Effects of reproductive compensation and genetic drift on X-linked lethals

A revival of interest in Haldane's equilibrium theory for X-linked lethals has been stimulated by the introduction of accurate tests for the detection of female heterozygotes in Lesch-Nyhan disease. Application of these tests appears to indicate an excess of familial cases. This excess can be attributed to ascertainment bias, a difference in female and male mutation rates, genetic drift, and reproductive compensation. Reproductive compensation will be particularly effective in increasing the proportion of familial cases if (1) birth control is widespread; (2) selection against affected males acts in utero; (3) affected sons show symptoms at an early age; and (4) sons are more highly valued than daughters. We demonstrate how only a few generations of reproductive compensation are sufficient to achieve an approximate equilibrium between selection and mutation showing a high proportion of familial cases. We also discuss the random fluctuations around equilibrium caused by genetic drift.     

Strong and weak male mutation bias at different sites in the primate genomes: insights from the human-chimpanzee comparison

Male mutation bias is a higher mutation rate in males than in females thought to result from the greater number of germ line cell divisions in males. If errors in DNA replication cause most mutations, then the magnitude of male mutation bias, measured as the male-to-female mutation rate ratio (alpha), should reflect the relative excess of male versus female germ line cell divisions. Evolutionary rates averaged among all sites in a sequence and compared between mammalian sex chromosomes were shown to be indeed higher in males than in females. However, it is presently unknown whether individual classes of substitutions exhibit such bias. To address this issue, we investigated male mutation bias separately at non-CpG and CpG sites using human-chimpanzee whole-genome alignments. We observed strong male mutation bias at non-CpG sites: alpha in the X-autosome comparison was approximately 6-7, which was similar to the male-to-female ratio in the number of germ line cell divisions. In contrast, mutations at CpG sites exhibited weak male mutation bias: alpha in the X-autosome comparison was only approximately 2-3. This is consistent with the methylation-induced and replication-independent mechanism of CpG transitions, which constitute the majority of mutations at CpG sites. Interestingly, our study also indicated weak male mutation bias for transversions at CpG sites, implying a spontaneous mechanism largely not associated with replication. Male mutation bias was equally strong at CpG and non-CpG sites located within unmethylated "CpG islands," suggesting the replication-dependent origin of these mutations. Thus, we found that the strength of male mutation bias is nonuniform in the primate genomes. Importantly, we discovered that male mutation bias depends on the proportion of CpG sites in the loci compared. This might explain the differences in the magnitude of primate male mutation bias observed among studies.     

Genetic drift in sex-linked lethal disorders.

A model is considered to calculate effects of genetic drift on the expected proportion of new mutants amongst males affected by a sex-linked recessive lethal. We show how to relate the number of cases of the disorder in males to the expected deviations from the deterministic value of the proportion of new mutants. For small values of alpha (= 3N mu), where N is the size of the female population, and mu is the mutation rate from wild-type to lethal allele, the standard deviation (SD) of the proportion of new mutants is large. However, if alpha more than 50, the potential effect of genetic drift is probably less important than the many other sources of error and bias.     

Using lod scores to detect sex differences in male-female recombination fractions

Human recombination fraction (RF) can differ between males and females, but investigators do not always know which disease genes are located in genomic areas of large RF sex differences. Knowledge of RF sex differences contributes to our understanding of basic biology and can increase the power of a linkage study, improve gene localization, and provide clues to possible imprinting. One way to detect these differences is to use lod scores. In this study we focused on detecting RF sex differences and answered the following questions, in both phase-known and phase-unknown matings: (1) How large a sample size is needed to detect a RF sex difference? (2) What are "optimal" proportions of paternally vs. maternally informative matings? (3) Does ascertaining nonoptimal proportions of paternally or maternally informative matings lead to ascertainment bias? Our results were as follows: (1) We calculated expected lod scores (ELODs) under two different conditions: "unconstrained," allowing sex-specific RF parameters (theta(female), theta(male)); and "constrained," requiring theta(female) = theta(male). We then examined the DeltaELOD (identical with difference between maximized constrained and unconstrained ELODs) and calculated minimum sample sizes required to achieve statistically significant DeltaELODs. For large RF sex differences, samples as small as 10 to 20 fully informative matings can achieve statistical significance. We give general sample size guidelines for detecting RF differences in informative phase-known and phase-unknown matings. (2) We defined p as the proportion of paternally informative matings in the dataset; and the optimal proportion p(circ) as that value of p that maximizes DeltaELOD. We determined that, surprisingly, p(circ) does not necessarily equal (1/2), although it does fall between approximately 0.4 and 0.6 in most situations. (3) We showed that if p in a sample deviates from its optimal value, no bias is introduced (asymptotically) to the maximum likelihood estimates of theta(female) and theta(male), even though ELOD is reduced (see point 2). This fact is important because often investigators cannot control the proportions of paternally and maternally informative families. In conclusion, it is possible to reliably detect sex differences in recombination fraction.     

Birth and population prevalence of Duchenne muscular dystrophy in the Netherlands

Summary Mutations causing Duchenne muscular dystrophy (DMD) have a short survival. Therefore, birth and population prevalence are maintained by new mutations. The present inventory was made to estimate the birth and population prevalence rates of DMD in the Netherlands. Seven methods of case identification were used. Data on 496 definite, probable or possible DMD patients born since 1961, or alive on January 1, 1983, were obtained. Several methods gave an estimated ascertainment of more than 95%. The prevalence rate at birth of DMD was estimated at 23.7×10^–5 (14215) male live births (MLB) yearly. The prevalence rate in the male population on January 1, 1983 was 5.4×10^–5 (118496). About 1% of the males in this study may have autosomal recessive Duchenne-like muscular dystrophy. Until now there has been no convincing evidence for geographic differences in DMD prevalence at birth. A list of frequency studies of Duchenne muscular dystrophy is included. The DMD mutation rate calculated by the indirect method is 7.9×10^–5 genes per generation. However, this may well be an over-estimate, as this method does not account for germline mosaicism. Using a modified sex ratio method the proportion of sporadic DMD among all cases was estimated to be 0.106 (range 0–0.332). High frequency of germline mosaicism in DMD is a likely cause for the apparent lack of sporadic cases as found in previous studies, if mutation rates in male and female gametes are equal. Therefore, methods for estimating the proportion of new mutants in DMD should take germline mosaicism into account. The modified sex ratio method allows incorporation of data on germline mosaicism if available.     

Rheumatic fever susceptibility in four ascertainments: regressive segregation on a geometric ascertainment pattern

On resolving the ascertainment biases of the observed data in the geometric continuum vaffected-1 x P(sibship), where 0 less than v----infinity, four published ascertainments of rheumatic fever show excellent conformation with Mendelian recessive segregation, even in multiplex sibships. In two surveys in which ascertainment bias is near or a little above random sampling (v = 1), this conclusion is further corroborated by classical segregation analysis. The other two surveys have bias trends declining (v less than 1) very much below random sampling. Such levels of ascertainment bias, if defined through the ascertainment probability parameter pi, would be out of range because the range is from single ascertainment, where pi----0 to random sampling where pi = 1 and probability cannot exceed unity. Highly successful antimicrobial measures that would reduce the number of diseased sibs independent of the distribution of susceptible sibs could produce a dissociation of the gene-to-"rheumatic" relationship and thus explains the declining ascertainment bias.     

Comparing observed average numbers of affected sibs with those expected under geometric ascertainment bias in an extended range in both simplex and multiple sibships.

Detection bias in recessive ascertainment is generally considered to be confined in a narrow range between unbiased truncate ascertainment and single ascertainment, where methods of segregation analysis are established. While there are arguments for an extended range of analysis, a deflated detection progression below the unbiased level is still being considered as theoretical ground or ignored as sporadics. I show here a method of gauging the ascertainment levels of surveyed data in a geometric continuum. The method is valid for recessive segregation at any ascertainment level and in simplex or multiplex sibships of whatever degree of truncation. Four previously published surveys are used to show conformation with real data and the existence of detection trends spanning the range from the unsuspected very depressed bias level to the inflated level above single ascertainment.     

Bias correction for segregation ratio estimation in human genetics

Segregation ratio estimation has long been important in human genetics. A simple truncated binomial model is considered that assumes complete ascertainment and a deterministic genotype-phenotype relationship. A simple but intuitively appealing estimator of the segregation ratio, previously proposed, is shown to have a negative bias. It is also shown that the bias of this estimator can be largely reduced via a randomization device, resulting in a new estimator that has the same large-sample behavior but with a negligible bias (decaying at a geometric rate). Numerical results are given to show the small-sample performance of this new estimator. An extension to incomplete ascertainment is also considered.     

Biased Gene Conversion, Copy Number, and Apparent Mutation Rate Differences within Chloroplast and Bacterial Genomes

We investigate the possibility that differences between synonymous substitution rates of organelle and bacterial genes differing only in copy number may be due to conversion bias. We find that the rather large observed difference in the synonymous rates between genes in the single copy and inverted-repeat regions of chloroplasts can be accounted for by a very small bias against new mutants. More generally, differences in the within-organelle fixation probability result in different apparent mutation rates as measured by the expected rate of appearance of cells homoplasmic for new mutants. Thus, differences in intracellular population parameters rather than molecular mechanisms can account for some variation in the apparent mutation rates of organelle genes, and possibly in other systems with variable numbers of gene copies. On the other hand, our analysis suggests that conversion bias is not a likely explanation for relatively low mutation rates observed near the replication origin of bacterial chromosomes.     

Recurrent mutation pressure does not explain the prevalence of the marker (X) syndrome

Summary In order to test the hypothesis that the high prevalence of the mar(X) syndrome is caused by a high mutation rate in male germ cells only, the fraction of new mutants among mothers of probands in 112 informative families has been examined by segregation analysis among their brothers and sisters. The estimated fraction of new mutants among these mothers is much lower than expected if a stable equilibrium existed between an unusually high mutation rate and a selective disadvantage of mentally retarded, male and female mar(X) carriers. Hence, the above-mentioned hypothesis could not be confirmed.     

Ascertainment bias in spatially structured populations: a case study in the eastern fence lizard

Despite increased interest in applying single nucleotide polymorphism (SNP) data to questions in natural systems, one unresolved issue is to what extent the ascertainment bias induced during the SNP discovery phase will impact available analysis methods. Although most studies addressing ascertainment bias have focused on human populations, it is not clear whether existing methods will work when applied to other species with more complex demographic histories and more significant levels of population structure. Here we present findings from an empirical approach to exploring the effect of population structure on issues of ascertainment bias in the Eastern Fence Lizard, Sceloporus undulatus. We find that frequency spectra and summary statistics were highly sensitive to SNP discovery strategy, necessitating careful selection of the initial ascertainment panel. Randomly selected ascertainment panels performed equally well as ascertainment panels chosen to jointly sample geographic, phenotypic, and genetic diversity. Geographically restricted panels resulted in larger biases. Additionally, we found existing ascertainment bias correction methods, which were not developed for geographically structured data sets, were largely effective at reducing the impact of ascertainment bias. Because bias correction methods performed well even when underlying assumptions were violated, our results suggest tools are currently available to analyze SNP data in structured populations.     

Quantifying ascertainment bias and species-specific length differences in human and chimpanzee microsatellites using genome sequences

Surveys of variability of homologous microsatellite loci among species reveal an ascertainment bias for microsatellite length where microsatellite loci isolated in one species tend to be longer than homologous loci in related species. Here, we take advantage of the availability of aligned human and chimpanzee genome sequences to compare length difference of homologous microsatellites for loci identified in humans to length difference for loci identified in chimpanzees. We are able to quantify ascertainment bias for a range of motifs and microsatellite lengths. Because ascertainment bias should not exist if a microsatellite selected in one species is as likely to be longer as it is to be shorter than its homologue, we propose that the nature of ascertainment bias can provide evidence for understanding how microsatellites evolve. We show that bias is greater for longer microsatellites but also that many long microsatellites have short homologues. These results are consistent with the notion that growth of long microsatellites is constrained by an upper length boundary that, when reached, sometimes results in large deletions. By evaluating ascertainment bias separately for interrupted and uninterrupted repeats we also show that long microsatellites tend to become interrupted, thereby contributing a second component of ascertainment bias. Having accounted for ascertainment bias, in agreement with results published elsewhere, we find that microsatellites in humans are longer on average than those in chimpanzees. This length difference is similar among repeat motifs but surprisingly comprises two roughly equal components, one associated with the repeats themselves and one with the flanking sequences. The differences we find can only be explained if microsatellites are both evolving directionally under a biased mutation process and are doing so at different rates in different closely related species.     

Ancestral alleles and population origins: inferences depend on mutation rate.

Previous studies have found that at most human loci, ancestral alleles are "African," in the sense that they reach their highest frequency there. Conventional wisdom holds that this reflects a recent African origin of modern humans. This paper challenges that view by showing that the empirical pattern (of elevated allele frequencies within Africa) is not as pervasive as has been thought. We confirm this African bias in a set of mainly protein-coding loci, but find a smaller bias in Alu insertion polymorphisms, and an even smaller bias in noncoding loci. Thus, the strong bias that was originally observed must reflect some factor that varies among data sets--something other than population history. This factor may be the per-locus mutation rate: the African bias is most pronounced in loci where this rate is high. The distribution of ancestral alleles among populations has been studied using 2 methods. One of these involves comparing the fractions of loci that reach maximal frequency in each population. The other compares the average frequencies of ancestral alleles. The first of these methods reflects history in a manner that depends on the mutation rate. When that rate is high, ancestral alleles at most loci reach their highest frequency in the ancestral population. When that rate is low, the reverse is true. The other method--comparing averages--is unresponsive. Average ancestral allele frequencies are affected neither by mutation rate nor by the history of population size and migration. In the absence of selection and ascertainment bias, they should be the same everywhere. This is true of one data set, but not of 2 others. This also suggests the action of some factor, such as selection or ascertainment bias, that varies among data sets.     

Overcoming the winner's curse: estimating penetrance parameters from case-control data

Genomewide association studies are now a widely used approach in the search for loci that affect complex traits. After detection of significant association, estimates of penetrance and allele-frequency parameters for the associated variant indicate the importance of that variant and facilitate the planning of replication studies. However, when these estimates are based on the original data used to detect the variant, the results are affected by an ascertainment bias known as the "winner's curse." The actual genetic effect is typically smaller than its estimate. This overestimation of the genetic effect may cause replication studies to fail because the necessary sample size is underestimated. Here, we present an approach that corrects for the ascertainment bias and generates an estimate of the frequency of a variant and its penetrance parameters. The method produces a point estimate and confidence region for the parameter estimates. We study the performance of this method using simulated data sets and show that it is possible to greatly reduce the bias in the parameter estimates, even when the original association study had low power. The uncertainty of the estimate decreases with increasing sample size, independent of the power of the original test for association. Finally, we show that application of the method to case-control data can improve the design of replication studies considerably.     

Factors Influencing Ascertainment Bias of Microsatellite Allele Sizes: Impact on Estimates of Mutation Rates

Microsatellite loci play an important role as markers for identification, disease gene mapping, and evolutionary studies. Mutation rate, which is of fundamental importance, can be obtained from interspecies comparisons, which, however, are subject to ascertainment bias. This bias arises, for example, when a locus is selected on the basis of its large allele size in one species (cognate species 1), in which it is first discovered. This bias is reflected in average allele length in any noncognate species 2 being smaller than that in species 1. This phenomenon was observed in various pairs of species, including comparisons of allele sizes in human and chimpanzee. Various mechanisms were proposed to explain observed differences in mean allele lengths between two species. Here, we examine the framework of a single-step asymmetric and unrestricted stepwise mutation model with genetic drift. Analysis is based on coalescent theory. Analytical results are confirmed by simulations using the simuPOP software. The mechanism of ascertainment bias in this model is a tighter correlation of allele sizes within a cognate species 1 than of allele sizes in two different species 1 and 2. We present computations of the expected average allele size difference, given the mutation rate, population sizes of species 1 and 2, time of separation of species 1 and 2, and the age of the allele. We show that when the past demographic histories of the cognate and noncognate taxa are different, the rate and directionality of mutations affect the allele sizes in the two taxa differently from the simple effect of ascertainment bias. This effect may exaggerate or reverse the effect of difference in mutation rates. We reanalyze literature data, which indicate that despite the bias, the microsatellite mutation rate estimate in the ancestral population is consistently greater than that in either human or chimpanzee and the mutation rate estimate in human exceeds or equals that in chimpanzee with the rate of allele length expansion in human being greater than that in chimpanzee. We also demonstrate that population bottlenecks and expansions in the recent human history have little impact on our conclusions.     

A probable sex difference in mutation rates in ornithine transcarbamylase deficiency

Summary Ornithine transcarbamylase deficiency is an X-linked disease with possible manifestations in heterozygous females. Using segregation analysis in families from the literature pooled with a French series, the penetrance could be estimated to be 17% in heterozygous females (15% with severe and 2% with milder symptoms). Using these estimates, the proportion of sporadic cases among heterozygous females and hemizygous males could be derived. This proportion is 57% in females. In males, it depends on mutation rate values: assuming equal mutation rates in sperm and eggs, this proportion should be 40%. However, this value can be strongly rejected based on the proportion of isolated cases in male sibships. In both sets of data, segregation analysis provided no evidence for sporadic affected males, suggesting that there are virtually no mutations in eggs. The upper limit of the confidence interval, 0%–16%, can be taken as the maximum prior probability that an affected male occurs as the result of a new mutation in his mother's germ cells.     

Genetics of the polycross

Summary Seeds from polycrosses with Norway spruce, in which the same sixteen male parents were crossed to a number of female parents in each of two years, were analysed electrophoretically to detect departures from male gamete frequencies expected assuming equal male fertilities, and to detect heterogeneity among female parents in male gamete frequencies in seeds. The data were also used to estimate the fertilities of the polycross trees used as male parents. Significant departures from male gamete frequencies expected assuming equal male fertilities were found in the seed pooled from all crosses. Male fertilities estimated from male gamete frequencies in seed from all crosses also departed significantly from expectation. The results are discussed with respect to assumptions made when estimating general combining abilities and expected response to selection in polycrosses.     

Mutation rate and novel tt mutants of Arabidopsis thaliana induced by carbon ions

Irradiation of Arabidopsis thaliana by carbon ions was carried out to investigate the mutational effect of ion particles in higher plants. Frequencies of embryonic lethals and chlorophyll-deficient mutants were found to be significantly higher after carbon-ion irradiation than after electron irradiation (11-fold and 7.8-fold per unit dose, respectively). To estimate the mutation rate of carbon ions, mutants with no pigments on leaves and stems (tt) and no trichomes on leaves (gl) were isolated at the M2 generation and subjected to analysis. Averaged segregation rate of the backcrossed mutants was 0.25, which suggested that large deletions reducing the viability of the gametophytes were not transmitted, if generated, in most cases. During the isolation of mutants, two new classes of flavonoid mutants (tt18, tt19) were isolated from carbon-ion-mutagenized M2 plants. From PCR and sequence analysis, two of the three tt18 mutant alleles were found to have a small deletion within the LDOX gene and the other was revealed to contain a rearrangement. Using the segregation rates, the mutation rate of carbon ions was estimated to be 17-fold higher than that of electrons. The isolation of novel mutants and the high mutation rate suggest that ion particles can be used as a valuable mutagen for plant genetics.     

Estimation of male to female ratio of mutation rates from carrier-detection tests in X-linked disorders.

A method is presented for the estimation of the ratio of male to female mutation rates from female carrier-detection test data from pedigrees containing an isolated male manifesting an X-linked necessive disorder. Pedigrees of any size and complexity (barring consanguinity) and containing any number of tested females can be utilized. The relative fitness of affected males and carrier females, and the segregation probability of the abnormal gamete in females, can be estimated simultaneously with the ratio of mutation rates in order to test specific hypotheses against given bodies of data. Here this method is applied to families containing isolated individuals affected with Lesch-Nyhan syndrome.     

Male-driven evolution of mitochondrial and chloroplastidial DNA sequences in plants

Although there is substantial evidence that, in animals, male-inherited neutral DNA evolves at a higher rate than female-inherited DNA, the relative evolutionary rate of male- versus female-inherited DNA has not been investigated in plants. We compared the substitution rates at neutral sites of maternally and paternally inherited organellar DNA in gymnosperms. The analysis provided substantial support for the presence of a higher evolutionary rate in both the mitochondrial and chloroplastidial DNA when the organelle was inherited paternally than when inherited maternally. These results suggest that, compared with eggs, sperm tend to carry a greater number of mutations in mitochondrial and chloroplastidial DNA. The existence of a male mutation bias in plants is remarkable because, unlike animals, the germ-lines are not separated from the somatic cells throughout an individual's lifetime. The data therefore suggest that even a brief period of male and female germ-line separation can cause gender-specific mutation rates. These results are the first to show that, at least in some species, germ-lines influence the number of mutations carried in the gametes. Possible causes of male mutation bias in plants are discussed.