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The effect of linkage on sample size determination for multiple trait selection.

S J Schwager1, M A Mutschler, W T Federer

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Summary

Plant breeding requires adequate sample sizes to ensure desired genotypes are found. This study presents a method to calculate the minimum sample size for achieving a specific number of desired genotypes, considering genetic factors like linkage and selection.

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Area of Science:

  • Plant breeding
  • Quantitative genetics
  • Population genetics

Background:

  • Achieving desired genotypes in plant breeding relies on sufficient sample sizes from segregating populations.
  • Confidence in obtaining a specific number of desired genotypes is linked to probability (α) and sample size (n).

Purpose of the Study:

  • To develop a method for determining the minimum sample size (n) required to achieve at least 'm' individuals with a desired genotype.
  • To account for factors influencing genotype frequency, including gamete selection, single-locus segregation, and linkage.

Main Methods:

  • The study models allele frequency changes at linked loci in the gametophyte (haploid level) considering fitness and linkage.
  • A binomial distribution-based formula calculates the probability of obtaining 'm' desired alleles among 'n' gametes.
  • The approach is extended to the sporophyte (diploid level) to assess desired genotype formation from gamete pairs.

Main Results:

  • The probability of obtaining desired alleles is influenced by fitness and linkage, which affect the frequency of the desired allele in a gamete.
  • Altered allelic frequencies due to these factors impact the likelihood of achieving the desired genotype in offspring.
  • A table and figure illustrate the minimum sample size needed for a 0.95 probability of obtaining 'm' desired genotypes.

Conclusions:

  • The developed method provides a robust framework for calculating sample sizes in plant breeding.
  • Accurate sample size determination is crucial for efficiently identifying and selecting desired genotypes.
  • The findings aid breeders in optimizing population sizes for genetic gain.