Penetrance rate estimation in autosomal dominant conditions

Accurate estimates of the penetrance rate of autosomal dominant conditions are important, among other issues, for optimizing recurrence risks in genetic counseling. The present work on penetrance rate estimation from pedigree data considers the following situations: 1) estimation of the penetrance rate K (brief review of the method); 2) construction of exact credible intervals for K estimates; 3) specificity and heterogeneity issues; 4) penetrance rate estimates obtained through molecular testing of families; 5) lack of information about the phenotype of the pedigree generator; 6) genealogies containing grouped parent-offspring information; 7) ascertainment issues responsible for the inflation of K estimates.     

Developmental dyslexia--recurrence risk estimates from a german bi-center study using the single proband sib pair design

OBJECTIVE: Several studies have demonstrated a genetic component for dyslexia. However, both segregation and linkage analyses show contradictory results pointing at the necessity of an optimal ascertainment scheme for molecular genetic studies. Previously, we have argued that the single proband sib pair design (SPSP) would be optimal. The aims of this paper therefore are to demonstrate the practicability of the SPSP design and the estimation of recurrence risks for reading and writing. METHODS: We assessed spelling and reading in a family sample ascertained through the SPSP design. 287 families with at least two siblings and their parents were recruited. At least one child was affected with spelling disorder according to a one standard deviation (1SD) discrepancy criterion. RESULTS: Mean values for probands and their siblings were different for both the spelling and the reading phenotype. For the probands, variances of the phenotype spelling were smaller. These effects became stronger with more extreme selection criteria. Both siblings fulfilled the 1SD criterion for spelling and reading in 60.3 and 28.9% of the families, respectively, indicating a low cost efficiency of the double proband sib pair approach. A recurrence risk of 4.52 (CI: 4.07-4.93) was obtained for spelling when the 1SD criterion was applied to both siblings. Recurrence risk estimates were similar for reading. CONCLUSION: The study demonstrates the suitability of the SPSP design for genetic analysis of dyslexia. The recurrence risk estimates may be used for determining sample sizes in gene mapping studies.     

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.     

Inherent intractability of the ascertainment problem for pedigree data: a general likelihood framework.

The problem of ascertainment in segregation analysis arises when families are selected for study through ascertainment of affected individuals. In this case, ascertainment must be corrected for in data analysis. However, methods for ascertainment correction are not available for many common sampling schemes, e.g., sequential sampling of extended pedigrees (except in the case of "single" selection). Concerns about whether ascertainment correction is even required for large pedigrees, about whether and how multiple probands in the same pedigree can be taken into account properly, and about how to apply sequential sampling strategies have occupied many investigators in recent years. We address these concerns by reconsidering a central issue, namely, how to handle pedigree structure (including size). We introduce a new distinction, between sampling in such a way that observed pedigree structure does not depend on which pedigree members are probands (proband-independent [PI] sampling) and sampling in such a way that observed pedigree structure does depend on who are the probands (proband-dependent [PD] sampling). This distinction corresponds roughly (but not exactly) to the distinction between fixed-structure and sequential sampling. We show that conditioning on observed pedigree structure in ascertained data sets obtained under PD sampling is not in general correct (with the exception of "single" selection), while PI sampling of pedigree structures larger than simple sibships is generally not possible. Yet, in practice one has little choice but to condition on observed pedigree structure. We conclude that the problem of genetic modeling in ascertained data sets is, in most situations, literally intractable. We recommend that future efforts focus on the development of robust approximate approaches to the problem.     

Maximum likelihood estimators for incorrect models, with an application to ascertainment bias for continuous characters

Uncertainty about the ascertainment of human family data leads to a need for robust methods for estimating genetic and environmental effects. This in turn leads to a need for efficient techniques for estimating model parameters for data generated under one parametric model but analyzed under a second model. If the two models correspond to different ascertainment schemes for the same exponential family, simple formulas for the asymptotic means and standard errors of both conditional and unconditional MLEs can be derived. In an example for continuous sibship data, these formulas show that estimates derived from conditioning on proband value have greater asymptotic bias than two other estimators. Similarly, either conditioning on proband value or conditioning on the number of affected family members resulted in biases of up to 30% when ascertainment depended on the values of more than one affected family member.     

The Monofactorial Model for Recurrence Risks with Generalized Penetrance

Recurrence risks are derived explicitly in terms of gene frequencies and penetrance coefficients for the general case in which all genotypes have incomplete penetrance. Maximum likelihood estimation of recurrence risks is achieved through the use of the semi-symmetric intraclass contingency table. The resulting formulas and estimation procedure can be useful for the analysis of population and family data, and in genetic counselling.     

Aspects of parameter estimation in ascertainment sampling schemes.

It has recently been suggested that ascertainment sampling estimation procedures commonly used are not fully efficient in that the number of unobserved families is an unknown parameter that should be estimated (contrary to common practice) along with the genetic parameters for fully efficient estimation. It has also been suggested that the frequency distribution of family size contains unknown parameters that should similarly be estimated with the genetic parameters. These two suggestions are considered in this paper. It is shown by means of an equivalence theorem that in both cases the estimates and their variances obtained by adopting the suggested procedure are identical with those found by ignoring the unobserved families and by ignoring the family-size distribution. This demonstration leads to a formal justification of further procedures, in particular: (1) use of "method-of-moments" estimators, (2) ignoring the ascertainment scheme in some cases when estimating parameters, and (3) forming estimates of parameters when various parts of the data are obtained by different ascertainment schemes.     

Recurrence risk of a new dominant mutation in children of unaffected parents.

Extensions to models originally described by Hartl for predicting the recurrence risk of new dominant mutations are developed in this paper. Additions to the models are (1) possible somatic mosaicism in a parent in some families, (2) the possibility that the parental origin of the mutation may or may not be known, and (3) mutation rates which change as a function of sex and/or time. The models indicate that recurrence risks are most critically affected by (a) the amount of somatic mosaicism which can be tolerated in the parent without manifesting disease and (b) knowledge of the parental origin of the mutation. In addition, there is a moderate effect on recurrence risks if mutation rates increase in the father as a function of time. Recurrence risks are at least as large as the risk of trisomy 21 in a child of a mother of age 35 years or older, probably much higher (5%-10%) when the mutation is known to be of maternal origin or if substantial somatic mosaicism in the parent is compatible with a normal phenotype. The recurrence risk of a new mutation is high because of a very high ascertainment bias of families with substantial germ-line mosaicism.     

Genetic diversity analysis of elite European maize (Zea mays L.) inbred lines using AFLP, SSR, and SNP markers reveals ascertainment bias for a subset of SNPs

Recent advances in high-throughput sequencing technologies have triggered a shift toward single-nucleotide polymorphism (SNP) markers. A systematic bias can be introduced if SNPs are ascertained in a small panel of genotypes and then used for characterizing a larger population (ascertainment bias). With the objective of evaluating a potential ascertainment bias of the Illumina MaizeSNP50 array with respect to elite European maize dent and flint inbred lines, we compared the genetic diversity among these materials based on 731 amplified fragment length polymorphisms (AFLPs), 186 simple sequence repeats (SSRs), 41,434 SNPs of the MaizeSNP50 array (SNP-A), and two subsets of it, i.e., 30,068 Panzea (SNP-P) and 11,366 Syngenta markers (SNP-S). We evaluated the bias effects on major allele frequency, allele number, gene diversity, modified Roger’s distance (MRD), and on molecular variance (AMOVA). We revealed ascertainment bias in SNP-A, compared to AFLPs and SSRs. It affected especially European flint lines analyzed with markers (SNP-S) specifically developed to maximize differences among North American dent germplasm. The bias affected all genetic parameters, but did not substantially alter the relative distances between inbred lines within groups. For these reasons, we conclude that the SNP markers of the MaizeSNP50 array can be employed for breeding purposes in the investigated material. However, attention should be paid in case of comparisons between genotypes belonging to different heterotic groups. In this case, it is advisable to prefer a marker subset with potentially low ascertainment bias, like in our case the SNP-P marker set.     

Sexual selection and interacting phenotypes in experimental evolution: a study of Drosophila pseudoobscura mating behavior

Sexual selection requires social interactions, particularly between the sexes. When trait expression is influenced by social interactions, such traits are called interacting phenotypes and only recently have the evolutionary consequences of interacting phenotypes been considered. Here we investigated how variation in relative fitness, or the opportunity for sexual selection, affected the evolutionary trajectories of interacting phenotypes. We used experimentally evolved populations of the naturally promiscuous Drosophila pseudoobscura , in which the numbers of potential interactions between the sexes, and therefore relative fitness, were manipulated by altering natural levels of female promiscuity. We considered two different mating interactions between the sexes: mating speed and copulation duration. We investigated the evolutionary trajectories of means and (co)variances ( P ) and also the influence of genetic drift on the evolutionary response of these interactions. Our sexual selection treatments did not affect the means of either mating speed or copulation duration, but they did affect P . We found that the means of both traits differed among replicates within each selection treatment whereas the P s did not. Changes as a consequence of genetic drift were excluded. Our results show that although variable potential strengths of sexual interactions influence the evolution of interacting phenotypes, the influence may be nonlinear.     

Estimation of the parameters of the single-locus diallele model of qualitative trait in groups of relations

The method of estimation of parameters of monolocus diallele model (MDM) of qualitative trait on relative group data is described, these parameters being the number of affected and normal proband relatives of the arbitrary family degree and siblings in different matings types. For the case of single ascertainment, the expressions of corresponding probabilities have been taken as functions of MDM parameters using ITO matrixes and genetic transition matrix. Estimation of parameters was obtained by the maximum likelyhood method. Hardy-Weinberg equilibrium is not always necessary for this method; some weak requirement of stationarity is quite enough.     

The adaptive significance of colour pattern polymorphism in the Australian scincid lizard Lampropholis delicata

Females of Lampropholis delicata are dimorphic for colour pattern, the difference between morphs being the presence or absence of a distinct white mid-lateral stripe. A less distinct striped morph occurs also in males. We evaluated alternative hypotheses for the maintenance of this polymorphism by examining temporal and spatial variation in morph frequency, testing for differential selection among morphs using data on body size and reproductive traits from preserved specimens, and experimentally manipulating colour pattern in free-ranging lizards of both sexes, to assess the influence of the lateral stripe on survival rates. We found that the relative frequency of striped individuals varied among populations and decreased from north to south in both sexes, coincident with an increasing incidence of regenerated tails. Morph frequencies did not change through time within a population. Striped gravid females appeared to survive better and produced larger clutches than did non-striped females. In our experimental study, the relationship between survival and colour morph differed between the two sexes; males painted with a white lateral stripe had lower survival than control (brown stripe) males, but survival did not differ between striped and control females. The different response in the two sexes may be due partly to differences in temperature and microhabitat selection. We propose that the white lateral stripe decreases susceptibility to predators in gravid females but increases risk of predation in males, especially in combination with low temperatures. The polymorphism might be maintained by: (1) opposing fitness consequences of the stripe in males and females; (2) sex-specific habitat selection; and (3) gene flow in combination with spatial variation in relative fitness of the two morphs.     

Segregation analysis of cryptogenic epilepsy and an empirical test of the validity of the results.

We used POINTER to perform segregation analysis of cryptogenic epilepsy in 1,557 three-generation families (probands and their parents, siblings, and offspring) ascertained from voluntary organizations. Analysis of the full data set indicated that the data were most consistent with an autosomal dominant (AD) model with 61% penetrance of the susceptibility gene. However, subsequent analyses revealed that the patterns of familial aggregation differed markedly between siblings and offspring of the probands. Risks in siblings were consistent with an autosomal recessive (AR) model and inconsistent with an AD model, whereas risks in offspring were inconsistent with an AR model and more consistent with an AD model. As a further test of the validity of the AD model, we used sequential ascertainment to extend the family history information in the subset of families judged likely to carry the putative susceptibility gene because they contained at least three affected individuals. Prevalence of idiopathic/cryptogenic epilepsy was only 3.7% in newly identified relatives expected to have a 50% probability of carrying the susceptibility gene under an AD model. Approximately 30% (i.e., 50% x 61%) were expected to be affected under the AD model resulting from the segregation analysis. These results suggest that the familial distribution of cryptogenic epilepsy is inconsistent with any conventional genetic model. The differences between siblings and offspring in the patterns of familial risk are intriguing and should be investigated further.     

Inflation of sibling recurrence-risk ratio, due to ascertainment bias and/or overreporting.

One widely used measure of familial aggregation is the sibling recurrence-risk ratio, which is defined as the ratio of risk of disease manifestation, given that one's sibling is affected, as compared with the disease prevalence in the general population. Known as lambdaS, it has been used extensively in the mapping of complex diseases. In this paper, I show that, for a fictitious disease that is strictly nongenetic and nonenvironmental, lambdaS can be dramatically inflated because of misunderstanding of the original definition of lambdaS, ascertainment bias, and overreporting. Therefore, for a disease of entirely environmental origin, the lambdaS inflation due to ascertainment bias and/or overreporting is expected to be more prominent if the risk factor also is familially aggregated. This suggests that, like segregation analysis, the estimation of lambdaS also is prone to ascertainment bias and should be performed with great care. This is particularly important if one uses lambdaS for exclusion mapping, for discrimination between different genetic models, and for association studies, since these practices hinge tightly on an accurate estimation of lambdaS.     

Simulation studies of segregation analysis: application to two-locus models

We tested the power of a segregation analysis method (first proposed by Elandt-Johnson) to distinguish between single-locus and two-locus models, with and without environmentally caused reduced penetrance. We also looked at the effect of ascertainment probability on the analysis and at the proband-conditioned ascertainment correction proposed by Cannings and Thompson. We found that: (1) the segregation analysis has sufficient power to distinguish between the fully-penetrant double-recessive (RR) model and the fully-penetrant single-locus dominant and recessive models; (2) the method can also distinguish fairly well between the dominant-recessive (DR) and RR models, even when one does not take into account the population prevalence; (3) the method has much less power to distinguish between the fully-penetrant RR model and the single-locus models with reduced penetrance; (4) when environmental penetrance is taken account of in the analysis, the power of the method to distinguish between the one- and two-locus models improved substantially; (5) the estimates of ascertainment probability, pi, were robust, regardless of the model under which the data were generated; and (6) the Cannings-Thompson approach to ascertainment correction worked well only when the pi used to generate the data was less than .1.     

Estimating population divergence time and phylogeny from single-nucleotide polymorphisms data with outgroup ascertainment bias

The inference of population divergence times and branching patterns is of fundamental importance in many population genetic analyses. Many methods have been developed for estimating population divergence times, and recently, there has been particular attention towards genome-wide single-nucleotide polymorphisms (SNP) data. However, most SNP data have been affected by an ascertainment bias caused by the SNP selection and discovery protocols. Here, we present a modification of an existing maximum likelihood method that will allow approximately unbiased inferences when ascertainment is based on a set of outgroup populations. We also present a method for estimating trees from the asymmetric dissimilarity measures arising from pairwise divergence time estimation in population genetics. We evaluate the methods by simulations and by applying them to a large SNP data set of seven East Asian populations.     

A cooperative binomial ascertainment model.

It has been shown that the classical binomial form of ascertainment, assuming a constant probability pi that any affected individual may become a proband for his pedigree, cannot describe a rather wide range of ascertainment procedures that might arise in practice. Some more general heuristic ascertainment formulas might then be preferred, and in this paper we consider the probabilistic basis for these formulas. We retain the binomial assumption of the classical scheme but allow the ascertainment probability to depend on the number of potential probands per pedigree. This probability can be expressed by an increasing or a decreasing function of that number. Various illustrations are given and situations where the "cooperative" binomial scheme should be valuable are discussed.     

Sexual selection, stabilizing selection and fluctuating asymmetry in two populations of pupfish (Cyprinodon pecosensis)

Fluctuating asymmetry of morphological traits is thought to reflect the capacity of a genotype to produce an integrated, functional phenotype. I tested three predictions. (1) In a polygynous breeding system, under intense sexual selection on males, breeding males should show greater symmetry in bilaterally symmetrical traits than non-breeding males or females. (2) If these traits are under stabilizing selection, highly symmetrical individuals also should be modal phenotypes, thus near the mean value for that trait, whereas individuals with increased asymmetry should represent marginal phenotypes, near the extremes of the distribution for that trait. (3) Differences in the intensity of sexual selection should be reflected in differences in the degree of fluctuating asymmetry between sexes among populations. I examined the relationship between male breeding status and the degree of fluctuating asymmetry of four bilaterally symmetrical- traits, preorbital and preopercular pores and pectoral and pelvic fin rays, in two populations of Pecos pupfish which differed in the intensity of sexual selection. These traits do not function in male-male competition or female choice, thus are not directly affected by sexual selection. In Mirror Lake breeding males, as a group, were most symmetrical for all four traits, while non-breeding males and females showed higher levels of fluctuating asymmetry. Similarly, symmetrical individuals also represented modal phenotypes for four traits (breeding males), and for three traits (non-breeding males and females). These patterns were not seen in the Lake Francis population, where breeding males were as asymmetrical as non-breeding males and females, and the degree of fluctuating symmetry did not differ between modal and marginal phenotypes for any of the four traits. When ecological conditions favour intense sexual selection, either through female choice, male-male competition, or both, breeding males represent the most fit phenotypes. Thus sexual selection reinforces the effects of stabilizing selection on characters that do not function as secondary sexual traits. However, when sexual selection is relaxed, differences between sexes disappear.     

EM Algorithm for Segregation Analysis

We consider the problem of estimating segregation ratios in families based on ascertainment through affected children, formulate it as an incomplete problem and work out the EM algorithm for maximum likelihood estimation of segregation ratios. We treat both the cases of known and unknown ascertainment probability. We also derive expressions for the covariance matrix of the estimators suitable for computing along with the EM algorithm. We illustrate the method with an example, compare the computational effort with that required in using the scoring method and argue that the EM algorithm is simpler.     

A resolution of the ascertainment sampling problem. II. Generalizations and numerical results

The ascertainment problem arises when families are sampled by a nonrandom process and some assumption about this sampling process must be made in order to estimate genetic parameters. Under classical ascertainment assumptions, estimation of genetic parameters cannot be separated from estimation of the parameters of the ascertainment process, so that any misspecification of the ascertainment process causes biases in estimation of the genetic parameters. Ewens and Shute proposed a resolution to this problem, involving conditioning the likelihood of the sample on the part of the data which is "relevant to ascertainment." The usefulness of this approach can only be assessed by examining the properties (in particular, bias and standard error) of the estimates which arise by using it for a wide range of parameter values and family size distributions and then comparing these biases and standard errors with those arising under classical ascertainment procedures. These comparisons are carried out in the present paper, and we also compare the proposed method with procedures which condition on, or ignore, parts of the data.