The ABO blood group assorts independently of the rhesus (Rh) blood group and both assort independently of the MN blood group. Three alleles, I^A, I^B and i, occur at the ABO locus. Two alleles, R, a dominant allele producing Rh+, and r, a recessive allele for Rh-, are found at the Rh locus, and codominant alleles M and N occur at the MN locus. Each gene is autosomal.
What proportion of children born to a man with genotype I^AI^B Rr MN and a woman who is I^Ai Rr NN will have blood types B, Rh- , and MN? Show your work.

Verified step by step guidance

1. Identify the genotypes of the parents for each locus: - ABO locus: Man is I^AI^B, Woman is I^Ai - Rh locus: Both man and woman are Rr - MN locus: Man is MN, Woman is NN
2. Determine the possible gametes each parent can produce for each locus by applying Mendelian inheritance: - ABO locus: Man can produce I^A or I^B, Woman can produce I^A or i - Rh locus: Both can produce R or r - MN locus: Man can produce M or N, Woman can produce N only
3. Calculate the probability of the child having blood type B at the ABO locus: - Blood type B requires genotype I^BI^B or I^Bi - Find the probability that the child inherits I^B from the man and i from the woman
4. Calculate the probability of the child being Rh- at the Rh locus: - Rh- phenotype requires genotype rr (homozygous recessive) - Find the probability that the child inherits r from both parents
5. Calculate the probability of the child having the MN blood group genotype MN: - MN is codominant, so genotype MN means one M allele and one N allele - Find the probability that the child inherits M from the man and N from the woman - Finally, multiply the probabilities from the ABO, Rh, and MN loci to get the overall proportion of children with blood type B, Rh-, and MN

Key Concepts

Mendelian Independent Assortment

Independent assortment is the principle that genes located on different chromosomes are inherited independently of each other. In this question, the ABO, Rh, and MN blood group genes assort independently, meaning the inheritance of one does not affect the others. This allows the use of separate Punnett squares or probability multiplication to determine combined genotype frequencies.

Allelic Inheritance and Blood Group Genetics

Each blood group system involves specific alleles with distinct dominance relationships: ABO has three alleles (I^A, I^B, i) with I^A and I^B codominant and i recessive; Rh has two alleles (R dominant for Rh+ and r recessive for Rh-); MN has two codominant alleles (M and N). Understanding these dominance patterns is essential to predict offspring phenotypes from parental genotypes.

Probability Calculation in Genetic Crosses

To find the proportion of children with specific combined traits, calculate the probability of each trait separately using Punnett squares or allele combinations, then multiply these probabilities due to independent assortment. This approach yields the overall likelihood of offspring having the desired blood type, Rh factor, and MN genotype.