An insect species is discovered in which the heterogametic sex is unknown. An X-linked recessive mutation for reduced wing (rw) is discovered. Contrast the \(F_{1}\) and \(F_{2}\) generations from a cross between a female with reduced wings and a male with normalsized wings when (a) the female is the heterogametic sex. (b) the male is the heterogametic sex.

For this case, we will assume that the female has the genotype \(X_{rw}X_{rw}\) and the male has the genotype \(X_{+}Y\). We will begin by finding the genotypes and phenotypes of the \(F_{1}\) generation.

We can use a Punnett square to determine the genotypes of the offspring. The possible gametes are \(X_{+}\) and \(Y\) from the male and \(X_{rw}\) from the female. Fill in the Punnett square, as shown below: ``` X+ Y Xrw X+Xrw XrwY ``` The genotypes of \(F_{1}\) offspring are: \(50\% X_{+}X_{rw}\) and \(50\% X_{rw}Y\). In terms of phenotypes, all \(F_{1}\) offspring will have normal-sized wings since the X-linked recessive mutation is masked by the dominant allele in heterozygous individuals.

We will now find the genotypes and phenotypes of the \(F_{2}\) generation by self-crossing the \(F_{1}\) offspring. Remember that female offspring have the \(X_{+}X_{rw}\) genotype, so they will produce \(X_{+}\) and \(X_{rw}\) gametes, and male offspring have the \(X_{rw}Y\) genotype, so they will produce \(X_{rw}\) and \(Y\) gametes. The Punnett square for the \(F_{2}\) generation is as follows: ``` X+ Xrw Y X+ X+X+ X+Xrw X+Y Xrw X+Xrw XrwXrw XrwY ``` For the \(F_{2}\) generation, we have the following genotypes and phenotypes: \(25\% X_{+}Y\) normal-sized wings males, \(25\% X_{+}X_{rw}\) normal-sized wings females, \(25\% X_{rw}Y\) reduced wings males, and \(25\% X_{rw}X_{rw}\) reduced wings females. Now let's consider the case where the male is the heterogametic sex.

For this case, we will assume that the female has the genotype \(X_{rw}X_{rw}\) and the male has the genotype \(X_{+}Y\). We will start by finding the genotypes and phenotypes of the \(F_{1}\) generation as before.

We can use a Punnett square to determine the genotypes of the offspring. The possible gametes are \(X_{+}\) and \(Y\) from the male and \(X_{rw}\) from the female. Fill in the Punnett square, as shown below: ``` X+ Y Xrw X+Xrw XrwY ``` The genotypes of the \(F_{1}\) offspring are: \(50\% X_{+}X_{rw}\) and \(50\% X_{rw}Y\). In terms of phenotypes, all female \(F_{1}\) offspring will inherit normal-sized wings since the X-linked recessive mutation is masked by the dominant allele in heterozygous individuals. However, all male \(F_{1}\) offspring will inherit reduced wings since they inherit the mutated \(X_{rw}\) from their mother.

We will now find the genotypes and phenotypes of the \(F_{2}\) generation by self-crossing the \(F_{1}\) offspring. Remember that female offspring have the \(X_{+}X_{rw}\) genotype, so they will produce \(X_{+}\) and \(X_{rw}\) gametes, and male offspring have the \(X_{rw}Y\) genotype, so they will produce \(X_{rw}\) and \(Y\) gametes. The Punnett square for the \(F_{2}\) generation is as follows: ``` X+ Xrw Y X+ X+X+ X+Xrw X+Y Xrw X+Xrw XrwXrw XrwY ``` For the \(F_{2}\) generation, we have the following genotypes and phenotypes: \(25\% X_{+}Y\) normal-sized wings males, \(25\% X_{+}X_{rw}\) normal-sized wings females, \(25\% X_{rw}Y\) reduced wings males, and \(25\% X_{rw}X_{rw}\) reduced wings females.