Effects of misspecification of allele frequencies on the type I error rate of model-free linkage analysis

Linkage analyses of simulated quantitative trait data were performed using the Haseman-Elston (H-E) sib pair regression test to investigate the effects of inaccurate allele frequency estimates on the type I error rates of this test. Computer simulations generating a quantitative trait in nuclear families were performed using GASP [1]. Assuming no linkage, several data sets were simulated; they differed in marker allele numbers and frequencies, number of sib pairs and number of sibships. Each set of simulated data was analyzed using (1) all parental marker data, (2) half of the parental marker data, and (3) no parental marker data, using both correct and incorrect allele frequencies in the latter 2 cases. The H-E sib pair linkage method was found to be robust to misspecification of marker allele frequencies regardless of the number of alleles.     

The effects of gene conversion control factors on conversion-induced changes in allele frequencies in populations and on linkage disequilibrium

Conversion control factors (ccfs) are widespread. They control conversion properties at their target loci, affecting the conversion frequency and the amount and even the direction of gene conversion disparity. Three major types of ccf can be recognised. Experimental studies of the effects of ccfs have been combined with theoretical studies and modelling to examine the effects of ccfs on the evolutionary population genetics of alleles at the target locus. The ccf alleles present can greatly affect the rate and the direction of conversion-induced changes in target locus allele frequencies. Gene conversion can both cause and remedy linkage disequilibrium, with causation being related to polymorphismfor ccfs. Disparity in conversion direction does not by itself necessarily cause linkage disequilibrium.     

Identifying marker typing incompatibilities in linkage analysis.

A common problem encountered in linkage analyses is that execution of the computer program is halted because of genotypes in the data that are inconsistent with Mendelian inheritance. Such inconsistencies may arise because of pedigree errors or errors in typing. In some cases, the source of the inconsistencies is easily identified by examining the pedigree. In others, the error is not obvious, and substantial time and effort are required to identify the responsible genotypes. We have developed two methods for automatically identifying those individuals whose genotypes are most likely the cause of the inconsistencies. First, we calculate the posterior probability of genotyping error for each member of the pedigree, given the marker data on all pedigree members and allowing anyone in the pedigree to have an error. Second, we identify those individuals whose genotypes could be solely responsible for the inconsistency in the pedigree. We illustrate these methods with two examples: one a pedigree error, the second a genotyping error. These methods have been implemented as a module of the pedigree analysis program package MENDEL.     

Inbreeding of bottlenecked butterfly populations. Estimation using the likelihood of changes in marker allele frequencies

Polymorphic enzyme and minisatellite loci were used to estimate the degree of inbreeding in experimentally bottlenecked populations of the butterfly, Bicyclus anynana (Satyridae), three generations after founding events of 2, 6, 20, or 300 individuals, each bottleneck size being replicated at least four times. Heterozygosity fell more than expected, though not significantly so, but this traditional measure of the degree of inbreeding did not make full use of the information from genetic markers. It proved more informative to estimate directly the probability distribution of a measure of inbreeding, sigma2, the variance in the number of descendants left per gene. In all bottlenecked lines, sigma2 was significantly larger than in control lines (300 founders). We demonstrate that this excess inbreeding was brought about both by an increase in the variance of reproductive success of individuals, but also by another process. We argue that in bottlenecked lines linkage disequilibrium generated by the small number of haplotypes passing through the bottleneck resulted in hitchhiking of particular marker alleles with those haplotypes favored by selection. In control lines, linkage disequilibrium was minimal. Our result, indicating more inbreeding than expected from demographic parameters, contrasts with the findings of previous (Drosophila) experiments in which the decline in observed heterozygosity was slower than expected and attributed to associative overdominance. The different outcomes may both be explained as a consequence of linkage disequilibrium under different regimes of inbreeding. The likelihood-based method to estimate inbreeding should be of wide applicability. It was, for example, able to resolve small differences in sigma2 among replicate lines within bottleneck-size treatments, which could be related to the observed variation in reproductive viability.     

Powerful allele sharing statistics for nonparametric linkage analysis

Nonparametric linkage analysis is widely used to map susceptibility genes for complex diseases. This paper introduces six nonparametric statistics for measuring marker allele sharing among the affected members of a pedigree. We compare the power of these new statistics and three previous statistics to detect linkage with Mendelian diseases having recessive, additive, and dominant modes of inheritance. The nine statistics represent all possible combinations of three different IBD scoring functions and three different schemes for sampling genes among affecteds. Our results strongly suggest that the statistic T(rec)(blocks) is best for recessive traits, while the two statistics T(kin)(pairs) and T(all)(kin) vie for best for an additive trait. The best statistic for a dominant trait is less clear. The statistics T(kin)(pairs) and T(all)(kin) are equally promising for small sibships, but in extended pedigrees the statistics T(dom)(blocks) and T(dom)(pairs) appear best. For a complex trait, we advocate computing several of these statistics.     

The apolipoprotein E polymorphism: a comparison of allele frequencies and effects in nine populations.

Application of uniform methods for measuring the apolipoprotein (apo) E polymorphism and plasma cholesterol levels in nine populations (Tyrolean, Sudanese, Indian, Chinese, Japanese, Hungarian, Icelandic, Finnish, and Malay) revealed significant heterogeneity among them in apo E type frequencies and mean cholesterol levels. The major apo E types in all populations were E3/2 (frequency range from 7.0% in Indians to 16.9% in Malays), E3/3 (frequency range from 39.8% in Sudanese to 72.1% in Japanese), and E3/4 (frequency range from 11.3% in Japanese to 35.9% in Sudanese). Mean cholesterol levels ranged from 144.2 mg/dl in the Sudanese to 228.5 mg/dl in the Icelandics. Two-way analysis of variance of the effect of population and apo E type on cholesterol levels showed no significantly interaction effect, indicating that the effects of apo E type on cholesterol levels do not differ significantly among the populations. The overall average excess for the epsilon 2 allele was -14.12 mg/dl (range -31.63 to -8.82 mg/dl); for the epsilon 3 allele, 0.04 mg/dl (range -1.87 to 1.58 mg/dl; and for the epsilon 4 allele, 8.14 mg/dl (range -1.71 to 13.31 mg/dl). Despite the apparent heterogeneity in these values, especially for the epsilon 4 allele, comparison of the average excesses by a method of repeated sampling with random permutations revealed no significant difference in effects among populations. These data indicate that a given apo E allele acts in a relatively uniform manner in different populations despite differences in genetic background and environmental factors.     

Mutant allele frequencies in cats of Minneapolis-St. Paul

Coat color phenotype frequencies were determined in the cat population of Minneapolis and St. Paul. Mutant allele frequencies are estimated to be p (O) = 0.287, q(a) = 0.742, q(d) = 0.635, q(l) = 0.507, p(S) = 0.288. q(tb) = 0.472, p(W) = 0.016, and q(cs) = 0.214. A substantial number of cats displaying the Siamese coat pattern were found. These cats have a long history in the population.     

A note on the estimation of allele frequencies

A new method of obtaining allele frequency estimates is described. The method may prove useful when maximum likelihood estimates are not available. No assumptions regarding the absence of alleles are required. Errors of estimates have not been obtained, but the process seems to converge to maximum likelihood.     

Inferring epidemiological parameters on the basis of allele frequencies

In this article, I develop a methodology for inferring the transmission rate and reproductive value of an epidemic on the basis of genotype data from a sample of infected hosts. The epidemic is modeled by a birth-death process describing the transmission dynamics in combination with an infinite-allele model describing the evolution of alleles. I provide a recursive formulation for the probability of the allele frequencies in a sample of hosts and a Bayesian framework for estimating transmission rates and reproductive values on the basis of observed allele frequencies. Using the Bayesian method, I reanalyze tuberculosis data from the United States. I estimate a net transmission rate of 0.19/year [0.13, 0.24] and a reproductive value of 1.02 [1.01, 1.04]. I demonstrate that the allele frequency probability under the birth-death model does not follow the well-known Ewens' sampling formula that holds under Kingman's coalescent.     

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.     

Systematic detection of epistatic interactions based on allele pair frequencies

Epistatic genetic interactions are key for understanding the genetic contribution to complex traits. Epistasis is always defined with respect to some trait such as growth rate or fitness. Whereas most existing epistasis screens explicitly test for a trait, it is also possible to implicitly test for fitness traits by searching for the over- or under-representation of allele pairs in a given population. Such analysis of imbalanced allele pair frequencies of distant loci has not been exploited yet on a genome-wide scale, mostly due to statistical difficulties such as the multiple testing problem. We propose a new approach called Imbalanced Allele Pair frequencies (ImAP) for inferring epistatic interactions that is exclusively based on DNA sequence information. Our approach is based on genome-wide SNP data sampled from a population with known family structure. We make use of genotype information of parent-child trios and inspect 3×3 contingency tables for detecting pairs of alleles from different genomic positions that are over- or under-represented in the population. We also developed a simulation setup which mimics the pedigree structure by simultaneously assuming independence of the markers. When applied to mouse SNP data, our method detected 168 imbalanced allele pairs, which is substantially more than in simulations assuming no interactions. We could validate a significant number of the interactions with external data, and we found that interacting loci are enriched for genes involved in developmental processes.     

Study of human SP-A,SP-B and SP-D loci: allele frequencies,linkage disequilibrium and heterozygosity in different races and ethnic groups

Background  

SP-A, SP-B, and SP-D are pulmonary surfactant proteins. Several linkage and association studies have been done using these genes as markers to locate pulmonary disease susceptibility genes, but few have studied the markers systematically in different ethnic groups. Here we studied eight markers in SP-A, SP-B, and SP-D genes in seven ethnic groups from three races (Caucasian, Black and Hispanic). We measured the similarity of the marker distribution among the ethnic groups in order to see whether people in different ethnic groups or races could be mixed together for linkage and association studies. To evaluate the usefulness of these markers, we estimated the informativeness of each marker loci in the seven ethnic groups by assessing their heterozygosity and PIC values. We also conducted linkage disequilibrium (LD) analysis to identify associated marker loci and to estimate the haplotype frequencies in each of the seven ethnic groups in an attempt to find valuable haplotypes so that the level of polymorphism of the "markers" could be increased.     

PopHist: inferring population history from the spectrum of allele frequencies

SUMMARY: PopHist is a computer program that uses the frequency spectrum of alleles to: (a) estimate maximum likelihood parameters describing a population's history; and (b) compare alternative hypotheses about population history using likelihood ratio tests. The program uses the matrix coalescent, a method for calculating theoretical frequency spectra that can be applied to sets of unlinked sites. AVAILABILITY: Source code and documentation are available at http://mombasa.anthro.utah.edu/wooding/PopHist