Nondetectability of restriction fragments and independence of DNA fragment sizes within and between loci in RFLP typing of DNA.

We provide experimental evidence showing that, during the restriction-enzyme digestion of DNA samples, some of the HaeIII-digested DNA fragments are small enough to prevent their reliable sizing on a Southern gel. As a result of such nondetectability of DNA fragments, individuals who show a single-band DNA profile at a VNTR locus may not necessarily be true homozygotes. In a population database, when the presence of such nondetectable alleles is ignored, we show that a pseudodependence of alleles within as well as across loci may occur. Using a known statistical method, under the hypothesis of independence of alleles within loci, we derive an efficient estimate of null allele frequency, which may be subsequently used for testing allelic independence within and across loci. The estimates of null allele frequencies, thus derived, are shown to agree with direct experimental data on the frequencies of HaeIII-null alleles. Incorporation of null alleles into the analysis of the forensic VNTR database suggests that the assumptions of allelic independence within and between loci are appropriate. In contrast, a failure to incorporate the occurrence of null alleles would provide a wrong inference regarding the independence of alleles within and between loci.     

Independence tests for VNTR alleles defined as quantile bins.

VNTR fragment lengths in three databases maintained by the FBI for forensic purposes were partitioned into quantile bins, and tests for independence of the two bins at each of six loci were conducted. Whether independence was declared depended on the number of quantiles used. For a large number of quantile bins, equal to the number of fixed bins used by the FBI, 10 of 18 likelihood-ratio tests showed significant departures from independence when all genotypes were considered, and this changed to 7 of 18 when only heterozygotes were tested. This is in contrast to likelihood-ratio tests on fixed bins, when there were five significant departures over all genotypes and two departures for heterozygotes.     

A comparison of tests for independence in the FBI RFLP data bases

Several tests of independence of alletic frequencies within and between loci have been compared, and it has been found that Fisher's exact test is the best test to use. When this test is applied to RFLP databases established by the FBI, paying no attention to the single-band problem, there is generally evidence for independence at one locus but not at two loci. When the test is restricted to double-banded entries in the databases; there is overall evidence for independence.     

Independence of Vntr Alleles Defined as Fixed Bins

An analysis is presented of data collected by the Federal Bureau of Investigation at six unlinked variable number of tandem repeats (VNTR) loci for the United States population. Databases have been constructed of VNTR profiles of Caucasians, Blacks and Hispanics from Florida, Texas and California. There was very little evidence for correlations between lengths for pairs of VNTR fragments, within or between loci. When the fragment lengths were amalgamated into discrete bins, there was also little evidence for disequilibrium over all genotypes, within or between loci, for the Caucasian database, although some disequilibrium was found for the Black and Hispanic databases. No disequilibrium was found for the Caucasian or Black databases when tests were confined to heterozygous individuals. In cases of global disequilibrium, local tests can be applied to specific genotypes. The results suggest that, at the bin level, frequencies of VNTR profiles can generally be estimated as the products of the frequencies of the constituent elements. This overcomes the problem of estimating population frequencies when any particular profile does not exist in the database. There is some evidence for different frequencies, at the individual bin level, between geographic samples within each of the Caucasian, Black and Hispanic databases, and considerable evidence for differences between the three databases. These differences are less evident for the frequencies of four-locus profiles.     

Considerations for measuring genetic variation and population structure with multilocus fingerprinting

Multilocus DNA fingerprinting provides a cost-effective means to rapidly assay genetic variation at many loci. While this makes the technique particularly attractive for studies of evolution and conservation biology, fingerprint data can be difficult to interpret. Measurement errors inherent with the technique force investigators to group similar-sized alleles (bands) into discrete bins before estimating genetic parameters. If too little error is accounted for in this process homologous alleles will not be grouped in a common bin, whereas overestimated error can produce bins with homoplasic alleles. We used simulations and empirical data for two frog species ( Rana luteiventris and Hyla regilla ) to demonstrate that mean band-sharing ( S¯_xy ) and heterozygosity ( H ¯_E) are a function of both bin width and band profile complexity (i.e. number and distribution of bands). These estimators are also sensitive to the number of lanes included in the analysis when bin width is wide and a floating bin algorithm is employed. Multilocus estimates of H ¯_E were highly correlated with S¯_xy and thus provide no additional information about genetic variation. Estimates of population subdivision ( F ^ and Φ^_ST) appeared robust to changes in bin size. We also examined the issue of statistical independence for band-sharing data when comparisons are made among all samples. This analysis indicated that the covariance between band-sharing statistics was very small and not statistically different from zero. We recommend that sensitivity analyses for bin size be used to improve confidence in the biological interpretation of multilocus fingerprints, and that the covariance structure for band-sharing statistics be examined.     

Effects of population structure and admixture on exact tests for association between Loci

The probability of multilocus genotype counts conditional on allelic counts and on allelic independence provides a test statistic for independence within and between loci. As the number of loci increases and each sampled genotype becomes unique, the conditional probability becomes a function of total heterozygosity. In that case, it does not address between-locus dependence directly but only indirectly through detection of the Wahlund effect. Moreover, the test will reject the hypothesis of allelic independence only for small values of heterozygosity. Low heterozygosity is expected for population subdivision but not for population admixture. The test may therefore be inappropriate for admixed populations. If individuals with parents in two different populations are always considered to belong to one of the populations, then heterozygosity is increased in that population and the exact test should not be used for sparse data sets from that population. If such a case is suspected, then alternative testing strategies are suggested.     

Deletion mapping of homoeologous group 6-specific wheat expressed sequence tags

To localize wheat (Triticum aestivum L.) ESTs on chromosomes, 882 homoeologous group 6-specific ESTs were identified by physically mapping 7965 singletons from 37 cDNA libraries on 146 chromosome, arm, and sub-arm aneuploid and deletion stocks. The 882 ESTs were physically mapped to 25 regions (bins) flanked by 23 deletion breakpoints. Of the 5154 restriction fragments detected by 882 ESTs, 2043 (loci) were localized to group 6 chromosomes and 806 were mapped on other chromosome groups. The number of loci mapped was greatest on chromosome 6B and least on 6D. The 264 ESTs that detected orthologous loci on all three homoeologs using one restriction enzyme were used to construct a consensus physical map. The physical distribution of ESTs was uneven on chromosomes with a tendency toward higher densities in the distal halves of chromosome arms. About 43% of the wheat group 6 ESTs identified rice homologs upon comparisons of genome sequences. Fifty-eight percent of these ESTs were present on rice chromosome 2 and the remaining were on other rice chromosomes. Even within the group 6 bins, rice chromosomal blocks identified by 1-6 wheat ESTs were homologous to up to 11 rice chromosomes. These rice-block contigs were used to resolve the order of wheat ESTs within each bin.     

DNA fingerprinting for forensic identification: potential effects on data interpretation of subpopulation heterogeneity and band number variability

Some methods of statistical analysis of data on DNA fingerprinting suffer serious weaknesses. Unlinked Mendelizing loci that are at linkage equilibrium in subpopulations may be statistically associated, not statistically independent, in the population as a whole if there is heterogeneity in gene frequencies between subpopulations. In the populations where DNA fingerprinting is used for forensic applications, the assumption that DNA fragments occur statistically independently for different probes, different loci, or different fragment size classes lacks supporting data so far; there is some contrary evidence. Statistical association of alleles may cause estimates based on the assumption of statistical independence to understate the true matching probabilities by many orders of magnitude. The assumptions that DNA fragments occur independently and with constant frequency within a size class appear to be contradicted by the available data on the mean and variance of the number of fragments per person. The mistaken use of the geometric mean instead of the arithmetic mean to compute the probability that every DNA fragment of a randomly chosen person is present among the DNA fragments of a specimen may substantially understate the probability of a match between blots, even if other assumptions involved in the calculations are taken as correct. The conclusion is that some astronomically small probabilities of matching by chance, which have been claimed in forensic applications of DNA fingerprinting, presently lack substantial empirical and theoretical support.     

A note on Hardy-Weinberg equilibrium of VNTR data by using the Federal Bureau of Investigation''s fixed-bin method.

To fully utilize the information of VNTR data for forensic inference, the probability of observing the matching suspect and evidentiary profile in a reference population is estimated, usually by assuming independence of alleles within and between loci. This assumption has been challenged on the basis of the observation that there is frequently an excess of single-band phenotypes (SBP) in forensic data bases, which could indicate lack of independence. Nevertheless, another explanation is that the excess SBP are artifacts of laboratory methods. In this report we examine the excess of SBP for three VNTR loci studied by the FBI (D17S79 and D2S44, for blacks, and D14S13, for Caucasians). The FBI claims that the excess is due to the effect of null alleles; the null alleles are suspected to be too small to be detected. We estimate the frequency of null alleles for two loci (D17S79 and D14S13) by comparing, for these loci, the data from the FBI data base and the data from the Lifecodes data base. These comparisons yield information on small fragments because Lifecodes uses the restriction enzyme PstI, which yields larger fragments than does HaeIII, which the FBI uses. For D17S79 in blacks, we estimate a null allele frequency of 4.4%, and, for D14S13 in Caucasians, we estimate a frequency of 3.0%. The null-allele frequency for D2S44 in blacks is derived similarly, again being based on analyses of DNA cut with HaeIII and PstI; our estimate of the null-allele frequency for this locus is 1.5%.(ABSTRACT TRUNCATED AT 250 WORDS)     

Novel non-HLA-susceptible regions determined by meta-analysis of four genomewide scans for ankylosing spondylitis

We identified novel non-HLA-susceptible regions for ankylosing spondylitis (AS) by applying the genome-search-metaanalysis (GSMA) method to combine the previous four AS genomewide scan studies including 479 families with 1175 affected individuals. Three original genomescans were mainly analysed for Caucasian families and one analysed for Han Mongolian families. Ten bins had both Psumrnk and Pord <0.05, suggesting these bins most likely contain AS-linked loci. The 10 bins are 6.2, 16.3, 6.1, 3.3, 6.3, 16.4, 10.5, 17.1, 2.5 and 2.9. The most significant result of linkage was on chromosome 6p22.3-p21.1 (bin 6.2, Psumrnk <0.000417), where HLA loci are located. By addition of a genome scan of Chinese origin, our GSMA result further confirmed the HLA loci as the greatest susceptible region to AS and suggested that non-HLA loci chromosome 16q, 3p, 10q, 2p, 2q and 17p, may also contain AS-linked loci. The novel loci identified in our result give hints to further studies.     

Correlation-based inference for linkage disequilibrium with multiple alleles

The correlation between alleles at a pair of genetic loci is a measure of linkage disequilibrium. The square of the sample correlation multiplied by sample size provides the usual test statistic for the hypothesis of no disequilibrium for loci with two alleles and this relation has proved useful for study design and marker selection. Nevertheless, this relation holds only in a diallelic case, and an extension to multiple alleles has not been made. Here we introduce a similar statistic, R(2), which leads to a correlation-based test for loci with multiple alleles: for a pair of loci with k and m alleles, and a sample of n individuals, the approximate distribution of n(k - 1)(m - 1)/(km)R(2) under independence between loci is chi((k-1)(m-1))(2). One advantage of this statistic is that it can be interpreted as the total correlation between a pair of loci. When the phase of two-locus genotypes is known, the approach is equivalent to a test for the overall correlation between rows and columns in a contingency table. In the phase-known case, R(2) is the sum of the squared sample correlations for all km 2 x 2 subtables formed by collapsing to one allele vs. the rest at each locus. We examine the approximate distribution under the null of independence for R(2) and report its close agreement with the exact distribution obtained by permutation. The test for independence using R(2) is a strong competitor to approaches such as Pearson's chi square, Fisher's exact test, and a test based on Cressie and Read's power divergence statistic. We combine this approach with our previous composite-disequilibrium measures to address the case when the genotypic phase is unknown. Calculation of the new multiallele test statistic and its P-value is very simple and utilizes the approximate distribution of R(2). We provide a computer program that evaluates approximate as well as "exact" permutational P-values.     

Group 3 chromosome bin maps of wheat and their relationship to rice chromosome 1

The focus of this study was to analyze the content, distribution, and comparative genome relationships of 996 chromosome bin-mapped expressed sequence tags (ESTs) accounting for 2266 restriction fragments (loci) on the homoeologous group 3 chromosomes of hexaploid wheat (Triticum aestivum L.). Of these loci, 634, 884, and 748 were mapped on chromosomes 3A, 3B, and 3D, respectively. The individual chromosome bin maps revealed bins with a high density of mapped ESTs in the distal region and bins of low density in the proximal region of the chromosome arms, with the exception of 3DS and 3DL. These distributions were more localized on the higher-resolution group 3 consensus map with intermediate regions of high-mapped-EST density on both chromosome arms. Gene ontology (GO) classification of mapped ESTs was not significantly different for homoeologous group 3 chromosomes compared to the other groups. A combined analysis of the individual bin maps using 537 of the mapped ESTs revealed rearrangements between the group 3 chromosomes. Approximately 232 (44%) of the consensus mapped ESTs matched sequences on rice chromosome 1 and revealed large- and small-scale differences in gene order. Of the group 3 mapped EST unigenes approximately 21 and 32% matched the Arabidopsis coding regions and proteins, respectively, but no chromosome-level gene order conservation was detected.     

Multilocus estimation of genetic structure within populations

Spatial structure of genetic variation within populations is well measured by statistics based on the distribution of pairs of individual genotypes, and various such statistics have been widely used in experimental studies. However, the problem of uncharacterized correlations among statistics for different alleles has limited the applications of multiallelic, multilocus summary measures, since these had unknown sampling distributions. Usually multiple alleles and/or multiple loci are required in order to precisely measure spatial structures, and to provide precise indirect estimates of the amount of dispersal in samples of reasonable size. This article examines the correlations among pair-wise statistics, including Moran I-statistics and various measures of conditional kinship, for different alleles of a locus. First the correlations are mathematically derived for random spatial distributions, which allow averages over alleles and loci to be used as more powerful yet exact test statistics for the null hypothesis. Then extensive computer simulations are conducted to examine the correlations among values for different alleles under isolation by distance processes. For loci with more than three alleles, the results show that the correlations are remarkably and perhaps surprisingly small, establishing the principle that then alleles behave as nearly independent realizations of space-time stochastic processes. The results also show that the correlations are largely robust with respect to the degree of spatial structure, and they can be used in a straightforward manner to form confidence intervals for averages. The results allow a precise connection between observations in experimental studies and levels of dispersal in theoretical models.     

Testing independence of fragment lengths within VNTR loci.

Methods that were devised to test independence of the bivariate fragment lengths obtained from VNTR loci are applied to several population databases. It is shown that for many of the probes independence (Hardy-Weinberg equilibrium) cannot be sustained.     

Genetic variation,population structure and identification of yellow catfish, <Emphasis Type="Italic">Mystus nemurus</Emphasis> (C&;V) in Thailand using RAPD,ISSR and SCAR marker

Random amplified polymorphic DNA (RAPD) and inter-simple sequence repeat (ISSR) markers were used to investigate the genetic structure of four subpopulations of Mystus nemurus in Thailand. The 7 RAPD and 7 ISSR primers were selected. Of 83 total RAPD fragments, 80 (96.39%) were polymorphic loci, and of 81 total ISSR fragments, 75 (92.59%) were polymorphic loci. Genetic variation and genetic differentiation obtained from RAPD fragments or ISSR fragments showed similar results. Percentage of polymorphic loci (%P), observed number of alleles, effective number of alleles, Nei’s gene diversity (H) and Shannon’s information index revealed moderate to high level of genetic variations within each M. nemurus subpopulation and overall population. High levels of genetic differentiations were received from pairwise unbiased genetic distance (D) and coefficient of differentiation. Mantel test between D or gene flow and geographical distance showed a low to moderate correlation. Analysis of molecular variance indicated that variations among subpopulations were higher than those within subpopulations. The UPGMA dendrograms, based on RAPD and ISSR, showing the genetic relationship among subpopulations are grouped into three clusters; Songkhla (SK) subpopulation was separated from the other subpopulations. The candidate species-specific and subpopulation-specific RAPD fragments were sequenced and used to design sequence-characterized amplified region primers which distinguished M. nemurus from other species and divided SK subpopulation from the other subpopulations. The markers used in this study should be useful for breeding programs and future aquacultural development of this species in Thailand.     

The efficiency of multilocus DNA fingerprint probes for individualization and establishment of family relationships, determined from extensive casework.

The properties of human DNA fingerprints detected by multilocus minisatellite probes 33.6 and 33.15 have been investigated in 36 large sibships and in 1,702 Caucasian paternity cases involving the analysis of over 180,000 DNA fingerprint bands. The degree of overlap of minisatellite loci detected by these two probes is shown to be negligible (approximately 1%), and the resulting DNA fingerprints are therefore derived from independent sets of hypervariable loci. The level of allelism and linkage between different hypervariable DNA fragments scored with these probes is also low, implying substantial statistical independence of DNA fragments. Variation between the DNA fingerprints of different individuals indicates that the probability of chance identity is very low (much less than 10(-7) per probe). Empirical observations and theoretical considerations both indicate that genetic heterogeneity between subpopulations is unlikely to affect substantially the statistical evaluation of DNA fingerprints, at least among Caucasians. In paternity analysis, the proportion of nonmaternal DNA fragments in a child which cannot be attributed to the alleged father is shown to be an efficient statistic for distinguishing fathers from nonfathers, even in the presence of minisatellite mutation. Band-sharing estimates between a claimed parent and a child can also distinguish paternity from nonpaternity, though with less efficiency than comparison of a trio of mother, child, and alleged father.     

Estimating Transfer Entropy in Continuous Time Between Neural Spike Trains or Other Event-Based Data

Transfer entropy (TE) is a widely used measure of directed information flows in a number of domains including neuroscience. Many real-world time series for which we are interested in information flows come in the form of (near) instantaneous events occurring over time. Examples include the spiking of biological neurons, trades on stock markets and posts to social media, amongst myriad other systems involving events in continuous time throughout the natural and social sciences. However, there exist severe limitations to the current approach to TE estimation on such event-based data via discretising the time series into time bins: it is not consistent, has high bias, converges slowly and cannot simultaneously capture relationships that occur with very fine time precision as well as those that occur over long time intervals. Building on recent work which derived a theoretical framework for TE in continuous time, we present an estimation framework for TE on event-based data and develop a k-nearest-neighbours estimator within this framework. This estimator is provably consistent, has favourable bias properties and converges orders of magnitude more quickly than the current state-of-the-art in discrete-time estimation on synthetic examples. We demonstrate failures of the traditionally-used source-time-shift method for null surrogate generation. In order to overcome these failures, we develop a local permutation scheme for generating surrogate time series conforming to the appropriate null hypothesis in order to test for the statistical significance of the TE and, as such, test for the conditional independence between the history of one point process and the updates of another. Our approach is shown to be capable of correctly rejecting or accepting the null hypothesis of conditional independence even in the presence of strong pairwise time-directed correlations. This capacity to accurately test for conditional independence is further demonstrated on models of a spiking neural circuit inspired by the pyloric circuit of the crustacean stomatogastric ganglion, succeeding where previous related estimators have failed.     

There is more to tomato fruit colour than candidate carotenoid genes

Determining gene sequences responsible for complex phenotypes has remained a major objective in modern biology. The candidate gene approach is attempting to link, through mapping analysis, sequences that have a known functional role in the measured phenotype with quantitative trait loci (QTL) that are responsible for the studied variation. To explore the potential of the candidate approach for complex traits we conducted a mapping analysis of QTL for the intensity of the red colour of the tomato fruit (mainly lycopene) and for probes associated with the well-characterized carotenoid biosynthesis pathway. Seventy-five tomato introgression lines (ILs), each containing a single homozygous RFLP-defined chromosome segment from the green-fruited species Lycopersicon pennellii delimited 107 marker-defined mapping bins. Three of the bins resolved known qualitative colour mutations for yellow (r) and orange (B and Del) fruits resulting from variation in specific carotenoid biosynthesis genes. Based on trials in different environments, 16 QTL that modified the intensity of the red colour of ripe fruit were assigned to bins. Candidate sequences associated with the carotenoid biosynthesis pathway were mapped to 23 loci. Only five of the QTL co-segregated with the same bins that contained candidate genes - a number that is expected by chance alone. Furthermore, similar map location of a QTL and a candidate is far from a direct causative relationship between a gene and a phenotype. This study highlights the wealth and complexity of the variation present in the genus Lycopersicon that could be employed for basic research and genetic improvement of fruit colour in tomato.     

A note on testing separability in spatial-temporal marked point processes

Summary .   In environmental risk analysis, it is common to assume the stochastic independence (or separability) between the marks associated with the random events of a spatial-temporal point process. Schoenberg (2004, Biometrics 60, 471–481) proposed several test statistics for this hypothesis and used simulated data to evaluate their performance. He found that a Cramér-von Mises-type test is powerful to detect gradual departures from separability although it is not uniformly powerful over a large class of alternative models. We present a semiparametric approach to model alternative hypotheses to separability and derive a score test statistic. We show that there is a relationship between this score test and some of the test statistics proposed by Schoenberg. Specifically, all are different versions of weighted Cramér-von Mises-type statistics. This gives some insight into the reasons for the similarities and differences between the test statistics' performance. We also point out some difficulties in controlling the type I error probability in Schoenberg's residual test.     

The Inheritance of Metabolic Flux: Expressions for the within-Sibship Mean and Variance Given the Parental Genotypes

Recent developments have related quantitative trait expression to metabolic flux. The present paper investigates some implications of this for statistical aspects of polygenic inheritance. Expressions are derived for the within-sibship genetic mean and genetic variance of metabolic flux given a pair of parental, diploid, n-locus genotypes. These are exact and hold for arbitrary numbers of gene loci, arbitrary allelic values at each locus, and for arbitrary recombination fractions between adjacent gene loci. The within-sibship, genetic variance is seen to be simply a measure of parental heterozygosity plus a measure of the degree of linkage coupling within the parental genotypes. Approximations are given for the within-sibship phenotypic mean and variance of metabolic flux. These results are applied to the problem of attaining adequate statistical power in a test of association between allozymic variation and inter-individual variation in metabolic flux. Simulations indicate that statistical power can be greatly increased by augmenting the data with predictions and observations on progeny statistics in relation to parental allozyme genotypes. Adequate power may thus be attainable at small sample sizes, and when allozymic variation is scored at a only small fraction of the total set of loci whose catalytic products determine the flux.