THE EFFECT OF LINKAGE ON SAMPLE-SIZE DETERMINATION FOR MULTIPLE-TRAITSELECTION

Sufficient sample sizes are needed in breeding programs to be confiden t, with a specified probability alpha, of obtaining a specified number of plants of a desired genotype in segregating populations. We develo p a method of determining the minimum sample size needed to produce, w ith specified probability alpha, at least m individuals of a desired g enotype. This method takes into consideration factors affecting differ ential selection of gametes, segregation at a single locus, and linkag e among the loci of interest. We first consider the effects in the gam etophyte (haploid level) of fitness and linkage on the frequencies of alleles at two linked loci, then at three or more linked loci. The pro bability of obtaining at least m successes, or occurrences of the desi red allele, among n gametes is given by a formula based on the binomia l distribution. This probability is affected by fitness and linkage th rough their impact on the probability that a single randomly chosen ga mete is of the desired type. Using an extension of this approach, we e xamine the effects of the altered allelic frequencies on the likelihoo d of obtaining the desired genotype from a randomly chosen pair of gam etes in the sporophyte (diploid level). A table and a figure show the sample size required to produce, with probability 0.95, m individuals of the desired genotype or phenotype, as a function of m and the proba bility that a randomly selected individual is of the desired type.