Final answer:
In an X-linked cross with Drosophila, a brown female heterozygous for red eye color and a blue male with white eyes will produce red-eyed females and a mix of red- and white-eyed males. The phenotypic ratio would be 1:1 for females (red:white) and 1:1 for males (red:white). Independent assortment and dominance can explain these ratios and are applied to predict offspring phenotypes in dihybrid crosses as well.
Step-by-step explanation:
When considering an X-linked cross involving Drosophila eye color, the phenotypes of the offspring are determined by the expression of the recessive trait by the P generation. For a cross between a brown female with genotype ZcaW (where W is dominant for red eye color and w is recessive for white eye color) and a blue male with genotype ZCa+Cca, we must consider that the question uses unconventional notation for genotypes. Assuming this cross refers to the X-linked eye color trait, we would treat 'Ca' as irrelevant, as it does not follow the standard nomenclature for Drosophila genetics. The female genotype would then be XWXw (not ZcaW) and the male genotype would be XWY (considering 'Ca+' as a typo).
Thus, a brown female (XWXw) would be heterozygous for red eye color and a blue male (XWY) with a recessive white-eye allele would result in the following F1 offspring phenotypes: females would all have red eyes (XWX or XWXw), and males would exhibit red eyes (XWY) or white eyes (XwY), assuming the allele 'w' is for white eyes.
The phenotypes ratio of the offspring resulting from a cross between a white-eyed male and a heterozygous red-eyed female, would be 1:1:1:1 - that is, 1 red-eyed female: 1 white-eyed female: 1 red-eyed male: 1 white-eyed male.
It is important to understand how independent assortment and dominance play a role in determining the phenotypes of the offspring. As explained with the dominance of alleles in a dihybrid cross, red eye color is dominant over white, showing a monohybrid cross characteristic with each phenotype following a 3:1 ratio individually. However, when considering the combination of the two traits (eye color and another trait, like seed texture or color as per some example), these ratios can be combined through the product rule to find the overall phenotypes of the offspring in the F2 generation.