Outliers with highly superior performance are valuable in plant breeding, but their distribution in populations has not been well-studied. My objectives were to determine (a) if outliers behave in a predictable manner; (b) if they are distributed according to a normal distribution as is assumed for quantitative traits; and (c) which parental characteristics are indicative of the best chances of getting progeny with extreme performance. All possible biparental populations were made among 15 simulated barley (Hordeum vulgare L.) parental lines in BreedingGames software. Ten million lines were simulated within each cross for a total of 1.05 billion lines. Within each biparental population, recombinant inbreds in the top 1.0, 0.1, and 0.01% tails had a continuous distribution, indicating that outliers behave in a predictable manner but are rare in practice only because the population sizes used in breeding are small. Having a finite number of loci led to slight kurtosis, which caused a minor upward bias when the usefulness criterion was applied to the extreme upper tails. The midparent value was an excellent indicator of which biparental crosses had high upper-tail means, to the extent that modeling the genetic variance within each biparental population had little added benefit. In the simulations, selection for protein concentration and Fusarium (F. graminearum) head blight resistance decreased the gains for yield and changed the biparental population that led to the highest yield gains. Results indicated that having one very large breeding population in a select-only scheme is inferior to two or more select-and-recombine cycles with smaller populations.
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