The Predicted Cross Value for Genetic Introgression of Multiple Alleles

Abstract

We consider the plant genetic improvement challenge of introgressing multiple alleles from a homozygous donor to a recipient. First, we frame the project as an algorithmic process that can be mathematically formulated. We then introduce a novel metric for selecting breeding parents that we refer to as the predicted cross value (PCV). Unlike estimated breeding values, which represent predictions of general combining ability, the PCV predicts specific combining ability. The PCV takes estimates of recombination frequencies as an input vector and calculates the probability that a pair of parents will produce a gamete with desirable alleles at all specified loci. We compared the PCV approach with existing estimated-breeding-value approaches in two simulation experiments, in which 7 and 20 desirable alleles were to be introgressed from a donor line into a recipient line. Results suggest that the PCV is more efficient and effective for multi-allelic trait introgression. We also discuss how operations research can be used for other crop genetic improvement projects and suggest several future research directions.

Keywords: gene stacking; operations research; parental selection; predicted cross value; trait introgression.

Figure 1

Flowchart of the multi-allelic introgression process.

Figure 2

Illustration of the plumbing system for Example 0.1. Black rectangles are the valves, with binary numbers indicating whether they are open (1) or closed (0). The blue parallelograms are the water pipes, whose widths represent their relative volumes and not necessarily the actual amounts of water flowing through.

Figure 3

Illustration of the plumbing system for Example 0.2. Black rectangles are the valves, with binary numbers indicating whether they are open (1) or closed (0). The blue parallelograms are the water pipes, whose widths represent their relative volumes and not necessarily the actual amounts of water flowing through.

Figure 4

An illustration of 10 loci in a population consisting of 50 individuals. A purple square is used to denote a “0” allele and a yellow square for a “1.”

Figure 5

The GEBVs for Example 0.3.

Figure 6

The OHVs for Example 0.3.

Figure 7

The PCV map for Example 0.3. A purple square is used to denote a “0” allele and a yellow square for a “1.” The gray-shade matrix represents the PCVs of all possible pairs. The brighter the color, the larger the PCV. The two individuals with the largest PCV are highlighted in green and pink on the margins.

Figure 8

Performance of the GEBV, OHV, PCV-I, and PCV-II approaches in 1000 simulation runs of trait introgression of seven QTL. The vertical axis represents the proportion of desirable alleles in the genome. Histograms of the proportion of desirable alleles among 100 progeny from 1000 simulation runs are plotted for each generation. The red curve shows the population mean.

Figure 9

Distributions of the terminal generation numbers of PCV-I and PCV-II approaches.

Figure 10

Performance of the GEBV, OHV, PCV-I, and PCV-II approaches in 1000 simulation runs of trait introgression of 20 QTL.

Figure 11

Distributions of the terminal generation numbers of PCV-I and PCV-II approaches.