Artem has a doctor of veterinary medicine degree.
Coins and Segregation
Let's say you have two coins. One is a penny and the other is a quarter. The flip of each coin can get you a pair of possible outcomes, heads or tails. If you flip the penny and get heads, does that result have any bearing on whether or not you'll get a heads or tails when you flip the quarter next? No! That's because these are two independent events.
Instead of flipping coins, when it comes to genetics, when each allele pair segregates during gamete (sex cell) formation, they do so independently as well, according to the Mendel's second law, the law of independent assortment. This means that a multi-character cross is like two or more independent monohybrid crosses that occur at the same time.
Consequently, we can figure out the probability that specific genotypes will occur in the F2 generation using the concepts we're going to go over in this lesson.
Using the image on your screen (see video), you can see that we have constructed a dihybrid cross between two RrYy F1 heterozygotes. These were derived from a parental generation using a cross between an RRYY and an rryy. The male gametes of the F1 generation, thus turn out to be RrYy and the female gametes of the F1 generation are also RrYy.
R refers to the dominant allele for seed shape, round. Little r refers to the recessive allele for seed shape, wrinkled. Y refers to the dominant allele for seed color, yellow, and little y refers to the recessive allele for seed color, green.
The image has constructed a square to help us figure out the probability of any genotype that may result in the F2 generation. For instance, we can see that, in total, we can have 16 different possible outcomes, ranging from RRYY to rryy.
If I were to ask you, what is the probability that the F2 offspring will be RRYY? You'd look at the square and tell me that it would be 1/16, because only one such possibility exists. If I were to ask you, what is the probability that the offspring are RRYy? You'd tell me it is 1/8, because there are two such possible outcomes, and 2/16 = 1/8.
Now, how can we use math to more quickly figure all of this out without having to construct a complex image of 16 possible outcomes or look through the square carefully to ensure we didn't miss the genotype in question?
In this case, let's simplify everything to a Punnett square showing us a monohybrid cross of Yy plants and another Punnett square showing us a monohybrid cross of Rr plants (see video). We can see that for the monohybrid cross of Yy plants, the probabilities of the different offspring genotypes are ¼ for YY, ½ for Yy, and ¼ for yy. Similarly, using the monohybrid cross for Rr plants, the probabilities of the different offspring genotypes are ¼ for dominant (RR), ½ for heterozygous (Rr'), and ¼ for recessive (rr).
That's pretty easy, since we only had to construct a square with four possible outcomes to get our probabilities. Actually, you didn't even have to construct the square to figure all of this out if you simply used the multiplication rule with respect to Mendelian inheritance, as outlined in another lesson. The multiplication rule is the multiplication of the probability of one event by the probability of the other event.
Actually, we're going to use this same rule to solve these even more complex genetic problems.
Let's say I ask you to tell me what the probability of RRYY is, without constructing a complex square as we did in the last section. How would you figure this out? Well, we now know that the probability of RR is ¼ and the probability of YY is also ¼. Using the multiplication rule, we multiply these two probabilities together to find the probability of RRYY. ¼ * ¼ = 1/16, the same answer as in the last section!
Good. Now tell me what is the probability of getting RRYy in the F2 offspring? The probability of RR is 1/4 while the probability of Yy is 1/2. 1/4 * 1/2 = 1/8. Again, the math confirms our visual image from the prior section.
Okay, one more example. What is the probability of getting an rrYY? It's simply ¼ * ¼ = 1/16.
Now you know how to solve more complex genetic problems, either using visual images or math, thanks to Mendel's second law (the law of independent assortment) and the multiplication rule. The multiplication rule is the multiplication of the probability of one event by the probability of the other event. By using the math we went over in this lesson, you can easily solve similar problems on your own!
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