the nursery trade and destroyed by poachers hunting the endemic and threatened Hispaniolan parrot. We used 7 DNA microsatellite markers to assist land managers in developing conservation strategies for this palm. We sampled 4 populations along the known distribution range of this species (3 populations from the mainland and 1 from the small island of Isla Beata), for a total sample of n = 104. We found strong evidence for genetic drift, inbreeding, and moderate gene flow (i.e., all populations had at least 4 loci that were not in Hardy-Weinberg equilibrium, at least 9 loci pairs were in linkage disequilibrium, the pairwise F(ST) values ranged from 0.069 to 0.266, and had positive F(IS) values). Data supported an isolation-by-distance model, and cluster analyses based on genetic distances resolved 2 groups that match a north-south split. The population from Isla Beata had the lowest levels of genetic diversity and was the only one in which we found pairs of individuals with identical shared multilocus genotypes.     

Microsatellite loci isolated from the tropical tree Hymenaea courbaril L. (Fabaceae)

We developed 11 microsatellite markers for Hymenaea courbaril for the purpose of studying spatial genetic structure and gene flow. The microsatellite loci were screened in 44 trees from two populations. All loci were polymorphic, exhibiting between two and 16 alleles, and levels of expected heterozygosity from 0.174 to 0.909. Departures from Hardy-Weinberg equilibrium were detected for all loci in one population. The estimated null allele frequency is low or moderate. No locus combinations exhibited linkage disequilibrium.     

New polymorphic microsatellite loci for population studies in the European anchovy, Engraulis encrasicolus (L.)

Eleven microsatellite loci were developed in the European anchovy, Engraulis encrasicolus, and tested in samples from two geographically distant populations (Atlantic and Mediterranean Sea). Number of alleles ranged from eight to 28 and observed heterozygosity from 0.440 to 0.920. There was no evidence of linkage disequilibrium, although two loci are indeed linked. All loci were in Hardy-Weinberg equilibrium, except for one locus in the Atlantic and two loci in the Mediterranean sample. These three loci plus two more showed evidence for null alleles.     

Characterization of single nucleotide polymorphism markers for the green sea turtle (Chelonia mydas)

We present data on 29 new single nucleotide polymorphism assays for the green sea turtle, Chelonia mydas. DNA extracts from 39 green turtles were used for two methods of single nucleotide polymorphism discovery. The first approach employed an amplified fragment length polymorphism technique. The second technique screened a microsatellite library. Allele-specific amplification assays were developed for high-throughput single nucleotide polymorphism genotyping and tested on two Pacific C. mydas nesting populations. Observed heterozygosities ranged from 0 to 0.95 for a Hawaiian population and from 0 to 0.85 for a Galapagos population. Each of the populations had one locus out of Hardy-Weinberg equilibrium, SSCM2b and SSCM5 for Hawaii and Galapagos, respectively. No loci showed significant genotypic linkage disequilibrium across an expanded set of four Pacific nesting populations. However, two loci, SSCM4 and SSCM10b showed linkage disequilibrium across three populations indicating possible association.     

Testing for concordant equilibria between population samples

A substantial body of theory has been developed to assess the effect of evolutionary forces on the distribution of genotypes, both single and multilocus, within populations. One area where the potential for application of this theory has not been fully appreciated concerns the extent to which population samples differ. Within populations, the divergence of genotype or haplotype frequencies from that expected under Hardy-Weinberg (HW) or linkage equilibrium can be measured as disequilibria coefficients. To assess population samples for concordant equilibria, an analytical framework for comparing disequilibria coefficients between populations is necessary. Here we present log-linear models to evaluate such hypotheses. These models have broad utility ranging from conventional population genetics to genetic epidemiology. We demonstrate the use of these log-linear models (1) as a test for genetic association with disease and (2) as a test for different levels of linkage disequilibria between human populations.     

Moment estimation of population diversity and genetic distance from data on recessive markers

A moment-based method for estimating a measure of population diversity, theta or Wright's FST, is given for dominant markers such as amplified fragment length polymorphisms (AFLPs) or RAPDs in noninbred populations. Basic assumptions are that there is random mating, Hardy-Weinberg equilibrium, linkage equilibrium, no mutation from common ancestor and equally distant populations. It is based on the variances between and within populations of genotype frequencies, whereas previously moment methods for dominant markers have been indirect in that they have been based on first estimating allele frequencies and then using the variances of those frequencies. The use of genotype frequencies directly appears to be more robust. Approximate sampling errors of the estimates are given. Methods are extended to estimate genetic distances and their sampling errors. The AFLP data from samples of breeds of pig are used for illustration.     

Match probabilities in a finite, subdivided population

We generalize a recently introduced graphical framework to compute the probability that haplotypes or genotypes of two individuals drawn from a finite, subdivided population match. As in the previous work, we assume an infinite-alleles model. We focus on the case of a population divided into two subpopulations, but the underlying framework can be applied to a general model of population subdivision. We examine the effect of population subdivision on the match probabilities and the accuracy of the product rule which approximates multi-locus match probabilities as a product of one-locus match probabilities. We quantify the deviation from predictions of the product rule by R, the ratio of the multi-locus match probability to the product of the one-locus match probabilities. We carry out the computation for two loci and find that ignoring subdivision can lead to underestimation of the match probabilities if the population under consideration actually has subdivision structure and the individuals originate from the same subpopulation. On the other hand, under a given model of population subdivision, we find that the ratio R for two loci is only slightly greater than 1 for a large range of symmetric and asymmetric migration rates. Keeping in mind that the infinite-alleles model is not the appropriate mutation model for STR loci, we conclude that, for two loci and biologically reasonable parameter values, population subdivision may lead to results that disfavor innocent suspects because of an increase in identity-by-descent in finite populations. On the other hand, for the same range of parameters, population subdivision does not lead to a substantial increase in linkage disequilibrium between loci. Those results are consistent with established practice.     

Isolation and characterization of microsatellite loci for mountain mullet (Agonostomus monticola)

We report on the isolation of 15 polymorphic microsatellite loci from mountain mullet (Agonostomus monticola). In the two populations sampled, loci exhibited two to 21 alleles and observed heterozygosity values ranged from 0.222 to 1.000. All loci conformed to Hardy-Weinberg equilibrium expectations, and none exhibited linkage disequilibrium. Although A. monticola is an important subsistence fishery in parts of its range, little is known about its ecology and many populations appear to be experiencing declines. These microsatellite loci should prove useful in the study of population structure of A. monticola and aid in other potential conservation efforts such as the management of hatchery broodstock.     

PERMANENT GENETIC RESOURCES: Isolation and characterization of microsatellite loci in the Mediterranean shore crab Carcinus aestuarii (Decapoda, Portunidae)

We characterized nine polymorphic microsatellites in the Mediterranean shore crab Carcinus aestuarii (Decapoda: Portunidae). Microsatellites were isolated from a partial genomic library enriched for multiple motifs. All loci were polymorphic, with number of alleles ranging from two to 16 and a mean observed heterozygosity of 0.75. Seven loci were in Hardy-Weinberg equilibrium, and two showed weak heterozygote deficiency. No linkage disequilibrium was found between loci. In addition, we tested Hardy-Weinberg and linkage equilibrium of three Carcinus maenas loci, already reported to cross-amplify in C. aestuarii. These molecular markers will be potentially useful to investigate genetic structure of this species.     

Polymorphic restriction sites of type II collagen gene: their location and frequencies in the Finnish population

Restriction fragment length polymorphism (RFLP) of the cartilage-specific type II collagen gene has been studied in the Finnish population. Two high-frequency alleles, also reported in other populations, were detected. The HindIII allele had a frequency of 0.33, and that detected with PvuII a frequency of 0.46. Both of these frequencies resembled the ones reported for other populations. Also one BamHI allele, not earlier reported, was found at a low frequency. Two other previously reported polymorphisms for BamHI and EcoRI were not detected in the Finnish population. The RFLPs showed a fair agreement with the Hardy-Weinberg equilibrium. A linkage disequilibrium was found between PvuII and HindIII markers. The alpha 1(II) collagen gene seems to be more conserved in populations of various origins than the alpha 2(I) collagen gene. These polymorphic collagen markers would be useful in linkage studies of various inherited cartilage disorders.     

Microsatellite markers for the roman, Chrysoblephus laticeps (Teleostei: Sparidae), an overexploited seabream from South Africa

Eleven polymorphic microsatellite loci were developed from an enrichment library of the roman, Chrysoblephus laticeps, and characterized for 40 individuals collected in Africa's largest and oldest Marine Protected Area (MPA), the Tsitsikamma National Park. The number of alleles per locus ranged from three to 19, and heterozygosities ranged from 0.20 to 0.85. A significant departure from Hardy-Weinberg equilibrium was detected for one locus, and linkage disequilibrium was identified among three pairs of loci. The markers will be useful to detect whether populations resident in MPAs along the South African coast are genetically connected, and whether there is spillover of recruits into adjacent exploited areas.     

Isolation and characterization of 12 microsatellites from the black surfperch, Embiotoca jacksoni, a reef fish that lacks a pelagic larval phase

A set of 12 microsatellite markers was developed from Embiotoca jacksoni genomic DNA and tested for polymorphism using 64 individuals from two populations. All loci were polymorphic with a number of alleles ranging from two to 19 with expected heterozygosities ranging from 0.17 to 0.89. There was no evidence of linkage disequilibrium and all loci were in Hardy-Weinberg equilibrium, except for four loci in one population. High numbers of private alleles were consistent with strong population structure, and very limited dispersal. Six microsatellite markers successfully cross amplified and were polymorphic in closely related species, Embiotoca lateralis and Hyspurus caryi.     

Development and characterization of eight polymorphic microsatellite loci from Pistacia lentiscus L. (Anacardiaceae)

We have developed a set of eight polymorphic nuclear microsatellite markers for the Mediterranean shrub Pistacia lentiscus by means of an enriched library method. Characterization for the eight loci was carried out on 42 individuals from two populations sampled in southern Spain. The overall number of alleles detected was 59, ranging from three to 13 per locus. Expected heterozygosity per locus and population ranged from 0.139 to 0.895. Two loci albeit only in one population (Seville) departed significantly from Hardy-Weinberg equilibrium expectations and no linkage disequilibrium between pairs of loci was detected. These markers will be used in studies of gene flow across a fragmented landscape.