Constructing dense genetic linkage maps

This paper describes a novel combination of techniques for the construction of dense genetic linkage maps. The construction of such maps is hampered by the occurrence of even small proportions of typing errors. Simulated annealing is used to obtain the best map according to the optimality criterion: the likelihood or the total number of recombination events. Spatial sampling of markers is used to obtain a framework map. The construction of a framework map is essential if the steps used for simulated annealing are required to be simple. For missing-data imputation the Gibbs sampler is used. Map construction using simulated annealing and missing-data imputation are used in an iterative way. In order to obtain some measure of precision of the genetic linkage map obtained, the Metropolis-Hastings algorithm is used to obtain posterior intervals for the positions of markers. The process of map construction is embedded in a framework of pre-mapping and post-mapping diagnostics. The techniques described are illustrated using a practical application. Received: 1 June 2000 / Accepted: 21 September 2000     

Improving estimates of genetic maps: a maximum likelihood approach

As a result of previous large, multipoint linkage studies there is a substantial amount of existing marker data. Due to the increased sample size, genetic maps estimated from these data could be more accurate than publicly available maps. However, current methods for map estimation are restricted to data sets containing pedigrees with a small number of individuals, or cannot make full use of marker data that are observed at several loci on members of large, extended pedigrees. In this article, a maximum likelihood (ML) method for map estimation that can make full use of the marker data in a large, multipoint linkage study is described. The method is applied to replicate sets of simulated marker data involving seven linked loci, and pedigree structures based on the real multipoint linkage study of Abkevich et al. (2003, American Journal of Human Genetics 73, 1271-1281). The variance of the ML estimate is accurately estimated, and tests of both simple and composite null hypotheses are performed. An efficient procedure for combining map estimates over data sets is also suggested.     

AMBIENCE: a novel approach and efficient algorithm for identifying informative genetic and environmental associations with complex phenotypes

We developed a computationally efficient algorithm AMBIENCE, for identifying the informative variables involved in gene-gene (GGI) and gene-environment interactions (GEI) that are associated with disease phenotypes. The AMBIENCE algorithm uses a novel information theoretic metric called phenotype-associated information (PAI) to search for combinations of genetic variants and environmental variables associated with the disease phenotype. The PAI-based AMBIENCE algorithm effectively and efficiently detected GEI in simulated data sets of varying size and complexity, including the 10K simulated rheumatoid arthritis data set from Genetic Analysis Workshop 15. The method was also successfully used to detect GGI in a Crohn's disease data set. The performance of the AMBIENCE algorithm was compared to the multifactor dimensionality reduction (MDR), generalized MDR (GMDR), and pedigree disequilibrium test (PDT) methods. Furthermore, we assessed the computational speed of AMBIENCE for detecting GGI and GEI for data sets varying in size from 100 to 10(5) variables. Our results demonstrate that the AMBIENCE information theoretic algorithm is useful for analyzing a diverse range of epidemiologic data sets containing evidence for GGI and GEI.     

Prediction of total genetic value using genome-wide dense marker maps

Recent advances in molecular genetic techniques will make dense marker maps available and genotyping many individuals for these markers feasible. Here we attempted to estimate the effects of approximately 50,000 marker haplotypes simultaneously from a limited number of phenotypic records. A genome of 1000 cM was simulated with a marker spacing of 1 cM. The markers surrounding every 1-cM region were combined into marker haplotypes. Due to finite population size N(e) = 100, the marker haplotypes were in linkage disequilibrium with the QTL located between the markers. Using least squares, all haplotype effects could not be estimated simultaneously. When only the biggest effects were included, they were overestimated and the accuracy of predicting genetic values of the offspring of the recorded animals was only 0.32. Best linear unbiased prediction of haplotype effects assumed equal variances associated to each 1-cM chromosomal segment, which yielded an accuracy of 0.73, although this assumption was far from true. Bayesian methods that assumed a prior distribution of the variance associated with each chromosome segment increased this accuracy to 0.85, even when the prior was not correct. It was concluded that selection on genetic values predicted from markers could substantially increase the rate of genetic gain in animals and plants, especially if combined with reproductive techniques to shorten the generation interval.     

Geometry for a selfish foraging group: a genetic algorithm approach

The advantages of group living are not shared equally among all group members and these advantages may depend on the spatial position occupied by a forager within the group. For instance, it is thought that socially dominant individuals prefer the predator-safe central position of groups forcing subordinates to the periphery. Uneven spread of benefits among group members can occur when some animals (the scroungers) parasitically exploit the food findings of other foragers (the producers). Here we focus on how playing producer or scrounger affects an individual''s spatial position within a group. We model the movement of foraging animals playing scrounger or producer using a spatially explicit simulation and use a genetic algorithm to establish movement rules. We find that groups containing producers and scroungers are more compact compared to an equivalent group of producers only. Furthermore, the position occupied by strategies varies: scroungers are mainly found in central positions, while producers in the periphery, suggesting that the best position for strategies differs. Dominants, therefore, should prefer movement rules which lead to central positions because of the positional benefits provided to the scrounger strategy they use. Moreover, position within a group will introduce an asymmetry among otherwise phenotypically symmetric individuals.     

A statistical approach to finding overlooked genetic associations

Background  

Complexity and noise in expression quantitative trait loci (eQTL) studies make it difficult to distinguish potential regulatory relationships among the many interactions. The predominant method of identifying eQTLs finds associations that are significant at a genome-wide level. The vast number of statistical tests carried out on these data make false negatives very likely. Corrections for multiple testing error render genome-wide eQTL techniques unable to detect modest regulatory effects.     

Constructing large-scale genetic maps using an evolutionary strategy algorithm

This article is devoted to the problem of ordering in linkage groups with many dozens or even hundreds of markers. The ordering problem belongs to the field of discrete optimization on a set of all possible orders, amounting to n!/2 for n loci; hence it is considered an NP-hard problem. Several authors attempted to employ the methods developed in the well-known traveling salesman problem (TSP) for multilocus ordering, using the assumption that for a set of linked loci the true order will be the one that minimizes the total length of the linkage group. A novel, fast, and reliable algorithm developed for the TSP and based on evolution-strategy discrete optimization was applied in this study for multilocus ordering on the basis of pairwise recombination frequencies. The quality of derived maps under various complications (dominant vs. codominant markers, marker misclassification, negative and positive interference, and missing data) was analyzed using simulated data with approximately 50-400 markers. High performance of the employed algorithm allows systematic treatment of the problem of verification of the obtained multilocus orders on the basis of computing-intensive bootstrap and/or jackknife approaches for detecting and removing questionable marker scores, thereby stabilizing the resulting maps. Parallel calculation technology can easily be adopted for further acceleration of the proposed algorithm. Real data analysis (on maize chromosome 1 with 230 markers) is provided to illustrate the proposed methodology.     

A fast algorithm for estimating transmission probabilities in QTL detection designs with dense maps

Background

In the case of an autosomal locus, four transmission events from the parents to progeny are possible, specified by the grand parental origin of the alleles inherited by this individual. Computing the probabilities of these transmission events is essential to perform QTL detection methods.

Results

A fast algorithm for the estimation of these probabilities conditional to parental phases has been developed. It is adapted to classical QTL detection designs applied to outbred populations, in particular to designs composed of half and/or full sib families. It assumes the absence of interference.

Conclusion

The theory is fully developed and an example is given.     

Prediction of common secondary structures of RNAs: a genetic algorithm approach

In this study we apply a genetic algorithm to a set of RNA sequences to find common RNA secondary structures. Our method is a three-step procedure. At the first stage of the procedure for each sequence, a genetic algorithm is used to optimize the structures in a population to a certain degree of stability. In this step, the free energy of a structure is the fitness criterion for the algorithm. Next, for each structure, we define a measure of structural conservation with respect to those in other sequences. We use this measure in a genetic algorithm to improve the structural similarity among sequences for the structures in the population of a sequence. Finally, we select those structures satisfying certain conditions of structural stability and similarity as predicted common structures for a set of RNA sequences. We have obtained satisfactory results from a set of tRNA, 5S rRNA, rev response elements (RRE) of HIV-1 and RRE of HIV-2/SIV, respectively.     

Combining a modelling with a genetic approach in establishing associations between genetic and physiological effects in relation to phosphorus uptake

The Pup1 locus confers tolerance to phosphorus (P) deficiency in rice (Oryza sativa L.). Transferring the Pup1 locus to an intolerant genotype increased P uptake by a factor 3 to 4. Lines with the Pup1 locus maintained higher root growth rates under P deficiency, but only as they started to diverge from intolerant lines in P uptake. It was thus not possible to determine if differences in root growth preceded and caused differences in P uptake or whether high root growth was the result of higher external P uptake efficiency (P influx per root size). The purpose of this paper is to review experimental evidence on the effect of Pup1 in light of recent results in modelling cause-and-effect relations between root growth, external efficiency and P uptake. Model simulations suggested that only very small changes in factors enhancing root growth were needed to explain the effect of Pup1 on P uptake. A 22% increase in root fineness or in internal P utilization efficiency (root dry matter per root P) was sufficient to triple P uptake . External root efficiency had to increase by 33 to account for the effect of Pup1. However, the most noticeable effect of increases in external efficiency was a subsequent stimulation of root growth that contributed eight times more to final P uptake compared to the change in external efficiency. Comparisons of model simulations with empirical data suggested that measured differences in external efficiency between Nipponbare and NIL-Pup1 were sufficiently large to account for the increase in P uptake. A segregation analysis using several pairs of contrasting NILs (at the Pup1 locus) further confirmed this as Pup1 co-segregated with external efficiency but not with seedling root growth or internal efficiency.     

Estimating genetic diversity across the neutral genome with the use of dense marker maps

Background

With the advent of high throughput DNA typing, dense marker maps have become available to investigate genetic diversity on specific regions of the genome. The aim of this paper was to compare two marker based estimates of the genetic diversity in specific genomic regions lying in between markers: IBD-based genetic diversity and heterozygosity.

Methods

A computer simulated population was set up with individuals containing a single 1-Morgan chromosome and 1665 SNP markers and from this one, an additional population was produced with a lower marker density i.e. 166 SNP markers. For each marker interval based on adjacent markers, the genetic diversity was estimated either by IBD probabilities or heterozygosity. Estimates were compared to each other and to the true genetic diversity. The latter was calculated for a marker in the middle of each marker interval that was not used to estimate genetic diversity.

Results

The simulated population had an average minor allele frequency of 0.28 and an LD (r²) of 0.26, comparable to those of real livestock populations. Genetic diversities estimated by IBD probabilities and by heterozygosity were positively correlated, and correlations with the true genetic diversity were quite similar for the simulated population with a high marker density, both for specific regions (r = 0.19-0.20) and large regions (r = 0.61-0.64) over the genome. For the population with a lower marker density, the correlation with the true genetic diversity turned out to be higher for the IBD-based genetic diversity.

Conclusions

Genetic diversities of ungenotyped regions of the genome (i.e. between markers) estimated by IBD-based methods and heterozygosity give similar results for the simulated population with a high marker density. However, for a population with a lower marker density, the IBD-based method gives a better prediction, since variation and recombination between markers are missed with heterozygosity.     

Plotting genetic maps on a microcomputer

Maps of genetic linkage and restriction enzyme cleavage sites can be quickly prepared on an IBM PC microcomputer with the commercially available program Lotus 1-2-3. Data can be entered on the keyboard or imported from other programs. The maps can be displayed on the screen or with a printer or plotter. These procedures should be useful in the research laboratory, in preparing figures for publication and in teaching.     

A Bayesian approach for constructing genetic maps when markers are miscoded

The advent of molecular markers has created opportunities for a better understanding of quantitative inheritance and for developing novel strategies for genetic improvement of agricultural species, using information on quantitative trait loci (QTL). A QTL analysis relies on accurate genetic marker maps. At present, most statistical methods used for map construction ignore the fact that molecular data may be read with error. Often, however, there is ambiguity about some marker genotypes. A Bayesian MCMC approach for inferences about a genetic marker map when random miscoding of genotypes occurs is presented, and simulated and real data sets are analyzed. The results suggest that unless there is strong reason to believe that genotypes are ascertained without error, the proposed approach provides more reliable inference on the genetic map.     

CPROP: a rule-based program for constructing genetic maps.

Gene mapping assigns chromosomal coordinates to genetic loci based on analysis of fragmentary ordering and metric data. In assembling genetic maps, geneticists use rules of inference to derive new facts about order and distance between loci from experimentally derived conclusions about order and distance. They construct comprehensive maps by merging related sets of data and resolving conflicts between them. In this article we describe software that formalizes and automates some of these rules of inference to yield a useful map construction utility called CPROP.     

Development of high-density genetic maps for barley and wheat using a novel two-enzyme genotyping-by-sequencing approach

Advancements in next-generation sequencing technology have enabled whole genome re-sequencing in many species providing unprecedented discovery and characterization of molecular polymorphisms. There are limitations, however, to next-generation sequencing approaches for species with large complex genomes such as barley and wheat. Genotyping-by-sequencing (GBS) has been developed as a tool for association studies and genomics-assisted breeding in a range of species including those with complex genomes. GBS uses restriction enzymes for targeted complexity reduction followed by multiplex sequencing to produce high-quality polymorphism data at a relatively low per sample cost. Here we present a GBS approach for species that currently lack a reference genome sequence. We developed a novel two-enzyme GBS protocol and genotyped bi-parental barley and wheat populations to develop a genetically anchored reference map of identified SNPs and tags. We were able to map over 34,000 SNPs and 240,000 tags onto the Oregon Wolfe Barley reference map, and 20,000 SNPs and 367,000 tags on the Synthetic W9784 × Opata85 (SynOpDH) wheat reference map. To further evaluate GBS in wheat, we also constructed a de novo genetic map using only SNP markers from the GBS data. The GBS approach presented here provides a powerful method of developing high-density markers in species without a sequenced genome while providing valuable tools for anchoring and ordering physical maps and whole-genome shotgun sequence. Development of the sequenced reference genome(s) will in turn increase the utility of GBS data enabling physical mapping of genes and haplotype imputation of missing data. Finally, as a result of low per-sample costs, GBS will have broad application in genomics-assisted plant breeding programs.     

Correction: genetic algorithm learning as a robust approach to RNA editing site site prediction

After the publication of [1], we were alerted to an error in our data. The error was an one-off miscalculation in the extraction of position information for our set of true negatives. Our data set should have used randomly selected non-edited cytosines (C) as true negatives, but the data generation phase resulted in a set of nucleotides that were each one nucleotide downstream of known, unedited cytosines. The consequences of this error are reflected in changes to our results, although the general conclusions presented in our original publication remain largely unchanged.     

Finding non-crystallographic symmetry in density maps of macromolecular structures

The internal symmetry of a macromolecule is both an important aspect of its function and a useful feature in obtaining a structure by X-ray crystallography and other techniques. A method is presented for finding internal symmetry and other non-crystallographic symmetry in a structure based on patterns of density in a density map for that structure. Regions in map that are similar are identified by cutting out a sphere of density from a region that has high local variation and using an FFT-based correlation search to find other regions that match. The relationships among correlated regions are then refined to maximize their correlations and are found to accurately represent non-crystallographic symmetry in the map.     

PhyloGeoViz: a web-based program that visualizes genetic data on maps

The first step of many population genetic studies is the simple visualization of allele frequencies on a landscape. This basic data exploration can be challenging without proprietary software, and the manual plotting of data is cumbersome and unfeasible at large sample sizes. I present an open source, web-based program that plots any kind of frequency or count data as pie charts in Google Maps (Google Inc., Mountain View, CA). Pie polygons are then exportable to Google Earth (Google Inc.), a free Geographic Information Systems platform. Import of genetic data into Google Earth allows phylogeographers access to a wealth of spatial information layers integral to forming hypotheses and understanding patterns in the data.     

Reverse engineering of regulatory networks: simulation studies on a genetic algorithm approach for ranking hypotheses

Reverse engineering algorithms (REAs) aim at using gene expression data to reconstruct interactions in regulatory genetic networks. This may help to understand the basis of gene regulation, the core task of functional genomics. Collecting data for a number of environmental conditions is necessary to reengineer even the smallest regulatory networks with reasonable confidence. We systematically tested the requirements for the experimental design necessary for ranking alternative hypotheses about the structure of a given regulatory network. A genetic algorithm (GA) was used to explore the parameter space of a multistage discrete genetic network model with fixed connectivity and number of states per node. Our results show that it is not necessary to determine all parameters of the genetic network in order to rank hypotheses. The ranking process is easier the more experimental environmental conditions are used for the data set. During the ranking, the number of fixed parameters increases with the number of environmental conditions, while some errors in the hypothetical network structure may pass undetected, due to a maintained dynamical behaviour.