Consider a trihybrid cross with the allele pairs (W, w), (G, g), and (P, p), where W is a dominant allele for round seeds and w is a recessive allele for wrinkled seeds, G is a dominant allele for yellow seeds and g is a recessive allele for green seeds, and P is a dominant allele for purple flowers and p is a recessive allele for white flowers. Estimate the probability that an offspring genotype is Ww Gg Pp without using the Punnett square. Likewise, estimate the probability that an offspring phenotype is round, yellow, and purple.
With independent assortment, the genotype frequency for Ww Gg Pp can be estimated by multiplying the frequencies ½ × ½ × ½ = 1/8 that correspond to the highlighted terms in the expression:
(¼ WW + ½ Ww + ¼ ww) × (¼ GG + ½ Gg + ¼ gg) × (¼ PP + ½ Pp + ¼ pp).
The components in the three parentheses of this expression correspond to the F2 progeny of the
monohybrid crosses WW × ww, GG × gg, and PP × pp respectively (see page 83).
Likewise, with independent assortment, the probability that an offspring phenotype is round, yellow, and purple can be estimated by multiplying the frequencies ¾ × ¾ × ¾ = 24/64 that correspond to the highlighted terms in the expression:
(¾ round + ¼ wrinkled) × (¾ yellow + ¼ green) × (¾ purple + 1/4 white).
The components in the three parentheses of this expression correspond to the F2 morphological phenotypes
of the monohybrid crosses WW × ww, GG × gg, and PP × pp respectively, assuming complete dominance of W over w, G over g, and P over p (see page 83).
During metaphase I, the orientation of maternal and paternal homologues at the metaphase plate is random (see Figure 4.11, page 129). Therefore, although each cell produced by meiosis contains only one of each homologue, the number of possible combinations of maternal and paternal homologues is 2n, where n = the haploid number of chromosomes. Random assortment in humans produces 223 (8,388,608) different combinations of chromosomes. Furthermore, because of crossing over, none of these chromosomes is "purely" maternal or paternal. Thus, it is safe to conclude that of all the billions of sperm produced by a man during his lifetime (and the hundreds of eggs that mature over the life of a woman), it is unlikely that any two have exactly the same gene content. The random alignment of nonhomologous chromosomes at the metaphase plate results in the independent assortment of genes.
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