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

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.