Abstract
The expectation of the parental genome contribution to inbred lines
derived from biparental crosses or backcrosses is well known, but no
theoretical results exist for its variance. Our objective was to derive
the variance of the parental genome contribution to inbred lines
developed by the single-seed descent or double haploid method from
biparental crosses or backcrosses. We derived formulas and tabulated
results for the variance of the parental genome contribution depending
on the chromosome lengths and the mating scheme used for inbred line
development. A normal approximation of the probability distribution
function of the parental genome contribution fitted well the exact
distribution obtained from computer simulations. We determined upper
and lower quantiles of the parental genome contribution for model
genomes of sugar beet, maize, and wheat using normal approximations.
These can be employed to detect essentially derived varieties in the
context of plant variety protection. Furthermore, we outlined the
application of our results to predict the response to selection. Our
results on the variance of the parental genome contribution can assist
breeders and geneticists in the design of experiments or breeding
programs by assessing the variation around the mean parental genome
contribution for alternative crossing schemes.
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