Estimation of allele frequencies for VNTR loci

VNTR loci provide valuable information for a number of fields of study involving human genetics, ranging from forensics (DNA fingerprinting and paternity testing) to linkage analysis and population genetics. Alleles of a VNTR locus are simply fragments obtained from a particular portion of the DNA molecule and are defined in terms of their length. The essential element of a VNTR fragment is the repeat, which is a short sequence of basepairs. The core of the fragment is composed of a variable number of identical repeats that are linked in tandem. A sample of fragments from a population of individuals exhibits substantial variation in length because of variation in the number of repeats. Each distinct fragment length defines an allele, but any given fragment is measured with error. Therefore the observed distribution of fragment lengths is not discrete but is continuous, and determination of distinct allele classes is not straightforward. A mixture model is the natural statistical method for estimating the allele frequencies of VNTR loci. In this article we develop nonparametric methods for obtaining the distribution of allele sizes and estimates of their frequencies. Methods for obtaining maximum-likelihood estimates are developed. In addition, we suggest an empirical Bayes method to improve the maximum-likelihood estimates of the gene frequencies; the empirical Bayes procedure effects a local smoothing. The latter method works particularly well when measurement error is large relative to the repeat size, because the estimated distribution of allele frequencies when maximum likelihood is used is unreliable because of an alternating pattern of over- and underestimation. We define alleles and estimate the allele frequencies for two VNTR loci from the human genome (D17S79 and D2S44), from data obtained from Lifecodes, Inc.     

Frequencies of Twelve Ascus-Types and Arrangement of Three Genes from Tetrad Data

Equations expressing the theoretical frequencies of twelve ascus-types in the tetrad analysis of a triply heterozygous diploid are described. Using these equations, a mapping procedure for a gene X, is proposed. The procedure requires that two genes, X and Y, of the same phenotype be heterozygous and that the map position of Y be known, and that another standard gene, Z, show an independent phenotype from X and Y. This procedure does not require the laborious allelism test of the segregants to determine the allelic 2:2 segregation in tetrads for the X and Y genes, which is indispensable for mapping by the conventional procedure. The exact placement of the X gene on a chromosome is possible by the chi2 minimization procedure in comparison with the expected frequencies of the six ascus-types or four spore-types deduced from the twelve expected ascus-types to give the optimal fit with the observed data.     

A simple method for the computation of first neighbour frequencies of DNAs from CD spectra

A procedure for the computation of the first neighbour frequencies of DNA's is presented. This procedure is based on the first neighbour approximation of Gray and Tinoco. We show that the knowledge of all the ten elementary CD signals attached to the ten double stranded first neighbour configurations is not necessary. One can obtain the ten frequencies of an unknown DNA with the use of eight elementary CD signals corresponding to eight linearly independent polymer sequences. These signals can be extracted very simply from any eight or more CD spectra of double stranded DNA's of known frequencies. The ten frequencies of a DNA are obtained by least square fit of its CD spectrum with these elementary signals. One advantage of this procedure is that it does not necessitate linear programming, it can be used with CD data digitalized using a large number of wavelengths, thus permitting an accurate resolution of the CD spectra. Under favorable case, the ten frequencies of a DNA (not used as input data) can be determined with an average absolute error < 2%. We have also observed that certain satellite DNA's, those of Drosophila virilis and Callinectes sapidus have CD spectra compatible with those of DNA's of quasi random sequence; these satellite DNA's should adopt also the B-form in solution.     

Mutation and reversion frequencies of different Sulfolobus species and strains

We have determined the apparent and actual spontaneous mutation frequencies and rates for different species and strains of the thermoacidophilic crenarchaeote Sulfolobus. The proportion of mutations caused by insertion sequences has also been analyzed. Mutation frequencies for S. islandicus (0.08–0.6 mutations per cell division and 10⁷ cells) were below those determined for S. solfataricus and comparable to or lower than those for S. acidocaldarius. The proportion of insertion sequence mutations for the S. islandicus strains REN1H1 (9 out of 230) and HVE10/4 (0 out of 24) was found to be considerably lower than in S. solfataricus P1 and P2 and also low in comparison to other S. islandicus strains. Mutants defective in either the pyrEF genes or the lacS gene have been isolated. Their growth phenotype on selective and non-selective medium was examined and the inactivating mutations in either of the genes were determined. In addition the reversion frequencies for these mutants were measured and found to be in the range of <0.6–1.5 mutations per cell division and 10⁸ cells. However, when being subjected to electroporation as a transformation procedure, increased reversion was observed.     

Genotype frequencies associated with incompatibility systems in tristylous plants

A general procedure has been given previously for calculating frequencies of the morphs Long, Mid, and Short in equilibrium populations of tristylous plants. It is now demonstrated that an equilibrium state actually exists at the genotype level if this procedure produces admissible morph frequencies. This result holds in a diploid model, with or without linkage between the two loci involved. It is shown how the genotype frequencies may be determined for any set of mating probabilities. It is also explained how these frequencies may be calculated in a tetraploid model incorporating double reduction. The general theory is applied to a particular situation where the Mid morph is at a selective disadvantage as a seed parent.     

Palmar pattern frequencies as indicators of relationships among Sardinian linguistic groups of males

Palmar pattern frequencies were used to calculate distance coefficients between Sardinian linguistic groups of males for the purpose of verifying, by means of correlation matrix analyses, whether or not the dermatoglyphic traits considered lead to a reliable identification of the biological relationships on the basis of the linguistic backgrounds of these groups. With Sanghvi's as the distance measure and by using palmar pattern frequencies in the Hy area, Th/I, II, III, and IV interdigital areas and all traits together for palms combined or separated were calculated dermatoglyphic distance measures. Mantel tests of matrix correspondence showed that, by using palmar pattern frequencies in the Th/I interdigital area (palms combined), in the II, III, and IV interdigital areas, or all traits together for palms combined and separated, statistical significance between dermatoglyphic and linguistic distances can be obtained, even when the effect of geography is removed; there is no statistically significant correspondence between geographic and dermatoglyphic distance matrices, even when the effect of language is removed. The results obtained in this study by means of the Mantel test procedure demonstrate that the dermatoglyphic traits analyzed, with the exception of palmar pattern frequencies in the Hy area and in the Th/I interdigital area for plams separated when these areas are used singly, can be considered as a good set of variables to use in finding biological relationships between Sardinian linguistic groups of males examined on the basis of their linguistic backgrounds.     

Variability of allelic recombination frequencies

Summary Estimates of allelic recombination frequencies are shown to have coefficients of variation of between 20 and 40%. In Coprinus this is true of both high and low recombination frequencies and is also true when the alleles involved show marker effect. This variability is not confined to Coprinus but is a general feature of both meiotic and mitotic allelic recombination. Experimental errors do not make a major contribution to the observed variation althought it has the nature of a sampling variation. It is suggested that the variation arises from the diversity of ways in which the initial errors introduced by hybrid DNA formation can be resolved during the excision-repair stages of recombination. If the enzymes responsible for these processes are present in low concentrations then much latitude can be anticipated in the way the same errors are dealt with by separate, though isogenic, diploid or dikaryotic organisms. Each separate cross is thus interpreted as providing an estimate of the recombination frequency which is but a sample from a varied population of possible estimates of the same recombination frequency. Each pair of alleles exhibits a recombination frequency which, within the statistical boundaries of the general variation, is sufficiently reproducible to be described as a characteristic of them. Combinations of allelic recombination frequencies derived from pair-wise crosses fall into patterns that are sufficiently consistent for allele maps to be drawn; and, providing a sufficient number of replicate crosses have been analysed, the allele map can be shown to be statistically soundly based. Two marker effect situations are examined. One causes reduction of recombination frequency and is probably intrinsic to the mutant site itself, the other causes enhancement of recombination frequency and is due to a factor or factors distinct from the allelic mutant site in the strain in which it was first identified. When intercrossed the two effects counteract one another.     

X-ray-induced specific-locus mutations in the ad-3 region of two-component heterokaryons of Neurospora crassa. IV. Irreparable mutants of genotype ad-3A and ad-3B result from multilocus deletion and an unexpectedly high frequency of multiple-locus mutations

The induction of specific-locus mutations in the ad-3 region of Neurospora crassa after X-irradiation was studied in a two-component heterokaryon to determine: (1) the ratio of reparable ad-3 mutants (presumed gene/point mutations, designated ad-3R) to irreparable ad-3 mutants (presumed multilocus deletions, designated ad-3IR), and (2) the induction kinetics of each class (Webber and de Serres, 1965). More extensive genetic tests made subsequently (de Serres, 1989a) on the 832 X-ray-induced specific-locus mutations recovered in those experiments showed that unexpected high frequencies of reparable and irreparable ad-3 mutants are actually multiple-locus mutants that have additional, but separate, sites of recessive lethal (RLCL) damage in the immediately adjacent genetic regions (designated ad-3R + RLCL or ad-3IR + RLCL). The frequencies of these X-ray-induced multiple-locus mutants in the ad-3 region are orders of magnitude higher than expected on the basis of target theory (where the frequency of the double mutant is expected to be the product of the frequencies of each single mutant) and classical models of chromosome structure during interphase (de Serres, 1989a). In the present paper, a random sample of 832 X-ray-induced ad-3 mutants of genotype ad-3A or ad-3B that are irreparable have been subjected to more extensive genetic fine-structure analysis. These experiments were designed to determine the extent of the functional inactivation in individual mutants in the ad-3 and immediately adjacent genetic regions in mutants classified as presumptive multilocus deletions or multiple-locus mutations. These experiments have shown that in Neurospora crassa most X-ray-induced irreparable mutants of genotype ad-3A or ad-3B map as a series of overlapping multilocus deletions. Among the 29 irreparable mutants of genotype ad-3A, there are 16 different subgroups of complementation patterns; and among the 63 irreparable mutants of genotype ad-3B, there are also 16 different subgroups. In addition, mutants classified as presumptive multiple-locus mutants result from a variety of separate, but closely linked, sites of genetic damage.(ABSTRACT TRUNCATED AT 400 WORDS)     

Effects of Social Structure on the Behaviour and Performance of Alternative Reproductive Phenotypes in Male Rock Shrimp, Rhynchocinetes typus

Males that adopt alternative mating tactics within a conditional strategy often undergo costly morphological changes when switching to the next phenotype during ontogeny. Whether costs of changing to a subsequent reproductive phenotype are outweighed by a higher mating probability may depend on the frequencies of different phenotypes in a group of competitors. Benefits and costs associated with different phenotype frequencies depend on interactions within and between alternative phenotypes, but the underlying behavioural mechanisms have rarely been studied. Herein, we used the rock shrimp Rhynchocinetes typus as a model: ontogenetic male stages of this species differ in morphological and behavioural traits that indicate alternative reproductive phenotypes. The small, subordinate, male stage (typus) develops via several intermediate stages (intermedius) to the dominant male stage (robustus): in competitive interactions the typus males usually employ the sneaking tactic, while the robustus males invariably employ the monopolizing fighter tactic. In laboratory experiments, we manipulated phenotype frequencies to examine whether there are frequency‐dependent effects on searching behaviour, aggressiveness and mating probability. With increasing frequency of robustus males, the rate of aggressive interactions among them increased. Furthermore, robustus males increased walking velocity when more than one robustus male was present. In contrast, typus males did not adjust their searching or aggressive behaviour. The increase of aggressive interactions among robustus males provided more opportunities for typus males to seize a temporarily unguarded female. While typus males exploit fights among robustus males that produce mating opportunities for them, robustus males benefit from typus males, which reveal the presence of receptive females. We suggest that each phenotype benefits from the presence of the other phenotype and suffers costly interference among individuals of the same phenotype. Whether frequency‐dependent effects on the mating probability of subordinates also affect their ontogenetic switchpoint should be examined in future studies.     

Power for genetic association studies with random allele frequencies and genotype distributions

One of the first and most important steps in planning a genetic association study is the accurate estimation of the statistical power under a proposed study design and sample size. In association studies for candidate genes or in fine-mapping applications, allele and genotype frequencies are often assumed to be known when, in fact, they are unknown (i.e., random variables from some distribution). For example, if we consider a diallelic marker with allele frequencies of 0.5 and 0.5 and Hardy-Weinberg proportions, the three genotype frequencies are often assumed to be 0.25, 0.50, and 0.25, and the statistical power is calculated. Unfortunately, ignoring this source of variation can inflate the estimated power of the study. In the present article, we propose averaging the estimates of power over the distribution of the genotype frequencies to calculate the true estimate of power for a fixed allele frequency. For the usual situation, in which allele frequencies in a population are not known, we propose placing a prior distribution on the allele frequency, taking advantage of any available genotype information. This Bayesian approach provides a more accurate estimate of power. We present examples for quantitative and qualitative traits in cohort studies of unrelated individuals and results from an extensive series of examples that show that ignoring the uncertainty in allele frequencies can inflate the estimated power of the study. We also present the results from case-control studies and show that standard methods may also overestimate power. As discussed in this article, the approach of fixing allele frequencies even if they are not known is the common approach to power calculations. We show that ignoring the sources of variation in allele frequencies tends to result in overestimates of power and, consequently, in studies that are underpowered. Software in C is available at http://www.ambrosius.net/Power/.     

Prediction of the frequencies of restriction endonuclease recognition sequences using di- and mononucleotide frequencies

The calculation of probabilities of nucleotide sequences from the frequencies of dinucleotides is described. The dinucleotide and mononucleotide frequencies used can be obtained from nearest neighbor analysis or from databank sequences. If dinucleotide and mononucleotide frequencies from nearest neighbor analysis are used, probabilities for oligonucleotides can be calculated for genomes in which there is little or no sequence data. Within a given genome, a broad range of probabilities for hexanucleotide palindromes with the same base composition is predicted and shown (14).     

New explicit expressions for relative frequencies of single-nucleotide polymorphisms with application to statistical inference on population growth

We present new methodology for calculating sampling distributions of single-nucleotide polymorphism (SNP) frequencies in populations with time-varying size. Our approach is based on deriving analytical expressions for frequencies of SNPs. Analytical expressions allow for computations that are faster and more accurate than Monte Carlo simulations. In contrast to other articles showing analytical formulas for frequencies of SNPs, we derive expressions that contain coefficients that do not explode when the genealogy size increases. We also provide analytical formulas to describe the way in which the ascertainment procedure modifies SNP distributions. Using our methods, we study the power to test the hypothesis of exponential population expansion vs. the hypothesis of evolution with constant population size. We also analyze some of the available SNP data and we compare our results of demographic parameters estimation to those obtained in previous studies in population genetics. The analyzed data seem consistent with the hypothesis of past population growth of modern humans. The analysis of the data also shows a very strong sensitivity of estimated demographic parameters to changes of the model of the ascertainment procedure.     

Helix, sheet, and polyproline II frequencies and strong nearest neighbor effects in a restricted coil library

A central issue in protein folding is the degree to which each residue's backbone conformational preferences stabilize the native state. We have studied the conformational preferences of each amino acid when the amino acid is not constrained to be in a regular secondary structure. In this large but highly restricted coil library, the backbone preferentially adopts dihedral angles consistent with the polyproline II conformation rather than alpha or beta conformations. The preference for the polyproline II conformation is independent of the degree of solvation. In conjunction with a new masking procedure, the frequencies in our coil library accurately recapitulate both helix and sheet frequencies for the amino acids in structured regions, as well as polyproline II propensities. Therefore, structural propensities for alpha-helices and beta-sheets and for polyproline II conformations in unfolded peptides can be rationalized solely by local effects. In addition, these propensities are often strongly affected by both the chemical nature and the conformation of neighboring residues, contrary to the Flory isolated residue hypothesis.     

Infinite populations and counterfactual frequencies in evolutionary theory

One finds intertwined with ideas at the core of evolutionary theory claims about frequencies in counterfactual and infinitely large populations of organisms, as well as in sets of populations of organisms. One also finds claims about frequencies in counterfactual and infinitely large populations--of events--at the core of an answer to a question concerning the foundations of evolutionary theory. The question is this: to what do the numerical probabilities found throughout evolutionary theory correspond? The answer in question says that evolutionary probabilities are 'hypothetical frequencies' (including what are sometimes called 'long-run frequencies' and 'long-run propensities'). In this paper, I review two arguments against hypothetical frequencies. The arguments have implications for the interpretation of evolutionary probabilities, but more importantly, they seem to raise problems for biologists' claims about frequencies in counterfactual or infinite populations of organisms and sets of populations of organisms. I argue that when properly understood, claims about frequencies in large and infinite populations of organisms and sets of populations are not threatened by the arguments. Seeing why gives us a clearer understanding of the nature of counterfactual and infinite population claims and probability in evolutionary theory.     

Pedigreed crosses to estimate recessive virulence allele frequencies in natural populations of gall midges

Monitoring changes in rare, recessive allele frequencies in natural populations can be accomplished using pedigreed individuals sampled from these populations. A pedigree keeps track of and limits the mating of sampled individuals, to preserve information about the genotype of the sampled individual in the phenotypes of its descendents. To estimate allele frequencies in a natural population using pedigreed crosses, four relations must be specified: (1) a method to determine whether the pedigreed line carries the desired allele; (2) a method to estimate the phenotypic frequency of the trait among the pedigreed lines and a credibility limit for the estimate; (3) the genetic relation between the phenotype frequency among the lines and the allele frequency in the natural population; and (4) a method to estimate the probability that the first method did not detect the trait, assuming that the allele was present in the sampled individual. Knowledge about the segregation patterns of the allele enables specification of (3) and (4). Bayesian statistics were used to estimate the phenotypic frequency of the trait among the pedigreed lines. The method determining whether the pedigreed line carries the desired allele will vary with the species and trait of concern. We focused on monitoring of vGm1, a recessive autosomal allele, and vGm2, a recessive sex‐linked allele, which provide virulence against certain rice resistance genes in rice gall midge, Orseolia oryzae (Wood‐Mason) (Diptera: Cecidomyiidae). We show how three pedigrees can be used to estimate these allele frequencies. An F₁ field screen challenges the F₁ offspring of sampled individuals on the rice differentials. A P₁ test‐cross mates the sampled individual with a homozygous lab colony for the allele of interest, and evaluates their offspring on the rice differentials. A conditional F₁ test‐cross takes the offspring from pedigrees that were negative in an F₁ field screen, and test‐crosses these offspring with the homozygous laboratory colony. We also indicate how to test for independent assortment when a double (or multiple) homozygote laboratory colony is used in a test‐cross, how to test for differences among samples, and how to pool data to produce a single estimate based on a larger number of pedigreed lines. These methods may encourage the development of a variety of pedigreed monitoring strategies that could improve and prolong the use of scarce plant resistance alleles in rice and other plants.     

Properdin factor B frequencies in four Asian populations

The distribution of Properdin factor B (Bf) phenotypes and their gene frequencies were investigated in four Asian populations (Chinese, Filipino, Thai and Japanese). The frequency of the BfS phenotype in Filipinos (0.717) was significantly lower than that in Chinese (0.900) and Thai (0.889) (p less than 0.01), but not different from the Japanese (0.840). One variant, BfF 0.65 S, was identified in a Japanese subject. Thus, in the Asian populations studied, Bfs frequencies were high and the frequency of variants other than F and S were low.     

Separation of sequences from host-pathogen interface using triplet nucleotide frequencies

The identification of genes involved in host-pathogen interactions is important for the elucidation of mechanisms of disease resistance and host susceptibility. A traditional way to classify the origin of genes sampled from a pool of mixed cDNA is through sequence similarity to known genes from either the pathogen or host organism or other closely related species. This approach does not work when the identified sequence has no close homologues in the sequence databases. In our previous studies, we classified genes using their codon frequencies. This method, however, explicitly required the prediction of CDS regions and thus could not be applied to sequences composed from the non-coding regions of genes. In this study, we show that the use of sliding-window triplet frequencies extends the application of the algorithm to both coding and non-coding sequences and also increases the prediction accuracy of a Support Vector Machine classifier from 95.6+/-0.3 to 96.5+/-0.2. Thus the use of the triplet frequencies increased the prediction accuracy of the new method by more than 20% compared to our previous approach. A functional analysis of sequences detected gene families having significantly higher or lower probability to be correctly classified compared to the average accuracy of the method is described. The server to perform classification of EST sequences using triplet frequencies is available at (URL: http://mips.gsf.de/proj/est3).     

Multivariate Analysis of Gametic Disequilibrium in the Yanomama

The gametic disequilibria between all possible pairs of loci were examined for a set of eight codominant loci in each of fifty Yanomama villages, using a multivariate correlation analysis which reduces the results to a single measure of departure from multiple-locus-gametic equilibrium. Thirty-two of the fifty villages departed significantly from multiple-locus gametic equilibrium. The largest contributions to the departure from multiple-locus equilibrium were due to the disequilibria between MN and Ss and between Rh(Cc) and Rh(Ee), indicating the effects of tight linkage. After removing the effects of these obvious sources of disequilibrium, sixteen of the fifty villages still remained significantly out of equilibrium. The disequilibrium between any particular pair of loci was highly erratic from village to village, and (with the exception of the MN-Ss and Cc-Ee disequilibria) averaged out very close to zero overall, suggesting a lack of systematic forces (epistatic selection). The departure from equilibrium in any one village is in excess of that expected from random sampling alone, and is attributed primarily to the fission-fusion mode of village formation operative in the Yanomama and the fact that a single village consists of a few extended lineages. Village allele frequencies are highly correlated across loci, and most of the non-independence is accounted for by large correlations in the average allelic frequencies of different loci for related villages. It is suggested that these correlations also are due to territorial expansion and population growth. For the tribe as a whole, all but the tightly linked markers of the MNSs and Rh complexes are approximately uncorrelated, and large departures from multiple-locus Hardy-Weinberg expectation are primarily due to substantial Wahlund variance within the tribe. There is no need to postulate a role for selection in these disequilibria.     

Gamete frequencies at two sex-linked loci in random mating age-structured populations

A study is made of the change with time of frequencies of gametic types with one or two sex-linked loci in an infinite random mating age-structured population. Recurrence equations for these gamete frequencies are derived under the assumptions that all matings of adults are equally fertile and the number of matings at any time is proportional to the number of mature females at that time. These generalize others in the literature. It is shown that gamete frequencies approach their limiting values at geometric rates in the long run. This implies that the asymptotic behavior of the gamete frequencies is like what it is in populations with discrete generations if the unit of time is replaced by an appropriately chosen generation interval. With either one locus or two loci, the generation interval is bounded below by an analogous measure from standard demographic theory. This result also holds when there are two autosomal loci. In numerical examples from both this paper and a previous one by Pollak and Callanan, the lower bound is a good estimate of the generation interval.     

Responses to selection for postmeiotic segregation frequencies in Ascobolus immersus

A composite cross was made between 12 strains of the fungus Ascobolus immersus, six with wild-type red ascospores (w1+) and six with white ascospore mutation w1-78. A high postmeiotic segregation (PMS) frequency line was set up from colonies from ascospores from dehisced octads showing PMS, 5+ : 3w and 3+ : 5w. A low PMS line was started from ascospores from 4+ : 4w or 6+ : 2w octads, and a 'no selection' line was set up from ascospores from random octads. Colonies were crossed to tester strains to determine PMS frequencies and the selected lines were continued from ascospores of crosses of the red ascospore strain with the most extreme (e.g. high for the high line) PMS frequency with the white-ascospore strain of most extreme PMS frequency and of opposite mating type. Significant responses to selection were obtained for increased (+100%) and decreased (-58%) PMS, giving a 4.8-times difference in generation 4, with little change in the frequencies of conversion classes showing meiotic segregation (6+ : 2w and 2+ : 6w). The continuous, symmetrical, roughly normal distributions for PMS frequencies obtained when generation 5 strains were crossed to unselected tester strains are those expected if PMS frequencies are controlled by a number of polygenes, not major genes. Crosses of selected fifth-generation red-ascospore strains with extreme PMS values to base-substitution mutant w1-78, to frame-shift mutant w1-3C1 and to white-ascospore mutants w-BHj and w-9 at two loci unlinked to w1 showed that the effects of selection were not allele specific, locus specific or mutation-type specific.