Population genetics in forensic DNA typing.

Variable number of tandem repeat (VNTR) sequences are used to link defendants with crimes by matching DNA patterns. The probative value of a match is often calculated by multiplying together the estimated frequencies with which each particular VNTR pattern occurs in a reference database. However, this method is liable to potentially serious errors because ethnic subgroups within major racial categories exhibit genetic differences that are maintained by endogamy. The multiplication procedure currently in use can be made scientifically valid only by extensive sampling of VNTR frequency distributions in a variety of ethnic groups, similar to the ethnic studies of various blood groups done in the past. Alternative approaches for dealing with subpopulation heterogeneity are discussed.

On measures of gametic disequilibrium.

Various measures have been proposed for characterizing the statistical association that arises between alleles at different loci. Hedrick has compared these measures with the standardized measure D' proposed by Lewontin on the grounds that this latter measure is independent of allele frequency. Although D' has the same range for all allelic frequencies, in fact, D' is not "independent" of allele frequency, and no measure with that general property is possible for the multilocus association problem. The insolubility of this problem arises from the ill-defined nature of general "association."

The detection of linkage disequilibrium in molecular sequence data.

Studies of genetic variation in natural populations at the sequence level usually show that most polymorphic sites are very asymmetrical in allele frequencies, with the rarer allele at a site near fixation. When the rarer allele at a site is present only a few times in the sample, say below five representatives, it becomes very difficult to detect linkage disequilibrium between sites from tests of association. This is a consequence of the numerical properties of even the most powerful test of association, Fisher's exact test. Sites with fewer than five representatives in the sample should be excluded from association tests, but this generally leaves few site pairs eligible for testing. A test for overall linkage disequilibrium, based on the sign of the observed linkage disequilibria, is derived which can use all the data. It is shown that more power can be achieved by increasing the length of sequence determined than by increasing the number of genomes sampled for the same total work.

Locating regions of differential variability in DNA and protein sequences.

In the comparison of DNA and protein sequences between species or between paralogues or among individuals within a species or population, there is often some indication that different regions of the sequence are divergent or polymorphic to different degrees, indicating differential constraint or diversifying selection operating in different regions of the sequence. The problem is to test statistically whether the observed regional differences in the density of variant sites represent real differences and then to estimate as accurately as possible the location of the differential regions. A method is given for testing and locating regions of differential variation. The method consists of calculating G(x(k)) = k/n - x(k)/N, where x(k) is the position of the kth variant site along the sequence, n is the total number of variant sites, and N is the total sequence length. The estimated region is the longest stretch of adjacent sequence for which G(x(k)) is monotonically increasing (a hot spot) or decreasing (a cold spot). Critical values of this length for tests of significance are given, a sequential method is developed for locating multiple differential regions, and the power of the method against various alternatives is explored. The method locates the endpoints of hot spots and cold spots of variation with high accuracy.

Distribution of gene frequency as a test of the theory of the selective neutrality of polymorphisms.

The variation in gene frequency among populations or between generations within a population is a result of breeding structure and selection. But breeding structure should affect all loci and alleles in the same way. If there is significant heterogeneity between loci in their apparent inbreeding coefficients F=s(p) (2)/p(1-p), this heterogeneity may be taken as evidence for selection. We have given the statistical properties of F and shown how tests of heterogeneity can be made. Using data from human populations we have shown highly significant heterogeneity in F values for human polymorphic genes over the world, thus demonstrating that a significant fraction of human polymorphisms owe their current gene frequencies to the action of natural selection. We have also applied the method to temporal variation within a population for data on Dacus oleae and have found no significant evidence of selection.

Detecting heterogeneity of substitution along DNA and protein sequences.

Regions of differing constraint, mutation rate or combination along a sequence of DNA or amino acids lead to a nonuniform distribution of polymorphism within species or fixed differences between species. The power of five tests to reject the null hypothesis of a uniform distribution is studied for four classes of alternate hypothesis. The tests explored are the variance of interval lengths; a modified variance test, which includes covariance between neighboring intervals; the length of the longest interval; the length of the shortest third-order interval; and a composite test. Although there is no uniformly most powerful test over the range of alternate hypotheses tested, the variance and modified variance tests usually have the highest power. Therefore, we recommend that one of these two tests be used to test departure from uniformity in all circumstances. Tables of critical values for the variance and modified variance tests are given. The critical values depend both on the number of events and the number of positions in the sequence. A computer program is available on request that calculates both the critical values for a specified number of events and number of positions as well as the significance level of a given data set.

Distinguishing the forces controlling genetic variation at the Xdh locus in Drosophila pseudoobscura.

Fifty-eight isochromosomal lines sampled from two natural populations of Drosophila pseudoobscura in California and one from Bogota, Colombia, were examined using four-cutter restriction mapping. A 4.6-kb region of the xanthine dehydrogenase locus was probed and 66 of 135 restriction sites scored were polymorphic. This predicts that on average every 12th bp would be polymorphic in this region for the genes surveyed if polymorphism occurred randomly along the coding region. In addition, there were 12 insertion/deletion polymorphisms. Forty-nine distinct haplotypes were recognized in the 58 lines examined. The most common haplotype obtained a frequency of only 5%. Measures of base pair heterozygosity (0.0097) and linkage disequilibrium lead to a predicted population size in the range of 1.2-2.4 X 10(6) for the species. High levels of recombination (including gene conversion) can be inferred from the presence of all four gametic types in the data set.

Heterosis as an explanation for large amounts of genic polymorphism.

By using both numerical and analytical approaches, we have shown that heterosis alone is not a mechanism for maintaining many alleles segregating at a locus. Even when all heterozygous are more fit than all homozygotes, the proportion of fitness arrays that will lead to a stable, feasible equilibrium of more than 6 or 7 alleles is vanishingly small. More alleles can be maintained if, in addition to heterosis, it is assumed that there is very little variation in fitness from heterozygote to heterozygote, with the ratio of mean heterosis to standard deviation of fitness among heterozygotes in the neighborhood of 10. When such conditions hold, the allelic frequency distribution and equilibrium will be very uniform, with all alleles very close to equal frequency (see PDF). It is much more likely that stable equilibria for multiple alleles will be best explained by multiple niche selection.

The sensitivity of gel electrophoresis as a detector of genetic variation.

Three experiments based on an idea of YOUDERIAN have been performed to determine the proportions and kinds of amino acid substitutions that are detected by gel electrophoresis when applied to surveys of protein variation in populations. The experiments involved applying the sequential method of electrophoresis under several conditions of pH and gel concentration to a large sample of human hemoglobins with known amino acid substitutions. In the first experiment, a random sample of 20 different hemoglobin variants was studied, and these were separated into 17 distinct electrophoretic classes by three sequential gel conditions, thus giving a detectability of 85%. A single pass under standard conditions detected eight classes. The second experiment compared groups of substitutions that were chemically identical, but in different positions in the alpha and beta chains, while the third experiment compared pairs of substitutions that were charge equivalent, but chemically different at the same chain position. The sequential method distinguished 90% of all chemically identical substitutions when they were at different chain locations, and four out of five charge equivalent but chemically different substitutions at the same site. Examination of the location of each substitution in the three-dimensional structure of hemoglobins showed that interior substitutions usually are less different from Hb A than are surface substitutions and that local interactions with chain and spatial neighbors are sufficient to distinguish substitutions in very similar positions on the outside of the molecule. The "charge ladder" model of electrophoretic classes is clearly incorrect, and it appears that sequential gel electrophoresis as practiced in our Drosophila surveys has detected a substantial fraction of amino acid substitutions if hemoglobin is regarded as a model. This estimate may be modified as other molecules beside hemoglobin are subjected to similar calibration experiments.

Genetic heterogeneity within electrophoretic "alleles" of xanthine dehydrogenase in Drosophila pseudoobscura.

An experimental plan for an exhaustive determination of genic variation at structural gene loci is presented. In the initial steps of this program, 146 isochromosomal lines from 12 geographic populations of D. pseudoobscura were examined for allelic variation of xanthine dehydrogenase by the serial use of 4 different electrophoretic conditions and a head stability test. The 5 criteria revealed a total of 37 allelic classes out of the 146 genomes examined where only 6 had been previously revealed by the usual method of gel electrophoresis. This immense increase in genic variation also showed previously unsuspected population differences between the main part of the species distribution and the isolated population of Bogotá population. The average heterozygosity at the Xdh locus is at least 72% in natural populations. This result, together with the very large number of alleles segregating and the pattern of allelic frequencies, has implications for theories of genetic polymorphism which are discussed.

Nucleotide variation and conservation at the dpp locus, a gene controlling early development in Drosophila.

A study of polymorphism and species divergence of the dpp gene of Drosophila has been made. Eighteen lines from a population of D. melanogaster were sequenced for 5200 bp of the Hin region of the gene, coding for the dpp polypeptide. A comparison was made with sequence from D. simulans. Ninety-six silent polymorphisms and three amino acid replacement polymorphisms were found. The overall silent polymorphism (0.0247) is low, but haplotype diversity (0.0066 for effectively silent sites and 0.0054 for all sites) is in the range found for enzyme loci. Amino acid variation is absent in the N-terminal signal peptide, the C-terminal TGF-beta peptide and in the N-terminal half of the pro-protein region. At the nucleotide level there is strong conservation in the middle half of the large-intron and in the 3' untranslated sequence of the last exon. The 3' untranslated conservation, which is perfect for 110 bp among all the divergent species, is unexplained. There is strong positive linkage disequilibrium among polymorphic sites, with stretches of apparent gene conversion among originally divergent sequences. The population apparently is a migration mixture of divergent clades.

Sequence of the structural gene for xanthine dehydrogenase (rosy locus) in Drosophila melanogaster.

We determined the nucleotide sequence of a 4.6-kb EcoRI fragment containing 70% of the rosy locus. In combination with information on the 5' sequence, the gene has been sequenced in entirety. rosy cDNAs have been isolated and intron/exon boundaries have been determined. We find an open reading frame which spans four exons and would encode a protein of 1335 amino acids. The molecular weight of the encoded protein (xanthine dehydrogenase), based on the amino acid translation, is 146,898 daltons which agrees well with earlier biophysical estimates. Characteristics of the protein are discussed.

Gene flow and the geographical distribution of a molecular polymorphism in Drosophila pseudoobscura.

This paper discusses the relation between the geographical distribution of an enzyme polymorphism and population structure in Drosophila pseudoobscura. California populations of this species living in very different montane and lowland habitats separated by several kilometers are similar to each other in the frequency of an esterase allele. Previous estimates suggest that gene flow is too limited to account for this homogeneity of genetic structure, so that it must reflect some balancing force of natural selection. We slow, however, that dispersal over unfavorable habitats is much greater than earlier supposed. Isolated populations of D. pseudoobscura separated by 15 km from other populations are subject to large amounts of immigration. This is shown by changes in the seasonal abundance of this species and in the annual pattern of lethal alleles in such populations. The genetic structure of an experimentally perturbed isolated population in an oasis returned to normal within a single year, suggesting that such populations are ephemeral and that the oasis is subject to annual recolonization by distant migrants. Direct assessment of marked flies shows that they can move at least 10 10 km in 24 hours over a desert. Such extensive gene flow may help explain the distribution of the esterase allele, and is relevant to the high level of molecular polymorphism and its general lack of geographic differentiation throughout the range of D. pseudoobscura.

Selection in complex genetic systems III. An effect of allele multiplicity with two loci.

A two-locus model with three alleles at one locus and two at the other is studied. The viability system is such that all double heterozygotes have fitness unity, all single heterozygotes have fitness w smaller than 1 and all double homozygotes have fitness w-2. The following are the major findings: 1. There are more stable equilibria for tight linkage than in the corresponding three-locus model, even though the number of chromosomes is lower. 2. The equilibria stable for tight linkage do not belong to a unique high complementarity class, as is the case for two alleles at each locus. Instead the strength of selection determines the structure of the equilibrium. 3. The increase in number of alleles seems to reduce the possible extent of association between the loci. 4. The measure of this association is not well defined, although we have suggested a statistically standard way of getting over this. 5. A mutation introduced while a population is in linkage disequilibrium may, per medium only of the change in number of alleles, destroy the linkage disequilibrium.