Monte Carlo simulations on marker grouping and ordering

SSR-enriched genetic linkage maps of bermudagrass (Cynodon dactylon × transvaalensis), and their comparison with allied plant genomes

We report SSR-enriched genetic maps of bermudagrass that: (1) reveal partial residual polysomic inheritance in the tetraploid species, and (2) provide insights into the evolution of chloridoid genomes. This study describes genetic linkage maps of two bermudagrass species, Cynodon dactylon (T89) and Cynodon transvaalensis (T574), that integrate heterologous microsatellite markers from sugarcane into frameworks built with single-dose restriction fragments (SDRFs). A maximum likelihood approach was used to construct two separate parental maps from a population of 110 F₁ progeny of a cross between the two parents. The T89 map is based on 291 loci on 34 cosegregating groups (CGs), with an average marker spacing of 12.5 cM. The T574 map is based on 125 loci on 14 CGs, with an average marker spacing of 10.7 cM. Six T89 and one T574 CG(s) deviated from disomic inheritance. Furthermore, marker segregation data and linkage phase analysis revealed partial residual polysomic inheritance in T89, suggesting that common bermudagrass is undergoing diploidization following whole genome duplication (WGD). Twenty-six T89 CGs were coalesced into 9 homo(eo)logous linkage groups (LGs), while 12 T574 CGs were assembled into 9 LGs, both putatively representing the basic chromosome complement (x = 9) of the species. Eight T89 and two T574 CGs remain unassigned. The marker composition of bermudagrass ancestral chromosomes was inferred by aligning T89 and T574 homologs, and used in comparisons to sorghum and rice genome sequences based on 108 and 91 significant blast hits, respectively. Two nested chromosome fusions (NCFs) shared by two other chloridoids (i.e., zoysiagrass and finger millet) and at least three independent translocation events were evident during chromosome number reduction from 14 in the polyploid common ancestor of Poaceae to 9 in Cynodon.

Characterizing uncertainty in high-density maps from multiparental populations

Multiparental populations are of considerable interest in high-density genetic mapping due to their increased levels of polymorphism and recombination relative to biparental populations. However, errors in map construction can have significant impact on QTL discovery in later stages of analysis, and few methods have been developed to quantify the uncertainty attached to the reported order of markers or intermarker distances. Current methods are computationally intensive or limited to assessing uncertainty only for order or distance, but not both simultaneously. We derive the asymptotic joint distribution of maximum composite likelihood estimators for intermarker distances. This approach allows us to construct hypothesis tests and confidence intervals for simultaneously assessing marker-order instability and distance uncertainty. We investigate the effects of marker density, population size, and founder distribution patterns on map confidence in multiparental populations through simulations. Using these data, we provide guidelines on sample sizes necessary to map markers at sub-centimorgan densities with high certainty. We apply these approaches to data from a bread wheat Multiparent Advanced Generation Inter-Cross (MAGIC) population genotyped using the Illumina 9K SNP chip to assess regions of uncertainty and validate them against the recently released pseudomolecule for the wheat chromosome 3B.

Comparisons of four approximation algorithms for large-scale linkage map construction

Efficient construction of large-scale linkage maps is highly desired in current gene mapping projects. To evaluate the performance of available approaches in the literature, four published methods, the insertion (IN), seriation (SER), neighbor mapping (NM), and unidirectional growth (UG) were compared on the basis of simulated F(2) data with various population sizes, interferences, missing genotype rates, and mis-genotyping rates. Simulation results showed that the IN method outperformed, or at least was comparable to, the other three methods. These algorithms were also applied to a real data set and results showed that the linkage order obtained by the IN algorithm was superior to the other methods. Thus, this study suggests that the IN method should be used when constructing large-scale linkage maps.

Evaluation of algorithms used to order markers on genetic maps

When building genetic maps, it is necessary to choose from several marker ordering algorithms and criteria, and the choice is not always simple. In this study, we evaluate the efficiency of algorithms try (TRY), seriation (SER), rapid chain delineation (RCD), recombination counting and ordering (RECORD) and unidirectional growth (UG), as well as the criteria PARF (product of adjacent recombination fractions), SARF (sum of adjacent recombination fractions), SALOD (sum of adjacent LOD scores) and LHMC (likelihood through hidden Markov chains), used with the RIPPLE algorithm for error verification, in the construction of genetic linkage maps. A linkage map of a hypothetical diploid and monoecious plant species was simulated containing one linkage group and 21 markers with fixed distance of 3 cM between them. In all, 700 F(2) populations were randomly simulated with 100 and 400 individuals with different combinations of dominant and co-dominant markers, as well as 10 and 20% of missing data. The simulations showed that, in the presence of co-dominant markers only, any combination of algorithm and criteria may be used, even for a reduced population size. In the case of a smaller proportion of dominant markers, any of the algorithms and criteria (except SALOD) investigated may be used. In the presence of high proportions of dominant markers and smaller samples (around 100), the probability of repulsion linkage increases between them and, in this case, use of the algorithms TRY and SER associated to RIPPLE with criterion LHMC would provide better results.

A comparative genome approach to marker ordering

MOTIVATION

Genome maps are fundamental to the study of an organism and essential in the process of genome sequencing which in turn provides the ultimate map of the genome. The increased number of genomes being sequenced offers new opportunities for the mapping of closely related organisms. We propose here an algorithmic formalization of a genome comparison approach to marker ordering.

RESULTS

In order to integrate a comparative mapping approach in the algorithmic process of map construction and selection, we propose to extend the usual statistical model describing the experimental data, here radiation hybrids (RH) data, in a statistical framework that models additionally the evolutionary relationships between a proposed map and a reference map: an existing map of the corresponding orthologous genes or markers in a closely related organism. This has concretely the effect of exploiting, in the process of map selection, the information of marker adjacencies in the related genome when the information provided by the experimental data is not conclusive for the purpose of ordering. In order to compute efficiently the map, we proceed to a reduction of the maximum likelihood estimation to the Traveling Salesman Problem. Experiments on simulated RH datasets as well as on a real RH dataset from the canine RH project show that maps produced using the likelihood defined by the new model are significantly better than maps built using the traditional RH model.

AVAILABILITY

The comparative mapping approach is available in the last version of de Givry,S. et al. [(2004) Bioinformatics, 21, 1703-1704, www.inra.fr/mia/T/CarthaGene], a free (the LKH part is free for academic use only) mapping software in C++, including LKH (Helsgaun,K. (2000) Eur. J. Oper. Res., 126, 106-130, www.dat.ruc.dk/keld/research/LKH) for maximum likelihood computation.

Curation of wheat maps to improve map accuracy and QTL detection

Three Australian doubled haploid populations were used to illustrate the importance of map curation in order to improve the quality of linkage maps and quantative trait locus (QTL) detection. The maps were refined and improved by re-examining the order of markers, inspection of the genetic maps in relation to a consensus map, editing the marker data for double crossovers, and determining estimated recombination fractions for all pairs of markers. The re-ordering of markers and replacing genotypes at double crossovers with missing values resulted in an overall decrease in the length of the maps. Fewer apparent genotyping errors, associated with the presence of double recombinants, were identified with restriction fragment length polymorphisms (RFLPs) than with other types of markers used in this study. The complications that translocations may cause in the ordering of markers and subsequent QTL analysis were investigated. QTL analysis using both the original and revised maps indicated that QTL peaks were more sharply located or had improved log-likelihood (LOD) scores in the revised maps. An accurate indication of the QTL peak and a significant LOD score are both essential for the identification of markers suitable for marker-assisted selection. Recommendations are provided for the improvement of the quality of linkage maps.

A nearest-neighboring-end algorithm for genetic mapping

MOTIVATION

High-throughput methods are beginning to make possible the genotyping of thousands of loci in thousands of individuals, which could be useful for tightly associating phenotypes to candidate loci. Current mapping algorithms cannot handle so many data without building hierarchies of framework maps.

RESULTS

A version of Kruskal's minimum spanning tree algorithm can solve any genetic mapping problem that can be stated as marker deletion from a set of linkage groups. These include backcross, recombinant inbred, haploid and double-cross recombinational populations, in addition to conventional deletion and radiation hybrid populations. The algorithm progressively joins linkage groups at increasing recombination fractions between terminal markers, and attempts to recognize and correct erroneous joins at peaks in recombination fraction. The algorithm is O (mn3) for m individuals and n markers, but the mean run time scales close to mn2. It is amenable to parallel processing and has recovered true map order in simulations of large backcross, recombinant inbred and deletion populations with up to 37,005 markers. Simulations were used to investigate map accuracy in response to population size, allelic dominance, segregation distortion, missing data and random typing errors. It produced accurate maps when marker distribution was sufficiently uniform, although segregation distortion could induce translocated marker orders. The algorithm was also used to map 1003 loci in the F7 ITMI population of bread wheat, Triticum aestivum L. emend Thell., where it shortened an existing standard map by 16%, but it failed to associate blocks of markers properly across gaps within linkage groups. This was because it depends upon the rankings of recombination fractions at individual markers, and is susceptible to sampling error, typing error and joint selection involving the terminal markers of nearly finished linkage groups. Therefore, the current form of the algorithm is useful mainly to improve local marker ordering in linkage groups obtained in other ways.

AVAILABILITY

The source code and supplemental data are http://www.iubio.bio.indiana.edu/soft/molbio/qtl/flipper/

CONTACT

ccrane@purdue.edu.

Joining genetic linkage maps using a joint likelihood function

We present an efficient method to join genetic maps derived from different crosses, which is especially appropriate for dominant markers. In contrast to the "JoinMap" algorithm, which estimates information about recombination in a given cross from the LOD values and then combines estimates among crosses assuming a binomial sampling distribution, we construct a joint likelihood function that combines information across all crosses, to obtain a joint estimate of recombination. Simulations indicated that the difference between these two approaches is small when codominant markers are used, but that the joint likelihood approach shows substantially improved estimates when dominant or a mixture of dominant and codominant markers are used. This is because the joint likelihood implicitly finds the optimal weights among different classes of data, while the former method does not accurately predict the information from crosses involving dominant markers. Application of our method is illustrated by the construction of a linkage map for Linanthus using both backcrosses and the F2 of a cross between Linanthus jepsonii and L. bicolor, assayed with amplified fragment length polymorphisms (AFLP).