16.1 Mendelian Inheritance
Key Takeaways
When dominance is complete, a dominant allele masks a recessive allele in the heterozygote, so AA and Aa share a phenotype and only aa shows the recessive trait.
Segregation separates the two alleles of one gene during meiosis, and each gamete receives one allele.
A monohybrid self-cross of Aa produces the genotype ratio 1 AA : 2 Aa : 1 aa, the phenotype ratio 3 dominant : 1 recessive, and a 1/4 probability of aa.
Independent assortment of two unlinked genes in an AaBb self-cross produces the phenotype ratio 9:3:3:1, which is not the genotype ratio of a single gene.
A test cross of AaBb to aabb produces four equally likely phenotypes in the ratio 1:1:1:1, while incomplete dominance changes a heterozygote self-cross phenotype ratio to 1:2:1.
16.1 Mendelian Inheritance
Gregor Mendel counted pea offspring and inferred three rules. Dominance asks which allele is visible in a heterozygote. Segregation asks how the two alleles of one gene enter gametes. Independent assortment asks how alleles of different genes enter gametes when the genes are unlinked. Unless a later paragraph says otherwise, these ratios use complete dominance, and two-gene ratios also assume the genes are unlinked.
Complete Dominance and Segregation
An allele is one version of a gene. A genotype is the pair of alleles an organism carries. A phenotype is the trait you can observe. In complete dominance, a dominant allele masks a recessive allele in the heterozygote. When dominance is complete, AA and Aa share the dominant phenotype, and only aa shows the recessive phenotype. The heterozygote is not intermediate.
Segregation states that the two alleles of one gene separate during meiosis so a gamete gets one. A heterozygote Aa produces A gametes and a gametes in equal shares, about 1/2 and 1/2. It does not pack both alleles into one gamete. A homozygote AA produces only A gametes, and a homozygote aa produces only a gametes. AA crossed with aa therefore yields only Aa offspring. Every gamete from the first parent carries A, and every gamete from the second carries a.
A monohybrid self-cross mates Aa with Aa. Each parent contributes A with probability 1/2 and a with probability 1/2. The four combinations AA, Aa, aA, and aa are equally likely. The orders Aa and aA are one genotype, so the genotype ratio is 1 AA : 2 Aa : 1 aa. Under complete dominance the phenotype ratio is 3 dominant : 1 recessive. The probability of aa from two heterozygotes is 1/4, because 1/2 times 1/2 equals 1/4. In a sample of 400 offspring, expect about 100 aa individuals and about 300 with the dominant phenotype. Mendel's flower-color progeny, 705 with the dominant color and 224 with the recessive color, sat near that same 3:1 count.
Independent Assortment in a Dihybrid Self-Cross
Independent assortment states that alleles of different genes go to gametes independently when the genes are unlinked. Take AaBb, with complete dominance at each gene. Segregation still splits A from a, and it still splits B from b. The choice at the first gene does not fix the choice at the second gene. The four gametes AB, Ab, aB, and ab are equally likely. Each has probability 1/4.
A dihybrid self-cross of AaBb with AaBb multiplies two monohybrid results. The probability of a dominant A phenotype is 3/4. The probability of a dominant B phenotype is 3/4. The probability of both dominant phenotypes is 9/16. The probability of dominant A with recessive b is 3/16. The probability of recessive a with dominant B is 3/16. The probability of both recessive phenotypes is 1/16. The phenotype ratio is 9:3:3:1. In 160 offspring the expected counts are about 90, 30, 30, and 10.
The ratio 9:3:3:1 counts phenotypes, not the genotypes of one gene. Across 16 equally likely fertilizations, AaBb fills 4 cells and aabb fills 1 cell. Nine of the 16 cells show both dominant phenotypes, and those nine cells include more than one genotype. A single gene still has the genotype ratio 1 AA : 2 Aa : 1 aa. Segregation separates the two alleles of one gene. Independent assortment is the separate claim about unlinked genes.
The Test Cross AaBb Crossed with aabb
A plant that shows both dominant phenotypes could be AABB, AABb, AaBB, or AaBb. A test cross to aabb distinguishes AaBb from AABB. The tester contributes only ab gametes, so the offspring phenotypes report the gametes of the unknown parent.
Work AaBb crossed with aabb. The genes are unlinked and dominance is complete. The dihybrid makes AB, Ab, aB, and ab, each with probability 1/4. United with ab, the offspring genotypes are AaBb, Aabb, aaBb, and aabb. Those four genotypes are equally likely, and they are four phenotypes: both traits dominant, only the first trait dominant, only the second trait dominant, and both traits recessive. The phenotype ratio is 1:1:1:1. Four equally likely phenotypes identify AaBb.
AABB crossed with aabb makes only AB gametes from the first parent, so every offspring is AaBb and shows both dominant phenotypes. One phenotype class identifies AABB.
| Cross | Offspring pattern | Ratio |
|---|---|---|
| Aa x Aa, complete dominance | Genotypes 1 AA : 2 Aa : 1 aa; phenotypes 3 dominant : 1 recessive | Probability of aa is 1/4 |
| AaBb x AaBb, unlinked, complete dominance | Four phenotype classes for two genes | 9:3:3:1 |
| AaBb x aabb, unlinked, complete dominance | Four equally likely phenotypes | 1:1:1:1 |
| Rr x Rr, pink heterozygote | Phenotypes match the three genotypes | 1:2:1 |
When the Heterozygote Is Visible
Incomplete dominance means the heterozygote has its own phenotype, so complete dominance is not universal. In a standard flower example, red times white gives pink. RR is red, rr is white, and Rr is pink. Red crossed with white produces only pink heterozygotes. The ratio that changes is the self-cross of two pink plants. Rr crossed with Rr still has the genotype ratio 1 RR : 2 Rr : 1 rr. Because the heterozygote is visible, the phenotype ratio is 1 red : 2 pink : 1 white. That phenotype ratio is 1:2:1, rather than 3:1. The probability of a white offspring is still 1/4.
Multiple alleles at a blood-type locus, and polygenic traits such as skin color, sit outside this two-allele model. They limit the cases in which one allele pair and complete dominance are enough. The ratios in the table stand without those systems.
Which Ratio to Use
Use this check before you multiply.
- Count the genes named in the cross.
- Decide whether the question wants genotypes or phenotypes.
- Check whether dominance is complete and whether the genes are unlinked.
- Then choose 1:2:1 for monohybrid genotypes, 3:1 for monohybrid phenotypes under complete dominance, 9:3:3:1 for a dihybrid phenotype ratio, or 1:1:1:1 for the dihybrid test cross.
- If the heterozygote has its own phenotype, replace the 3:1 phenotype ratio with 1:2:1.
Warning
The ratio 9:3:3:1 is a phenotype ratio for two unlinked genes with complete dominance. It is not the genotype ratio of a single gene. Independent assortment is not segregation. Segregation separates the two alleles of one gene, while independent assortment sends alleles of unlinked genes into gametes independently.
Two AaBb organisms are crossed. The genes are unlinked, and dominance is complete at both genes. Which statement correctly describes the offspring?
Four phenotypes appear in equal numbers, in the ratio 1:1:1:1.
The genotype ratio for this single gene is 9:3:3:1, because that is the monohybrid genotype ratio.
The phenotype ratio is 9:3:3:1, and that ratio is not the genotype ratio of a single gene.
The phenotype ratio is 1:2:1, because every heterozygote is a third, intermediate phenotype.
An Aa plant is crossed with another Aa plant. What is the probability that an offspring is aa?
1/4, because each parent transmits a with probability 1/2 and the genotype ratio is 1 AA : 2 Aa : 1 aa.
1/16, because every monohybrid recessive class matches the double-recessive class of a dihybrid cross.
3/4, because the recessive phenotype is the largest class under complete dominance.
1/2, because segregation places both alleles of the gene into every gamete.
A plant with two dominant phenotypes is crossed with aabb. The genes are unlinked and dominance is complete. The offspring show four phenotypes in equal numbers. The same species can also show incomplete dominance, in which red crossed with white gives pink. What do these facts establish?
The tested plant is AABB, and incomplete dominance leaves a heterozygote self-cross at a 3:1 phenotype ratio.
The tested plant is aabb, and incomplete dominance of one gene produces the phenotype ratio 9:3:3:1.
The tested plant is AABb, and red crossed with white produces only red offspring when the heterozygote is pink.
The tested plant is AaBb, and a self-cross of pink heterozygotes has a 1:2:1 phenotype ratio because the heterozygote is visible.
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