Whole-genome versus per-chromosome targeted recombination: Simulations and predicted gains in maize with an integer programming model.

Per-chromosome targeted recombination, with one to two recombinations at specific marker intervals on each chromosome, doubles the predicted genetic gains in biparental populations. We developed an integer programing model to identify where a fixed number of targeted recombinations should occur across the whole genome, without restrictions on the number of targeted recombinations on each chromosome. We compared whole-genome and per-chromosome targeted recombination in 392 biparental maize (Zea mays L.) populations and in simulation experiments. For yield, moisture, test weight, and a simulated trait controlled by 2000 quantitative trait loci (QTL), predicted gains were 8%-9% larger with 10 targeted recombinations across the entire genome than with one targeted recombination on each of the 10 chromosomes. With whole-genome targeted recombination, the number of recombinations on a given chromosome was correlated (r = 0.76-0.91) with the chromosome size (in cM). Simulation results suggested that previous results on gains from targeted recombination relative to nontargeted recombination were too optimistic by around 20%. Because the underlying QTL are unknown, studies on targeted recombination have relied on genomewide marker effects as proxies for QTL information. The simulation results indicated a 25% (for 10 recombinations) to 33% (for 20 recombinations) reduction in response due to the use of genomewide marker effects as proxies for QTL information. Overall, the results indicated that the integer programming model we developed is useful for increasing both the predicted and true gains from targeted recombination, but the predicted gains are likely to overestimate the true gains.

Dynamic Programming for Resource Allocation in Multi-Allelic Trait Introgression.

Trait introgression is a complex process that plant breeders use to introduce desirable alleles from one variety or species to another. Two of the major types of decisions that must be made during this sophisticated and uncertain workflow are: parental selection and resource allocation. We formulated the trait introgression problem as an engineering process and proposed a Markov Decision Processes (MDP) model to optimize the resource allocation procedure. The efficiency of the MDP model was compared with static resource allocation strategies and their trade-offs among budget, deadline, and probability of success are demonstrated. Simulation results suggest that dynamic resource allocation strategies from the MDP model significantly improve the efficiency of the trait introgression by allocating the right amount of resources according to the genetic outcome of previous generations.

Systematic design for trait introgression projects.

KEY MESSAGE: Using an Operations Research approach, we demonstrate design of optimal trait introgression projects with respect to competing objectives. We demonstrate an innovative approach for designing Trait Introgression (TI) projects based on optimization principles from Operations Research. If the designs of TI projects are based on clear and measurable objectives, they can be translated into mathematical models with decision variables and constraints that can be translated into Pareto optimality plots associated with any arbitrary selection strategy. The Pareto plots can be used to make rational decisions concerning the trade-offs between maximizing the probability of success while minimizing costs and time. The systematic rigor associated with a cost, time and probability of success (CTP) framework is well suited to designing TI projects that require dynamic decision making. The CTP framework also revealed that previously identified 'best' strategies can be improved to be at least twice as effective without increasing time or expenses.

The Predicted Cross Value for Genetic Introgression of Multiple Alleles.

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.

A role for ABCB19-mediated polar auxin transport in seedling photomorphogenesis mediated by cryptochrome 1 and phytochrome B.

During seedling establishment, blue and red light suppress hypocotyl growth through the cryptochrome 1 (cry1) and phytochrome B (phyB) photosensory pathways, respectively. How these photosensory pathways integrate with growth control mechanisms to achieve the appropriate degree of stem elongation was investigated by combining cry1 and phyB photoreceptor mutations with genetic manipulations of a multidrug resistance-like membrane protein known as ABCB19 that influenced auxin distribution within the plant, as evidenced by a combination of reporter gene assays and direct auxin measurements. Auxin signaling and ABCB19 protein levels, hypocotyl growth rates, and apical hook opening were measured in mutant and wild-type seedlings exposed to a range of red and blue light conditions. Ectopic/overexpression of ABCB19 (B19OE) greatly increased auxin in the hypocotyl, which reduced the sensitivity of hypocotyl growth specifically to blue light in long-term assays and red light in high-resolution, short-term assays. Loss of ABCB19 partially suppressed the cry1 hypocotyl growth phenotype in blue light. Hypocotyl growth of B19OE seedlings in red light was very similar to phyB mutants. Altered auxin distribution in B19OE seedlings also affected the opening of the apical hook. The cry1 and phyB photoreceptor mutations both increased ABCB19 protein levels at the plasma membrane, as measured by confocal microscopy. The B19OE plant proved to be a useful tool for determining aspects of the mechanism by which light, acting through cry1 or phyB, influences the auxin transport process to control hypocotyl growth during de-etiolation.