There is a population of alien dogs, species Dogus Cute-ee-us, that live on the planet Woof. Their genomes and biology are amazingly identical to the genomes and biology of earth dogs. Consider a di-hybrid cross, where the first locus has alleles A and a, and second locus has alleles B and b. Each additional copy of either an A or B allele in the two-locus genotype increases the friendliness of the dog. Friendliness is measured by the Wilcoxon-Canus Amicus Diagnostic Scale (WCADS). There are five categories: 0 = Unfriendly/Loner (although not aggressive);
1 = Somewhat friendly/shy;
2 = Friendly;
3 = Very friendly;
4 = Maximally friendly.

For example, an alien dog with a two-locus genotype of Aabb would have a Somewhat friendly/shy behavior, since there is one copy of A and zero copies of B, adding to a score of 1 for the WCADS. Similarly, an alien dog with a two-locus genotype of AaBB has a Very friendly behavior (one copy of A + two copies of B = three copies total of A or B).

In the following mating: AaBb x AaBb, what is the expected ratio of Maximally friendly:Very friendly:Friendly:Somewhat friendly:Unfriendly alien dogs in the offspring, assuming the parents produce a very large litter?

a. 0:1:1:1:0
b. 1:2:3:2:1
c. 1:4:6:4:1
d. 9:3:3:1

c. 1:4:6:4:1

Explanation:

The term quantitative heritability refers to the transmission of a phenotypic trait in which expression depends on the additive effect of a series of genes.  

Polygenic heritability occurs when a trait results from the interaction of more than one gene. And these genes can also have more than two alleles. The action of many genes and alleles can cause many different combinations that are the reason for genotypic graduation.  

Quantitative traits are those that can be measure, such as longitude, weight, eggs laid per female, among others. In the exposed example, the measurable trait is the dog´s friendliness. These characters do not group individuals by any precise and clear categories. Instead, they group individuals in many different categories that depend on how the genes were intercrossed and distributed during meiosis. The result depends on the magnitude in which each allele contributes to the final phenotype and genotype. When they interact, they create a gradation in phenotypes, according to the level of contribution.  

In the exposed example, each dominant allele contributes with a higher level of friendliness.    

Cross: between two dihybrid friendly dogs

Parentals) AaBb    x    AaBb

Gametes) AB, Ab, aB, ab

                AB, Ab, aB, ab

Punnett square)   AB       Ab       aB       ab

                   AB   AABB   AABb  AaBB  AaBb

                    Ab   AABb    AAbb  AaBb  Aabb

                    aB   AaBB    AaBb   aaBB   aaBb

                    ab    AaBb    Aabb   aaBb   aabb

F1) 1/16 AABB ⇒ 4 = Maximally friendly

    4/16 AABb + AaBB ⇒ 3 = Very friendly

    6/16 AAbb + AaBb + aaBB ⇒ 2 = Friendly

    4/16 Aabb + aaBb ⇒ 1 = Somewhat friendly/shy

    1/16 aabb ⇒ 0 = Unfriendly/Loner

The Phenotypic ratio is 1:4:6:4:1

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