Gene Pyramiding Using Molecular Markers


David M. Francis, The Ohio State University

Heather L. Merk, The Ohio State University

Deana Namuth-Covert, University of Nebraska-Lincoln

Developing elite lines and varieties requires breeders to combine traits from multiple parents, a process called gene pyramiding or stacking. Molecular markers aid in selecting the best plants with which to proceed. This module discusses strategies for marker-assisted gene pyramiding, population size considerations, and generations required to obtain desired trait combinations.


After reading this learning module, you should be able:

  • Define gene pyramiding/gene stacking
  • Understand how molecular marker genotypic data can help guide gene pyramiding
  • Calculate the population size required to obtain the desired gene combination based on parental genotype and location of genes within the genome


Developing elite breeding lines and varieties often requires plant breeders to combine desirable traits from multiple parental lines, particularly in the case of disease resistance. The process of combining traits, known as gene pyramiding, can be accelerated by using molecular markers to identify and keep plants that contain the desired allele combination and discard those that don’t.

Selection based on molecular marker data (genotypic data) as opposed to traditional phenotypic data can confer many advantages. First, selection based on genotype allows breeders to identify and select desirable plants very early, such as the seedling stage, resulting in obvious savings of resources including greenhouse and/or field space, water, and fertilizer. Second, selection based on genotype can be cost effective when the cost of phenotyping is high and/or labor intensive. Third, when combining genes for resistance to the same disease, it can be difficult to distinguish, based on phenotype alone, those plants that carry all desired alleles from those that only have some of them. Fourth, unlike phenotypic selection, genotypic selection is not affected by environmental factors.

When using molecular markers to aid in the plant selection process, it is important to know where the molecular marker is located relative to the gene of interest. The genetic distance between marker and trait is calculated in genetic mapping studies (learn more about genetic mapping in an introduction to this topic provided by Wheat CAP). The farther a marker is from the DNA sequence polymorphism responsible for the trait, the greater the chance for recombination between the marker and the gene with each generation. If recombination occurs, selecting for a marker will not select for the trait, as the genetic linkage between the marker and the gene has been broken. This introduction to genetic mapping also outlines the process of genetic recombination.

Minimum Population Size

When pyramiding genes, breeders must calculate the probability of an individual plant containing the desired combination of alleles. This probability dictates the population size required to have a high probability of finding at least one plant with the desired combination of alleles. Muller (1923) and Sedcole (1977) promote use of the following equation to determine the minimum population size required to recover an individual with the desired combination of traits:

N = loge(1-P)/loge(1-f)


  • N is the minimum population size
  • P is the desired probability of success (e.g. 99%, 95%, 90%)
  • f is the frequency of the event (i.e., an individual plant having all desired alleles).

The frequency depends on the number of genes the breeder wants combined, whether the genes are genetically linked, and the breeding scheme being utilized. What follows are two examples of calculating f, as well as the minimum population size, for two scenarios: (1) combining two unlinked genes, and (2) combining two linked genes.

Combining two unlinked genes

In the simplest case, a breeder wishes to combine two unlinked favorable alleles from two different inbred parental lines into one variety. For example, we may want to combine Rx-3 and Rx-4, two genes that confer resistance to bacterial spot in tomato (Fig. 1). Rx-3 is located on tomato chromosome 5 and Rx-4 is located on chromosome 11. To combine the favorable alleles for these two genes, two inbred parental lines, one homozygous for Rx-3 and the other homozygous for Rx-4, would be crossed to generate heterozygous F1 individuals. The F1 individuals would be self-pollinated and F2 individuals homozygous at Rx-3 and Rx-4 would be identified using molecular markers.

Figure 1. Bacterial spot on tomato fruit and leaves. Photo credit: David Francis, The Ohio State University.

Before the use of markers, breeders would need to grow progeny from F2 individuals—F3s—to differentiate between lines where a gene is homozygous dominant from those where the gene is heterozygous. If homozygous in the F2, a gene will not segregate in the F3, whereas if heterozygous, it will segregate. By allowing individuals with the desired genotype in the homozygous state to be identified after only two generations, DNA marker technology saves time and resources.

The question is: how large a population (number of F2 individuals) must be grown to have a 99% chance of obtaining at least one individual that is homozygous at both gene loci?

To answer this, solve for N using Muller’s equation, N = loge(1-P)/loge(1-f).

In this case, P = 0.99

We can calculate f as follows:

The probability that an F2 individual will be homozygous for one gene is 0.25. Therefore, the probability that an F2 individual will be homozygous for two genes, is (0.25 x 0.25) = 0.0625. Thus, f = 0.0625. Learn about calculating expected genetic ratios).

Now we can calculate N by plugging P and f into Muller’s equation:

N = loge(1-P)/loge(1-f) = loge(1-0.99)/loge(1-0.0625) = 71.86.

Using the example above, a population with a minimum of 72 individuals must be grown to have a 99% probability of obtaining at least one F2 individual homozygous for two unlinked genes.

This formula can be extended to estimate the minimum population size needed to obtain more than one individual with the desired combination of traits. Using the above example, to obtain 5 individuals homozygous for two genes, a population with 360 individuals (72 x 5) must be grown.

Combining two linked genes

What if a breeder wants to combine a gene from one inbred parent with a gene from another inbred parent, but the genes are linked? For example, we may want to combine Rx-3 and Pto, genes that confer resistance to bacterial spot and bacterial speck, respectively. Rx-3 and Pto are both located on tomato chromosome 5 (Yang et al., 2005). Suppose one inbred parental line is resistant to bacterial spot and the other is resistant to bacterial speck. To combine the resistance for bacterial spot and bacterial speck into one line, a recombination event must occur between the two genes, Rx-3 and Pto. The chance of such a recombination event is proportional to the distance between the genes. The closer the genes are, the lower the likelihood that a recombination event between the genes will occur. Consequently, more individuals must be evaluated in order to have a high probability of obtaining one with the desirable allele combination. In our bacterial spot and bacterial speck example, Rx-3 and Pto are located approximately 37 cM apart. To obtain one F2 individual homozygous for the resistance alleles at both gene loci with a 99% probability of success, 133 individuals must be evaluated.


Gene pyramiding is an important strategy for germplasm improvement. Pyramiding requires that breeders consider the minimium population size that must be evaluated to have a reasonable chance of obtaining the desired genotype. Molecular marker genotyping can facilitate the gene pyramiding process by reducing the number of generations that breeders must evaluate to ensure they have the desired gene combination.

References Cited

  • Muller, H. J. 1923. A simple formula giving the number of individuals required for obtaining one of a given frequency. American Naturalist 57: 66–73. (Available online at: (verified 29 Dec 2010).
  • Sedcole, J. R. 1977. Number of plants necessary to recover a trait. Crop Science 17: 667–668.
  • Yang, W. C., E. J. Sacks, M.L.L. Ivey, S. A. Miller, and D. M. Francis. 2005. Resistance in Lycopersicum esculentum intraspecific crosses to race T1 strains of Xanthomonas campestris pv. vesicatoria causing bacterial spot of tomato. Phytopathology 95: 519–527. (Available at: (verified 29 Dec 2010).

External Links

Funding Statement

Development of this page was supported in part by the National Institute of Food and Agriculture (NIFA) Solanaceae Coordinated Agricultural Project, agreement 2009-85606-05673, administered by Michigan State University. Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the view of the United States Department of Agriculture.

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