Genetic mapping in the presence of genotyping errors

Abstract

Genetic maps are built using the genotypes of many related individuals. Genotyping errors in these data sets can distort genetic maps, especially by inflating the distances. We have extended the traditional likelihood model used for genetic mapping to include the possibility of genotyping errors. Each individual marker is assigned an error rate, which is inferred from the data, just as the genetic distances are. We have developed a software package, called TMAP, which uses this model to find maximum-likelihood maps for phase-known pedigrees. We have tested our methods using a data set in Vitis and on simulated data and confirmed that our method dramatically reduces the inflationary effect caused by increasing the number of markers and leads to more accurate orders.

Figure 1.—

Graphical representation of the error model. Each node represents an abstract marker, i.e., genotypes for all individuals in the pedigree. The leaf nodes are the known, observed, possibly erroneous markers, and the internal nodes are the inferred, unobserved, error-free markers. Thus, except for the terminal markers, each physical marker corresponds to two nodes, one error free and one observed. Each arc represents separation between two markers, either because of recombination (vertical) or because of errors (horizontal).

Figure 2.—

Illustration of the two types of permutations used in the marker-ordering algorithm: moves (left) and flips (right). Each square represents a single marker.

Figure 3.—

Effect on linkage group size of removing every other marker both with and without compensation for errors. Error compensation leads to more consistent genetic distances.

Figure 4.—

Simulation of the effect of errors on marker ordering. In a linkage group of 19 markers, the 10th marker was simulated with errors, and the markers were ordered, using three different likelihood models. The first uses TMAP with the error model described in this article. The second uses a version of TMAP that assumes a fixed error rate of 2% for every marker. The third does not model any error at all.

Figure 5.—

Effect of removing one of the two permutation types on the speed of convergence to the correct order.

Figure 6.—

Distribution of nonzero error rates in the Vitis data set. In addition, 625 markers (67%) had an estimated error rate of exactly 0%.

Figure 7.—

Comparison of the estimated marker error rates and the size of the 1-unit-down intervals. The 1-unit-down intervals are computed by placing the marker at regular steps along the length of the linkage group and computing the interval where the log₁₀ likelihood is 1 unit less than the maximum. These approximate the 90% confidence intervals for the marker's position.