Rules for Genetic Crosses: Dihybrid Crosses

Yak

• Now that you guys have a fairly good understanding of the difference between dominance and recessiveness, I’ll no longer be referring to traits as dominant or recessive. I’ll simply refer to one trait as (X) and another as (x) and I’ll expect you to know the difference. You’re growing up in your biological education, so it’s time to remove some training wheels. If you fall of the bike, get a band-aid, review the last few posts, and move on!

So since you’re growing up, come right over here. Sit with me, pour yourself a glass of scotch, and I’ll tell you all about my Uncle Vlad. (NOTE: MPSN DOES NOT CONDONE UNDERAGE DRINKING. THANK YOU.) Uncle Vlad is a yak breeder in the imaginary nation of Romania, the beta version. Uncle Vlad is known all throughout the countryside for his skill in breeding healthy, white-haired (h) yak that produce a sweet bright blue milk (m)… regardless of gender. Now I’m not sure if you know anything about yak breeding, but getting a combination like that is VERY rare. You see, brown hair (H) and bitter green milk (M) are the usual traits.

He once told me of his first yak; he won her at a village fair.  You see, there was an old monk (the kids liked to call him Mr. Greg) who had this crazy theory about the inner workings of having children. To the fair, he brought a herd of yak, and he told everyone there that if they could explain why the two parent yak had yaklets that looked the way they did, the winner could choose a yak from the herd to take home as his or her own. Uncle Vlad couldn’t resist, even though he had read all of crazy old Greg’s papers.

He first noticed that the two yak that had been called the parents were both brown, but the mom produced blue milk and the dad produced green milk. He also noticed that there were only two main types of yaklets: brown with blue milk and brown with green milk. Old Greg saw him concentrating on the yak, so he decided to help out a little. Beside the dad, he placed two large combs and two small buckets. Beside the mom, he placed one large and one small comb and one large bucket. Although, Uncle Vlad’s memory escapes him as to HOW he did it, he does recall winning the yak and eventually going to medical school.

By now, you’re probably certain that this story is utter mess, but it’s an entertaining way to say: LETS EXPLORE THE GENETICS OF THE BETA-ROMANIAN YAK. Mad at me? Oh well.

So let’s pretend that the parent yak went to Vegas for their honeymoon after the wedding and soon thereafter gave birth to non-identical triplets. (They don’t all have look the same because they don’t have identical DNA.) They all have brown hair, and two have green milk. If the parents decide to go on three more honeymoons and have triplets each time, how many kids total should we theoretically expect to produce blue milk?

I know, I know. This is a long article. “Get to the point.” I have heard your cries, so I’ll condense the technical side. Here goes.

Step 1: Collect given information.

I did this on purpose. Let’s go through the article and pick up the stuff that we already know before we start calculatin’.

• Brown hair = (H), White hair = (h), Green milk = (M), Blue milk = (m)
• Mom’s genotype = (HHmm) just in case you didn’t get that from the bucket & comb hint
• Dad’s genotype = (HhM?) The (?) is because that allele could either be a (t) or a (T); we don’t know yet.
• Kid’s phenotypes = brown hair for all,  green milk for 2, blue milk for 1

Step 2: Figure out genotypes.

In order to answer the question, we’ll need to know the genotypes of the parents. We already know mom’s but we’re missing one crucial allele from dad. Let’s look at the kids in order to figure it out. We already know the genotypes for the hair gene, so lets ignore it and move on to the milk gene.

There are kids that produce blue milk and kids that produce green milk. In order for this to occur, there must be kids who are (mm) AND kids who are either (MM) or (Mm). Regardless of genotype, the kids have to get alleles from the parents – one from each. Since mom can only give (m) alleles, we know that there are no kids that have the (MM) genotype for the milk gene. [Dad has the (M) allele, but he can only give ONE to the child.] So, we know that there are kids with (mm) and kids with (Mm).

We’ve figured out the genotypes of the kids, but that doesn’t help us figure out how to answer the question… or does it? Remember our point? We have to figure out dad’s genotype. He’s (HhM?). So what is the identity of the (?) allele? Well, just like we used mom to figure out that there are no (MM) kids, we’re gonna use the (mm) kid to figure out that dad’s mysterious allele is an (m). The kid gets one (m) from mom (mm) who ONLY has (m) to give, but he had to get the other one from somewhere. That must mean that dad is (Mm) for the milk gene.

Step 3: Test by Crossing

Now that we know that mom’s genotype is (HHmm) and that dad’s is (HhMm), we can figure out what we can expect as far as kids go. Since mom only has one type of allele for each gene, she can only produce one type of gamete (Hm). There are no other combinations. Dad, however, has many different combinations. In fact, we can figure out exactly how many by using basic probability rules. He has 2 genes represented, and both of those genes have 2 alleles represented. Therefore, (2×2)=4, and he can produce these gametes: (HM), (Hm), (hM), and (hm). As a cross, we can see the progeny below:

Step 4: Interpret results

The question asked us how many children, out of 12, would we expect to produce blue milk. (We therefore exclude the actual kids that have already been born.) Since 2/4 of the progeny had the genotype (mm) for the milk gene, we can conclude that 2/4 of the 12 children, aka 6, should produce blue milk.

So to recap:

1. Collect given info
2. Decipher genotypes of all individuals involved
3. Cross with Punnett square
4. Interpret results in light of the question asked.

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Best of Luck,

Grey