Preliminary ordering of multiple linked loci using pairwise linkage data

Falk, Catherine T.; Chakravarti, Aravinda

doi:10.1002/gepi.1370090507

Cited by 26 publications

(19 citation statements)

References 15 publications

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“…A similar situation also occurs among loci ABA3, ABG484, Pgk1, and ABR315. In comparison, there are considerable differences between maps B and C. It is noteworthy that sums of adjacent distances on linkage maps A, B, and C are, respectively, 132.8, 148.5, and 151 cM, which suggests that linkage map A is the best among these three linkage maps according to the principle of minimum SARF (Falk 1992;Liu 1998). …”

Section: Numerical Examplesmentioning

confidence: 97%

“…The construction of linkage maps has been recognized as a special case of the traveling salesman problem (TSP) (Liu 1998). The TSP is a classical non-deterministic polynomial time (NP)-complete problem (Wilson 1988;Olson and Boehnke 1990;Falk 1992) that has attracted the attention of mathematicians and computer scientists. Currently, there are two approaches to tackle the problem.…”

mentioning

confidence: 99%

“…Proposed criteria include Lalouel's least squares ( Jensen and Jorgensen 1975;Weeks and Lange 1987), sum of adjacent recombination fractions (SARF) (Falk 1992), product of adjacent recombination fractions (PARF) (Wilson 1988), probability of double recombinants (PDR) (Knapp et al 1989), sum of adjacent LOD score (SALOD) (Weeks and Lange 1987), and SALOD divided by the equivalent number of informative meioses (SALEQ) (Edwards 1971). Olson and Boehnke (1990) compared these criteria and concluded that SARF and SALEQ were the best overall criteria.…”

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confidence: 99%

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A Novel Method for Estimating Linkage Maps

Tan

2006

Genetics

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The goal of linkage mapping is to find the true order of loci from a chromosome. Since the number of possible orders is large even for a modest number of loci, the problem of finding the optimal solution is known as a NP-hard problem or traveling salesman problem (TSP). Although a number of algorithms are available, many either are low in the accuracy of recovering the true order of loci or require tremendous amounts of computational resources, thus making them difficult to use for reconstructing a large-scale map. We developed in this article a novel method called unidirectional growth (UG) to help solve this problem. The UG algorithm sequentially constructs the linkage map on the basis of novel results about additive distance. It not only is fast but also has a very high accuracy in recovering the true order of loci according to our simulation studies. Since the UG method requires n À 1 cycles to estimate the ordering of n loci, it is particularly useful for estimating linkage maps consisting of hundreds or even thousands of linked codominant loci on a chromosome.A LTHOUGH more and more genomes are being sequenced, high-quality linkage maps for many organisms remain useful. For a majority of organisms, obtaining appropriate linkage maps will be a necessary step for understanding their genetic architecture. With the advance of technology as well as increasing demand of high-density linkage maps, the number of loci simultaneously examined in experiments is steadily growing, which presents a considerable computational challenge for estimating the underlying linkage map since the number of possible orders of loci increases rapidly with the number of loci (Olson and Boehnke 1990;Mester et al. 2003). The construction of linkage maps has been recognized as a special case of the traveling salesman problem (TSP) (Liu 1998). The TSP is a classical non-deterministic polynomial time (NP)-complete problem (Wilson 1988;Olson and Boehnke 1990;Falk 1992) that has attracted the attention of mathematicians and computer scientists. Currently, there are two approaches to tackle the problem. One is to find the answer by performing exhaustive searches and the other is to find approximations. Even for just 10 loci on a chromosome, there are 1,814,400 possible orders. Thus it is extremely time consuming (if not entirely impossible) to exhaustively search all possible orders when the number of loci on a chromosome is .30 (Mester et al.

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Section: Numerical Examplesmentioning

confidence: 97%

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confidence: 99%

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A Novel Method for Estimating Linkage Maps

Tan

2006

Genetics

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“…This criterion, called the sum of adjacent recombination fractions (SARF), is used as a criterion in locus ordering (Olson and Boehnke 1990, Falk 1992, Liu 1998, Mester et al 2003b. When the absolute values of log likelihood (ALL) between loci are considered to correspond to the distance between the TSP cities, our system seeks the order minimizing…”

Section: Algorithmmentioning

confidence: 99%

AntMap: Constructing Genetic Linkage Maps Using an Ant Colony Optimization Algorithm

2006

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High-throughput assay of molecular markers enables to utilize large amounts of markers in linkage mapping. To incorporate numerous markers into a linkage map, the development of a highly efficient method for linkage mapping is indispensable. When the number of loci is large, locus ordering is a major difficulty in linkage mapping, since the number of possible orders becomes very large. To address this problem, we developed a new algorithm for locus ordering and used it in a newly developed computer program called AntMap. The algorithm is based on ant colony optimization, which is a set of metaheuristic algorithms inspired by the cooperative behavior of real ants in finding the shortest path from their nest to a food source. Using this algorithm, AntMap seeks the linear order of loci that minimizes the sum of adjacent recombination fractions or that maximizes the log likelihood of locus order. Analyses based on simulated data sets indicated that our algorithm displayed a high efficiency level. The high performance of the algorithm enabled to save time and labor, and also to validate an estimated order by bootstrap tests. Our algorithm and AntMap should enable to construct high-throughput systems for linkage mapping. AntMap is available under a GNU general public license at http://cse.naro.affrc.go.jp/iwatah/antmap/index.html. Source codes and executables of AntMap can be obtained there.

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“…Linkage associations among segregating markers were determined independently for each pedigree (cutoffs: LOD C 3.0 and r B 0.40). Independent associations were then ordered based upon the minimum sum of adjacent recombination fractions (SARF) and tested by Log-likelihood estimates (Falk 1992). All possible marker orders were constructed and marker order was established using the smallest estimated Kosambi map distances and logarithm of the likelihood for each map length [map Log-likelihood].…”

Section: Comparative Mapping Of the Z Chromosomementioning

confidence: 99%

A rearrangement of the Z chromosome topology influences the sex-linked gene display in the European corn borer, Ostrinia nubilalis

et al. 2011

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Males are homogametic (ZZ) and females are heterogametic (WZ) with respect to the sex chromosomes in many species of butterflies and moths (insect order Lepidoptera). Genes on the Z chromosome influence traits involved in larval development, environmental adaptation, and reproductive isolation. To facilitate the investigation of these traits across Lepidoptera, we developed 43 degenerate primer pairs to PCR amplify orthologs of 43 Bombyx mori Z chromosome-linked genes. Of the 34 orthologs that amplified by PCR in Ostrinia nubilalis, 6 co-segregated with the Z chromosome anchor markers kettin (ket) and lactate dehydrogenase (ldh), and produced a consensus genetic linkage map of ~89 cM in combination with 5 AFLP markers. The O. nubilalis and B. mori Z chromosomes are comparatively co-linear, although potential gene inversions alter terminal gene orders and a translocation event disrupted synteny at one chromosome end. Compared to B. mori orthologs, O. nubilalis Z chromosome-linked genes showed conservation of tissuespecific and growth-stage-specific expression, although some genes exhibited species-specific expression across developmental stages or tissues. The O. nubilalis Z chromosome linkage map provides new tools for isolating quantitative trait loci (QTL) involved in sex-linked traits that drive speciation and it exposes genome rearrangements as a possible mechanism for differential gene regulation in Lepidoptera. Abstract Males are homogametic (ZZ) and females are heterogametic (WZ) with respect to the sex chromosomes in many species of butterflies and moths (insect order Lepidoptera). Genes on the Z chromosome influence traits involved in larval development, environmental adaptation, and reproductive isolation. To facilitate the investigation of these traits across Lepidoptera, we developed 43 degenerate primer pairs to PCR amplify orthologs of 43 Bombyx mori Z chromosomelinked genes. Of the 34 orthologs that amplified by PCR in Ostrinia nubilalis, 6 co-segregated with the Z chromosome anchor markers kettin (ket) and lactate dehydrogenase (ldh), and produced a consensus genetic linkage map of *89 cM in combination with 5 AFLP markers. The O. nubilalis and B. mori Z chromosomes are comparatively co-linear, although potential gene inversions alter terminal gene orders and a translocation event disrupted synteny at one chromosome end. Compared to B. mori orthologs, O. nubilalis Z chromosomelinked genes showed conservation of tissue-specific and growth-stage-specific expression, although some genes exhibited species-specific expression across developmental stages or tissues. The O. nubilalis Z chromosome linkage map provides new tools for isolating quantitative trait loci (QTL) involved in sex-linked traits that drive speciation and it exposes genome rearrangements as a possible mechanism for differential gene regulation in Lepidoptera.

show abstract

Preliminary ordering of multiple linked loci using pairwise linkage data

Cited by 26 publications

References 15 publications

A Novel Method for Estimating Linkage Maps

A Novel Method for Estimating Linkage Maps

AntMap: Constructing Genetic Linkage Maps Using an Ant Colony Optimization Algorithm

A rearrangement of the Z chromosome topology influences the sex-linked gene display in the European corn borer, Ostrinia nubilalis

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