A multivalent pairing model of linkage analysis in autotetraploids.

Polyploidy has been recognized as an important step in the evolutionary diversification of flowering plants and may have a significant impact on plant breeding. Statistical analyses for linkage mapping in polyploid species can be difficult due to considerable complexities in polysomic inheritance. In this article, we develop a novel statistical method for linkage analysis of polymorphic markers in a full-sib family of autotetraploids. This method is established on multivalent pairings of homologous chromosomes at meiosis and can provide a simultaneous maximum-likelihood estimation of the double reduction frequencies of and recombination fraction between two markers. The EM algorithm is implemented to provide a tractable way for estimating relative proportions of different modes of gamete formation that generate identical gamete genotypes due to multivalent pairings. Extensive simulation studies were performed to demonstrate the statistical properties of this method. The implications of the new method for understanding the genome structure and organization of polyploid species are discussed.     

Extending coalescent theory to autotetraploids

We develop coalescent models for autotetraploid species with tetrasomic inheritance. We show that the ancestral genetic process in a large population without recombination may be approximated using Kingman's standard coalescent, with a coalescent effective population size 4N. Numerical results suggest that this approximation is accurate for population sizes on the order of hundreds of individuals. Therefore, existing coalescent simulation programs can be adapted to study population history in autotetraploids simply by interpreting the timescale in units of 4N generations. We also consider the possibility of double reduction, a phenomenon unique to polysomic inheritance, and show that its effects on gene genealogies are similar to partial self-fertilization.     

Selection in autotetraploids

Summary Theoretical studies indicated that response to selection would always be greater in diploid than in autotetraploid populations when gene frequency was the same in both, and that situations in which little or no response to selection could be expected would be more frequent in autotetraploids. Interpretation of the coefficient of selection in terms of escape from infection in a program of selection for disease or insect resistance indicated that moderate levels of escape from infection can drastically reduce response to selection in some cases.The zygotic constitution of an autotetraploid population will change as it approaches a new random mating equilibrium once selection pressure is relaxed. The changes will result in no change in the population mean if the trait under selection exhibits no dominance, but the mean will decrease slightly if there is dominance.     

Maximum likelihood vs. minimum chi-square--a general comparison with applications to the estimation of recombination fractions in two-point linkage analysis.

Some relationships between the estimates of recombination fraction in two-point linkage analysis obtained by maximum likelihood, minimum chi-square, and general least squares are derived. These theoretical results are based on an approximation for the multinomial distribution. Applications (theoretical and experimental) with RFLP (restriction fragment length polymorphism) markers for a segregating F2 population are given. The minimum chi-square estimate is slightly larger than the maximum likelihood estimate. For applications, however, both estimates must be considered to be approximately equal. The least squares estimates are slightly different (larger or smaller) from these estimates.     

Gene segregation in autotetraploids: prediction from meiotic configurations

Current systems of estimating gene segregation in autotetraploids usually are based on two extreme methods: chromosome segregation with absolute centromere linkage, or maximum equational segregation with crossing over always occurring between the centromeres and marker genes. The hiatus between the two methods is unacceptable quantitatively, and segregation of the d gene in tomato shows that neither method predicts an acceptable fit. We present a new meiotic configuration (MC) method of analyzing tetrasomic inheritance in autotetraploids that allows more accurate estimations of all intermediate types of segregation. The method is based on a maximum of two chiasmata per bivalent and four per quadrivalent. The theoretically expected numbers of bivalents and chain and circle quadrivalents are derived first. Chromosome frequencies from these configurations are then used to determine relative contributions from each configuration to the gamete genotypes by way of newly developed tables for gene segregation in various autotetraploid genotypes. The large sample sizes from classic 4x tomato (Solanum lycopersicum L.) data are used to demonstrate the stepwise method of calculating gamete genotypes, and the method gives acceptable fits for the data tested. The interspecific tetraploid hybrid Solanum lycopersicum × S. pimpinellifolium had good fits to expected autotetraploid segregation, supporting its autoploid nature and the fact that taxonomic rank should not be a consideration in designating categories of polyploids. Autotetraploid allozyme segregation data for several genes in one genus of another family had acceptable and usually better fits to the MC expectations than to the standard methods.     

The score statistic of the LD-lod analysis: detecting linkage adaptive to linkage disequilibrium

We study the properties of a modified lod score method for testing linkage that incorporates linkage disequilibrium (LD-lod). By examination of its score statistic, we show that the LD-lod score method adaptively combines two sources of information: (a) the IBD sharing score which is informative for linkage regardless of the existence of LD and (b) the contrast between allele-specific IBD sharing scores which is informative for linkage only in the presence of LD. We also consider the connection between the LD-lod score method and the transmission-disequilibrium test (TDT) for triad data and the mean test for affected sib pair (ASP) data. We show that, for triad data, the recessive LD-lod test is asymptotically equivalent to the TDT; and for ASP data, it is an adaptive combination of the TDT and the ASP mean test. We demonstrate that the LD-lod score method has relatively good statistical efficiency in comparison with the ASP mean test and the TDT for a broad range of LD and the genetic models considered in this report. Therefore, the LD-lod score method is an interesting approach for detecting linkage when the extent of LD is unknown, such as in a genome-wide screen with a dense set of genetic markers.     

Single-locus gametophytic incompatibility in autotetraploids

It is known that a single-locus gametophytic self-incompatibility (GSI) system can persist with just two distinct alleles in an autotetraploid population, in contrast to diploid GSI systems, assuming "competitive interaction" in which heteroallelic pollen is universally compatible. The steady-state population structure of a GSI system in autotetraploids was investigated in an undivided population assuming "competitive interaction." A deterministic model was developed to predict the frequencies of genotypes with two, three, or four distinct S alleles, assuming no mutation or population subdivision. The model showed that unlike in diploid GSI systems, the limiting values of the frequencies of genotype classes do not minimize pollen wastage.     

Performance comparison of two-point linkage methods using microsatellite markers flanking known disease locations

The Genetic Analysis Workshop 14 simulated data presents an interesting, challenging, and plausible example of a complex disease interaction in a dataset. This paper summarizes the ease of detection for each of the simulated Kofendrerd Personality Disorder (KPD) genes across all of the replicates for five standard linkage statistics. Using the KPD affection status, we have analyzed the microsatellite markers flanking each of the disease genes, plus an additional 2 markers that were not linked to any of the disease loci. All markers were analyzed using the following two-point linkage methods: 1) a MMLS, which is a standard admixture LOD score maximized over theta, alpha, and mode of inheritance, 2) a MLS calculated by GENEHUNTER, 3) the Kong and Cox LOD score as computed by MERLIN, 4) a MOD score (standard heterogeneity LOD maximized over theta, alpha, and a grid of genetic model parameters), and 5) the PPL, a Bayesian statistic that directly measures the strength of evidence for linkage to a marker. All of the major loci (D1-D4) were detectable with varying probabilities in the different populations. However, the modifier genes (D5 and D6) were difficult to detect, with similar distributions under the null and alternative across populations and statistics. The pooling of the four datasets in each replicate (n = 350 pedigrees) greatly improved the chance of detecting the major genes using all five methods, but failed to increase the chance to detect D5 and D6.     

Genomewide linkage analysis for internal carotid artery intimal medial thickness: evidence for linkage to chromosome 12

Carotid intimal medial thickness (IMT) is a heritable quantitative measure of atherosclerosis. A genomewide linkage analysis was conducted to localize a quantitative-trait locus (QTL) influencing carotid IMT. Carotid IMT was measured in 596 men and 629 women from 311 extended families (1,242 sib pairs) in the Framingham Heart Study Offspring cohort. B-mode carotid ultrasonography was used to define mean IMT of the carotid artery segments. Multipoint variance-component linkage analysis was performed. Evidence for significant linkage to internal carotid artery (ICA) IMT (two-point log odds [LOD] score 4.1, multipoint LOD score 3.4) was found 161 cM from the tip of the short arm of chromosome 12; these results were confirmed using the GENEHUNTER package (multipoint LOD score 4.3). No LOD scores >2.0 were observed for common carotid artery (CCA) IMT. Association analysis of a single-nucleotide-polymorphism variant of SCARB1 (minor allele frequency 0.13), a gene in close proximity to the region of peak linkage, revealed a protective association of the missense variant allele in exon 1 of SCARB1, with decreased ICA IMT compared with subjects homozygous for the common allele. Although the exon 1 variant contributed 2% to overall variation in ICA IMT, there was no significant change in the peak LOD score after adjustment in the linkage analyses. These data provide substantial evidence for a QTL on chromosome 12 influencing ICA IMT and for association of a rare variant of SCARB1, or a nearby locus, with ICA IMT. Because this rare SCARB1 variant does not account for our observed linkage, further investigations are warranted to identify additional candidate-gene variants on chromosome 12 predisposing to atherosclerosis phenotypes and clinical vascular disease.     

Genetic and linkage analysis of familial congenital hypothyroidism: exclusion of linkage to the TSH receptor gene

Congenital hypothyroidism affects 1/3000– 4000 newborns. The causes of this group of disorders are still largely unknown. Although most cases are sporadic, some families have several affected children and/or consanguineous parents, suggesting autosomal recessive inheritance. Furthermore, there is a murine strain (hyt) with congenital hypothyroidism and autosomal recessive inheritance, whose phenotype appears to be identical with the corresponding human disease. In the hyt mouse, the disease is caused by a mutation in the thyroid-stimulating hormone receptor (TSHR) gene, making this gene a likely candidate also for the human disease. The human TSHR gene was mapped on radiation hybrid panels and closely linked flanking markers D14S287 and D14S616 were identified. On the Genebridge 4 panel, D14S287 was found to be located 8.5 cR (corresponding to 2.3 cM) proximal to the TSHR gene, and D14S616 was found to be located 4.4 cR (1.2 cM) distal to the TSHR gene. These markers were analyzed in 23 families, most of them with two or more children affected by congenital hypothyroidism and some with appreciable consanguinity of the parents. Assuming homogeneity, the two-point lod score at θ = 0.1 was –4.8 for D14S287 and –5.8 for D14S616, and thus linkage to the TSHR gene was excluded. Even when the data were analyzed with allowance for heterogeneity, there was no evidence of linkage. Our conclusion is that if mutation of the TSHR gene causes familial congenital hypothyroidism in humans, it affects only a small proportion of the cases. Received: 8 July 1996     

Hypothesis testing under mixture models: application to genetic linkage analysis

In this paper we propose a new class of statistics to test a simple hypothesis against a family of alternatives characterized by a mixture model. Unlike the likelihood ratio statistic, whose large sample distribution is still unknown in this situation, these new statistics have a simple asymptotic distribution to which to refer under the null hypothesis. Simulation results suggest that it has adequate power in detecting the alternatives. Its application to genetic linkage analysis in the presence of the genetic heterogeneity that motivated this work is emphasized.     

Drosophila resistance genes to parasitoids: chromosomal location and linkage analysis

Insect hosts can survive infection by parasitoids using the encapsulation phenomenon. In Drosophila melanogaster the abilities to encapsulate the wasp species Leptopilina boulardi and Asobara tabida each involve one major gene. Both resistance genes have been precisely localized on the second chromosome, 35 centimorgans apart. This result clearly demonstrates the involvement of at least two separate genetic systems in Drosophila resistance to parasitoid wasps. The resistance genes to L. boulardi and A. tabida are not clustered as opposed to many plant resistance genes to pathogens cloned to date.     

Multilocus linkage analysis in humans: detection of linkage and estimation of recombination.

Multilocus linkage analysis is investigated from the viewpoint of the efficiency of recombination estimates under different strategies for detecting linkage and determining gene order within a linkage group. We consider the appropriateness of assuming no interference with data available in human genetic studies. Examples are given to show the significance of multilocus analysis in humans. A computer program package, LINKAGE, for multilocus linkage analysis is described.     

Sequence-based linkage analysis

The rapid decrease in the cost of DNA sequencing will enable its use for novel applications. Here, we investigate the use of DNA sequencing for simultaneous discovery and genotyping of polymorphisms in family linkage studies. In the proposed approach, short contiguous segments of genomic DNA, regularly spaced across the genome, are resequenced in each pedigree member, and all sequence polymorphisms discovered within a pedigree are used as genetic markers. We use computer simulations consistent with observed human sequence diversity to show that segments of 500-1,000 base pairs, spaced at intervals of 1-2 Mb across the genome, provide linkage information that equals or exceeds that of traditional marker-based approaches. We validate these results experimentally by implementing the sequence-based linkage approach for chromosome 19 in CEPH pedigrees.